This type of MDM can be expected to have the interesting optical features not only in the negative refraction index but also in the mode properties. The above mentioned waveguide structure can commonly accommodate only surface plasmon mode. When the thickness of guiding layer is increased to millimeter-scale, such waveguide can accommodate thousands of guided modes, and ultrahigh-order modes (UHM) can be excited. In this case the MDM is commonly called symmetrical metal-cladding waveguide (SMCW) [5]. To our knowledge, however, there have been few investigations about the UHM properties of the SMCW. In this chapter, we have reported the UHM properties of the SMCW and their applications on optical devices. The UHM of SMCW can be excited by free space coupling [6] in small incident angle. In section 2, we present some details of the UHM properties such as large mode spacing, sensitive to the change of waveguide parameters, and slow wave effect. Section 3 introduces applications on optical devices such as modulators, filters and sensors, which are closely related to the UHM in guiding layer.

© 2012 Chen, licensee InTech. This is an open access chapter 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. © 2012 The Author(s). Licensee InTech. This chapter is 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.

#### **2. Properties of SMCW**

The SMCWs are the millimeter-scale guiding layers (dielectric constant *ε1*, thickness *d*) sandwiched between two metal films (Fig.1). The upper metal film (dielectric constant ε2, thickness *h*) of several dozens of nanometer acts as coupling layer as well as a metal cladding; and the base metal layer (dielectric constant ε2) acts as a substrate of the waveguide, which is thick enough to prevent the influence of the glass flat on guiding layer. For modulation applications, the upper and base metal films also serve as electrodes of the device. If the light incidents from air to the guiding layer directly, it can meet the coupling condition and couple the mode with effective index less than 1. The allowed range of the effective index in SMCW can be reached from 0 to n1 for the guided modes, where n1= (ε1)1/2 is the refractive index of the guiding slab. This range is much wider than that available to the usual waveguides. The principle model of free-space coupling is shown in Fig.2. When the beam incomes from the air to the metal surface, it will generate evanescent field in the metal. Since the upper metal film is thin (dozens of nanometer), the tail of evanescent field can reach the interface of guided wave layer of the metal. It will generate an opposite evanescent field on the interface. Due to the interaction between two evanescent fields from opposite directions, the incident light can be coupled into waveguide.

Optical Devices Based on Symmetrical Metal Cladding Waveguides 129

*k j* (2)

sin (3)

(1)

**2.1. The attenuated total reflection spectrum**

the four-layer optical system for TE mode is written as [7]

constant of guided modes are, respectively, expressed as follows:

2

2

*r*

*h*=30nm, and *d*= 0.38mm.

When a laser beam cast on the upper metal layer with resonant conditions, a large part of the light energy is transferred in the guiding layer, resulting in the attenuated total reflection (ATR) spectrum, which describes the relation between reflectivity and incident angle or wavelength of the reflected light. We take TE mode for example. The reflection coefficient of

32 32 21 1 21 2 21 1 2

here rij=(κi-κj)/(κi+κj), is the complex Fresnel reflection coefficient for the boundary between media i and j, in which the normal components of the wave vectors and propagation

> 2 2 0 ,( 1,2,3) *j j*

> > 0 3

here k0=2π/λ is the wavenumber in vacuum; ε3 is the dielectric constant at medium in which the light incident and reflected; *β* is the propagation constant of the guided modes; *θ* and *λ* are the incident angle and wavelength, respectively. As shown in Fig.3, when the energy of the incident light is coupled into the guided modes, the intensity of the reflected light R=|r|2 decreases dramatically, and a series of reflection dips in the ATR spectrum are produced.

**Figure 3.** Simulated ATR curve with the following parameters: *ε2*=-28+i1.8, *ε*1=2.278, *λ*= 859.8nm,

The experimental arrangement for measuring ATR spectrum is shown schematically in Fig.4. The SMCW is fixed on a computer controlled *θ/2θ* goniometer. After passing through the polarizer and mirror, a collimated laser light beam is incident into the structure. Angular scan is carried out by a computer-controlled *θ/2θ* goniometer. As the goniometer rotates, the

*k*

21 1 32 21 2 32 21 1 2

*r i d rr i h rr i d i h*

1 exp(2 ) exp(2 ) exp(2 )exp(2 ) *r rr i d r i h r i d i h*

exp(2 ) exp(2 ) exp(2 )exp(2 )

**Figure 1.** Symmetrical metal-cladding waveguide structure

**Figure 2.** Principle model of free-space coupling

#### **2.1. The attenuated total reflection spectrum**

128 Optical Devices in Communication and Computation

The SMCWs are the millimeter-scale guiding layers (dielectric constant *ε1*, thickness *d*) sandwiched between two metal films (Fig.1). The upper metal film (dielectric constant ε2, thickness *h*) of several dozens of nanometer acts as coupling layer as well as a metal cladding; and the base metal layer (dielectric constant ε2) acts as a substrate of the waveguide, which is thick enough to prevent the influence of the glass flat on guiding layer. For modulation applications, the upper and base metal films also serve as electrodes of the device. If the light incidents from air to the guiding layer directly, it can meet the coupling condition and couple the mode with effective index less than 1. The allowed range of the effective index in SMCW can be reached from 0 to n1 for the guided modes, where n1= (ε1)1/2 is the refractive index of the guiding slab. This range is much wider than that available to the usual waveguides. The principle model of free-space coupling is shown in Fig.2. When the beam incomes from the air to the metal surface, it will generate evanescent field in the metal. Since the upper metal film is thin (dozens of nanometer), the tail of evanescent field can reach the interface of guided wave layer of the metal. It will generate an opposite evanescent field on the interface. Due to the interaction between two evanescent fields from

opposite directions, the incident light can be coupled into waveguide.

**Figure 1.** Symmetrical metal-cladding waveguide structure

**Figure 2.** Principle model of free-space coupling

**2. Properties of SMCW**

When a laser beam cast on the upper metal layer with resonant conditions, a large part of the light energy is transferred in the guiding layer, resulting in the attenuated total reflection (ATR) spectrum, which describes the relation between reflectivity and incident angle or wavelength of the reflected light. We take TE mode for example. The reflection coefficient of the four-layer optical system for TE mode is written as [7]

$$r = \frac{r\_{32} - r\_{32}r\_{21}^2 \exp(2i\kappa\_1 d) + r\_{21} \exp(2i\kappa\_2 h) - r\_{21} \exp(2i\kappa\_1 d) \exp(2i\kappa\_2 h)}{1 - r\_{21}^2 \exp(2i\kappa\_1 d) + r\_{32}r\_{21} \exp(2i\kappa\_2 h) - r\_{32}r\_{21} \exp(2i\kappa\_1 d) \exp(2i\kappa\_2 h)} \tag{1}$$

here rij=(κi-κj)/(κi+κj), is the complex Fresnel reflection coefficient for the boundary between media i and j, in which the normal components of the wave vectors and propagation constant of guided modes are, respectively, expressed as follows:

$$\kappa\_j = \sqrt{k\_0^2 \varepsilon\_j - \beta^2} \text{ ( $j = 1, 2, 3$ )}\tag{2}$$

$$
\beta = k\_0 \sqrt{\varepsilon\_3} \sin \theta \tag{3}
$$

here k0=2π/λ is the wavenumber in vacuum; ε3 is the dielectric constant at medium in which the light incident and reflected; *β* is the propagation constant of the guided modes; *θ* and *λ* are the incident angle and wavelength, respectively. As shown in Fig.3, when the energy of the incident light is coupled into the guided modes, the intensity of the reflected light R=|r|2 decreases dramatically, and a series of reflection dips in the ATR spectrum are produced.

**Figure 3.** Simulated ATR curve with the following parameters: *ε2*=-28+i1.8, *ε*1=2.278, *λ*= 859.8nm, *h*=30nm, and *d*= 0.38mm.

The experimental arrangement for measuring ATR spectrum is shown schematically in Fig.4. The SMCW is fixed on a computer controlled *θ/2θ* goniometer. After passing through the polarizer and mirror, a collimated laser light beam is incident into the structure. Angular scan is carried out by a computer-controlled *θ/2θ* goniometer. As the goniometer rotates, the

incident angle will change, while the photodiode keeps consistently monitoring the reflected light intensity to scan the reflectance curve. The reflected light intensity is captured by a photodiode fixed on the 2*θ* plate of the goniometer and converted into a voltage signal. At small incident angles, UHM resonance will occur and couple the incident light energy into the SMCW by the free space coupling technique. Then in the reflective curve, a series of resonance dips take place in the angular spectrum, as illustrated in Fig.3.

Optical Devices Based on Symmetrical Metal Cladding Waveguides 131

(8)

(9)

(10)

(11)

(12)

(7)

Furthermore, when d reaches millimeter-scale, the waveguide can accommodate thousands of guided modes. For example, use the parameters: ε2 = −28 + i1.8, ε1 = 2.278, λ= 859.8nm, *h* = 30 nm, and *d* = 0.38 mm, *m* is 1333 for the highest mode. However, the maximum of the absolute value of the second term on the right in Eq. (4) is *π*. It will not generate much error if ignoring it, and the approximate dispersion equation of the UHMs for both TE and TM modes is [5]

2 *h Nm m*( 0,1,2,......)

where N = *β/k0* is the effective index of the UHM. Eq. (7) implies that when N is close to zero,

Because UHMs have a short retention time in waveguide layer, any tiny change of *λ*, n1 and *d* will cause the sensitive change of *N*. If we define sensitivity *SN* as the derivative of

> *N N S*

> > 1 *N n n N*

*N*

1

2 2 1 *N n N*

2 2 1 *N n N d Nd*

From above mentioned three equations, sensitivity is in inverse proportion to effective index *N*. Therefore, we can obtain high sensitivity when UHM is excited. According to ray optics theory, with the same propagation distance, the small incident angle means that UHM will experience more times reflection and light propagation distance will be longer, resulting in a series of special features different from low-order modes. This property is extremely useful

Finally, according to Eq. (4), tiny change of wavelength can generate great change of effective index, illustrating that UHM has strong dispersion property and consequent slow

> *dN c d n n dn d*

In the equation, group velocity expression is totally different from those conventional slow light schemes, which is composed of two contributions that are shown in Eq. (12): one

11 1

light effect. Using Eq. (7), we can also obtain the group velocity of UHM:

*g*

where *ξ* represents *λ*, *n1* or *d.* By the total differential of Eq. (7), we can get:

2

1

effective index to certain characteristic parameter, that is

the UHM exhibits polarization insensibility.

to design sensors and modulators.

