In step 2, the insertion loss caused by the misalignment of the offset was calculated by using another Marcuse equation [3]. Another target insertion loss of 20 dB was determined in order to exceed the loss budget between network devices. The insertion loss became 20 dB when *θ*

A sample made of the solid refractive index matching material (silicone resin) was fabricated based on the above parameters. Experiments were carried out with mechanical splices and samples of solid matching material. A groove was dug with the same shape as the sample, and the sample was tilted at 16° to the optical axis of the fiber, as shown in Fig. 12(a). A state was maintained whereby fiber end B always touched the sample, and fiber end A gradually moved toward the sample (Fig. 12(b)-(d)). The insertion and return losses were measured for different gap widths. Figure 12(b) shows the state in which fiber end A did not touch the sample. Figure 12(c) shows the state where fiber end A just touched the sample, and fiber end A was close to fiber end B, and Fig. 12(d) shows the state where the very narrow gap between the fiber ends

Figure 13(a) and (b) show the insertion and return loss results at wavelengths of 1.31 and 1.55 μm, respectively. When fiber end A did not touch the sample, the insertion loss always exceeded 20 dB. Moreover, the return losses were constant at 15 dB. When fiber end A just touched the sample, the insertion losses decreased to 2.5 and 2.3 dB, and the return losses increased to 51.7 and 48.6 dB at wavelengths of 1.31 and 1.55 μm, respectively. In addition,

to 120 μm. The insertion loss then became 2 dB.

56 Current Developments in Optical Fiber Technology

was 16°.

was filled by the sample.

Field installable connections that have incorrectly cleaved fiber ends might lead to insertion losses of more than 40 dB induced by temperature changes, which may eventually result in faults in the optical networks. Therefore, it is important to use correctly cleaved fiber ends to prevent network failures caused by improper optical fiber connections. This means that we need a technique for inspecting cleaved optical fiber ends.

Cleaved optical fiber ends are usually inspected before fusion splicing with a CCD camera and a video monitor installed in fusion splice machines [22]. On the other hand, cleaved optical fiber ends are not usually inspected when mechanical splices and field installable connectors are assembled. These connections are easy to assemble and does not require electric power. Therefore, an inspection method is needed for these connections. A fiber optic Fabry-Perot interferometer based sensor for inspecting cleaved optical fiber ends has been proposed [23-24].

The basic concept of the proposed sensor for inspecting cleaved optical fiber ends is shown in Fig. 14. Figure 14(a) and (b), respectively, show fiber connections in which a fiber with a flattened end for detection is used in the inspection of incorrectly cleaved (uneven) and correctly cleaved (flat) fiber ends. The ratio of the reflected light power (*Pr* or *Pr'*) to the incident light power (*Pi* or *Pi '*) within each connection is measured. Two optical fibers are connected with an air gap *S* remaining between them. Misalignments of the offset and tilt between the fibers and the mode field mismatch are not taken into account. Under both conditions, Fresnel reflections occur at the fiber ends because of refractive discontinuity. In Fig. 14(a), the reflected light from the uneven end spreads in every direction, and the back-reflection efficiency ratio, *Pr/Pi* , is determined using the Fresnel reflection at the fiber end for detection in air. The Fresnel reflection *R0* is defined by the following equation.

2

Faults and Novel Countermeasures for Optical Fiber Connections in Fiber-To-The-Home Networks

(1)

59

(2)

*'*) is defined by the

http://dx.doi.org/10.5772/54241

1

1 *n n R n n* æ ö - = ç ÷ + è ø

> 2 0

4 sin (2 / ) (1 ) 4 sin (2 / )

 l

p

 l

*R R nS* p

The return losses in dB are derived by multiplying the log of the reflection functions by -10. Here *S* and λ denote the gap size and wavelength, respectively. According to Equation (2), the return loss depends on *S* and λ. Figure 15 shows the calculated return losses from the uneven (incorrectly cleaved) and flat (correctly cleaved) fiber ends. The dashed and solid lines in the figure represent the calculations for the uneven and flat ends based on Equations (1) and (2), respectively. Here, the refractive indices *n1* and *n* were 1.454 and 1.0, and the gap size used for Equation (2) was 10 μm. The return losses of the uneven end were independent of wavelength and had a constant value of 14.7 dB. The return losses of the flat end varied greatly and periodically and resulted in a worst value of ~8.7 dB because of the Fabry-Perot interference.

2 2 0 0

= - +

In Fig. 14(b), some of the incident light is multiply reflected in the gap. The phase of the multiply reflected light changes whenever it is reflected, which interferes with the back-reflected light at the optical fiber connection. These multiple reflections between fiber ends are considered to behave like a Fabry-Perot interferometer [25-27]. Two flat fiber ends make up a Fabry-Perot

0

interferometer. Based on the model, the returned efficiency *R* (= *Pr'/Pi*

*R nS R*

**Figure 15.** Return losses from uneven (dashed line) and flat (solid line) fiber ends

following equation.

Here *n1* and *n* denote the refractive indices of the fiber core and air, respectively.

**Figure 13.** Results of (a) insertion loss and (b) return loss

**Figure 14.** Basic concept of proposed sensor: (a) inspecting uneven fiber end, and (b) inspecting flat fiber end

Faults and Novel Countermeasures for Optical Fiber Connections in Fiber-To-The-Home Networks http://dx.doi.org/10.5772/54241 59

$$R\_0 = \left(\frac{n\_1 - n}{n\_1 + n}\right)^2\tag{1}$$

Here *n1* and *n* denote the refractive indices of the fiber core and air, respectively.

In Fig. 14(b), some of the incident light is multiply reflected in the gap. The phase of the multiply reflected light changes whenever it is reflected, which interferes with the back-reflected light at the optical fiber connection. These multiple reflections between fiber ends are considered to behave like a Fabry-Perot interferometer [25-27]. Two flat fiber ends make up a Fabry-Perot interferometer. Based on the model, the returned efficiency *R* (= *Pr'/Pi '*) is defined by the following equation.

$$R = \frac{4R\_0 \sin^2(2\pi nS/\lambda)}{\left(1 - R\_0\right)^2 + 4R\_0 \sin^2(2\pi nS/\lambda)}\tag{2}$$

**Figure 15.** Return losses from uneven (dashed line) and flat (solid line) fiber ends

**Figure 13.** Results of (a) insertion loss and (b) return loss

58 Current Developments in Optical Fiber Technology

**Figure 14.** Basic concept of proposed sensor: (a) inspecting uneven fiber end, and (b) inspecting flat fiber end

The return losses in dB are derived by multiplying the log of the reflection functions by -10. Here *S* and λ denote the gap size and wavelength, respectively. According to Equation (2), the return loss depends on *S* and λ. Figure 15 shows the calculated return losses from the uneven (incorrectly cleaved) and flat (correctly cleaved) fiber ends. The dashed and solid lines in the figure represent the calculations for the uneven and flat ends based on Equations (1) and (2), respectively. Here, the refractive indices *n1* and *n* were 1.454 and 1.0, and the gap size used for Equation (2) was 10 μm. The return losses of the uneven end were independent of wavelength and had a constant value of 14.7 dB. The return losses of the flat end varied greatly and periodically and resulted in a worst value of ~8.7 dB because of the Fabry-Perot interference. The return loss values at wavelengths of 1.31 and 1.55 μm were 11.2 and 18.9 dB, respectively. Even if the gap size and wavelength period were changed, the return losses varied as greatly as the values at a 10-μm gap [28]. These results indicate that an inspected fiber end can be considered uneven or flat depending on whether or not the measured return losses from the fiber end at two wavelengths are both ~14.7 dB.

Two levers are provided for manually operating only the left V-groove. The left lever moves the left V-groove along the Y-axis at 10 μm per pitch up to a maximum distance of 250 μm. Similarly, the right lever moves the left V-groove along the X-axis at 10 μm per pitch up to a

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In the experiments, the gap between the fiber for detection and the fiber under test was set at 40 μm, and each scanning distance was set at 10 μm. Typical experimental results are shown in Fig. 18. In the figure, (a) and (c) show the flat parts of the inspected fiber end found using the proposed inspection sensor and (b) and (d) show SEM images of the flat end. The fiber ends seen in Fig. 18(a) and (c) were found to be correctly and incorrectly cleaved, respectively. The experimental image with a correctly cleaved fiber end shows that the flat parts form a circle with a diameter of about 140 μm, which is slightly larger than the actual 125-μm-diameter fiber end. This is because the mode field area of light may radiate from the fiber end for detection. In contrast, the experimental results for the incorrectly cleaved fiber end show that half the fiber end parts are flat and half are uneven. The results obtained with the proposed

inspection method and those obtained by SEM observation are in good agreement.

The above results show that the proposed sensor made it possible to determine accurately whether the fiber ends were correctly or incorrectly cleaved for all the samples examined. Since the proposed sensor for cleaved optical fiber ends is based on the Fabry-Perot interferometer

maximum distance of 250 μm.

**Figure 17.** Fabricated fiber stage

**Figure 16.** Experimental setup including fiber stage

Based on the above principle, we have designed the inspection sensor shown in Fig. 16. This sensor is composed of two light sources emitting at different wavelengths, an optical power meter, an optical coupler, and a fiber stage. In this proposed sensor, one light source is turned on and the other is turned off. The return loss values are measured separately at two wave‐ lengths. The fiber stage is the most important component because a Fabry-Perot interferometer must be created in it by the fiber for detection and the fiber under test. The other equipment can be adapted from commercially available devices. Therefore, we fabricated a new fiber stage with the following characteristics to implement the proposed technique, as shown in Fig. 17. The dimensions of the fabricated fiber stage are 90 x 100 x 110 mm, which is small enough to be portable in the field. It is also suitable for operation in an outside environment because it does not require a power source. Manual driving was adopted for moving the fiber ends. Two V-grooves for the alignment of two fiber ends were used to create a Fabry–Perot interferometer. These two V-grooves were originally one V-groove that was divided into two. By using the same V-groove for alignment, any tilting of the two fibers along their Z-axes can be reduced. The X- and Y-axes for the scanning direction of the fiber ends were chosen from several alternatives, the direction of the radius, spirally, or with one stroke, due to the streamlining of the fiber stage mechanism. The minimum distance the V-groove can move was designed to be 10 μm along both the X- and Y-axes. The stage was designed to move along both the X- and Y-axes to a maximum distance of 250 μm to cover the entire end of 125-μm-diameter fibers. Two levers are provided for manually operating only the left V-groove. The left lever moves the left V-groove along the Y-axis at 10 μm per pitch up to a maximum distance of 250 μm. Similarly, the right lever moves the left V-groove along the X-axis at 10 μm per pitch up to a maximum distance of 250 μm.

**Figure 17.** Fabricated fiber stage

The return loss values at wavelengths of 1.31 and 1.55 μm were 11.2 and 18.9 dB, respectively. Even if the gap size and wavelength period were changed, the return losses varied as greatly as the values at a 10-μm gap [28]. These results indicate that an inspected fiber end can be considered uneven or flat depending on whether or not the measured return losses from the

Based on the above principle, we have designed the inspection sensor shown in Fig. 16. This sensor is composed of two light sources emitting at different wavelengths, an optical power meter, an optical coupler, and a fiber stage. In this proposed sensor, one light source is turned on and the other is turned off. The return loss values are measured separately at two wave‐ lengths. The fiber stage is the most important component because a Fabry-Perot interferometer must be created in it by the fiber for detection and the fiber under test. The other equipment can be adapted from commercially available devices. Therefore, we fabricated a new fiber stage with the following characteristics to implement the proposed technique, as shown in Fig. 17. The dimensions of the fabricated fiber stage are 90 x 100 x 110 mm, which is small enough to be portable in the field. It is also suitable for operation in an outside environment because it does not require a power source. Manual driving was adopted for moving the fiber ends. Two V-grooves for the alignment of two fiber ends were used to create a Fabry–Perot interferometer. These two V-grooves were originally one V-groove that was divided into two. By using the same V-groove for alignment, any tilting of the two fibers along their Z-axes can be reduced. The X- and Y-axes for the scanning direction of the fiber ends were chosen from several alternatives, the direction of the radius, spirally, or with one stroke, due to the streamlining of the fiber stage mechanism. The minimum distance the V-groove can move was designed to be 10 μm along both the X- and Y-axes. The stage was designed to move along both the X- and Y-axes to a maximum distance of 250 μm to cover the entire end of 125-μm-diameter fibers.

fiber end at two wavelengths are both ~14.7 dB.

60 Current Developments in Optical Fiber Technology

**Figure 16.** Experimental setup including fiber stage

In the experiments, the gap between the fiber for detection and the fiber under test was set at 40 μm, and each scanning distance was set at 10 μm. Typical experimental results are shown in Fig. 18. In the figure, (a) and (c) show the flat parts of the inspected fiber end found using the proposed inspection sensor and (b) and (d) show SEM images of the flat end. The fiber ends seen in Fig. 18(a) and (c) were found to be correctly and incorrectly cleaved, respectively. The experimental image with a correctly cleaved fiber end shows that the flat parts form a circle with a diameter of about 140 μm, which is slightly larger than the actual 125-μm-diameter fiber end. This is because the mode field area of light may radiate from the fiber end for detection. In contrast, the experimental results for the incorrectly cleaved fiber end show that half the fiber end parts are flat and half are uneven. The results obtained with the proposed inspection method and those obtained by SEM observation are in good agreement.

The above results show that the proposed sensor made it possible to determine accurately whether the fiber ends were correctly or incorrectly cleaved for all the samples examined. Since the proposed sensor for cleaved optical fiber ends is based on the Fabry-Perot interferometer and a new fiber stage, it allows us to determine whether 10 x 10 μm areas of a cleaved optical fiber end are flat or uneven. The measured results of the inspected flat and uneven fiber ends were in good agreement with those obtained using an SEM.

developing the tool. For the clear view requirement, the fiber ends or connector endfaces under test should be viewable with both the naked eye and a camera. Naked-eye inspection is easily applicable and effective during fiber end preparation and assembly procedures. Camera inspection is effective because it allows us to photograph an inspected cleaved fiber end or connector endface. To meet the portability requirement, the tool must be compact and easy to carry to any location including aerial sites. For the ease of operation requirement, the tool should not require any focal adjustment of a microscope, and the tool must be as easy as

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Several concrete specifications were determined on the basis of these requirements, as listed in Table 1. The tool must be small enough to carry with one hand. Its total weight should be less than 500 g. It should include a microscope that has a lens with a magnification power of a few hundred times. The target fiber is a 125-μm bare/250-μm coated fiber, which is placed in the FA holder used in field installable connectors or a holder for mechanical splicing. The target connectors are SC, MU, FA, and FAS connectors. The tool uses a cell phone equipped with a CCD camera and small video monitor. This enables the inspected fiber end to be photographed and sent over a cell phone network. LED light sources are used to allow visibility

The tool is designed to inspect both cleaved fiber ends and connector endfaces. Schematic views of the inspection method for a cleaved fiber end and an optical connector endace are shown in Fig. 19(a) to (c). The fundamental optical microscope system for the tool is shown in Fig. 19(a). The microscope system is composed of an objective lens, an eyepiece lens for a cell phone camera or a naked eye, a sample that can be inspected, and an LED light source. Their components must be arranged in a line at designated lengths. In this figure, Sob, La, Sey, fob, and fey indicate the distance from the objective lens to the object point, the distance between the objective and eyepiece lenses, the distance from the eyepiece lens to the viewpoint for a cell phone camera or the naked eye, the focal distance of the objective lens, and the focal distance of the eyepiece lens, respectively. Here, Sob is designed to be slightly larger than fob, and Sey is

possible to handle to prevent the need for complex operations in the field.

in dark places. A rechargeable battery is used for the LED light sources.

**Table 1.** Specifications of new inspection tool

#### **4.3. Simple tool for inspecting optical fiber ends**

The conventional inspection method for a cleaved fiber end involves checking it regularly (about once a week) to ensure good cleaving quality by using a CCD camera and the video monitor of a fusion splicer. If the cleaved fiber end is imperfect, first the fiber cleaver blade is replaced. If no improvements result from this countermeasure, the fiber cleaver itself must be repaired by the manufacturer. In contrast, the conventional inspection method for optical fiber connector endfaces is to check the surface before connecting the mated connector. This method uses a CCD camera and the video monitor of a specialized piece of inspection equipment [29]. If the connector endface is contaminated, it must be cleaned with a special cleaner. These methods using a CCD camera and a video monitor are expensive and unsuit‐ able for use with straightforward fiber connections in the field. Therefore, a simple and eco‐ nomical inspection tool for cleaved fiber ends and connector endfaces suitable for use in the field have been proposed [30-31].

**Figure 18.** Experimental results of correctly cleaved fiber end: (a) result with proposed sensor and (b) result of SEM observation, and experimental results for incorrectly cleaved fiber end: (c) result with proposed sensor and (d) result of SEM observation

There are three important requirements for an inspection tool, namely it must provide a clear view, be portable, and easy to operate. We took these requirements into consideration when developing the tool. For the clear view requirement, the fiber ends or connector endfaces under test should be viewable with both the naked eye and a camera. Naked-eye inspection is easily applicable and effective during fiber end preparation and assembly procedures. Camera inspection is effective because it allows us to photograph an inspected cleaved fiber end or connector endface. To meet the portability requirement, the tool must be compact and easy to carry to any location including aerial sites. For the ease of operation requirement, the tool should not require any focal adjustment of a microscope, and the tool must be as easy as possible to handle to prevent the need for complex operations in the field.

Several concrete specifications were determined on the basis of these requirements, as listed in Table 1. The tool must be small enough to carry with one hand. Its total weight should be less than 500 g. It should include a microscope that has a lens with a magnification power of a few hundred times. The target fiber is a 125-μm bare/250-μm coated fiber, which is placed in the FA holder used in field installable connectors or a holder for mechanical splicing. The target connectors are SC, MU, FA, and FAS connectors. The tool uses a cell phone equipped with a CCD camera and small video monitor. This enables the inspected fiber end to be photographed and sent over a cell phone network. LED light sources are used to allow visibility in dark places. A rechargeable battery is used for the LED light sources.

**Table 1.** Specifications of new inspection tool

and a new fiber stage, it allows us to determine whether 10 x 10 μm areas of a cleaved optical fiber end are flat or uneven. The measured results of the inspected flat and uneven fiber ends

The conventional inspection method for a cleaved fiber end involves checking it regularly (about once a week) to ensure good cleaving quality by using a CCD camera and the video monitor of a fusion splicer. If the cleaved fiber end is imperfect, first the fiber cleaver blade is replaced. If no improvements result from this countermeasure, the fiber cleaver itself must be repaired by the manufacturer. In contrast, the conventional inspection method for optical fiber connector endfaces is to check the surface before connecting the mated connector. This method uses a CCD camera and the video monitor of a specialized piece of inspection equipment [29]. If the connector endface is contaminated, it must be cleaned with a special cleaner. These methods using a CCD camera and a video monitor are expensive and unsuit‐ able for use with straightforward fiber connections in the field. Therefore, a simple and eco‐ nomical inspection tool for cleaved fiber ends and connector endfaces suitable for use in the

**Figure 18.** Experimental results of correctly cleaved fiber end: (a) result with proposed sensor and (b) result of SEM observation, and experimental results for incorrectly cleaved fiber end: (c) result with proposed sensor and (d) result of

There are three important requirements for an inspection tool, namely it must provide a clear view, be portable, and easy to operate. We took these requirements into consideration when

were in good agreement with those obtained using an SEM.

**4.3. Simple tool for inspecting optical fiber ends**

62 Current Developments in Optical Fiber Technology

field have been proposed [30-31].

SEM observation

The tool is designed to inspect both cleaved fiber ends and connector endfaces. Schematic views of the inspection method for a cleaved fiber end and an optical connector endace are shown in Fig. 19(a) to (c). The fundamental optical microscope system for the tool is shown in Fig. 19(a). The microscope system is composed of an objective lens, an eyepiece lens for a cell phone camera or a naked eye, a sample that can be inspected, and an LED light source. Their components must be arranged in a line at designated lengths. In this figure, Sob, La, Sey, fob, and fey indicate the distance from the objective lens to the object point, the distance between the objective and eyepiece lenses, the distance from the eyepiece lens to the viewpoint for a cell phone camera or the naked eye, the focal distance of the objective lens, and the focal distance of the eyepiece lens, respectively. Here, Sob is designed to be slightly larger than fob, and Sey is designed to be slightly larger than fey. The figure also shows the light path. An LED light source emitting an almost parallel light beam, is used in this microscope system. After passing through the inspected sample, the light is focused at the back focal plane of the objective lens. It then proceeds to and is magnified by the eyepiece lens before passing into a cell phone camera or a naked eye. The magnified image of the inspected sample can be observed with the cell phone monitor or with the naked eye by using appropriate lenses and by designating appropriate distances; Sob, La, and Sey. With normal optical microscopes, the inspected sample is placed on the stage and must be adjusted to Sob and aligned at the object point while La and Sey are designated as constants. By contrast, with this microscope system, the inspected sample, which in placed in a special holder, can always be positioned at the object point without active alignment, i.e., without focal length adjustment. This special holder is described in detail in the following section. For the cleaved fiber inspection shown in Fig. 19(b), the side of the cleaved fiber end is designed to be viewed through the objective lens of the microscope system with the use of the LED light source. The distance between the fiber end and the objective lens a is designed to be equal to Sob. The fiber end, LED, and lens are designed to align passively and to set at each designated distance and not require focal adjustment. However, for the optical-fiber connector inspection in Fig. 19(c), the endface of the connector is designed to be viewed through the objective lens by using a half-mirror and another LED light source. The summation of the distance between the connector endface and the half-mirror b and that between the half-mirror and the object lens c is designed to be equal to Sob. The connector end, LED, half-mirror, and lens are also designed to align passively and to set at each designated distance and not require focal adjustment.

The fiber ends or connector endfaces under test can be viewed through the top of the body

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**Figure 19.** Basic concept of inspection method with developed tool: (a) fundamental optical microscope system and

The conventional fiber end preparation procedure for an FAS connector has six steps: (1) cut the support wire of the dropped cable, (2) strip the cable coating, (3) place the fiber in the FA holder, (4) strip the fiber coating, (5) clean the stripped fiber (bare fiber) with alcohol, and (6) cut the bare optical fiber with a fiber cleaver. The assembly procedure comprises the next three steps: (7) insert the properly prepared bare optical fiber into the mechanical splice part in the FAS connector, (8) join it to the built-in optical fiber, and (9) fix the position of the bare optical fiber. The inspection procedure for the proposed inspection tool (i)-(iii) for a cleaved fiber end can be conducted between the fiber end preparation and assembly procedures, i.e., between steps (6) and (7). This indicates that the proposed inspection tool can work well with the

inspecting (b) cleaved fiber end (side) and (c) connector endface (front)

conventional fiber end preparation and assembly procedures.

(step ii) using the cell phone monitor (step iii).

On the basis of the described specifications and design, we developed a simple, mobile and cost-effective tool. The outer components of the proposed inspection tool and the internal makeup of the optical microscope system are shown in Fig. 20. It is composed of three main parts: a body that includes a microscope that has objective and eyepiece lenses and LED light sources, a cell phone and its attachment, and special holders for cleaved fiber ends or connector endfaces. The cell phone is equipped with a CCD camera and a small video monitor. This inspection tool is simple and light, and weighs about 500 g including the cell phone. The optical microscope system is also shown in this figure. The eyepiece lens, objective lens, and object point of the cleaved fiber end are aligned in the body of the tool. The two LEDs for the cleaved fiber end and connector endface are also installed in the body. The half-mirror is aligned in the special holder for the connector endface. The inspection procedure is as follows.

The special holders and body are designed to automatically align the inspected cleaved fiber end or connector end at each of the object points after step (ii). The attachment for a cell phone is also designed to automatically align the camera in the cell phone at the viewpoint after step (iii). This structure and procedure result in the inspection tool not requiring focal adjustment. The fiber ends or connector endfaces under test can be viewed through the top of the body (step ii) using the cell phone monitor (step iii).

designed to be slightly larger than fey. The figure also shows the light path. An LED light source emitting an almost parallel light beam, is used in this microscope system. After passing through the inspected sample, the light is focused at the back focal plane of the objective lens. It then proceeds to and is magnified by the eyepiece lens before passing into a cell phone camera or a naked eye. The magnified image of the inspected sample can be observed with the cell phone monitor or with the naked eye by using appropriate lenses and by designating appropriate distances; Sob, La, and Sey. With normal optical microscopes, the inspected sample is placed on the stage and must be adjusted to Sob and aligned at the object point while La and Sey are designated as constants. By contrast, with this microscope system, the inspected sample, which in placed in a special holder, can always be positioned at the object point without active alignment, i.e., without focal length adjustment. This special holder is described in detail in the following section. For the cleaved fiber inspection shown in Fig. 19(b), the side of the cleaved fiber end is designed to be viewed through the objective lens of the microscope system with the use of the LED light source. The distance between the fiber end and the objective lens a is designed to be equal to Sob. The fiber end, LED, and lens are designed to align passively and to set at each designated distance and not require focal adjustment. However, for the optical-fiber connector inspection in Fig. 19(c), the endface of the connector is designed to be viewed through the objective lens by using a half-mirror and another LED light source. The summation of the distance between the connector endface and the half-mirror b and that between the half-mirror and the object lens c is designed to be equal to Sob. The connector end, LED, half-mirror, and lens are also designed to align passively and to set at each designated

On the basis of the described specifications and design, we developed a simple, mobile and cost-effective tool. The outer components of the proposed inspection tool and the internal makeup of the optical microscope system are shown in Fig. 20. It is composed of three main parts: a body that includes a microscope that has objective and eyepiece lenses and LED light sources, a cell phone and its attachment, and special holders for cleaved fiber ends or connector endfaces. The cell phone is equipped with a CCD camera and a small video monitor. This inspection tool is simple and light, and weighs about 500 g including the cell phone. The optical microscope system is also shown in this figure. The eyepiece lens, objective lens, and object point of the cleaved fiber end are aligned in the body of the tool. The two LEDs for the cleaved fiber end and connector endface are also installed in the body. The half-mirror is aligned in

the special holder for the connector endface. The inspection procedure is as follows.

**i.** The cleaved optical fiber or the optical connector to be inspected is placed in the

The special holders and body are designed to automatically align the inspected cleaved fiber end or connector end at each of the object points after step (ii). The attachment for a cell phone is also designed to automatically align the camera in the cell phone at the viewpoint after step (iii). This structure and procedure result in the inspection tool not requiring focal adjustment.

distance and not require focal adjustment.