**Figure 4.** Experimental arrangement for measuring ATR spectrum

#### **2.2. Ultrahigh-order mode**

Disregarding the effects resulting from the limited thickness of the metal film, dispersion equation of the guided modes in SMCW can be written as

$$\kappa\_1 h = m\pi + 2\tan^{-1}(\rho \frac{a\_2}{\kappa\_1}), \quad m = 0, 1, 2, \ldots \tag{4}$$

where attenuated coefficient in the metal α2=iκ2, m is the mode ordinal number of guided mode. The parameters relevant to polarization are given by:

$$\rho = \begin{cases} 1 & \text{TE Polarization} \\ \varepsilon\_1 / \varepsilon\_2 & \text{TM Polarization} \end{cases} \tag{5}$$

According to Eq. (4), we can deduce an approximate formula:

$$
\Delta m \propto \sin 2\theta \Lambda \theta \tag{6}
$$

Since *Δm*=1, when the incident angle is small, a bigger *Δθ* can be obtained. So the mode spacing effect of UHMs is evident. Such property is convenient to comb filter design for optical communication applications.

Furthermore, when d reaches millimeter-scale, the waveguide can accommodate thousands of guided modes. For example, use the parameters: ε2 = −28 + i1.8, ε1 = 2.278, λ= 859.8nm, *h* = 30 nm, and *d* = 0.38 mm, *m* is 1333 for the highest mode. However, the maximum of the absolute value of the second term on the right in Eq. (4) is *π*. It will not generate much error if ignoring it, and the approximate dispersion equation of the UHMs for both TE and TM modes is [5]

130 Optical Devices in Communication and Computation

incident angle will change, while the photodiode keeps consistently monitoring the reflected light intensity to scan the reflectance curve. The reflected light intensity is captured by a photodiode fixed on the 2*θ* plate of the goniometer and converted into a voltage signal. At small incident angles, UHM resonance will occur and couple the incident light energy into the SMCW by the free space coupling technique. Then in the reflective curve, a series of

Disregarding the effects resulting from the limited thickness of the metal film, dispersion

1 2

1 *h m* 2tan ( ), 0,1,2,...... *m*

1 *TEPolarization*

*TM Polarization*

(4)

(5)

(6)

where attenuated coefficient in the metal α2=iκ2, m is the mode ordinal number of guided

*m* sin2

Since *Δm*=1, when the incident angle is small, a bigger *Δθ* can be obtained. So the mode spacing effect of UHMs is evident. Such property is convenient to comb filter design for

resonance dips take place in the angular spectrum, as illustrated in Fig.3.

**Figure 4.** Experimental arrangement for measuring ATR spectrum

equation of the guided modes in SMCW can be written as

1

mode. The parameters relevant to polarization are given by:

According to Eq. (4), we can deduce an approximate formula:

optical communication applications.

1 2

**2.2. Ultrahigh-order mode**

$$\frac{2\pi}{\lambda}h \cdot \sqrt{\varepsilon\_1 - N^2} = m\pi \qquad \text{ (}m = 0, 1, 2, ...\text{)}\tag{7}$$

where N = *β/k0* is the effective index of the UHM. Eq. (7) implies that when N is close to zero, the UHM exhibits polarization insensibility.

Because UHMs have a short retention time in waveguide layer, any tiny change of *λ*, n1 and *d* will cause the sensitive change of *N*. If we define sensitivity *SN* as the derivative of effective index to certain characteristic parameter, that is

$$\mathcal{S}\_N = \frac{\partial \mathcal{N}}{\partial \mathcal{L}}\tag{8}$$

where *ξ* represents *λ*, *n1* or *d.* By the total differential of Eq. (7), we can get:

$$\frac{\partial \mathbf{N}}{\partial n\_1} = \frac{n\_1}{N} \tag{9}$$

$$\frac{\partial \mathbf{N}}{\partial \lambda} = \frac{n\_1^2 - N^2}{N\lambda} \tag{10}$$

$$\frac{\partial \mathbf{N}}{\partial d} = \frac{n\_1^2 - \mathbf{N}^2}{\mathbf{N}d} \tag{11}$$

From above mentioned three equations, sensitivity is in inverse proportion to effective index *N*. Therefore, we can obtain high sensitivity when UHM is excited. According to ray optics theory, with the same propagation distance, the small incident angle means that UHM will experience more times reflection and light propagation distance will be longer, resulting in a series of special features different from low-order modes. This property is extremely useful to design sensors and modulators.

Finally, according to Eq. (4), tiny change of wavelength can generate great change of effective index, illustrating that UHM has strong dispersion property and consequent slow light effect. Using Eq. (7), we can also obtain the group velocity of UHM:

$$\nu\_{\mathcal{g}} = \frac{d\phi}{d\mathcal{\beta}} = \frac{N}{n\_1} \cdot \frac{c}{n\_1 + \alpha d n\_1 / d\phi} \tag{12}$$

In the equation, group velocity expression is totally different from those conventional slow light schemes, which is composed of two contributions that are shown in Eq. (12): one

originates from the first-order dispersion resembling the conventional slow light system, and factor *N/n1* can be called slow light factor which is related to the effective index of the UHMs. The deduced results offer us a new physical mechanism for realizing slow light that may not rely on the existence of a sharp single resonance or multiple resonances, but the effective index of the UHM for the small incident angle (θ→0).

#### **2.3. Propagation loss**

Once SMCW is used to achieving optical devices, the important concern relating to the SMCW is that metallic structures exhibit high losses at optical wavelengths. An issue arising is whether the UHMs could be efficiently confined to the guiding layer over a long distance transmission. To see this clearly, four types of metal cladding waveguides have been considered as shown in Fig.5. Fig.5(a) is a structure of three-layer metal cladding waveguide without considering metal and radiative loss. By using three-layer waveguide theory, for TE mode, propagation constant, *βa* , of guided modes for three-layer metal cladding waveguide without considering the metal absorption, can be expressed as:

$$\boldsymbol{\beta}^{a} = \frac{\pi}{\lambda d} \sqrt{4\varepsilon\_{1} d^{2} - \left(\mathbf{m}\_{0}\lambda\right)^{2}} \tag{13}$$

Optical Devices Based on Symmetrical Metal Cladding Waveguides 133

*eff*

(14)

*d*

*k* (15)

(17)

1

*k* (16)

(18)

is the vertical guiding wave

(19)

*h*

2 21 3 2 2 22 2 1 23 2

2 2 1 01 ( ) *a a*

2 2 2 0 2 ( ) *a a*

> 1/2 2 2

> > 2 2 / *a*

*r*

*aa a a*

*a a a aa*

4 ( ) exp( 2 ) Im( ) (( ) ( ) )(( ) ( ) )

>

> *k*

*eff d d*

vector of three-layer metal cladding waveguide without considering the metal absorption, *ε2r* and *ε2i* are real and imaginary parts of dielectric constant (*ε2=ε2r+jε2i*), and *deff* is the effective thickness. Δ*β*rad represents the difference of the eigen-propagation constant between three-layer waveguide and radiative waveguide coupling system. Because the radiative damping is inversely proportional to the exponential function of *h* as shown in Eq.

Fig.5(c) is a structure of three-layer metal cladding waveguide only with considering metal loss. Comparing Fig.5(a) with Fig.5(c) under the condition of |ε2r|>>ε2i at visible and near infrared wavelength, we can obtain that metal loss only affects the imaginary part of propagation constant in three-layer metal cladding waveguide. Then the intrinsic damping,

0 20 1

( ) Im( ) ( ( ))

21 2

where *β0* is the eigen-propagation constant of the guided mode for three-layer waveguide with semi-infinite-thick coupling layer. Table1 lists the propagation loss of two kinds of SMCW which thickness of guiding layer *d* is 0.5 mm and 1 mm, corresponding to UHM order *m* is 1421 and 2843, separately. The dielectric constant of Au and Ag at wavelength *λ*= 1053 nm is -40+2.5i and -48+1.6i, respectively. η presents the ratio of the remaining power after the guided mode transmits for *z*= 1 mm to the guided mode initial power and can be expressed as exp(-2*Δβz*). Then the propagation loss ζ can be expressed as -10/*z×lgη*. As shown in table 1, in sub-millimeter scale, the propagation losses of the guided modes are both less than 3 dB/mm, which is benefit for the design of optical devices. In addition, the

*i aa a a*

*k*

2 2

*a*

2

*eff*

*d*

3 03 *a a*

2 is the absorption constant of the cladding layer, a

(14), the radiative damping can be adjusted by changing the parameter *h*.

propagation loss property has little relation to polarization.

*rad*

with

and

Where a

Im(*β0*), can be written as [8]:

where m0 is mode order.

**Figure 5.** (a) three-layer metal cladding waveguide with ε2=ε2r and h→∞, (b) SMCW with ε2=ε2r and *h* ≠∞, (c) three-layer metal cladding waveguide with ε2=ε2r+iε2i and *h*→∞, (d) SMCW with ε2=ε2r+iε2i and *h*≠∞.

Fig.5(b) is a structure of SMCW only with considering radiative loss. Comparing Fig.5(b) with Fig.5(a) by using weak-coupling condition, which is satisfied with four-layer system [8], the radiative damping, Im(Δ*β*rad), can be expressed as,

#### Optical Devices Based on Symmetrical Metal Cladding Waveguides 133

$$\operatorname{Im}(\Delta \boldsymbol{\beta}^{\mathrm{rad}}) = \frac{4\alpha\_2^a (\kappa\_1^a)^2 \kappa\_3^a \exp(-2\alpha\_2^a \boldsymbol{h})}{((\kappa\_1^a)^2 + (\alpha\_2^a)^2)((\kappa\_3^a)^2 + (\alpha\_2^a)^2)\boldsymbol{\beta}^a d\_{\mathrm{eff}}} \tag{14}$$

with

132 Optical Devices in Communication and Computation

**2.3. Propagation loss**

mode, propagation constant, *βa*

where m0 is mode order.

and *h*≠∞.

effective index of the UHM for the small incident angle (θ→0).

without considering the metal absorption, can be expressed as:

originates from the first-order dispersion resembling the conventional slow light system, and factor *N/n1* can be called slow light factor which is related to the effective index of the UHMs. The deduced results offer us a new physical mechanism for realizing slow light that may not rely on the existence of a sharp single resonance or multiple resonances, but the

Once SMCW is used to achieving optical devices, the important concern relating to the SMCW is that metallic structures exhibit high losses at optical wavelengths. An issue arising is whether the UHMs could be efficiently confined to the guiding layer over a long distance transmission. To see this clearly, four types of metal cladding waveguides have been considered as shown in Fig.5. Fig.5(a) is a structure of three-layer metal cladding waveguide without considering metal and radiative loss. By using three-layer waveguide theory, for TE

1 0 4 (m ) *a d*

**Figure 5.** (a) three-layer metal cladding waveguide with ε2=ε2r and h→∞, (b) SMCW with ε2=ε2r and *h* ≠∞, (c) three-layer metal cladding waveguide with ε2=ε2r+iε2i and *h*→∞, (d) SMCW with ε2=ε2r+iε2i

Fig.5(b) is a structure of SMCW only with considering radiative loss. Comparing Fig.5(b) with Fig.5(a) by using weak-coupling condition, which is satisfied with four-layer system

[8], the radiative damping, Im(Δ*β*rad), can be expressed as,

*d*

, of guided modes for three-layer metal cladding waveguide

(13)

2 2

$$
\kappa\_1^a = \sqrt{k\_0^2 \varepsilon\_1 - (\mathcal{J}^a)^2} \tag{15}
$$

$$
\alpha\_2^a = \sqrt{(\beta^a)^2 - k\_0^2 \varepsilon\_{2r}} \tag{16}
$$

$$\kappa\_3^a = \left(k\_0^2 \varepsilon\_3 - \left(\mathcal{J}^a\right)^2\right)^{1/2} \tag{17}$$

and

$$d\_{eff} = d + \mathcal{D} / \alpha\_2^a \tag{18}$$

Where a 2 is the absorption constant of the cladding layer, a 1 is the vertical guiding wave vector of three-layer metal cladding waveguide without considering the metal absorption, *ε2r* and *ε2i* are real and imaginary parts of dielectric constant (*ε2=ε2r+jε2i*), and *deff* is the effective thickness. Δ*β*rad represents the difference of the eigen-propagation constant between three-layer waveguide and radiative waveguide coupling system. Because the radiative damping is inversely proportional to the exponential function of *h* as shown in Eq. (14), the radiative damping can be adjusted by changing the parameter *h*.

Fig.5(c) is a structure of three-layer metal cladding waveguide only with considering metal loss. Comparing Fig.5(a) with Fig.5(c) under the condition of |ε2r|>>ε2i at visible and near infrared wavelength, we can obtain that metal loss only affects the imaginary part of propagation constant in three-layer metal cladding waveguide. Then the intrinsic damping, Im(*β0*), can be written as [8]:

$$\operatorname{Im}(\beta^0) = \frac{\varepsilon\_{2i} k\_0^2 (\kappa\_1^a)^2}{\alpha\_2^a (\kappa\_1^a + (\alpha\_2^a)^2) \beta^a d\_{eff}} \tag{19}$$

where *β0* is the eigen-propagation constant of the guided mode for three-layer waveguide with semi-infinite-thick coupling layer. Table1 lists the propagation loss of two kinds of SMCW which thickness of guiding layer *d* is 0.5 mm and 1 mm, corresponding to UHM order *m* is 1421 and 2843, separately. The dielectric constant of Au and Ag at wavelength *λ*= 1053 nm is -40+2.5i and -48+1.6i, respectively. η presents the ratio of the remaining power after the guided mode transmits for *z*= 1 mm to the guided mode initial power and can be expressed as exp(-2*Δβz*). Then the propagation loss ζ can be expressed as -10/*z×lgη*. As shown in table 1, in sub-millimeter scale, the propagation losses of the guided modes are both less than 3 dB/mm, which is benefit for the design of optical devices. In addition, the propagation loss property has little relation to polarization.

134 Optical Devices in Communication and Computation

**Table 1.** Guided-mode propagation loss with different parameters

#### **2.4. The enhanced Goos–Hänchen effect**

When the weak coupling condition |exp(2i*κ2*h)|<<1 is satisfied, Eq. (1) can be rewritten as

$$r = \left| r \right| e^{i\phi} = r\_{32} \frac{\beta - \left[ \text{Re}\left(\boldsymbol{\beta}^{0}\right) + \text{Re}\left(\boldsymbol{\Delta}\boldsymbol{\beta}^{nd}\right) \right] - i \left[ \text{Im}\left(\boldsymbol{\beta}^{0}\right) - \text{Im}\left(\boldsymbol{\Delta}\boldsymbol{\beta}^{nd}\right) \right]}{\beta - \left[ \text{Re}\left(\boldsymbol{\beta}^{0}\right) + \text{Re}\left(\boldsymbol{\Delta}\boldsymbol{\beta}^{nd}\right) \right] - i \left[ \text{Im}\left(\boldsymbol{\beta}^{0}\right) + \text{Im}\left(\boldsymbol{\Delta}\boldsymbol{\beta}^{nd}\right) \right]} \right| \tag{20}$$

where *ϕ* is the phase difference between the reflected and incident waves. Re(β0), Im(β0) and Re(*Δβrad*), Im(*Δβrad*) are the real and imaginary parts of the parameters *β0* and *Δβrad*, respectively.

According to stationary phase method, the Goos-Hänchen (GH) shift L is expressed as:

$$L(\mathcal{A}) = -\frac{\mathcal{A}}{2\pi\sqrt{\varepsilon\_3}} \cdot \left. \frac{d\phi}{d\theta} \right|\_{\theta = \theta\_0} \tag{21}$$

Optical Devices Based on Symmetrical Metal Cladding Waveguides 135

(23)

(24)

(25)

is small, the radiative damping is larger than the intrinsic damping, positive lateral shift is obtained. The negative GH shift corresponds to the reverse case. Larger GH shift can be obtained when intrinsic damping approaches the radiative damping. The critical thickness can

where *n* and *κ* are the refractive index of the metal (*n*+*jκ*=(ε2)1/2). The critical thickness should

4 *cr h*

2 ln

*n*

be determined from Eq. (22) by letting denominator is equal to zero [8]:

**Figure 6.** Reflectivity and lateral beam shift with respect to the incident wavelength

through the photocurrents from the output electrodes x1 and x2 (see Fig.7):

To measure the shift while avoiding small spurious displacement, we use the wavelength interrogation-based method by combining a tunable laser and a one-dimensional position sensitive detector (PSD). The position of the incident light can be determined by the PSD

> 2 *a L*

12 1 2 12 1 2 *II VV II VV*

here I1 and I2 are the photocurrents of the output electrodes x1 and x2, respectively. V1 and V2 are the voltages converted from I1 and I2 after amplifier circuit. The analog voltages V1 and V2 are further converted into digital signals and collected by the computer (PC). Light

where *ΔL* is the displacement from the center of the PSD, a is the length of the PSD, *δ* is

be about 31nm using the parameters above.

defined as

where *θ0* is the fixed incident angle. Using (20), L at the resonance wavelength of ATR curve can be written as [9]

$$L(\mathcal{A}\_{\rm res}) = -\cos\theta\_0 \cdot \frac{2\operatorname{Im}(\Delta\mathcal{J}^{\rm rad})}{\operatorname{Im}(\mathcal{J}^0)^2 - \operatorname{Im}(\Delta\mathcal{J}^{\rm rad})^2} \tag{22}$$

With the parameters ε3=1, ε1=2.278, ε2=-28+1.8j, *θ*0=8.11, *d*=0.38μm, and *h*=22nm, the calculated GH shifts with respect to wavelength is shown in Fig.6. The reflectivity is also shown in Fig.6 for comparison. It is found from Fig.6 that the enhancement of the lateral shift of reflective light is closely relevant to the coupling of waveguide power. Reflectivity corresponds to the excitation of a guided mode with the change of the incident wavelength. When the incident wavelength gradually meets the condition of resonance, the reflectivity decreased sharply, most of the energy of the incident angle is coupled into waveguide, greatly enhance the reflective GH shift and forms a peak, and this peak of lateral shift corresponds to the minimum of the reflectivity. Moreover, as the radiative damping is inversely proportional to the exponential function of *h* from Eq. (14), we can adjust radiative damping by varying *h*. When h is small, the radiative damping is larger than the intrinsic damping, positive lateral shift is obtained. The negative GH shift corresponds to the reverse case. Larger GH shift can be obtained when intrinsic damping approaches the radiative damping. The critical thickness can be determined from Eq. (22) by letting denominator is equal to zero [8]:

134 Optical Devices in Communication and Computation

**Table 1.** Guided-mode propagation loss with different parameters

When the weak coupling condition |exp(2i*κ2*h)|<<1 is satisfied, Eq.  Re(β0), Im(β0) and Re(*Δβrad*), Im(*Δβrad*) are the real and imaginary parts of the parameters *β0* and *Δβrad*,

where *θ0* is the fixed incident angle. Using (20), L at the resonance wavelength of ATR curve

2Im( ) ( ) cos Im( ) Im( )

With the parameters ε3=1, ε1=2.278, ε2=-28+1.8j, *θ*0=8.11, *d*=0.38μm, and *h*=22nm, the calculated GH shifts with respect to wavelength is shown in Fig.6. The reflectivity is also shown in Fig.6 for comparison. It is found from Fig.6 that the enhancement of the lateral shift of reflective light is closely relevant to the coupling of waveguide power. Reflectivity corresponds to the excitation of a guided mode with the change of the incident wavelength. When the incident wavelength gradually meets the condition of resonance, the reflectivity decreased sharply, most of the energy of the incident angle is coupled into waveguide, greatly enhance the reflective GH shift and forms a peak, and this peak of lateral shift corresponds to the minimum of the reflectivity. Moreover, as the radiative damping is inversely proportional to the exponential function of *h* from Eq. (14), we can adjust radiative damping by varying *h*. When h

*res rad L*

32 0 0

According to stationary phase method, the Goos-Hänchen (GH) shift L is expressed as:

2 *d L*

( )

*i*

*rad rad*

(20)

(22)

*rad rad*

(21)

0 0

Re Re Im Im

Re Re Im Im

*i*

3 0

0 0 2 2

*rad*

*d*

**2.4. The enhanced Goos–Hänchen effect**

*i*

*r re r*

respectively.

can be written as [9]

$$h\_{cr} = \frac{\lambda}{4\pi\kappa} \ln\frac{2}{n} \tag{23}$$

where *n* and *κ* are the refractive index of the metal (*n*+*jκ*=(ε2)1/2). The critical thickness should be about 31nm using the parameters above.