64 Current Developments in Optical Fiber Technology

appropriate special holder.

**ii.** The special holder is installed at the center of the body.

**iii.** The attachment with the cell phone is installed on top of the body.

**Figure 19.** Basic concept of inspection method with developed tool: (a) fundamental optical microscope system and inspecting (b) cleaved fiber end (side) and (c) connector endface (front)

The conventional fiber end preparation procedure for an FAS connector has six steps: (1) cut the support wire of the dropped cable, (2) strip the cable coating, (3) place the fiber in the FA holder, (4) strip the fiber coating, (5) clean the stripped fiber (bare fiber) with alcohol, and (6) cut the bare optical fiber with a fiber cleaver. The assembly procedure comprises the next three steps: (7) insert the properly prepared bare optical fiber into the mechanical splice part in the FAS connector, (8) join it to the built-in optical fiber, and (9) fix the position of the bare optical fiber. The inspection procedure for the proposed inspection tool (i)-(iii) for a cleaved fiber end can be conducted between the fiber end preparation and assembly procedures, i.e., between steps (6) and (7). This indicates that the proposed inspection tool can work well with the conventional fiber end preparation and assembly procedures.

**Figure 21.** Experimental observation results on cell phone screen: (a) developed inspection tool with cell phone at‐ tached, (b) incorrectly cleaved fiber end, (c) correctly cleaved fiber end, (d) contamination on connector endface, and

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For conventional FAS connector procedures, the fiber end preparation and assembly proce‐ dures take 72 and 28% of the total installation time, respectively. With the proposed tool, inspection took 11% longer than with the conventional procedure. These results indicate that using the inspection tool may result in a slight increase of 11% in operation time compared with that required with conventional fiber end preparation and assembly procedures.

The fabricated inspection tool is compact, highly portable, and can inspect a fiber and clearly determine whether it has been cleaved correctly and whether contamination or scratches can be found on the connector endfaces. Thus, this tool will be highly practical for field use.

This chapter reported example faults and novel countermeasures with optical fiber connectors

After a brief introduction (section 1), section 2 described the FTTH network and optical fiber connectors and mechanical splices used in Japan, and section 3 reported example faults with these optical connections in FTTH networks. First, the faults with fiber connection using refractive-index matching material were reported in section 3.1. There are two major causes of these faults: one is a wide gap between fiber ends and the other is incorrectly cleaved fiber ends. Next, faults with fiber connection using physical contact were explained in section 3.2. This fault might occur when the connector endfaces are contaminated. The characteristics of

(e) uncontaminated connector endface

**5. Conclusion**

these faults were outlined.

and mechanical splices in FTTH networks.

**Figure 20.** Outer components of fabricated inspection tool and internal makeup of optical microscope system

The inspection results and operation time of the fabricated inspection tool were evaluated. Experimental observation results from the cell phone screen are shown in Fig. 21. The tool with a cell phone attached is shown in Fig. 21(a), and its observation results are shown in Fig. 21(b) to (e). The fiber end or connector endface in each photo is magnified about 100 times. These results indicate that the tool can be used to inspect and determine whether fiber ends have been cleaved incorrectly (Fig. 21(b)) or correctly (Fig. 21(c)), and whether there is contamination (Fig. 21(d)) or no contamination (Fig. 21(e)) on the connector endfaces.

Faults and Novel Countermeasures for Optical Fiber Connections in Fiber-To-The-Home Networks http://dx.doi.org/10.5772/54241 67

**Figure 21.** Experimental observation results on cell phone screen: (a) developed inspection tool with cell phone at‐ tached, (b) incorrectly cleaved fiber end, (c) correctly cleaved fiber end, (d) contamination on connector endface, and (e) uncontaminated connector endface

For conventional FAS connector procedures, the fiber end preparation and assembly proce‐ dures take 72 and 28% of the total installation time, respectively. With the proposed tool, inspection took 11% longer than with the conventional procedure. These results indicate that using the inspection tool may result in a slight increase of 11% in operation time compared with that required with conventional fiber end preparation and assembly procedures.

The fabricated inspection tool is compact, highly portable, and can inspect a fiber and clearly determine whether it has been cleaved correctly and whether contamination or scratches can be found on the connector endfaces. Thus, this tool will be highly practical for field use.

## **5. Conclusion**

**Figure 20.** Outer components of fabricated inspection tool and internal makeup of optical microscope system

66 Current Developments in Optical Fiber Technology

The inspection results and operation time of the fabricated inspection tool were evaluated.

Experimental observation results from the cell phone screen are shown in Fig. 21. The tool with

a cell phone attached is shown in Fig. 21(a), and its observation results are shown in Fig.

21(b) to (e). The fiber end or connector endface in each photo is magnified about 100 times.

These results indicate that the tool can be used to inspect and determine whether fiber ends

have been cleaved incorrectly (Fig. 21(b)) or correctly (Fig. 21(c)), and whether there is

contamination (Fig. 21(d)) or no contamination (Fig. 21(e)) on the connector endfaces.

This chapter reported example faults and novel countermeasures with optical fiber connectors and mechanical splices in FTTH networks.

After a brief introduction (section 1), section 2 described the FTTH network and optical fiber connectors and mechanical splices used in Japan, and section 3 reported example faults with these optical connections in FTTH networks. First, the faults with fiber connection using refractive-index matching material were reported in section 3.1. There are two major causes of these faults: one is a wide gap between fiber ends and the other is incorrectly cleaved fiber ends. Next, faults with fiber connection using physical contact were explained in section 3.2. This fault might occur when the connector endfaces are contaminated. The characteristics of these faults were outlined.

Novel countermeasures against these above-mentioned faults were introduced in section 4. In section 4.1, a new connection method using solid refractive index matching material was proposed as a countermeasure against faults caused by the wide gap between fiber ends. This connection method can provide an insertion loss of more than 20 dB or less than 2 dB when the gap between the fiber ends is wider or narrower than 120 μm, respectively. If there is a de‐ fective connection that has a wide gap, the insertion loss will always be extremely high. In such cases, communication services may be immobilized. With the connection method, engi‐ neers undertaking detection work can notice the defective connection immediately after instal‐ lation.

**References**

[1] Ministry of Internal Affairs and Communications, 2011 WHITE PAPER Information and Communications in Japan [online], Available at: http://www.soumu.go.jp/johot‐

Faults and Novel Countermeasures for Optical Fiber Connections in Fiber-To-The-Home Networks

http://dx.doi.org/10.5772/54241

69

[2] Matsuhashi K., Uchiyama Y., Kaiden T., Kihara M., Tanaka H., & Toyonaga M. "Fault cases and countermeasures against damage caused by wildlife to optical fiber cables in FTTH networks in Japan," in Proceeding of the 59th IWCS/Focus, Nov. 7-10,

[3] NTT East Corporation, "Fault cases and countermeasures for field assembly connec‐

[4] Kihara M., Nagano R., Uchino M., Yuki Y., Sonoda H., Onose H., Izumita H., & Ku‐ waki N., "Analysis on performance deterioration of optical fiber joints with mixture of refractive index matching material and air-filled gaps," in Proceedings of the OFC/

[5] Kihara M., Uchino M., Watanabe H., & Toyonaga M., "Fault analysis: optical per‐ formance investigation of optical fiber connections with imperfect physical contact,"

[6] Kihara M., "Optical performance analysis of single-mode fiber connections," in the book "Optical fiber communications and devices" edited by Moh. Yasin, Sulaiman W.

[7] Nakajima T., Terakawa K., Toyonaga M., & Kama M., "Development of optical con‐ nector to achieve large-scale optical network construction," in Proceedings of the 55th

[8] Hogari K., Nagase R., & Takamizawa K., "Optical connector technologies for optical access networks," IEICE Trans. Electron., Vol. E93-C, No. 7, 2010, pp. 1172–1179. [9] Sugita E., Nagase R., Kanayama K., & Shintaku T., "SC-type single-mode optical fi‐ ber connectors," IEEE/OSA J. Lightw. Technol., vol. 7, 1989, pp. 1689–1696.

[10] Nagase R., Sugita E., Iwano S., Kanayama K., & Ando Y., "Miniature optical connec‐ tor with small zirconia ferrule," IEEE Photon. Technol. Lett., vol. 3, No. 11, 1991, pp.

[12] Satake T., Nagasawa S., & Arioka R., "A new type of a demountable plastic molded single mode multifiber connector," IEEE/OSA J. Lightw. Technol., vol. LT-4, 1986, pp.

Harun and Hamzah Arof, ISBN 978-953-307-954-7, InTech, February 2, 2012.

IWCS/Focus, Nov. 12-15, 2006, Providence, Rhode Island, USA, pp. 439–443.

tors in optical access facilities," NTT Technical Review, vol. 9, No. 7, 2011.

susintokei/whitepaper/ja/h23/pdf/index.html (accessed 10 Aug. 2012).

2010, Providence, Rhode Island, USA, pp. 274-278.

NFOEC, March 22-26, 2009, San Diego, CA, USA, JWA4.

Opt. Lett., vol. 36, no. 24, 2011, pp. 4791-4793.

[11] "Optical fiber mechanical splice", US patent No.5963699.

1045–1047.

1232-1236.

In section 4.2, a fiber optic Fabry-Perot interferometer-based sensor was introduced as a coun‐ termeasure for detecting faults caused by incorrectly cleaved fiber ends. The sensor mainly uses laser diodes, an optical power meter, a 3-dB coupler, and an XY lateral adjustment fi‐ ber stage. Experimentally obtained fiber end images were in good agreement with scanning electron microscope observation images of incorrectly cleaved fiber ends.

In section 4.3, a novel tool for inspecting optical fiber ends was proposed as a countermeas‐ ure for detecting faults caused both by incorrectly cleaved fiber ends and by contaminated con‐ nector endfaces. The proposed tool has a simple structure and does not require focal adjustment. It can be used to inspect a fiber and clearly determine whether it has been cleaved correctly and whether contamination or scratches are present on the connector endfaces. The tool requires a slight increase of 11% in operation time compared with conventional fiber end preparation and assembly procedures. The proposed tool provides a simple and cost-effec‐ tive way of inspecting cleaved fiber ends and connector endfaces and is suitable for field use.

These results support the practical use of optical fiber connections in the construction and operation of optical network systems such as FTTH.

## **Acknowledgements**

This work was supported by the TASC, NTT East Corporation, Japan. The author is deeply grateful to the following members of the TASC for their support; to Y. Yajima for discussing the experiments related to fiber connection with refractive index matching ma‐ terial, to H. Onose for discussing the experiments related to contaminated connector end‐ faces, to H. Watanabe and M. Tanaka for helpful discussions regarding the new connection method using solid refractive index matching material and a fiber optic Fab‐ ry-Perot interferometer based sensor, and to M. Okada and M. Hosoda for discussions regarding the simple inspection tool.

## **Author details**

Mitsuru Kihara

NTT Access Network Service Systems Laboratories, Nippon Telegraph and Telephone Cor‐ poration, Japan

## **References**

Novel countermeasures against these above-mentioned faults were introduced in section 4. In section 4.1, a new connection method using solid refractive index matching material was proposed as a countermeasure against faults caused by the wide gap between fiber ends. This connection method can provide an insertion loss of more than 20 dB or less than 2 dB when the gap between the fiber ends is wider or narrower than 120 μm, respectively. If there is a de‐ fective connection that has a wide gap, the insertion loss will always be extremely high. In such cases, communication services may be immobilized. With the connection method, engi‐ neers undertaking detection work can notice the defective connection immediately after instal‐

In section 4.2, a fiber optic Fabry-Perot interferometer-based sensor was introduced as a coun‐ termeasure for detecting faults caused by incorrectly cleaved fiber ends. The sensor mainly uses laser diodes, an optical power meter, a 3-dB coupler, and an XY lateral adjustment fi‐ ber stage. Experimentally obtained fiber end images were in good agreement with scanning

In section 4.3, a novel tool for inspecting optical fiber ends was proposed as a countermeas‐ ure for detecting faults caused both by incorrectly cleaved fiber ends and by contaminated con‐ nector endfaces. The proposed tool has a simple structure and does not require focal adjustment. It can be used to inspect a fiber and clearly determine whether it has been cleaved correctly and whether contamination or scratches are present on the connector endfaces. The tool requires a slight increase of 11% in operation time compared with conventional fiber end preparation and assembly procedures. The proposed tool provides a simple and cost-effec‐ tive way of inspecting cleaved fiber ends and connector endfaces and is suitable for field use. These results support the practical use of optical fiber connections in the construction and

This work was supported by the TASC, NTT East Corporation, Japan. The author is deeply grateful to the following members of the TASC for their support; to Y. Yajima for discussing the experiments related to fiber connection with refractive index matching ma‐ terial, to H. Onose for discussing the experiments related to contaminated connector end‐ faces, to H. Watanabe and M. Tanaka for helpful discussions regarding the new connection method using solid refractive index matching material and a fiber optic Fab‐ ry-Perot interferometer based sensor, and to M. Okada and M. Hosoda for discussions

NTT Access Network Service Systems Laboratories, Nippon Telegraph and Telephone Cor‐

electron microscope observation images of incorrectly cleaved fiber ends.

operation of optical network systems such as FTTH.