**Figure 6.** Reflectivity and lateral beam shift with respect to the incident wavelength

To measure the shift while avoiding small spurious displacement, we use the wavelength interrogation-based method by combining a tunable laser and a one-dimensional position sensitive detector (PSD). The position of the incident light can be determined by the PSD through the photocurrents from the output electrodes x1 and x2 (see Fig.7):

$$
\Delta L = \frac{a}{2}\delta \tag{24}
$$

where *ΔL* is the displacement from the center of the PSD, a is the length of the PSD, *δ* is defined as

$$\delta = \frac{I\_1 - I\_2}{I\_1 + I\_2} = \frac{V\_1 - V\_2}{V\_1 + V\_2} \tag{25}$$

here I1 and I2 are the photocurrents of the output electrodes x1 and x2, respectively. V1 and V2 are the voltages converted from I1 and I2 after amplifier circuit. The analog voltages V1 and V2 are further converted into digital signals and collected by the computer (PC). Light displacement measurement using PSD can achieve high sensitivity and accuracy and will not be affected by the change of the light intensity.

Optical Devices Based on Symmetrical Metal Cladding Waveguides 137

**Figure 8.** Measured analog voltages V1 and V2 and calculated positive value of *δ* as a function of

optical devices based on SMCW have the potential applications in many fields.

The above mentioned properties of UHM in SMCW have been widely used to applications on optical devices. Here, we list several practical application examples, such as filter, sensor, modulator and slow wave device. Due to its excellent performance and simple structure,

As mentioned above, a sub-millimeter SMCW is capable of coupling the incident light with a fixed wavelength from free space into the glass slab directly. As the excitation of the guided modes results in resonant transfer of energy from the incident light, guided modes manifest themselves by a series of resonant dips in the reflectivity when the incident angle is varied. On the other hand, if a polychromatic light is used instead of a single-wavelength light, resonant dips at a fixed incident angle can also be achieved in a spectral plot of the reflectivity. In this way, a comb filter is built [11]. For a better understanding of how it works, we consider the UHMs of the sub-millimeter SMCW in the case of free space

> 1 2 *nd m* cos

where *ν* is the frequency of the light in free space. Without considering the material dispersion of the waveguide, we can express the channel spacing in frequency separated by

> 1 2 cos *c n d*

It is found that *θ* is a constant as the incident angle of the light is fixed, which means that the channel spacing is equal in frequency for this comb filter. Moreover, according to Eq. (26)

(26)

(27)

*c*

wavelength with (a) *h*=8nm and (b) *h*=50nm. The incident angle *θ* is 8.11o.

**3. Optical devices based on SMCW**

**3.1. Tunable comb filters**

coupling. Eq. (7) can be rewritten as

two neighboring guided modes as

The experimental arrangement for measuring GH shift is shown in Fig.7 [10]. After passing through two apertures (A1, A2) and a splitter (S1), a large part of the Guassian beam from a tunable laser was introduced onto the SMCW. Another part of the beam, which is reflected from S1, irradiated the second splitter (S2) and is detected by a wavemeter connected to a computer. We choose to excite the UHMs, because of the polarization independence of the UHMs, TE and TM incidences have nearly the same characteristics. The reflected light from the SMCW was first detected by a photodiode (PD). Angular scan was performed by rotating the goniometer and the ATR spectrum was generated. We selected the operation angle to be located at the maximum reflectivity near a certain dip of the spectrum (Position 1). The GH effect is not remarkable at this position due to the deviation of the resonance condition. The position of the reflected beam was set as the reference at this point. Then we moved the PD out of the light path (Position 2) without changing any position of the incident beam and let the reflected light beam cast onto the center of the PSD perpendicularly. Then by changing the wavelength through temperature tuning, the variation of *δ* can be measured obviously on the computer screen. To gain better understanding of GH shift measurement using PSD, Fig.8(a) and (b) show the two sets of measurement results when the wavelength of the incident light is changed artificially. The values of V1 and V2 are also measured and plotted in the two figures for comparison. Since the preliminarily setting of the light is at the center of PSD under the case of unresonance, which means the reference values of *δ* is equal to zero, the change of the value *δ* shown on the computer were the actual relative enhanced positive and negative lateral beam displacement under the case of resonance. Then the actual position *ΔL* can be obtained by using Eq. (24).

**Figure 7.** Experimental setup (A1 and A2, aperture; PD:photodiode; S1 and S2: splitter; 1-D PSD: onedimensional position sensitive detector and PC: computer).

**Figure 8.** Measured analog voltages V1 and V2 and calculated positive value of *δ* as a function of wavelength with (a) *h*=8nm and (b) *h*=50nm. The incident angle *θ* is 8.11o.

#### **3. Optical devices based on SMCW**

The above mentioned properties of UHM in SMCW have been widely used to applications on optical devices. Here, we list several practical application examples, such as filter, sensor, modulator and slow wave device. Due to its excellent performance and simple structure, optical devices based on SMCW have the potential applications in many fields.

#### **3.1. Tunable comb filters**

136 Optical Devices in Communication and Computation

by using Eq. (24).

not be affected by the change of the light intensity.

displacement measurement using PSD can achieve high sensitivity and accuracy and will

The experimental arrangement for measuring GH shift is shown in Fig.7 [10]. After passing through two apertures (A1, A2) and a splitter (S1), a large part of the Guassian beam from a tunable laser was introduced onto the SMCW. Another part of the beam, which is reflected from S1, irradiated the second splitter (S2) and is detected by a wavemeter connected to a computer. We choose to excite the UHMs, because of the polarization independence of the UHMs, TE and TM incidences have nearly the same characteristics. The reflected light from the SMCW was first detected by a photodiode (PD). Angular scan was performed by rotating the goniometer and the ATR spectrum was generated. We selected the operation angle to be located at the maximum reflectivity near a certain dip of the spectrum (Position 1). The GH effect is not remarkable at this position due to the deviation of the resonance condition. The position of the reflected beam was set as the reference at this point. Then we moved the PD out of the light path (Position 2) without changing any position of the incident beam and let the reflected light beam cast onto the center of the PSD perpendicularly. Then by changing the wavelength through temperature tuning, the variation of *δ* can be measured obviously on the computer screen. To gain better understanding of GH shift measurement using PSD, Fig.8(a) and (b) show the two sets of measurement results when the wavelength of the incident light is changed artificially. The values of V1 and V2 are also measured and plotted in the two figures for comparison. Since the preliminarily setting of the light is at the center of PSD under the case of unresonance, which means the reference values of *δ* is equal to zero, the change of the value *δ* shown on the computer were the actual relative enhanced positive and negative lateral beam displacement under the case of resonance. Then the actual position *ΔL* can be obtained

**Figure 7.** Experimental setup (A1 and A2, aperture; PD:photodiode; S1 and S2: splitter; 1-D PSD: one-

dimensional position sensitive detector and PC: computer).

As mentioned above, a sub-millimeter SMCW is capable of coupling the incident light with a fixed wavelength from free space into the glass slab directly. As the excitation of the guided modes results in resonant transfer of energy from the incident light, guided modes manifest themselves by a series of resonant dips in the reflectivity when the incident angle is varied. On the other hand, if a polychromatic light is used instead of a single-wavelength light, resonant dips at a fixed incident angle can also be achieved in a spectral plot of the reflectivity. In this way, a comb filter is built [11]. For a better understanding of how it works, we consider the UHMs of the sub-millimeter SMCW in the case of free space coupling. Eq. (7) can be rewritten as

$$\frac{2\pi\nu}{c}n\_1d\cos\theta = m\pi\tag{26}$$

where *ν* is the frequency of the light in free space. Without considering the material dispersion of the waveguide, we can express the channel spacing in frequency separated by two neighboring guided modes as

$$
\Delta\nu = \frac{c}{2n\_1 d\cos\theta} \tag{27}
$$

It is found that *θ* is a constant as the incident angle of the light is fixed, which means that the channel spacing is equal in frequency for this comb filter. Moreover, according to Eq. (26)

and (27), both the center wavelength and the channel spacing can be tuned by simply changing the incident angle. The parameters of SMCW that achieve comb filter are as follows: a glass (ZF7) slab (*d*=900μm); the thickness of the upper film *h*=20 nm. Fig.9 shows the output spectrum from the SMCW.

Optical Devices Based on Symmetrical Metal Cladding Waveguides 139

(29)

(32)

(33)

(34)

(28)

*I*

Combined (28) with (29), the sensitivity *S*I can be written by

*N*

*R*

dip, and *α* is the divergence half-angle of the laser beam.

index N can be expressed as

expressed as

with

*dR R N S d N*

Using the phase matching condition of resonance energy transfer, the effective refractive

*I R N R N R N S S S*

where SN is defined as the rate of change of the effective refractive index N with respect to certain characteristic parameter and determined by Eq.(9)-(11). As described in section 2.2, optical waveguide oscillating field sensor exhibits the substantial improvement: the UHMs of the SMCW with millimeter scale is selected to act the sensing probe, so *N*→0 and SN enhancement has been achieved. SR represents the slope of the dip at the operation angle θ0, which was usually set at the fall-off side. The absolute maximum values of the slopes are related to the width of the ATR reflection dips and the mode number. The larger the mode number, the wider the corresponding ATR dip, and the smaller the steepest slope. So the divergence angle of the incident light should be taken into consideration. To calculate the maximum value of sensitivity SI, Lorentzian function is used to approximate the reflection dip in the ATR spectrum. The FWHM is assumed to be larger than the divergence of the incident light in order to prevent profile distortion. According to Ref [12], SR can be

3 *N* sin

3 3

2 0 2 2 2

(31)

0 4( ) 2 exp( ) 2 ( )2

*S x x dx*

*xx Q*

*Q W* /

2( )/ *i x*

0 2( )/ *i sp x*

where *Rm* and *R0* are the values of the reflectivity when guided mode is and is not excited, respectively. θsp is the angle for exciting the guided mode, *W* is the half of the FWHM of the

Taking wavelength sensing for example [13], use the parameters: ε2 = −28 + i1.8, *ε1* = 2.278 at 859.8 nm*, h* = 30 nm, *α* = 0.4 mrad and *d* = 0.38 mm. The sensitivity *SI* with respect to the

*m*

*R Q R R*

  1 1 cos cos

(30)

**Figure 9.** Experimental and theoretical reflective spectrum of SMCW, with parameters ε2 = −132+ i12.56, *n1* = 1.765, *h* = 21 nm, *d* = 0.85 mm and *θ* = 6.1o

From Fig.9, we can see equally spaced loss peaks with a 3 dB line-width of 0.1 nm appear in the spectral plot from 1551 to 1556 nm. The wavelength spacing of these peaks is just 0.8 nm. The channel isolation, which is closely related to the thickness of the upper gold film of the waveguide, has been found to be 12 dB. Insertion loss is characterized by the maximum reflectivity, which is greater than 95% (~0.2 dB). The tunability of the filter can be obtained simply by slightly rotating the waveguide with respect to the incident light. Tuning of the center wavelength in the range of channel spacing can be easily obtained by changing several degrees of the incident angle according to Eq. (26).

#### **3.2. Optical sensors**

In this section, we propose oscillating wave sensors using SMCW structure. The thickness of guiding layer can be expanded to millimeter scale, which it can contain very sensitive UHM. The high sensitivity can be detected by measuring the intensity variation of the reflected light due to the movement of the corresponding synchronous angle by an optical sensor. In addition, an alternative approach is presented via measuring the enhanced GH shifts at excitement of UHM. This approach enables the possibility to obtain a higher resolution and prevent the disturbance caused by the power fluctuation of the light source.

#### *3.2.1. Sensitivity analysis*

If we using the intensity measurement interrogation to observe the response of the sensor, the sensitivity in SMCW can be defined as the rate of change of the reflectivity to center characteristics parameters which is expressed as:

Optical Devices Based on Symmetrical Metal Cladding Waveguides 139

$$S\_I = \frac{d\mathcal{R}}{d\xi} = \left(\frac{\partial\mathcal{R}}{\partial\theta}\right)\left(\frac{\partial\theta}{\partial\mathcal{N}}\right)\left(\frac{\partial\mathcal{N}}{\partial\xi}\right) \tag{28}$$

Using the phase matching condition of resonance energy transfer, the effective refractive index N can be expressed as

$$N = \sqrt{\varepsilon\_3} \sin \theta \tag{29}$$

Combined (28) with (29), the sensitivity *S*I can be written by

$$\mathbf{S}\_{I} = \left(\frac{\partial \mathbf{R}}{\partial \theta}\right) \left(\frac{\partial \theta}{\partial \mathbf{N}}\right) \left(\frac{\partial \mathbf{N}}{\partial \xi}\right) = \frac{1}{\sqrt{\varepsilon\_{3} \cos \theta}} \left(\frac{\partial \mathbf{R}}{\partial \theta}\right) \left(\frac{\partial \mathbf{N}}{\partial \xi}\right) \equiv \frac{1}{\sqrt{\varepsilon\_{3} \cos \theta}} \mathbf{S}\_{R} \mathbf{S}\_{N} \tag{30}$$

where SN is defined as the rate of change of the effective refractive index N with respect to certain characteristic parameter and determined by Eq.(9)-(11). As described in section 2.2, optical waveguide oscillating field sensor exhibits the substantial improvement: the UHMs of the SMCW with millimeter scale is selected to act the sensing probe, so *N*→0 and SN enhancement has been achieved. SR represents the slope of the dip at the operation angle θ0, which was usually set at the fall-off side. The absolute maximum values of the slopes are related to the width of the ATR reflection dips and the mode number. The larger the mode number, the wider the corresponding ATR dip, and the smaller the steepest slope. So the divergence angle of the incident light should be taken into consideration. To calculate the maximum value of sensitivity SI, Lorentzian function is used to approximate the reflection dip in the ATR spectrum. The FWHM is assumed to be larger than the divergence of the incident light in order to prevent profile distortion. According to Ref [12], SR can be expressed as

$$S\_R = \frac{\partial R}{\partial \theta} = \frac{4(R\_0 - R\_m)}{a\sqrt{2\pi}} \int\_{-\infty}^{\infty} \left| \frac{2Q^2}{\left(\mathbf{x} - \mathbf{x}\_0\right)^2 + 2Q^2} \right| \cdot \mathbf{x} \exp(-\mathbf{x}^2) d\mathbf{x} \tag{31}$$

with

138 Optical Devices in Communication and Computation

the output spectrum from the SMCW.

*n1* = 1.765, *h* = 21 nm, *d* = 0.85 mm and *θ* = 6.1o

**3.2. Optical sensors**

*3.2.1. Sensitivity analysis*

characteristics parameters which is expressed as:

several degrees of the incident angle according to Eq. (26).

and (27), both the center wavelength and the channel spacing can be tuned by simply changing the incident angle. The parameters of SMCW that achieve comb filter are as follows: a glass (ZF7) slab (*d*=900μm); the thickness of the upper film *h*=20 nm. Fig.9 shows

**Figure 9.** Experimental and theoretical reflective spectrum of SMCW, with parameters ε2 = −132+ i12.56,

From Fig.9, we can see equally spaced loss peaks with a 3 dB line-width of 0.1 nm appear in the spectral plot from 1551 to 1556 nm. The wavelength spacing of these peaks is just 0.8 nm. The channel isolation, which is closely related to the thickness of the upper gold film of the waveguide, has been found to be 12 dB. Insertion loss is characterized by the maximum reflectivity, which is greater than 95% (~0.2 dB). The tunability of the filter can be obtained simply by slightly rotating the waveguide with respect to the incident light. Tuning of the center wavelength in the range of channel spacing can be easily obtained by changing

In this section, we propose oscillating wave sensors using SMCW structure. The thickness of guiding layer can be expanded to millimeter scale, which it can contain very sensitive UHM. The high sensitivity can be detected by measuring the intensity variation of the reflected light due to the movement of the corresponding synchronous angle by an optical sensor. In addition, an alternative approach is presented via measuring the enhanced GH shifts at excitement of UHM. This approach enables the possibility to obtain a higher resolution and

If we using the intensity measurement interrogation to observe the response of the sensor, the sensitivity in SMCW can be defined as the rate of change of the reflectivity to center

prevent the disturbance caused by the power fluctuation of the light source.

$$Q = W / \alpha \tag{32}$$

$$\propto = \sqrt{2} \left( \theta\_i - \theta \right) / a \tag{33}$$

$$\propto\_0 = \sqrt{2}(\theta\_i - \theta\_{sp}) / a \tag{34}$$

where *Rm* and *R0* are the values of the reflectivity when guided mode is and is not excited, respectively. θsp is the angle for exciting the guided mode, *W* is the half of the FWHM of the dip, and *α* is the divergence half-angle of the laser beam.

Taking wavelength sensing for example [13], use the parameters: ε2 = −28 + i1.8, *ε1* = 2.278 at 859.8 nm*, h* = 30 nm, *α* = 0.4 mrad and *d* = 0.38 mm. The sensitivity *SI* with respect to the angle of incidence is shown in Fig.10. The UHMs are more sensitive than the low-order modes and are more applicable for sensing.

Optical Devices Based on Symmetrical Metal Cladding Waveguides 141

In the intensity interrogation (as illustrated in Fig. 11(a)), the sample is sealed by an O-ring sandwiched between two gold films that deposited on glass substrates. The two gold films and the sample cell form the SMCW structure. The upper gold film (35 nm in thickness) is deposited on a thin glass slide. The glass slide is 0.178 mm in thickness, with a RI of 1.50. The lower gold film (300 nm) is deposited on a glass plate. The lower glass plate's thickness is 2 mm with an RI of 1.50. The dielectric constants of the gold films are −11.4+i1.50 at the wavelength of 650 nm. The sample cell serves as the guiding layer of the waveguide sensor, and the thickness of the sample cell is governed by the thickness of the O-ring of about 1.99 mm. The aqueous sample could be pumped in and out of the sample cell by a peristaltic pump through the inlet and outlet on the lower substrate. The water sample with an RI of 1.333 can be used as the guiding layer of the waveguide. The guided wave concentrates and propagates in the sample layer as the oscillating field and hence a magnification in

*3.2.2. Refractive index sensing*

sensitivity is expected. Fig.11(b) is the sensor sample [14].

**Figure 11.** RI sensor of intensity interrogation (a) structural sketch; (b) actual picture

1

3 1

*R N S n S*

*n*

Then we can see that the use of a smaller incident angle (1.69° in the experiment) as a sensing probe can achieve higher sensitivity. The experimental results are shown in Fig.12. In this case, a 20 ppm NaCl concentration change (corresponding to 2.6×10−6 RIU) can cause a reflectance change of around 3%.With a standard error of 0.2% for the measurement of the optical intensity[15], its resolution with 1% noise level can reach up to 0.88×10-6 RIU for the

cos cos sin

1

  (36)

*R*

Based on sensitivity analysis, SI can be cast in the form of

*I*

ideal case.

**Figure 10.** *S*I versus incident angle *θ*

Similarly, in the GH shift interrogation, the sensitivity of the sensor is defined by the change rate of the GH shift (L) with respect to center characteristics parameters and it can be written as

$$\mathbf{S}\_{\rm GH} = \left(\frac{\partial L}{\partial \theta}\right) \left(\frac{\partial \theta}{\partial \mathbf{N}}\right) \left(\frac{\partial \mathbf{N}}{\partial \xi}\right) = \frac{1}{\sqrt{\varepsilon\_3} \cos \theta} \left(\frac{\partial L}{\partial \theta}\right) \left(\frac{\partial \mathbf{N}}{\partial \xi}\right) \equiv \frac{1}{\sqrt{\varepsilon\_3} \cos \theta} \mathbf{S}\_L \mathbf{S}\_N \tag{35}$$

Compared with the intensity interrogation, the only difference is the replacement of SR by SL. According to Eq. (22), if the intrinsic damping of the UHM is close to the radiative damping, a large GH shift can be observed [10]. The dependence of the GH shift on the effective index for a selected mode forms a resonance peak. High sensitivity *S*GH can be reached at the up and down sides of the peak. In addition, since the magnitude of the GH shift is irrelevant to the incident light intensity, a power fluctuation of the laser brings no disturbance to the resolution of the optical sensor.