**Acknowledgements**

**Author details**

Mitsuru Kihara

poration, Japan

regarding the simple inspection tool.

lation.

68 Current Developments in Optical Fiber Technology

[13] Kihara M., Nagano R., Izumita H., & Toyonaga M., "Unusual fault detection and loss analysis in optical fiber connections with refractive index matching material," Opti‐ cal Fiber Technol., vol. 18, 2012, pp. 167–175.

[26] Kashima N., "Passive optical components for optical fiber transmission," Norwood,

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[27] Kihara M., Tomita S., & Haibara T., "Influence of wavelength and temperature changes on optical performance of fiber connections with small gap," IEEE Photon.

[28] Kihara M., Uchino M., Omachi M., & Izumita H., "Analyzing return loss deteriora‐ tion of optical fiber joints with various air-filled gaps over a wide wavelength range," in Proceedings of the OFC/NFOEC, March 21-25, 2010, San Diego, CA, USA, NWE4.

[29] For example, JDSU Fiberscope (Fiber Optic Connector End Face Cleaning System), see URL: http://www.jdsu.com/en-us/Test-and-Measurement/Products/families/

[30] Okada M., Kihara M., Hosoda M., &Toyonaga M., "Simple inspection tool for cleaved optical fiber ends and optical fiber connector end surface," in Proceedings of

[31] Kihara M., Okada M., Hosoda M., Iwata T., Yajima Y., & Toyonaga M., "Tool for in‐ specting faults from incorrectly cleaved fiber ends and contaminated optical fiber

the 60th IWCS, Nov. 7-9, Charlotte, North Carolina, USA, 2011, 270-274.

connector end surfaces," Optical Fiber Technol., vol. 18, 2012, 470-479.

MA: Artech House, 1995.

Tech. Lett. 18, 2006, 2120-2122.

westover/Pages/default.aspx/

[26] Kashima N., "Passive optical components for optical fiber transmission," Norwood, MA: Artech House, 1995.

[13] Kihara M., Nagano R., Izumita H., & Toyonaga M., "Unusual fault detection and loss analysis in optical fiber connections with refractive index matching material," Opti‐

[14] Yajima Y., Watanabe H., Kihara M., & Toyonaga M., "Optical performance of field assembly connectors using incorrectly cleaved fiber ends," in Proceedings of the

[15] Berdinskikh T., Bragg J., Tse E., Daniel J., Arrowsmith P., Fisenko A., & Mahmoud S., "The contamination of fiber optics connectors and their effect on optical perform‐ ance," in Technical digest series of OFC 2002, March 17- 22, 2002, Anaheim, Califor‐

[16] Albeanu N., Aseere L., Berdinskikh T., Nguyen J., Pradieu Y., Silmser D., Tkalec H., & Tse E., "Optical connector contamination and its influence on optical signal per‐

[17] Berdinskikh T., Chen J., Culbert J., Fisher D., Huang S. Y., Roche B. J., Tkalec H., Wil‐ son D., & Ainley S. B., "Accumulation of particles near the core during repetitive fi‐ ber connector matings and de-matings" in Technical Digest of OFC/NFOEC2007,

[18] Marcuse D., "Loss analysis of optical fiber splice," Bell Sys. Tech. J, vol. 56, 1976, pp.

[19] Kihara M., Nagasawa S., & Tanifuji T., "Return loss characteristics of optical fiber connectors," IEEE/OSA J. Lightw. Technol., vol. 14, Sep. 1996, pp. 1986-1991.

[20] For example, CLETOP (Optical connector cleaner), see URL: http://www.ntt-at.com/

[21] Tanaka M., Watanabe H., Kihara M., & Takaya M., "New connection method using solid refractive index matching material," in Proceedings of the OECC2012, July 2-6,

[22] Tanifuji T., Kato Y., & Seikai S., "Realization of a low-loss splice for single-mode fi‐ bers in the field using an automatic arc-fusion splicing machine," in Proceedings of

[23] Kihara M., Watanabe H., Tanaka M., & Toyonaga M., "Fiber optic Fabry-Perot inter‐ ferometer based sensor for inspecting cleaved fiber ends," Microwave and Optical

[24] Watanabe H., Kihara M., Tanaka M., & Toyonaga M., "Inspection technique for cleaved optical fiber ends based on Fabry-Perot interferometer," IEEE/OSA J. Lightw.

[25] Yariv A., "Introduction to optical electronics," New York: Holt, Rinehart, and Win‐

the OFC, Feb. 28-March 2, 1983, New Orleans, Louisiana, USA, MG3.

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nia, pp. 617-618.

70 Current Developments in Optical Fiber Technology

703-718.

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2012, Busan, Korea, 4C2-5.

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formance," J SMTA, vol. 16, issue 3, 2003, pp. 40-49.

March 25-29, 2007, Anaheim, CA, USA, NThA6, pp. 1-11.

**Chapter 4**

**Multimode Graded-Index Optical Fibers**

**for Next-Generation Broadband Access**

Growing research interests are focused on the high-speed telecommunications and data communications networks with increasing demand for accessing to the Internet even from home. For instance, in Nov 2011 Strategy Analytics forecasted that there would be more than 807 million broadband fixed line subscriptions worldwide in 2017, based on a figure of 578 million at the end of 2011 showing a cumulative annual growth rate of around 8 percent [1]. This increasing demand for high-speed information transmission over the last two deca‐ des has been driven by the huge successes during the last decade of new multimedia serv‐ ices, commonly referred as Next-Generation Access (NGA) services, such as Internet Protocol Television (IPTV) or Video on Demand (VoD), as well as an increased data traffic driven by High-Definition TV (HDTV) and Peer-to-Peer (P2P) applications which have changed people's habits and their demands for service delivery. Consequently, consumer adoption of broadband access to facilitate use of the Internet for knowledge, commerce and, obviously, entertainment is contingent with the increment of the optical broadband access network capacity, which should extent into the customer's premises up to the terminals. Thus, steady increases in bandwidth requirements of access networks and local area net‐ works (LANs) have created a need for short-reach and medium-reach links supporting data rates of Gbps (such as Gigabit Ethernet, GbE), 10Gbps (such as 10-Gigabit Ethernet, 10GbE) and even higher (such as 40- and 100- Gigabit Ethernet standards, namely 40GbE and 100GbE respectively, which started in November 2007 and have been very ratified in June 2010). Detailed studies [2, 3] have defined the required bit-rates to be transmitted to the cus‐ tomer's premises for different profiles for the traffic flows, reaching a total future-proof

> © 2013 Sánchez Montero and Vázquez García; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is

© 2013 Sánchez Montero and Vázquez García; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

David R. Sánchez Montero and

Additional information is available at the end of the chapter

properly cited.

Carmen Vázquez García

http://dx.doi.org/10.5772/54245

**1. Introduction**

## **Multimode Graded-Index Optical Fibers for Next-Generation Broadband Access**

David R. Sánchez Montero and Carmen Vázquez García

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/54245

## **1. Introduction**

Growing research interests are focused on the high-speed telecommunications and data communications networks with increasing demand for accessing to the Internet even from home. For instance, in Nov 2011 Strategy Analytics forecasted that there would be more than 807 million broadband fixed line subscriptions worldwide in 2017, based on a figure of 578 million at the end of 2011 showing a cumulative annual growth rate of around 8 percent [1]. This increasing demand for high-speed information transmission over the last two deca‐ des has been driven by the huge successes during the last decade of new multimedia serv‐ ices, commonly referred as Next-Generation Access (NGA) services, such as Internet Protocol Television (IPTV) or Video on Demand (VoD), as well as an increased data traffic driven by High-Definition TV (HDTV) and Peer-to-Peer (P2P) applications which have changed people's habits and their demands for service delivery. Consequently, consumer adoption of broadband access to facilitate use of the Internet for knowledge, commerce and, obviously, entertainment is contingent with the increment of the optical broadband access network capacity, which should extent into the customer's premises up to the terminals. Thus, steady increases in bandwidth requirements of access networks and local area net‐ works (LANs) have created a need for short-reach and medium-reach links supporting data rates of Gbps (such as Gigabit Ethernet, GbE), 10Gbps (such as 10-Gigabit Ethernet, 10GbE) and even higher (such as 40- and 100- Gigabit Ethernet standards, namely 40GbE and 100GbE respectively, which started in November 2007 and have been very ratified in June 2010). Detailed studies [2, 3] have defined the required bit-rates to be transmitted to the cus‐ tomer's premises for different profiles for the traffic flows, reaching a total future-proof

properly cited.

© 2013 Sánchez Montero and Vázquez García; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is © 2013 Sánchez Montero and Vázquez García; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

very-high-bit-rate link in the order of 2Gbps per user. It is estimated that end-user access bandwidths could reach 1 Gbps by 2015, and 10 Gbps by 2020.

metropolitan area networks and is subsequently penetrating into the access networks. How‐ ever, it requires great care, delicate high-precision equipment, and highly-skilled personnel, being mainly deployed for long-haul fiber optic communications, constituting the so-called Optical Distribution Network (ODN) and the core telecommunication network of the next generation of optical broadband access networks. Nevertheless, as it comes closer to the end user and his residential area, the costs of installing and maintaining the fiber network become

Multimode Graded-Index Optical Fibers for Next-Generation Broadband Access

http://dx.doi.org/10.5772/54245

75

Also inside the customer's premises, there is a growing need for convergence of the multi‐ tude of communication networks. Presently, Unshielded Twisted copper Pair (UTP) cables are used for voice telephony, cat-5 UTP cables for high-speed data, coaxial cables for CATV2 and FM3 radio signals distribution, wireless Local Area Network (LAN) for high-speed data, FireWire for high-speed short-range signals, and also Power Line Communications (PLC) technology for control signals and lower-speed data. These different networks are each dedicated and optimised for a particular set of services, which also put different Quality-of-Service (QoS) demands, and suffer from serious shortcomings when they are considered to serve the increasing demand for broadband services. Also no cooperation between the net‐ works exists. A common infrastructure that is able to carry all the service types would alle‐ viate these problems. It is therefore not easy to upgrade services, to introduce new ones, nor to create links between services (e.g., between video and data). By establishing a common broadband in-house network infrastructure, in which a variety of services can be integrated, however, these difficulties can be surmounted. The transmission media used at present are not suited for provisioning high-bandwidth services at low cost. For instance, today's wiring in LANs is based mainly on copper cables (twisted pair or coaxial) and silica (glass) fiber of two kinds: singlemode optical fiber (SMF) and multimode optical fiber (MMF). Copper based technologies suffer strong susceptibility to electromagnetic interferences and have limited capacity for digital transmission as well as the presence of crosstalk. Compared to these copper based technologies, optical fiber has smaller volume, it is less bulky and has a smaller weight. In comparison with data transmission capability, optical fiber offers higher

On the other hand, optical fiber is extensively used for long-distance data transmission and it represents an alternative for transmission at the customer's premises as well. Optical fiber connections offer complete immunity to EMI and present increase security, since it is very difficult to intercept signals transmitted through the fiber. Moreover, optical communication systems based on silica optical fibers allow communication signals to be transmitted not on‐ ly over long distances with low attenuation but also at extremely high data rates, or band‐ width capacity. In SMF systems, this capability arises from the propagation of a single optical mode in the low-loss windows of silica located at the near-infrared wavelengths of 1.3μm, and 1.55μm. Furthermore, since the introduction of Erbium-Doped Fiber Amplifiers (EDFAs), the last decade has witnessed the emergence of SMF as the standard data trans‐

a driving factor, which seriously hampers the large-scale introduction of FTTx.

bandwidth at longer transmission distances.

2 CATV: Community Antena TeleVision.

3 FM: Frequency Modulation.

Related to this latter premise, a growing number of service providers are turning to solu‐ tions capable of exploiting the full potential of optical fiber for service delivery, being the copper based x-Digital Subscriber Line (xDSL) infrastructure progressively replaced by a fi‐ ber-based outside plant with thousands of optical ports and optical fiber branches towards residential and business users, constituting the core of the FTTx (Fiber to the Home/Node/ Curb/Business) deployments, see Fig. 1(a). These include passive optical networks (PONs), whose standardization has accelerated product availability and deployment. The ongoing evolution to deliver Gigabit per second Ethernet and the growing trend to migrate to Wave‐ length Division Multiplexing (WDM) schemes have benefited significantly from the Coarse WDM (CWDM) and Dense WDM (DWDM) optoelectronics technologies, as they provide a more efficient way to deliver traffic to Customer Premises Equipment (CPE) devices. These systems, commonly referred to as WDM-PON, are still under standardization process and field trials and are the basis of the so-called next-generation broadband optical access net‐ works to prepare for the future upgrade of the FTTx systems currently being deployed. A basic scheme of the WDM-PON architecture is depecited in Fig. 1(b). However, networking architectures such as PON, BPON, WDM-PON, etc. are outside the scope of this chapter. There is a widely-spread consensus concerning service providers that FTTx is the most pow‐ erful and future-proof access network architecture for providing broadband services to resi‐ dential users.

**Figure 1.** (a) Different FTTx network deployments. (b) Architecture of WDM-PON.

In the FTTx system concepts deployed up to now, singlemode optical fiber (SMF) is used, which has a tremendous bandwidth and thus a huge transport capacity for many services such as the ITU G.983.x ATM1 -PON system. Research is ongoing to further extend the capabil‐ ities of shared SMF access networks. The installation of SMF has now conquered the core and

1 ATM: Asynchronous Transfer Mode.

metropolitan area networks and is subsequently penetrating into the access networks. How‐ ever, it requires great care, delicate high-precision equipment, and highly-skilled personnel, being mainly deployed for long-haul fiber optic communications, constituting the so-called Optical Distribution Network (ODN) and the core telecommunication network of the next generation of optical broadband access networks. Nevertheless, as it comes closer to the end user and his residential area, the costs of installing and maintaining the fiber network become a driving factor, which seriously hampers the large-scale introduction of FTTx.

Also inside the customer's premises, there is a growing need for convergence of the multi‐ tude of communication networks. Presently, Unshielded Twisted copper Pair (UTP) cables are used for voice telephony, cat-5 UTP cables for high-speed data, coaxial cables for CATV2 and FM3 radio signals distribution, wireless Local Area Network (LAN) for high-speed data, FireWire for high-speed short-range signals, and also Power Line Communications (PLC) technology for control signals and lower-speed data. These different networks are each dedicated and optimised for a particular set of services, which also put different Quality-of-Service (QoS) demands, and suffer from serious shortcomings when they are considered to serve the increasing demand for broadband services. Also no cooperation between the net‐ works exists. A common infrastructure that is able to carry all the service types would alle‐ viate these problems. It is therefore not easy to upgrade services, to introduce new ones, nor to create links between services (e.g., between video and data). By establishing a common broadband in-house network infrastructure, in which a variety of services can be integrated, however, these difficulties can be surmounted. The transmission media used at present are not suited for provisioning high-bandwidth services at low cost. For instance, today's wiring in LANs is based mainly on copper cables (twisted pair or coaxial) and silica (glass) fiber of two kinds: singlemode optical fiber (SMF) and multimode optical fiber (MMF). Copper based technologies suffer strong susceptibility to electromagnetic interferences and have limited capacity for digital transmission as well as the presence of crosstalk. Compared to these copper based technologies, optical fiber has smaller volume, it is less bulky and has a smaller weight. In comparison with data transmission capability, optical fiber offers higher bandwidth at longer transmission distances.

On the other hand, optical fiber is extensively used for long-distance data transmission and it represents an alternative for transmission at the customer's premises as well. Optical fiber connections offer complete immunity to EMI and present increase security, since it is very difficult to intercept signals transmitted through the fiber. Moreover, optical communication systems based on silica optical fibers allow communication signals to be transmitted not on‐ ly over long distances with low attenuation but also at extremely high data rates, or band‐ width capacity. In SMF systems, this capability arises from the propagation of a single optical mode in the low-loss windows of silica located at the near-infrared wavelengths of 1.3μm, and 1.55μm. Furthermore, since the introduction of Erbium-Doped Fiber Amplifiers (EDFAs), the last decade has witnessed the emergence of SMF as the standard data trans‐

very-high-bit-rate link in the order of 2Gbps per user. It is estimated that end-user access

Related to this latter premise, a growing number of service providers are turning to solu‐ tions capable of exploiting the full potential of optical fiber for service delivery, being the copper based x-Digital Subscriber Line (xDSL) infrastructure progressively replaced by a fi‐ ber-based outside plant with thousands of optical ports and optical fiber branches towards residential and business users, constituting the core of the FTTx (Fiber to the Home/Node/ Curb/Business) deployments, see Fig. 1(a). These include passive optical networks (PONs), whose standardization has accelerated product availability and deployment. The ongoing evolution to deliver Gigabit per second Ethernet and the growing trend to migrate to Wave‐ length Division Multiplexing (WDM) schemes have benefited significantly from the Coarse WDM (CWDM) and Dense WDM (DWDM) optoelectronics technologies, as they provide a more efficient way to deliver traffic to Customer Premises Equipment (CPE) devices. These systems, commonly referred to as WDM-PON, are still under standardization process and field trials and are the basis of the so-called next-generation broadband optical access net‐ works to prepare for the future upgrade of the FTTx systems currently being deployed. A basic scheme of the WDM-PON architecture is depecited in Fig. 1(b). However, networking architectures such as PON, BPON, WDM-PON, etc. are outside the scope of this chapter. There is a widely-spread consensus concerning service providers that FTTx is the most pow‐ erful and future-proof access network architecture for providing broadband services to resi‐

**(a) (b)**

In the FTTx system concepts deployed up to now, singlemode optical fiber (SMF) is used, which has a tremendous bandwidth and thus a huge transport capacity for many services

ities of shared SMF access networks. The installation of SMF has now conquered the core and

bandwidths could reach 1 Gbps by 2015, and 10 Gbps by 2020.

74 Current Developments in Optical Fiber Technology

Access Loop Customer Premise

xDSLover copper Ethernet over fibre

Point to Point Existing in-building cabling (CAT5-DSL)

**Figure 1.** (a) Different FTTx network deployments. (b) Architecture of WDM-PON.

Fibre Point to Multipoint or Point to Point

xDSL over copper

Street Cabinet

Fibre Point to Multipoint or

dential users.

FibreTo The Central Office

FibreToThe

FibreToThe Building (FTTB)

FibreToThe Home (FTTH)

Central Office /AccesNode

Curb (FTTC) Fibre

such as the ITU G.983.x ATM1

1 ATM: Asynchronous Transfer Mode.

2 CATV: Community Antena TeleVision.

3 FM: Frequency Modulation.

mission medium for wide area networks (WANs), especially in terrestrial and transoceanic communication backbones. The success of the SMF in long-haul communication backbones has given rise to the concept of optical networking, which is a central theme with currently driving research and development activities in the field of photonics. The main objective is to integrate voice, video, and data streams over all-optical systems as communication sig‐ nals make their way from WANs down to the end user by Fiber-To-The-x (FTTx), offices, and in-homes.

tion to, as PF GIPOF has a relative low loss wavelength region ranging from 650nm to 1300nm (even theoretically in the third transmission window), it allows for WDM transmis‐ sion of several data channels. However, attenuation and bandwidth characteristics of the current state-of-the-art PF GIPOF are not at par with those of standard silica SMFs, but they still are superior to those of copper based technologies. Nevertheless, although these losses are coming down steadily due to ongoing improvements in the production processes of this still young technology, the higher than silica attenuation inhibits their use in relative long link applications, being mainly driven for covering in-building optical networks link lengths for in-building/home optical networks (with link lengths less than 1 km), and thus the loss per unit length is of less importance. It should be noted that available light sources for silica fiber based systems can be used with PF GIPOF systems. The same is true of connectors as

Multimode Graded-Index Optical Fibers for Next-Generation Broadband Access

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77

Therefore, it can be stated that polymer optical fiber technology has reached a level of devel‐ opment where it can successfully replace copper based technology and silica MMF for data transmission in short distance link applications such as in the office, in-home and LAN sce‐ narios. Moreover, PF GIPOF is forecasted to be able to support bit-rate distance products in the order of 10Gbps km [5]. Short distance communications system like in-home network and office LANs represent a unique opportunity for deployment of PF GIPOF based sys‐ tems for broadband applications. We can conclude that PF GIPOF technology is experienc‐ ing rapid development towards a mature solution for data transmission at short haul communications. The challenge remains in bringing this POF technology (transceiver, con‐

nectors,…) to a competitive price and performance level at the customer's premises.

Nevertheless, the potentials of these multimode fibers, both silica- and polymer-based, to support broadband radio-frequency, microwave and even millimetre wave transmission over short- and medium-reach distances are yet to be fully known. The belief is that a better understanding of the factors that affect the fiber bandwidth will prove very useful in in‐ creasing the bandwidth of silica MMF and PF GIPOF links in real situations. In the whole fiber network society to be realized in the near future, it is said that silica-based SMF fibers for long-haul backbone will be only several percents of the total use, and the remaining more than 90% would correspond to all-optical networks covering the last mile [6]. Link lengths may range from well below 1 km in LANs and residential houses, to only a few kilo‐ metres in larger building such as offices, hospitals, airport halls, etc. And it is now clear that the expected market is huge and researches and companies all over the world are competing

In this framework, the first part of this chapter, comprising sections 2 and 3 will briefly ad‐ dress the fundamentals of mutimode optical fibers as well as present transmission capacities. Like any communication channel, the multimode optical fiber also suffers from various signal distortions limiting its usefulness. The primary mechanisms contributing to the channel im‐ pairment in multimode fibers are discussed. Both silica-based MMFs and PF GIPOFs are es‐ sentially large-core optical waveguide supporting multiple transverse electromagnetic modes and they suffer from similar channel impairments. On the other hand, present capabilities of actual multimode optical fiber-based deployments are shown. In addition, different techni‐

in the case of Gigabit Ethernet equipment.

to find a solution to this issue.

Although conventional SMF solutions have the potential of achieving very large band‐ widths, they suffer from high connections costs compared to copper or wireless solutions. For this reason, SMF has not been widely adopted by the end user (premises) where most of the interconnections are needed and less cost-sharing between users is obtainable. The un‐ derlying factor is the fact that the SMF core is typically only a few micrometers in diameter with the requirement of precise connecting, delicate installation and handling. Yet as the op‐ tical network gets closer to the end user, the system is characterized by numerous connec‐ tions, splices, and couplings that make the use of thin SMF impractical. An alternative technology is then the use of conventional silica-based multimode optical fiber (MMF) with larger core diameters. This fact allows for easier light coupling from an optical source, large tolerance on axial misalignments, which results in cheaper connectors and associated equip‐ ment, as well as less requirements on the skills of the installation personnel. However, the use of MMFs is at a cost of a bandwidth penalty with regards to their SMF counterparts, mainly due to the introduction of modal dispersion. This is the reason why MMF is com‐ monly applied to short-reach and medium-reach applications due to its low intrinsic attenu‐ ation despite its limited bandwidth. In particular, in the access network, the use of MMF may yield a considerable reduction of installation costs although the bandwidth-times length product of SMF is significantly higher than that of MMF. As in the access network, the fiber link lengths are less than 10km, however, the bandwidth of presently commercially available silica MMFs is quite sufficient.

On the other hand, compared to multimode silica optical fiber, polymer optical fiber (POF) offers several advantages over conventional multimode optical fiber over short distances (ranging from 100m to 1000m) such as the even potential lower cost associated with its easi‐ ness of installation, splicing and connecting. This is due to the fact that POF is more flexible and ductile [4], making it easier to handle. Consequently, POF termination can be realized faster and cheaper than in the case of silica MMF. This POF technology could be used for data transmission in many applications areas ranging like in-home, fiber to the building, wireless LAN backbone or office LAN among others. In addition, improvement in the band‐ width of POF fiber can be obtained by grading the refractive index, thus introducing the socalled Graded-Index POFs (GIPOFs). Although by grading the index profile significantly enhanced characteristics have been obtained, the bandwidth and attenuation still limit the transmission distances and capacity. Reduction of loss has been achieved by using amor‐ phous perfluorinated polymers for the core material. This new type of POF has been named perfluorinated GIPOF (PF GIPOF). This new fiber with low attenuation and large band‐ width has opened the way for high capacity transmission over POF based systems. In addi‐ tion to, as PF GIPOF has a relative low loss wavelength region ranging from 650nm to 1300nm (even theoretically in the third transmission window), it allows for WDM transmis‐ sion of several data channels. However, attenuation and bandwidth characteristics of the current state-of-the-art PF GIPOF are not at par with those of standard silica SMFs, but they still are superior to those of copper based technologies. Nevertheless, although these losses are coming down steadily due to ongoing improvements in the production processes of this still young technology, the higher than silica attenuation inhibits their use in relative long link applications, being mainly driven for covering in-building optical networks link lengths for in-building/home optical networks (with link lengths less than 1 km), and thus the loss per unit length is of less importance. It should be noted that available light sources for silica fiber based systems can be used with PF GIPOF systems. The same is true of connectors as in the case of Gigabit Ethernet equipment.

mission medium for wide area networks (WANs), especially in terrestrial and transoceanic communication backbones. The success of the SMF in long-haul communication backbones has given rise to the concept of optical networking, which is a central theme with currently driving research and development activities in the field of photonics. The main objective is to integrate voice, video, and data streams over all-optical systems as communication sig‐ nals make their way from WANs down to the end user by Fiber-To-The-x (FTTx), offices,

Although conventional SMF solutions have the potential of achieving very large band‐ widths, they suffer from high connections costs compared to copper or wireless solutions. For this reason, SMF has not been widely adopted by the end user (premises) where most of the interconnections are needed and less cost-sharing between users is obtainable. The un‐ derlying factor is the fact that the SMF core is typically only a few micrometers in diameter with the requirement of precise connecting, delicate installation and handling. Yet as the op‐ tical network gets closer to the end user, the system is characterized by numerous connec‐ tions, splices, and couplings that make the use of thin SMF impractical. An alternative technology is then the use of conventional silica-based multimode optical fiber (MMF) with larger core diameters. This fact allows for easier light coupling from an optical source, large tolerance on axial misalignments, which results in cheaper connectors and associated equip‐ ment, as well as less requirements on the skills of the installation personnel. However, the use of MMFs is at a cost of a bandwidth penalty with regards to their SMF counterparts, mainly due to the introduction of modal dispersion. This is the reason why MMF is com‐ monly applied to short-reach and medium-reach applications due to its low intrinsic attenu‐ ation despite its limited bandwidth. In particular, in the access network, the use of MMF may yield a considerable reduction of installation costs although the bandwidth-times length product of SMF is significantly higher than that of MMF. As in the access network, the fiber link lengths are less than 10km, however, the bandwidth of presently commercially

On the other hand, compared to multimode silica optical fiber, polymer optical fiber (POF) offers several advantages over conventional multimode optical fiber over short distances (ranging from 100m to 1000m) such as the even potential lower cost associated with its easi‐ ness of installation, splicing and connecting. This is due to the fact that POF is more flexible and ductile [4], making it easier to handle. Consequently, POF termination can be realized faster and cheaper than in the case of silica MMF. This POF technology could be used for data transmission in many applications areas ranging like in-home, fiber to the building, wireless LAN backbone or office LAN among others. In addition, improvement in the band‐ width of POF fiber can be obtained by grading the refractive index, thus introducing the socalled Graded-Index POFs (GIPOFs). Although by grading the index profile significantly enhanced characteristics have been obtained, the bandwidth and attenuation still limit the transmission distances and capacity. Reduction of loss has been achieved by using amor‐ phous perfluorinated polymers for the core material. This new type of POF has been named perfluorinated GIPOF (PF GIPOF). This new fiber with low attenuation and large band‐ width has opened the way for high capacity transmission over POF based systems. In addi‐

and in-homes.