Moreover, the thickness of the upper metal cladding is also an important factor that must be considered when analyzing the sensitivity. The thicknesses of upper and bottom metal films are essential parameters in the determination of the sensitivity. If thickness *h* is excessively thick, it is difficult for the incident light power to be coupled into the planar waveguide structure. However, if thickness *h* is too thin, it is easy for the incident energy to be coupled into the waveguide. On the other hand, it is also easy for the light energy to be coupled out of the waveguide. As a consequence, there is an optimum solution to thickness *h* by which the highest sensitivity is obtained. Theoretical and experimental results show that the optimal thickness for the upper metal layer is within the range of about 31–33 nm if the maximum sensitivity is to be achieved. In the following section, refractive index (RI), displacement and light wavelength sensing with extremely high sensitivity are introduced.

#### *3.2.2. Refractive index sensing*

140 Optical Devices in Communication and Computation

**Figure 10.** *S*I versus incident angle *θ*

modes and are more applicable for sensing.

angle of incidence is shown in Fig.10. The UHMs are more sensitive than the low-order

Similarly, in the GH shift interrogation, the sensitivity of the sensor is defined by the change rate of the GH shift (L) with respect to center characteristics parameters and it can be written as

> *GH L N L N L N S S S*

Compared with the intensity interrogation, the only difference is the replacement of SR by SL. According to Eq. (22), if the intrinsic damping of the UHM is close to the radiative damping, a large GH shift can be observed [10]. The dependence of the GH shift on the effective index for a selected mode forms a resonance peak. High sensitivity *S*GH can be reached at the up and down sides of the peak. In addition, since the magnitude of the GH shift is irrelevant to the incident light intensity, a power fluctuation of the laser brings no

Moreover, the thickness of the upper metal cladding is also an important factor that must be considered when analyzing the sensitivity. The thicknesses of upper and bottom metal films are essential parameters in the determination of the sensitivity. If thickness *h* is excessively thick, it is difficult for the incident light power to be coupled into the planar waveguide structure. However, if thickness *h* is too thin, it is easy for the incident energy to be coupled into the waveguide. On the other hand, it is also easy for the light energy to be coupled out of the waveguide. As a consequence, there is an optimum solution to thickness *h* by which the highest sensitivity is obtained. Theoretical and experimental results show that the optimal thickness for the upper metal layer is within the range of about 31–33 nm if the maximum sensitivity is to be achieved. In the following section, refractive index (RI), displacement and light wavelength sensing with extremely high sensitivity are introduced.

*N*

disturbance to the resolution of the optical sensor.

3 3

1 1 cos cos

(35)

  In the intensity interrogation (as illustrated in Fig. 11(a)), the sample is sealed by an O-ring sandwiched between two gold films that deposited on glass substrates. The two gold films and the sample cell form the SMCW structure. The upper gold film (35 nm in thickness) is deposited on a thin glass slide. The glass slide is 0.178 mm in thickness, with a RI of 1.50. The lower gold film (300 nm) is deposited on a glass plate. The lower glass plate's thickness is 2 mm with an RI of 1.50. The dielectric constants of the gold films are −11.4+i1.50 at the wavelength of 650 nm. The sample cell serves as the guiding layer of the waveguide sensor, and the thickness of the sample cell is governed by the thickness of the O-ring of about 1.99 mm. The aqueous sample could be pumped in and out of the sample cell by a peristaltic pump through the inlet and outlet on the lower substrate. The water sample with an RI of 1.333 can be used as the guiding layer of the waveguide. The guided wave concentrates and propagates in the sample layer as the oscillating field and hence a magnification in sensitivity is expected. Fig.11(b) is the sensor sample [14].

**Figure 11.** RI sensor of intensity interrogation (a) structural sketch; (b) actual picture

Based on sensitivity analysis, SI can be cast in the form of

$$S\_I = \frac{1}{\sqrt{\varepsilon\_3} \cos \theta} \left(\frac{\partial R}{\partial \theta}\right) \left(\frac{\partial N}{\partial n\_1}\right) \equiv \frac{S\_R n\_1}{\cos \theta \cdot \sin \theta} \tag{36}$$

Then we can see that the use of a smaller incident angle (1.69° in the experiment) as a sensing probe can achieve higher sensitivity. The experimental results are shown in Fig.12. In this case, a 20 ppm NaCl concentration change (corresponding to 2.6×10−6 RIU) can cause a reflectance change of around 3%.With a standard error of 0.2% for the measurement of the optical intensity[15], its resolution with 1% noise level can reach up to 0.88×10-6 RIU for the ideal case.

Optical Devices Based on Symmetrical Metal Cladding Waveguides 143

Fig.14. The step change of 20 ppm NaCl solution in concentration, which corresponds to a variation of 2.64 ×10−6 RIU, induces a GH shift change of at least 20 μm. Considering the noise level in the experiment, the probing sensitivity of 2.0×10−7 RIU is resolved since the measurement variation of the GH shift is confined within 1.5 μm for each sample [16].

In the experimental setup, we propose to use a variable air gap produced by a calibrated piezoelectric translator (PZT) to act as the guiding layer of the optical waveguide. As shown in Fig.15, the sample for minute displacement measurement is composed of two parts: one is a glass prism on its base precoated with a thin gold film; the other is a 500 μm thick LiNbO3 slab sandwiched between two 400 nm thick gold films and serves as a PZT. The two components, separated by an air gap with a thickness of 100 mm, are rigidly mounted on a heavy platform. The gold films deposited on the prism and the upper surface of LiNbO3

**Figure 14.** The GH shifts with respect to solutions of different concentrations in the sample cell: (a) pure water, (b) 20ppm NaCl solution, (c) 40 ppm NaCl solution, (d) 60 ppm NaCl solution, and (e) 80 ppm

As soon as applying a dc voltage on the pair electrodes of the PZT, the air gap changes its thickness due to the piezoelectric effect of the LiNbO3 slab. As a result, the reflection dip shifts its peak position and result in a change of the reflectivity. According to the resolution of the reflectivity variation, displacement can be evaluated from the applied voltage and the piezoelectric coefficient of the LiNbO3 slab. In the intensity interrogation, SI can be cast in

> 1 sin cos cos sin *I R R N S S*

We can also use UHM as the sensing probe to achieve higher sensitivity. Test experiment has been performed with the waveguide parameters as follows: *ε1*=1.0, *ε2*=−11+i1.0, *ε3*=3.0, *d*=108 μm, *h*=40 nm, and *λ*=650 nm. Displacement sensitivity of proposed configuration is

3 3

  2

(37)

1 3

*d d*

*3.2.3. Displacement sensing*

NaCl solution

the form of

slab, together with the air gap form an SMCW.

**Figure 12.** Sensor response for NaCl water solution in the experiment. The left side of the curve is the scanned reflectance curve of the three highest guiding modes. The scan motor stopped at the fall-off of the fourth resonance dip. 20 ppm NaCl water solution is filled in the sample cell and the first measurement starts at A and is then paused. After pure water is pumped in the sample cell and the signal stabilized, measurement starts at B and then back to the 20 ppm NaCl sample measurement at C. The sensor response is enlarged in the inset.

**Figure 13.** RI sensor of GH shift interrogation (a) structural sketch; (b) actual picture

In the GH shift interrogation (as illustrated in Fig. 13), a glass prism is coated with a 20 nm thick gold film to serve as the coupling layer.  The air gap of 0.7 mm sandwiched between two gold films works as the guiding layer, where a gasket is used to form a sealed sample cell. With the help of a peristaltic pump, sample liquids to be detected flow into the cell through the inlet and the outlet tubes embedded in the substrate glass plate.

The expression of sensitivity SGH is similar to Eq. (36) by replacing SR with SL. So UHM is also selected as a sensing probe. Experiments are carried out with the waveguide parameters as follows: *θ*=4.60°, *ε3*=2.25, *ε2*=−28+1.8i, *h*=20 nm, and *d*=0.7 mm, for pure water (solid curve), *n1*=1.333 RIU. A series of NaCl solutions with the change step of 20 ppm in concentration is used as sample analyte to be probed. The experimental result is shown in Fig.14. The step change of 20 ppm NaCl solution in concentration, which corresponds to a variation of 2.64 ×10−6 RIU, induces a GH shift change of at least 20 μm. Considering the noise level in the experiment, the probing sensitivity of 2.0×10−7 RIU is resolved since the measurement variation of the GH shift is confined within 1.5 μm for each sample [16].

#### *3.2.3. Displacement sensing*

142 Optical Devices in Communication and Computation

The sensor response is enlarged in the inset.

**Figure 12.** Sensor response for NaCl water solution in the experiment. The left side of the curve is the scanned reflectance curve of the three highest guiding modes. The scan motor stopped at the fall-off of

the fourth resonance dip. 20 ppm NaCl water solution is filled in the sample cell and the first measurement starts at A and is then paused. After pure water is pumped in the sample cell and the signal stabilized, measurement starts at B and then back to the 20 ppm NaCl sample measurement at C.

**Figure 13.** RI sensor of GH shift interrogation (a) structural sketch; (b) actual picture

and the outlet tubes embedded in the substrate glass plate.