76 Current Developments in Optical Fiber Technology

available silica MMFs is quite sufficient.

Therefore, it can be stated that polymer optical fiber technology has reached a level of devel‐ opment where it can successfully replace copper based technology and silica MMF for data transmission in short distance link applications such as in the office, in-home and LAN sce‐ narios. Moreover, PF GIPOF is forecasted to be able to support bit-rate distance products in the order of 10Gbps km [5]. Short distance communications system like in-home network and office LANs represent a unique opportunity for deployment of PF GIPOF based sys‐ tems for broadband applications. We can conclude that PF GIPOF technology is experienc‐ ing rapid development towards a mature solution for data transmission at short haul communications. The challenge remains in bringing this POF technology (transceiver, con‐ nectors,…) to a competitive price and performance level at the customer's premises.

Nevertheless, the potentials of these multimode fibers, both silica- and polymer-based, to support broadband radio-frequency, microwave and even millimetre wave transmission over short- and medium-reach distances are yet to be fully known. The belief is that a better understanding of the factors that affect the fiber bandwidth will prove very useful in in‐ creasing the bandwidth of silica MMF and PF GIPOF links in real situations. In the whole fiber network society to be realized in the near future, it is said that silica-based SMF fibers for long-haul backbone will be only several percents of the total use, and the remaining more than 90% would correspond to all-optical networks covering the last mile [6]. Link lengths may range from well below 1 km in LANs and residential houses, to only a few kilo‐ metres in larger building such as offices, hospitals, airport halls, etc. And it is now clear that the expected market is huge and researches and companies all over the world are competing to find a solution to this issue.

In this framework, the first part of this chapter, comprising sections 2 and 3 will briefly ad‐ dress the fundamentals of mutimode optical fibers as well as present transmission capacities. Like any communication channel, the multimode optical fiber also suffers from various signal distortions limiting its usefulness. The primary mechanisms contributing to the channel im‐ pairment in multimode fibers are discussed. Both silica-based MMFs and PF GIPOFs are es‐ sentially large-core optical waveguide supporting multiple transverse electromagnetic modes and they suffer from similar channel impairments. On the other hand, present capabilities of actual multimode optical fiber-based deployments are shown. In addition, different techni‐ ques reported in literature to carry microwave and millimetre-wave over optical networks, surmounting the multimode fiber bandwidth bottleneck, are also briefly described.

important factor limiting the transmission of a digital signal across large distances. The at‐ tenuation coefficient usually use units of dB/km through the medium due to the relatively high quality of transparency of modern optical transmission media. Empirical research over the years has shown that attenuation in optical fiber is caused primarily by both scattering and absorption. However, the fundamentals of both attenuation mechanisms are outside the

Multimode Graded-Index Optical Fibers for Next-Generation Broadband Access

http://dx.doi.org/10.5772/54245

79

On the one hand, silica exhibits fairly good optical transmission over a wide range of wave‐ lengths. In the near-infrared (near IR) portion of the spectrum, particularly around 1.5 μm, silica can have extremely low absorption and scattering losses of the order of 0.2 dB/km. Such remarkably-low losses are possible only because ultra-pure silicon is available, being essential for manufacturing integrated circuits and discrete transistors. Nevertheless, fiber cores are usually doped with various materials with the aim of raising the core refractive in‐ dex thus achieving propagation of light inside the fiber (by means of total internal reflection mechanisms). A high transparency in the 1.4-μm region is achieved by maintaining a low concentration of hydroxyl groups (OH). Alternatively, a high OH concentration is better for

On the other hand, until recently, the only commercially available types of POF were based on non-fluorinated polymers such as PolyMethylMethAcrylate (PMMA) (better known as Plexiglass®), widely used as core material for graded-index fiber [11] in addition with the utilization of several kinds of dopants. Although firstly developed PMMA-GIPOFs were demonstrated to obtain very high transmission bandwidth compared to that of Step-Index (SI) counterparts, the use of PMMA is not attractive due to its strong absorption driving a serious problem in the PMMA-based POFs at the near-IR (near-infrared) to IR regions. This is because of the large attenuation due to the high harmonic absorption loss by carbon-hy‐ drogen (C-H) vibration (C-H overtone). As a result, PMMA-based POFs could only be used at a few wavelengths in the visible portion of the spectrum, typically 530nm and 650nm, with typical attenuations around 150dB/km at 650nm. Today, unfortunately, almost all giga‐ bit optical sources operate in the near-infrared (typically 850nm or 1300nm), where PMMA and similar polymers are essentially opaque. Nevertheless, in this scenario, undistorted bit streams of 2.5Gbps over 200m of transmission length were successfully demonstrated over

On the other hand, it has been reported that one can eliminate this absorption loss by substi‐ tuting the hydrogen atoms in the polymer molecule for heavier atoms [13]. In this case, if the absorption loss decreases with the substitution of hydrogen for deuterium or halogen atoms (such as fluorine), the possible distance for signal transmission would be limited by disper‐ sion, and not by attenuation. Many polymers have been researched and reported in litera‐ ture in order to improve the bandwidth performance given by the first PMMA-based graded-index polymer optical fibers [14]. Nevertheless, today, amorphous perfluorinated (PF) GIPOF is widely used because of its high bandwidth and low attenuation from the visi‐ ble to the near IR wavelengths compared to PMMA GIPOF [15]. As a result, it is immediate‐ ly compatible with gigabit transmission sources, and can be used over distances of hundreds of meters. This fact is achieved mainly by reducing the number of carbon-hydro‐

scope of this chapter.

PMMA-GIPOF [12].

transmission in the ultraviolet (UV) region.

The second part of this chapter, which comprises sections 4, 5 and 6, respectively, focuses on the frequency response mathematical framework and the experimental results, respectively, of both types of multimode optical fibers. Some of the key factors affecting the frequency characteristics of both fiber types are addressed and studied. Theoretical simulations and measurements are shown for standard silica-based MMF as well as for PF GIPOF. Although some of these issues are interrelated, they are separately identified for clarity.

Finally, the main conclusions of this chapter are reported in Section 7.

## **2. Fundamentals of multimode optical fibers**

Despite the above advantages, the use of multimode optical fiber has been resisted for some years by fiber-optic link designers in favour of their SMF counterparts since Epworth dis‐ covered the potentially catastrophic problem of modal noise [7]. Modal noise in laser-based MMF links has been recently more completely addressed and theoretical as well as experi‐ mental proofs have shown that long-wavelength operation of MMFs is robust to modal noise [8-10]. This explains the spectacular regain of interest for MMFs as the best solution for the cabling of the access, in-home networks and LANs. The question that needs answer now in view of increasing the usefulness of MMF concerns the improvement of their dispersion characteristics, which is related to their reduced bandwidth.

For the transmission of communication signals, attenuation and bandwidth are important parameters. Both parameters will be briefly described in the following subsections, focusing on their impact over multimode fibers. In any case, the optical signal is distorted and attenu‐ ated when it propagates over the fiber. These effects have to be modeled when describing the signal transmission. They behave quite differently in different types of fibers. Whereas signal distortions in singlemode fibers (SMFs) are primarily caused by chromatic dispersion, i.e. the different speeds of individual spectral parts, the description of dispersion in multi‐ mode fibers (MMFs) is considerably more complex. Not only does chromatic dispersion oc‐ cur in them, but also has the generally much greater modal (or intermodal) dispersion.

It should be noted that, apart from attenuation, an important characteristic of an optical fi‐ ber as a transmission medium is its bandwidth. Bandwidth is a measure of the transmission capacity of a fiber data link. As multimode fibers can guide many modes having different velocities, they produce a signal response inferior to that of SMFs, being this modal disper‐ sion effect the limiting bandwidth factor. So bandwidth and dispersion are two parameters closely related.

#### **2.1. Attenuation**

Attenuation in fiber optics, also known as transmission loss, is the reduction in the intensity of the light beam with respect to distance traveled through a transmission medium, being an important factor limiting the transmission of a digital signal across large distances. The at‐ tenuation coefficient usually use units of dB/km through the medium due to the relatively high quality of transparency of modern optical transmission media. Empirical research over the years has shown that attenuation in optical fiber is caused primarily by both scattering and absorption. However, the fundamentals of both attenuation mechanisms are outside the scope of this chapter.

ques reported in literature to carry microwave and millimetre-wave over optical networks,

The second part of this chapter, which comprises sections 4, 5 and 6, respectively, focuses on the frequency response mathematical framework and the experimental results, respectively, of both types of multimode optical fibers. Some of the key factors affecting the frequency characteristics of both fiber types are addressed and studied. Theoretical simulations and measurements are shown for standard silica-based MMF as well as for PF GIPOF. Although

Despite the above advantages, the use of multimode optical fiber has been resisted for some years by fiber-optic link designers in favour of their SMF counterparts since Epworth dis‐ covered the potentially catastrophic problem of modal noise [7]. Modal noise in laser-based MMF links has been recently more completely addressed and theoretical as well as experi‐ mental proofs have shown that long-wavelength operation of MMFs is robust to modal noise [8-10]. This explains the spectacular regain of interest for MMFs as the best solution for the cabling of the access, in-home networks and LANs. The question that needs answer now in view of increasing the usefulness of MMF concerns the improvement of their dispersion

For the transmission of communication signals, attenuation and bandwidth are important parameters. Both parameters will be briefly described in the following subsections, focusing on their impact over multimode fibers. In any case, the optical signal is distorted and attenu‐ ated when it propagates over the fiber. These effects have to be modeled when describing the signal transmission. They behave quite differently in different types of fibers. Whereas signal distortions in singlemode fibers (SMFs) are primarily caused by chromatic dispersion, i.e. the different speeds of individual spectral parts, the description of dispersion in multi‐ mode fibers (MMFs) is considerably more complex. Not only does chromatic dispersion oc‐ cur in them, but also has the generally much greater modal (or intermodal) dispersion.

It should be noted that, apart from attenuation, an important characteristic of an optical fi‐ ber as a transmission medium is its bandwidth. Bandwidth is a measure of the transmission capacity of a fiber data link. As multimode fibers can guide many modes having different velocities, they produce a signal response inferior to that of SMFs, being this modal disper‐ sion effect the limiting bandwidth factor. So bandwidth and dispersion are two parameters

Attenuation in fiber optics, also known as transmission loss, is the reduction in the intensity of the light beam with respect to distance traveled through a transmission medium, being an

surmounting the multimode fiber bandwidth bottleneck, are also briefly described.

some of these issues are interrelated, they are separately identified for clarity.

Finally, the main conclusions of this chapter are reported in Section 7.

**2. Fundamentals of multimode optical fibers**

78 Current Developments in Optical Fiber Technology

characteristics, which is related to their reduced bandwidth.

closely related.

**2.1. Attenuation**

On the one hand, silica exhibits fairly good optical transmission over a wide range of wave‐ lengths. In the near-infrared (near IR) portion of the spectrum, particularly around 1.5 μm, silica can have extremely low absorption and scattering losses of the order of 0.2 dB/km. Such remarkably-low losses are possible only because ultra-pure silicon is available, being essential for manufacturing integrated circuits and discrete transistors. Nevertheless, fiber cores are usually doped with various materials with the aim of raising the core refractive in‐ dex thus achieving propagation of light inside the fiber (by means of total internal reflection mechanisms). A high transparency in the 1.4-μm region is achieved by maintaining a low concentration of hydroxyl groups (OH). Alternatively, a high OH concentration is better for transmission in the ultraviolet (UV) region.

On the other hand, until recently, the only commercially available types of POF were based on non-fluorinated polymers such as PolyMethylMethAcrylate (PMMA) (better known as Plexiglass®), widely used as core material for graded-index fiber [11] in addition with the utilization of several kinds of dopants. Although firstly developed PMMA-GIPOFs were demonstrated to obtain very high transmission bandwidth compared to that of Step-Index (SI) counterparts, the use of PMMA is not attractive due to its strong absorption driving a serious problem in the PMMA-based POFs at the near-IR (near-infrared) to IR regions. This is because of the large attenuation due to the high harmonic absorption loss by carbon-hy‐ drogen (C-H) vibration (C-H overtone). As a result, PMMA-based POFs could only be used at a few wavelengths in the visible portion of the spectrum, typically 530nm and 650nm, with typical attenuations around 150dB/km at 650nm. Today, unfortunately, almost all giga‐ bit optical sources operate in the near-infrared (typically 850nm or 1300nm), where PMMA and similar polymers are essentially opaque. Nevertheless, in this scenario, undistorted bit streams of 2.5Gbps over 200m of transmission length were successfully demonstrated over PMMA-GIPOF [12].