In the GH shift interrogation (as illustrated in Fig. 13), a glass prism is coated with a 20 nm thick gold film to serve as the coupling layer.  The air gap of 0.7 mm sandwiched between two gold films works as the guiding layer, where a gasket is used to form a sealed sample cell. With the help of a peristaltic pump, sample liquids to be detected flow into the cell through the inlet

The expression of sensitivity SGH is similar to Eq. (36) by replacing SR with SL. So UHM is also selected as a sensing probe. Experiments are carried out with the waveguide parameters as follows: *θ*=4.60°, *ε3*=2.25, *ε2*=−28+1.8i, *h*=20 nm, and *d*=0.7 mm, for pure water (solid curve), *n1*=1.333 RIU. A series of NaCl solutions with the change step of 20 ppm in concentration is used as sample analyte to be probed. The experimental result is shown in In the experimental setup, we propose to use a variable air gap produced by a calibrated piezoelectric translator (PZT) to act as the guiding layer of the optical waveguide. As shown in Fig.15, the sample for minute displacement measurement is composed of two parts: one is a glass prism on its base precoated with a thin gold film; the other is a 500 μm thick LiNbO3 slab sandwiched between two 400 nm thick gold films and serves as a PZT. The two components, separated by an air gap with a thickness of 100 mm, are rigidly mounted on a heavy platform. The gold films deposited on the prism and the upper surface of LiNbO3 slab, together with the air gap form an SMCW.

**Figure 14.** The GH shifts with respect to solutions of different concentrations in the sample cell: (a) pure water, (b) 20ppm NaCl solution, (c) 40 ppm NaCl solution, (d) 60 ppm NaCl solution, and (e) 80 ppm NaCl solution

As soon as applying a dc voltage on the pair electrodes of the PZT, the air gap changes its thickness due to the piezoelectric effect of the LiNbO3 slab. As a result, the reflection dip shifts its peak position and result in a change of the reflectivity. According to the resolution of the reflectivity variation, displacement can be evaluated from the applied voltage and the piezoelectric coefficient of the LiNbO3 slab. In the intensity interrogation, SI can be cast in the form of

$$S\_I = \frac{1}{\sqrt{\varepsilon\_3} \cos \theta} \left(\frac{\partial \mathcal{R}}{\partial \theta}\right) \left(\frac{\partial \mathcal{N}}{\partial d}\right) \equiv \frac{\varepsilon\_1 - \varepsilon\_3 \sin^2 \theta}{\varepsilon\_3 \cos \theta \cdot \sin \theta \cdot d} \cdot S\_R \tag{37}$$

We can also use UHM as the sensing probe to achieve higher sensitivity. Test experiment has been performed with the waveguide parameters as follows: *ε1*=1.0, *ε2*=−11+i1.0, *ε3*=3.0, *d*=108 μm, *h*=40 nm, and *λ*=650 nm. Displacement sensitivity of proposed configuration is

shown in Fig.16. The waveguide thickness *d* is increased and decreased in steps by increasing and reducing the voltages applied on the electrodes of the PZT. The step-style change of voltage is 50 V. According to the piezoelectric coefficient of a Z-cut LiNbO3 slab, d33=33.45 pm/V, the value of the displacement resolution for the proposed configuration is determined as SI =50×33.45×10-3=1.7 nm, which corresponds to the reflectivity change of R=1%[17].

Optical Devices Based on Symmetrical Metal Cladding Waveguides 145

2

(38)

1 3

coefficient of the z-cut LiNbO3 is d33=8 ×10−12 m/v. Thus, the thickness change per step is determined as *Δd*=8×10−12×10 m=8×10−11 m, which leads to a GH shift change of 2 μm. The experimental ripple of each step is confined to 0.5 μm. With this noise level, the sensing

> 1 sin cos cos sin *I R R N S S*

It is found that the effective index is extremely sensitive to *λ* in the case of *N* → 0. The waveguide parameters are given as follows: *d* = 0.38 mm, ε2 = −28 + i1.8, ε1 = 2.278, and *h*= 31 nm. The initial wavelength was set to 859.800 nm. Once this value was stabilized, the reference wavelength was changed subsequently to 859.8005, 859.8010, 859.8015, and 859.8020 nm and decreased back to 859.8000 nm in steps. The step-style change of wavelength is 0.5 pm, with the average 2.5% change in the reflectivity *ΔR*. Considering a noise level of about 0.05% in Fig.18, a resolution of 0.2pm is finally obtained for the

**Figure 17.** Experimental sensitivity of the proposed configuration. Voltage applied on the PZT between

each step is 10 V, which leads to an 8×10−11 m change of the air gap thickness.

In the intensity interrogation, the wavelength sensitivity SI can be written as

3 3

resolution is evaluated to be 40 pm[18].

*3.2.4. Wavelength sensing*

reflectivity change of R=1%[13].

**Figure 15.** Displacement sensor of intensity interrogation (a) structural sketch; (b) actual picture

**Figure 16.** Experimental result of displacement measurement: (a) m-line obtained by angular scanning and displacement experimental result; (b) intensity export by applying step-styled voltages.

In the GH shift interrogation, the sensor structure is the same as Fig. 15. The experiment was performed with the following parameters: ε2=−28+1.8i, ε1=1, ε3=2.25, *d*=500 μm, and *h* =18 nm. The incident wavelength is adjusted to be 859.00 nm. The experimental result is shown in Fig.17. The voltage applied on the PZT between each step is 10 V, and the piezoelectric coefficient of the z-cut LiNbO3 is d33=8 ×10−12 m/v. Thus, the thickness change per step is determined as *Δd*=8×10−12×10 m=8×10−11 m, which leads to a GH shift change of 2 μm. The experimental ripple of each step is confined to 0.5 μm. With this noise level, the sensing resolution is evaluated to be 40 pm[18].

#### *3.2.4. Wavelength sensing*

144 Optical Devices in Communication and Computation

R=1%[17].

shown in Fig.16. The waveguide thickness *d* is increased and decreased in steps by increasing and reducing the voltages applied on the electrodes of the PZT. The step-style change of voltage is 50 V. According to the piezoelectric coefficient of a Z-cut LiNbO3 slab, d33=33.45 pm/V, the value of the displacement resolution for the proposed configuration is determined as SI =50×33.45×10-3=1.7 nm, which corresponds to the reflectivity change of

**Figure 15.** Displacement sensor of intensity interrogation (a) structural sketch; (b) actual picture

**Figure 16.** Experimental result of displacement measurement: (a) m-line obtained by angular scanning

In the GH shift interrogation, the sensor structure is the same as Fig. 15. The experiment was performed with the following parameters: ε2=−28+1.8i, ε1=1, ε3=2.25, *d*=500 μm, and *h* =18 nm. The incident wavelength is adjusted to be 859.00 nm. The experimental result is shown in Fig.17. The voltage applied on the PZT between each step is 10 V, and the piezoelectric

and displacement experimental result; (b) intensity export by applying step-styled voltages.

In the intensity interrogation, the wavelength sensitivity SI can be written as

$$\boldsymbol{S}\_{I} = \frac{1}{\sqrt{\varepsilon\_{3}} \cos \theta} \left( \frac{\partial \mathcal{R}}{\partial \theta} \right) \left( \frac{\partial \mathcal{N}}{\partial \mathcal{L}} \right) \equiv \frac{\varepsilon\_{1} - \varepsilon\_{3} \sin^{2} \theta}{\varepsilon\_{3} \cos \theta \cdot \sin \theta \cdot \mathcal{L}} \cdot \mathcal{S}\_{R} \tag{38}$$

It is found that the effective index is extremely sensitive to *λ* in the case of *N* → 0. The waveguide parameters are given as follows: *d* = 0.38 mm, ε2 = −28 + i1.8, ε1 = 2.278, and *h*= 31 nm. The initial wavelength was set to 859.800 nm. Once this value was stabilized, the reference wavelength was changed subsequently to 859.8005, 859.8010, 859.8015, and 859.8020 nm and decreased back to 859.8000 nm in steps. The step-style change of wavelength is 0.5 pm, with the average 2.5% change in the reflectivity *ΔR*. Considering a noise level of about 0.05% in Fig.18, a resolution of 0.2pm is finally obtained for the reflectivity change of R=1%[13].

**Figure 17.** Experimental sensitivity of the proposed configuration. Voltage applied on the PZT between each step is 10 V, which leads to an 8×10−11 m change of the air gap thickness.

Optical Devices Based on Symmetrical Metal Cladding Waveguides 147

4 1 33

1

(39)

(40)

electric field modulates refractive index of the EO polymer, resulting in the change of the effective refractive index for the guided modes, shifting the resonance dips along the angular direction in ATR spectrum. If we define γ33 as the EO coefficient of the polymer and E is the applied electric field across the EO polymer film. The refractive index change of

> 3 1 1 33 1 2 *n nE*

cos sin 2 *R R N S n*

*R n E n*

Therefore the reflected light is modulated by the applied electric field. Higher sensitivity is obtained at the midst of the fall-off of the resonance dip excited at smaller resonance angle with thicker guiding layer, so that enhanced modulation is realized by enabling the device

In the experiment, the gold film about 300nm was sputtered onto the surface of the K9 glass flat to serve as substrate and one electrode. A PMMA-based second-order nonlinear optical (NLO) side-chain material containing the disperse red chromophore was synthesized through copolymerization for electro-optic device. The polymer was dissolved in toluene, 25% polymer to 75% toluene by weight. A 12-thick polymer film was spin coated onto the gold film substrate, and then was tempered at 40o in a vacuum for 12 hours to remove the residual solvent. The refractive index of polymer is 1.52 at wavelength 832nm. In order to remove the centrosymmetric structure of the chromophores, the film was corona-poled in the air by an applied electric voltage of 4000V at 110o for 25 min with inter-electrode distance being 20mm, and cooled down to room temperature with the field still applied. Finally, the upper gold film about 30nm thick was deposited on the polymer film by sputtering technique to serve as the coupling layer and another electrode. The complex dielectric constant of the gold film is *ε2* = −28 + i1.6. The EO coefficient γ33 of polymer measured at 832 nm using improved ATR method is 11.9 pmV. A collimated TM-polarized beam with 832nm wavelength is used. The modulation working angle was chosen at the midst of the fall-off of the resonance dip excited at resonance angle 9.7o. A sinusoidal electrical field was applied across the two electrodes with 10 Vp-p driving voltage at 1MHz, the electro-optic modulation process was obtained. The oscilloscope traces of modulating voltage and reflected intensity versus time are shown, respectively, in Fig.20. The modulation depth was measured to be 8.7%. However, under the same electrical field the modulation depth was only 5.6% when the resonance dip at 28.9o was used, which is attributed to lower sensitivity at larger

At the midst of the fall-offs of resonance dip, where a considerably good linearity is

*R*

3 1

1

to operate with stronger modulation depth and lower driving voltage.

resonance angle. The total insertion loss of the sample was 1.08 dB[20].

guiding layer Δn1 is written as [19]:

observed, the change of the light reflectivity is:

**Figure 18.** Wavelength sensitivity of the proposed configuration. The shift in the ATR curve was measured by changing the wavelength in steps of 0.5 pm. The angle of incidence is 3.82°.