On the other hand, it has been reported that one can eliminate this absorption loss by substi‐ tuting the hydrogen atoms in the polymer molecule for heavier atoms [13]. In this case, if the absorption loss decreases with the substitution of hydrogen for deuterium or halogen atoms (such as fluorine), the possible distance for signal transmission would be limited by disper‐ sion, and not by attenuation. Many polymers have been researched and reported in litera‐ ture in order to improve the bandwidth performance given by the first PMMA-based graded-index polymer optical fibers [14]. Nevertheless, today, amorphous perfluorinated (PF) GIPOF is widely used because of its high bandwidth and low attenuation from the visi‐ ble to the near IR wavelengths compared to PMMA GIPOF [15]. As a result, it is immediate‐ ly compatible with gigabit transmission sources, and can be used over distances of hundreds of meters. This fact is achieved mainly by reducing the number of carbon-hydro‐ gen bonds that exist in the monomer unit by using partially fluorinated polymers. In 1998, the PF-based GIPOF had an attenuation of around 30dB/km at 1310nm. Attenuation of 15dB/km was achieved only three years after and lower and lower values of attenuation are being achieved. The theoretical limit of PF-based GIPOFs is ~0.5 dB/km at 1250-1390nm [16]. In the estimation, the attenuation factors are divided in two: material-inherent scattering loss and material-inherent absorption loss. The first factor is mainly given by the Rayleigh scattering, following the relation *αR* ∼(*λ*)−4 . The second factor is given by the absorption caused by molecular vibrations. A detailed explanation on the estimation processes is de‐ scribed [17].

slightly different times, leading to a wavelength-dependent pulse spreading, i.e. dispersion. As a matter of fact, the broader the spectral width (linewidth) of the optical source the great‐ er is the chromatic dispersion. In PF-based POFs the chromatic dispersion is much smaller than in silica MMF for wavelengths up to 1100nm. For wavelengths above 1100nm, the dis‐ persion of the PF-based GIPOF retains and the dispersion of silica MMF increases. The ex‐

chrom 2 ( ) ;

 l

where *D*(*λ*) is the material dispersion parameter (usually given in ps/nm⋅km), *Δλ* is the spectral width of the light source, and *L* is the length of the fiber. Fig. 3(a) depicts a typical material dispersion curve as a function of the operating wavelength. for a PF GIPOF as well as a silica-based MMF with a SiO2 core doped with 6.3mol-% GeO2 and a SiO2 cladding. It is clearly seen the better performance in terms of material dispersion of the PF GIPOF com‐

*t D LD*

ll

( ) ( ) 2

*d n*

l

D = ×D × =- × (1)

Multimode Graded-Index Optical Fibers for Next-Generation Broadband Access

**1 1.5 2 2.5 3 3.5 4 108**

**(b)**

**Index exponent (α)**

**PF GIPOF@λ=1300nm PF GIPOF@λ=850nm PF GIPOF@λ=650nm PMMA GIPOF@λ=650nm**

http://dx.doi.org/10.5772/54245

81

l

*c d* l

pared to the silica-based counterpart, especially in the range up to 1100nm. 10 Optical Fiber

**109**

**3‐dBo bandwidth, GHz over 100m**

**Figure 3.** (a) Typical material dispersion of the central core region for a silica-based MMF (blue solid line) and PF GIPOF (red dashed line). (b) Relation between the refractive index profile and bandwidth of 100m-long PF GIPOF. PMMA-

On the other hand, modal dispersion is caused by the fact that the different modes (light paths) within the fiber carry components of the signals at different velocities, which ultimate results in pulse overlap and a garbled communications signal. Lower order modes propa‐ gate mainly along the waveguide axis, while the higher-order modes follow a more zigzag path, which is longer. If a short light pulse is excited at the input of the fiber, the lowest or‐ der modes arrive first at the end of the fiber and the higher order modes arrive later. The output pulse will thus be built up of all modes, with different arrival times, so the pulse is

**1010**

**1011**

**1012**

pression of such dispersion is given by:

GIPOF at 650nm is plotted for comparison.

**-700 -600 -500 -400 -300 -200 -100 0 100**

**Material dispersion (ps/km.nm)**

broadened.

**400 600 800 1000 1200 1400 1600 -800**

**(a)**

**Silica MMF PF GIPOF**

**Wavelength (nm)**

#### **2.2. Dispersion**

As aforementioned, pulse broadening in MMFs is generally caused by modal dispersion and chromatic dispersion. For MMFs it is necessary to consider the factors of material, modal and profile dispersion. The latter considers the wavelength dependence on the relative re‐ fractive index difference in graded index fibers. Waveguide dispersion additionally occurs in singlemode fibers, whereas profile dispersion and modal dispersion do not.

**Figure 2.** Dispersion mechanisms in optical fibers.

All the kinds of dispersion appearing in optical fibers are summarized in Fig. 2. The mecha‐ nisms dependent on the propagation paths are marked in blue, whereas the wavelength-de‐ pendent processes are marked in red. Those mechanisms only affecting SMFs are outside from the scope of this work so they will be avoided. For multimode fibers modal dispersion and chromatic dispersion are the relevant processes to be considered.

In a generic description, chromatic dispersion is introduced by the effect that the speed of propagation of light of different wavelengths differs resulting in a wavelength dependence of the modal group velocity. The end result is that different spectral components arrive at slightly different times, leading to a wavelength-dependent pulse spreading, i.e. dispersion. As a matter of fact, the broader the spectral width (linewidth) of the optical source the great‐ er is the chromatic dispersion. In PF-based POFs the chromatic dispersion is much smaller than in silica MMF for wavelengths up to 1100nm. For wavelengths above 1100nm, the dis‐ persion of the PF-based GIPOF retains and the dispersion of silica MMF increases. The ex‐ pression of such dispersion is given by:

gen bonds that exist in the monomer unit by using partially fluorinated polymers. In 1998, the PF-based GIPOF had an attenuation of around 30dB/km at 1310nm. Attenuation of 15dB/km was achieved only three years after and lower and lower values of attenuation are being achieved. The theoretical limit of PF-based GIPOFs is ~0.5 dB/km at 1250-1390nm [16]. In the estimation, the attenuation factors are divided in two: material-inherent scattering loss and material-inherent absorption loss. The first factor is mainly given by the Rayleigh

caused by molecular vibrations. A detailed explanation on the estimation processes is de‐

As aforementioned, pulse broadening in MMFs is generally caused by modal dispersion and chromatic dispersion. For MMFs it is necessary to consider the factors of material, modal and profile dispersion. The latter considers the wavelength dependence on the relative re‐ fractive index difference in graded index fibers. Waveguide dispersion additionally occurs

All the kinds of dispersion appearing in optical fibers are summarized in Fig. 2. The mecha‐ nisms dependent on the propagation paths are marked in blue, whereas the wavelength-de‐ pendent processes are marked in red. Those mechanisms only affecting SMFs are outside from the scope of this work so they will be avoided. For multimode fibers modal dispersion

In a generic description, chromatic dispersion is introduced by the effect that the speed of propagation of light of different wavelengths differs resulting in a wavelength dependence of the modal group velocity. The end result is that different spectral components arrive at

and chromatic dispersion are the relevant processes to be considered.

in singlemode fibers, whereas profile dispersion and modal dispersion do not.

. The second factor is given by the absorption

scattering, following the relation *αR* ∼(*λ*)−4

80 Current Developments in Optical Fiber Technology

**Figure 2.** Dispersion mechanisms in optical fibers.

scribed [17].

**2.2. Dispersion**

$$
\Delta t\_{\text{chom}} = D(\lambda) \cdot \Delta \lambda \cdot L \; ; \; D\left(\lambda\right) = -\frac{\lambda}{c} \cdot \frac{d^2 n\left(\lambda\right)}{d\lambda^2} \tag{1}
$$

where *D*(*λ*) is the material dispersion parameter (usually given in ps/nm⋅km), *Δλ* is the spectral width of the light source, and *L* is the length of the fiber. Fig. 3(a) depicts a typical material dispersion curve as a function of the operating wavelength. for a PF GIPOF as well as a silica-based MMF with a SiO2 core doped with 6.3mol-% GeO2 and a SiO2 cladding. It is clearly seen the better performance in terms of material dispersion of the PF GIPOF com‐ pared to the silica-based counterpart, especially in the range up to 1100nm. 10 Optical Fiber

**Figure 3.** (a) Typical material dispersion of the central core region for a silica-based MMF (blue solid line) and PF GIPOF (red dashed line). (b) Relation between the refractive index profile and bandwidth of 100m-long PF GIPOF. PMMA-GIPOF at 650nm is plotted for comparison.

On the other hand, modal dispersion is caused by the fact that the different modes (light paths) within the fiber carry components of the signals at different velocities, which ultimate results in pulse overlap and a garbled communications signal. Lower order modes propa‐ gate mainly along the waveguide axis, while the higher-order modes follow a more zigzag path, which is longer. If a short light pulse is excited at the input of the fiber, the lowest or‐ der modes arrive first at the end of the fiber and the higher order modes arrive later. The output pulse will thus be built up of all modes, with different arrival times, so the pulse is broadened.

To overcome and compensate for modal dispersion, the refractive index of the fiber core (or, alternatively, graded index exponent of the fiber core) is graded parabola-like from a high index at the fiber core center to a low index in the outer core region, i.e. by forming a grad‐ ed-index (GI) fiber core profile. In such fibers, light travelling in a low refractive-index struc‐ ture has a higher speed than light travelling in a high index structure and the higher order modes bend gradually towards the fiber axis in a shorter period of time because the refrac‐ tive index is lower at regions away from the fiber core. The objective of the GI profile is to equalise the propagation times of the various propagating modes. Therefore, the time differ‐ ence between the lower order modes and the higher order modes is smaller, and so the broadening of the pulse leaving the fiber is reduced and, consequently, the transmission bandwidth can be increased over the same transmission length. For negligible modal disper‐ sion the ideal refractive index profile is around 2. This refractive index profile formed in the core region of multimode optical fibers plays a great role determining its bandwidth, be‐ cause modal dispersion is generally dominant in the multimode fiber although an optimum refractive index profile can produce the minimum modal dispersion, i.e. larger bandwidth being almost independent of the launching conditions [18]. Fig. 3(b) shows the calculated bandwidth of a PF-based GIPOF operating at different wavelengths, in which it is assumed that the source spectral width is 1nm, with regards to the refractive index profile, *α*. The da‐ ta of the bandwidth of a PMMA-based GIPOF at 650nm is also shown for comparison show‐ ing a maximum limited to approximately 1.8GHz for 100m by the large material dispersion. On the other hand, the smaller material dispersion of the PF polymer-based GIPOF permits a maximum bandwidth of 4GHz even at 650nm. Furthermore, when the signal wavelength is 1300nm, theoretical maximum bandwidth achieves 92GHz for 100m. The difference of the optimum index exponent value between 650nm and 1300nm wavelengths is caused by the inherent polarization properties of material itself. It should be mentioned that a uniform ex‐ citation has been assumed and no differential mode attenuation (DMA) and mode coupling (MC) effects have been considered. These effects will be briefly described later on.

Fig. 4(a), the chromatic dispersion will essentially limit the total bandwidth for *α*1 <*α* <*α*2, whilst for *α* <*α*1 or *α* >*α*2 the modal dispersion will cause the main limitation. In other words, when the index exponent is around the optimum value (*α*-resonance), the modal dispersion effect on the possible 3-dB bandwidth (and so on the bit rate) is minimized and the chromat‐ ic dispersion dominates this performance. On the other hand, when the index exponent is deviated from the optimum, the modal dispersion increases becoming the main source of

Multimode Graded-Index Optical Fibers for Next-Generation Broadband Access

Multimode Graded-Index Optical Fibers for Next-Generation Broadband Access

http://dx.doi.org/10.5772/54245

**1 1.5 2 2.5 3 3.5 4 108**

**Index exponent (α)**

13

83

bandwidth limitation.

**10-12**

**Total dispersion (seg/100m)**

**10-11**

**10-10**

**10-9**

or PMMA-based GIPOF fibers.

*2.2.1. Dispersion modelling approach*

**1 1.5 2 2.5 3 3.5 4 10-13**

**Index exponent (α)**

**10-12 10-11 10-10**

**2 2.05 2.1 2.15 2.2 2.25 2.3 2.35 2.4 2.45 2.5 10-13**

**109**

**3‐dBo bandwidth, Hz over 100m**

**Figure 4.** (a) Dispersion effects versus refractive index profile for a 100m-long PF GIPOF, assuming equal power in all modes and a 1300nm light source with 1nm of spectral linewidth. Inset: zoom near the optimum profile region. (b)

It is also noteworthy that, since the PF polymer has low material and profile dispersions and the wavelength dependence of the optimum profile is decreased, a high bandwidth per‐ formance can be maintained over a wide wavelength range, compared to multimode silica

The propagation characteristics of optical fibers are generally described by the wave equa‐ tion which results directly from Maxwell's equations and characterizes the wave propaga‐ tion in a fiber as a dielectric wave guide in the form of a differential equation. In order to solve the equation, the field distributions of all modes and the attendant propagation con‐

The wave equation is basically a vector differential equation which can, however, under the condition of weak wave guidance be transformed into a scalar wave equation in which the polarization of the wave plays no role whatsoever [19]. The prerequisite for the weak wave guiding is that the refractive indices between the core and cladding hardly differ, being ful‐ filled quite well in silica fibers when the difference in refractive index between the core and cladding region is below 1%. Calculations based on the scalar wave equation only show very small inaccuracies with regards to the group delay. Then, the equations which describe the electric and magnetic fields are decoupled so that you can write a scalar wave equation.

stants, which results from the use of the boundary conditions, have to be determined.

Corresponding 3-dBo bandwidth. (—) Total dispersion ; **(- -)** Modal dispersion ; (---) Chromatic dispersion.

**1010**

**1011**

**1012**

**1013**

**(a) (b)**

To summarize, the different types of dispersion that appear in a MMF and their relation to the fiber bandwidth are analyzed in Fig. 4. This figure reports the PF GIPOF chromatic and modal dispersion and the total bandwidth of a 100m-long link as a function of the refractive index profile, at a wavelength of 1300nm. Fig. 4(b) depicts the corresponding 3-dBo (3-dB optical bandwidth) baseband bandwidth, related to Fig. 4(a). These plots are based on the same analysis of Fig. 3, which assumed a uniform excitation and neglected both the DMA and mode coupling effects. From these figures, the chromatic bandwidth is seen to show lit‐ tle dependence on *α*, which means that the material dispersion is the dominant contribution (with regards to the profile dispersion) in the transmission window considered. On the oth‐ er hand, the modal bandwidth shows a highly peaked resonance with *α*. This is the well known characteristic feature of the grading. With the present choice of parameters values, that maximum bandwidth (i.e. minimum dispersion) approximately occurs at 2.18 at 1300nm, as shown in Fig. 4(a). Furthermore, the presence of crossover points (namely *α*1 and *α*2) shows that the total bandwidth may be limited either by the modal dispersion or the chromatic dispersion depending on the value of the refractive index profile. Focusing on

13

Fig. 4(a), the chromatic dispersion will essentially limit the total bandwidth for *α*1 <*α* <*α*2, whilst for *α* <*α*1 or *α* >*α*2 the modal dispersion will cause the main limitation. In other words, when the index exponent is around the optimum value (*α*-resonance), the modal dispersion effect on the possible 3-dB bandwidth (and so on the bit rate) is minimized and the chromat‐ ic dispersion dominates this performance. On the other hand, when the index exponent is deviated from the optimum, the modal dispersion increases becoming the main source of bandwidth limitation. Multimode Graded-Index Optical Fibers for Next-Generation Broadband Access

**Figure 4.** (a) Dispersion effects versus refractive index profile for a 100m-long PF GIPOF, assuming equal power in all modes and a 1300nm light source with 1nm of spectral linewidth. Inset: zoom near the optimum profile region. (b) Corresponding 3-dBo bandwidth. (—) Total dispersion ; **(- -)** Modal dispersion ; (---) Chromatic dispersion.

It is also noteworthy that, since the PF polymer has low material and profile dispersions and the wavelength dependence of the optimum profile is decreased, a high bandwidth per‐ formance can be maintained over a wide wavelength range, compared to multimode silica or PMMA-based GIPOF fibers.

#### *2.2.1. Dispersion modelling approach*

To overcome and compensate for modal dispersion, the refractive index of the fiber core (or, alternatively, graded index exponent of the fiber core) is graded parabola-like from a high index at the fiber core center to a low index in the outer core region, i.e. by forming a grad‐ ed-index (GI) fiber core profile. In such fibers, light travelling in a low refractive-index struc‐ ture has a higher speed than light travelling in a high index structure and the higher order modes bend gradually towards the fiber axis in a shorter period of time because the refrac‐ tive index is lower at regions away from the fiber core. The objective of the GI profile is to equalise the propagation times of the various propagating modes. Therefore, the time differ‐ ence between the lower order modes and the higher order modes is smaller, and so the broadening of the pulse leaving the fiber is reduced and, consequently, the transmission bandwidth can be increased over the same transmission length. For negligible modal disper‐ sion the ideal refractive index profile is around 2. This refractive index profile formed in the core region of multimode optical fibers plays a great role determining its bandwidth, be‐ cause modal dispersion is generally dominant in the multimode fiber although an optimum refractive index profile can produce the minimum modal dispersion, i.e. larger bandwidth being almost independent of the launching conditions [18]. Fig. 3(b) shows the calculated bandwidth of a PF-based GIPOF operating at different wavelengths, in which it is assumed that the source spectral width is 1nm, with regards to the refractive index profile, *α*. The da‐ ta of the bandwidth of a PMMA-based GIPOF at 650nm is also shown for comparison show‐ ing a maximum limited to approximately 1.8GHz for 100m by the large material dispersion. On the other hand, the smaller material dispersion of the PF polymer-based GIPOF permits a maximum bandwidth of 4GHz even at 650nm. Furthermore, when the signal wavelength is 1300nm, theoretical maximum bandwidth achieves 92GHz for 100m. The difference of the optimum index exponent value between 650nm and 1300nm wavelengths is caused by the inherent polarization properties of material itself. It should be mentioned that a uniform ex‐ citation has been assumed and no differential mode attenuation (DMA) and mode coupling

82 Current Developments in Optical Fiber Technology

(MC) effects have been considered. These effects will be briefly described later on.

To summarize, the different types of dispersion that appear in a MMF and their relation to the fiber bandwidth are analyzed in Fig. 4. This figure reports the PF GIPOF chromatic and modal dispersion and the total bandwidth of a 100m-long link as a function of the refractive index profile, at a wavelength of 1300nm. Fig. 4(b) depicts the corresponding 3-dBo (3-dB optical bandwidth) baseband bandwidth, related to Fig. 4(a). These plots are based on the same analysis of Fig. 3, which assumed a uniform excitation and neglected both the DMA and mode coupling effects. From these figures, the chromatic bandwidth is seen to show lit‐ tle dependence on *α*, which means that the material dispersion is the dominant contribution (with regards to the profile dispersion) in the transmission window considered. On the oth‐ er hand, the modal bandwidth shows a highly peaked resonance with *α*. This is the well known characteristic feature of the grading. With the present choice of parameters values, that maximum bandwidth (i.e. minimum dispersion) approximately occurs at 2.18 at 1300nm, as shown in Fig. 4(a). Furthermore, the presence of crossover points (namely *α*1 and *α*2) shows that the total bandwidth may be limited either by the modal dispersion or the chromatic dispersion depending on the value of the refractive index profile. Focusing on

The propagation characteristics of optical fibers are generally described by the wave equa‐ tion which results directly from Maxwell's equations and characterizes the wave propaga‐ tion in a fiber as a dielectric wave guide in the form of a differential equation. In order to solve the equation, the field distributions of all modes and the attendant propagation con‐ stants, which results from the use of the boundary conditions, have to be determined.

The wave equation is basically a vector differential equation which can, however, under the condition of weak wave guidance be transformed into a scalar wave equation in which the polarization of the wave plays no role whatsoever [19]. The prerequisite for the weak wave guiding is that the refractive indices between the core and cladding hardly differ, being ful‐ filled quite well in silica fibers when the difference in refractive index between the core and cladding region is below 1%. Calculations based on the scalar wave equation only show very small inaccuracies with regards to the group delay. Then, the equations which describe the electric and magnetic fields are decoupled so that you can write a scalar wave equation.

The models based on the solution of the wave equation in the form of a mode solver differ fundamentally only in regard to the solution method and whether or not you are proceeding from a more computer-intensive vector wave equation or the more usual scalar wave equa‐ tion. In the technical literature solutions for the vector wave equation with the aid of finite element method (FEM) [20], with finite differences (Finite Difference Time Domain Method - FDTD) [21] and the beam propagation method (BPM) [22] are well known. These are gener‐ ally used for very small, mostly singlemode waveguides in which polarization characteristics play a role. Multimode fibers (including polymer fibers) are quite large and the polarization of light counts for only a few centimeters. That is why analytical estimations of the scalar wave equation, the so-called WKB (Wentzel-Kramers-Brillouin, from whom the name derives) Method and Ray Tracing [23], are primarily used for the modeling of multi‐ mode fibers. In the latter, the propagating light through an optical system can be seen as the propagation of individual light rays following a slightly different path; these paths can be calculated using standard geometrical optics.

where *Ai*,*k* and *λi*,*k* are the oscillator strength and the oscillator wavelength, respectively

On the other hand, from the WKB analysis, the modal propagation constants can be approx‐ imately derived as following [26], in which each guided mode has its own propagation con‐

*M*

a l

1/2

ê ú ë û (5)

= - (6)

 a -

 a

1/2 2 2

l

2

+ é ù

 l

where *m* stands for the principal mode number [27] and *k* =2*π* / *λ* is the free space wave‐ number. This so-called principal mode number (mode group number or mode number) can be defined as *m*=2*μ* + *ν* + 1 in which the parameters *μ* and *ν* are referred to as radial and azi‐ muthal mode number, respectively. Physically, *μ* and *ν* represent the maximum intensities that may appear in the radial and azimuthal direction in the field intensities of a given mode. For a deeper analysis works reported in [28, 29] are recommended. On the other hand, *M* (*α*, *λ*) is the total number of mode groups that can be potentially guided in the fi‐

> 1 ( ) ( ) (,) 2

> > l a

( ) 2 ( ,) , 2 *d m m*

( ) ( )(4 ( )) ( ,) 1 1 2()

l el

a

*N m m m*

= - - D + é ù é ù æö æö ê ú ê ú = ç÷ ç÷ ê ú ê ú èø èø êë ú êû ë úû

p

*c d* lbl

2 2 1

a

D + + +

a

*c MM*

 l

× D =

l a l

As a consequence of Eq. 4, the delay time *τ*(*m*, *λ*) of a mode depends only on its principal mode number. It should be mentioned that the differences in modal delay are those that de‐ termine the modal dispersion. The delay time of the guided modes (or modal delay per unit

*n M a*

 p

al

t l

length) can be derived from Eq. 4 using the definition:

where *c* is the speed of light in vacuum, deriving in:

2 *m*

t tl l

where *ε*(*λ*) is the profile dispersion parameter given by [30]:

1/2 2 2

Multimode Graded-Index Optical Fibers for Next-Generation Broadband Access

http://dx.doi.org/10.5772/54245

(4)

85

(7)

a

+

a

(both parameters are often gathered under the term of Sellmeier constants).

1 ( ,) () 1 2() (,) *m m m nk*

= -D é ù æ ö ê ú = ç ÷ è ø ë û

 l

stant and therefore propagates at its own particular velocity:

b bl

ber, given by [26]:

Focusing on the WKB method, the latter primarily makes available expressions, that can be calculated efficiently, for describing the propagations constants and group delays of the propagating modes within the fiber. In this method, whereas the field distributions in step index profile fibers can be determined analytically, the refractive index distribution over the radius of a graded index fiber can generally be described with a power-law, as Eq. 2 states. Fibers with power-law profiles possess the characteristic that the modes can be put in mode groups which have the same propagation constant and also similar mode delay (at least for exponents close to *α* =2). The propagation times of the modes are only then dependent on the propagation constant and then the group delay can be determined with the aid of the WKB Method by differentiating the propagation constant from the angular frequency [24].

$$n\left(r,\lambda\right) = \begin{cases} n\_1\left(\lambda\right) \left[1 - 2\Lambda\left(\lambda\right)\left(\frac{r}{a}\right)^a\right]^{1/2} & \text{for } 0 \le r \le a\\ n\_1\left(\lambda\right) \left[1 - 2\Lambda\left(\lambda\right)\right]^{1/2} & \text{for } r \ge a \end{cases} \quad \text{with } \Lambda\left(\lambda\right) = \frac{n\_1^{2^\star}\left(\lambda\right) - n\_2^{2^\star}\left(\lambda\right)}{2n\_1^{2^\star}\left(\lambda\right)}\tag{2}$$

where *r* is the offset distance from the core center, *a* is the fiber core radius (i.e. the radius at which the index *n*(*r*, *λ*) reaches the cladding value *n*2(*λ*)=*n*1(*λ*) 1−2*Δ*(*λ*) 1/2 ), *n*1(*λ*) is the re‐ fractive index in the fiber core center, *λ* is the free space wavelength of the fiber excitation light, *α* is the refractive index exponent and *Δ*(*λ*) is the relative refractive index difference between the core and the cladding. It is usually assumed that the core and cladding refrac‐ tive index materials follow a three-term Sellmeier function of wavelength [25] given by:

$$m\_i(\mathcal{A}) = \left(1 + \sum\_{k=1}^3 \frac{A\_{i,k}\lambda^2}{\lambda^2 - \lambda\_{i,k}^2}\right)^{1/2} \quad \text{with i=1 (core), 2 (cladding)}\tag{3}$$

where *Ai*,*k* and *λi*,*k* are the oscillator strength and the oscillator wavelength, respectively (both parameters are often gathered under the term of Sellmeier constants).