For the GH shift measurement, the waveguide parameters are given as follows: *d* = 0.5 mm, *ε2* = −28 + i1.8, *ε1* = 1, *ε3* =2.25, *h* = 19.8 nm, and *θ*=4.263°. We first fix the wavelength (*λ*=859.003 nm). As shown in Fig.19, the change of wavelength 1 pm will cause the average variation of reflective light lateral shift about 10 μm.

**Figure 19.** Experiment result using GH shift measurement

#### **3.3. Optical modulators**

The configuration of electro-optic (EO) modulator is a SMCW on a glass (K9) flat. The cover and the substrate are both gold film, and the waveguide is EO polymer film. An applied electric field modulates refractive index of the EO polymer, resulting in the change of the effective refractive index for the guided modes, shifting the resonance dips along the angular direction in ATR spectrum. If we define γ33 as the EO coefficient of the polymer and E is the applied electric field across the EO polymer film. The refractive index change of guiding layer Δn1 is written as [19]:

146 Optical Devices in Communication and Computation

**Figure 18.** Wavelength sensitivity of the proposed configuration. The shift in the ATR curve was measured by changing the wavelength in steps of 0.5 pm. The angle of incidence is 3.82°.

variation of reflective light lateral shift about 10 μm.

**Figure 19.** Experiment result using GH shift measurement

**3.3. Optical modulators**

For the GH shift measurement, the waveguide parameters are given as follows: *d* = 0.5 mm, *ε2* = −28 + i1.8, *ε1* = 1, *ε3* =2.25, *h* = 19.8 nm, and *θ*=4.263°. We first fix the wavelength (*λ*=859.003 nm). As shown in Fig.19, the change of wavelength 1 pm will cause the average

The configuration of electro-optic (EO) modulator is a SMCW on a glass (K9) flat. The cover and the substrate are both gold film, and the waveguide is EO polymer film. An applied

$$
\Delta \mathfrak{m}\_1 = -\frac{1}{2} \mathfrak{m}\_1^3 \mathcal{V}\_{33} E \tag{39}
$$

At the midst of the fall-offs of resonance dip, where a considerably good linearity is observed, the change of the light reflectivity is: *R*

$$
\Delta R = \frac{1}{\sqrt{\varepsilon\_3} \cos \theta} \left( \frac{\partial R}{\partial \theta} \right) \left( \frac{\partial N}{\partial n\_1} \right)
\Delta n\_1 = \frac{S\_R n\_1^4 \gamma\_{33}}{\sin 2\theta} E \tag{40}
$$

Therefore the reflected light is modulated by the applied electric field. Higher sensitivity is obtained at the midst of the fall-off of the resonance dip excited at smaller resonance angle with thicker guiding layer, so that enhanced modulation is realized by enabling the device to operate with stronger modulation depth and lower driving voltage.

In the experiment, the gold film about 300nm was sputtered onto the surface of the K9 glass flat to serve as substrate and one electrode. A PMMA-based second-order nonlinear optical (NLO) side-chain material containing the disperse red chromophore was synthesized through copolymerization for electro-optic device. The polymer was dissolved in toluene, 25% polymer to 75% toluene by weight. A 12-thick polymer film was spin coated onto the gold film substrate, and then was tempered at 40o in a vacuum for 12 hours to remove the residual solvent. The refractive index of polymer is 1.52 at wavelength 832nm. In order to remove the centrosymmetric structure of the chromophores, the film was corona-poled in the air by an applied electric voltage of 4000V at 110o for 25 min with inter-electrode distance being 20mm, and cooled down to room temperature with the field still applied. Finally, the upper gold film about 30nm thick was deposited on the polymer film by sputtering technique to serve as the coupling layer and another electrode. The complex dielectric constant of the gold film is *ε2* = −28 + i1.6. The EO coefficient γ33 of polymer measured at 832 nm using improved ATR method is 11.9 pmV. A collimated TM-polarized beam with 832nm wavelength is used. The modulation working angle was chosen at the midst of the fall-off of the resonance dip excited at resonance angle 9.7o. A sinusoidal electrical field was applied across the two electrodes with 10 Vp-p driving voltage at 1MHz, the electro-optic modulation process was obtained. The oscilloscope traces of modulating voltage and reflected intensity versus time are shown, respectively, in Fig.20. The modulation depth was measured to be 8.7%. However, under the same electrical field the modulation depth was only 5.6% when the resonance dip at 28.9o was used, which is attributed to lower sensitivity at larger resonance angle. The total insertion loss of the sample was 1.08 dB[20].

Optical Devices Based on Symmetrical Metal Cladding Waveguides 149

**Figure 21.** Schematic layout of the SMCW for verifying slow light effect

delay [22].

*ε2* =−19 + 0.5i , *ε1* = 2.89, and *d* = 2 mm.

In the experimental arrangement, the source is a collimated light beam at a wavelength of 650 nm, which is modulated by an EO modulator to produce a signal of 1.0 GHz sinusoidal pulse train. Two photodiodes are setup to detect the light intensity. The first photodiode (PD1) takes in the reflected light beam, which serves as the reference beam. The second photodiode (PD2) is used to measure the time delay of the slowed light beam. The tunable delay is measured by an oscilloscope with the bandwidth of 2 GHz. We measure the delay times *Δt* at different fixed incident angles, which become larger as the incident angle *θ* becomes smaller. The experimental results are illustrated in Fig.23. After propagating through a 1.1-cm-long active region, a delay of 2.165 ns was achieved, that corresponds to group velocities less than 0.017c. Further decreasing the incident angle could generate more

**Figure 22.** Dispersion curves and group index characteristics of ultrahigh-order modes with parameters

**Figure 20.** Oscilloscope traces of modulating voltage versus time (upside) and the reflected intensity versus time (downside).

#### **3.4. Slow light devices**

The scheme diagram of the SMCW for verifying slow light effect is illustrated in Fig. 21. The advantages of this geometry are that the slow light properties can be tailored to the desired wavelength and the delay is tunable by varying the incident angle and the parameters of the guiding layer. This is important because the applications of slow light require a degree of tunability. These make the proposed slow light scheme useful and practical.

Test experiment has been performed with the waveguide parameters as follows: *ε1* = 2.89, *ε2* = −19 + 0.5i (silver lms), *ε3*=1.0, *d*=2mm (glass slab), *h*=30 nm, *λ*=632.8 nm, and *θ*=3°. An additional silver stripe (about 500nm thick and 1.1 cm wide) is fabricated in the middle of this layer to prevent light leakage. According to Eq.(19), one finds that Im(*β0*)=0.1158526mm−1, which shows that the signal power is about 10% after propagating along the guiding layer for about 1 cm. The proposed structure is completely different from the conventional Fabry-Perot cavity, and those similar folded optical delay lines where the incident ray of light bounces in the cavity between the two interfaces (mirrors) before it exits [21]. From Eq. (12), the slow light effect can be observed only when a specific UHM that propagates along the guiding layer is excited, thus the proposed slow light scheme does not rely on obtaining long optical paths. This proposed slow light mechanism can also be interpreted in terms of the anomalous dispersion of the UHMs, which is depicted in Fig.22. It is demonstrated in Fig.22 that anomalous dispersion curves of the proposed structure exhibit an extremely flattened region (slow light region) in the vicinity of zero wave number (N→0).

**Figure 21.** Schematic layout of the SMCW for verifying slow light effect

versus time (downside).

practical.

(N→0).

**3.4. Slow light devices**

**Figure 20.** Oscilloscope traces of modulating voltage versus time (upside) and the reflected intensity

The scheme diagram of the SMCW for verifying slow light effect is illustrated in Fig. 21. The advantages of this geometry are that the slow light properties can be tailored to the desired wavelength and the delay is tunable by varying the incident angle and the parameters of the guiding layer. This is important because the applications of slow light require a degree of tunability. These make the proposed slow light scheme useful and

Test experiment has been performed with the waveguide parameters as follows: *ε1* = 2.89, *ε2* = −19 + 0.5i (silver lms), *ε3*=1.0, *d*=2mm (glass slab), *h*=30 nm, *λ*=632.8 nm, and *θ*=3°. An additional silver stripe (about 500nm thick and 1.1 cm wide) is fabricated in the middle of this layer to prevent light leakage. According to Eq.(19), one finds that Im(*β0*)=0.1158526mm−1, which shows that the signal power is about 10% after propagating along the guiding layer for about 1 cm. The proposed structure is completely different from the conventional Fabry-Perot cavity, and those similar folded optical delay lines where the incident ray of light bounces in the cavity between the two interfaces (mirrors) before it exits [21]. From Eq. (12), the slow light effect can be observed only when a specific UHM that propagates along the guiding layer is excited, thus the proposed slow light scheme does not rely on obtaining long optical paths. This proposed slow light mechanism can also be interpreted in terms of the anomalous dispersion of the UHMs, which is depicted in Fig.22. It is demonstrated in Fig.22 that anomalous dispersion curves of the proposed structure exhibit an extremely flattened region (slow light region) in the vicinity of zero wave number In the experimental arrangement, the source is a collimated light beam at a wavelength of 650 nm, which is modulated by an EO modulator to produce a signal of 1.0 GHz sinusoidal pulse train. Two photodiodes are setup to detect the light intensity. The first photodiode (PD1) takes in the reflected light beam, which serves as the reference beam. The second photodiode (PD2) is used to measure the time delay of the slowed light beam. The tunable delay is measured by an oscilloscope with the bandwidth of 2 GHz. We measure the delay times *Δt* at different fixed incident angles, which become larger as the incident angle *θ* becomes smaller. The experimental results are illustrated in Fig.23. After propagating through a 1.1-cm-long active region, a delay of 2.165 ns was achieved, that corresponds to group velocities less than 0.017c. Further decreasing the incident angle could generate more delay [22].

**Figure 22.** Dispersion curves and group index characteristics of ultrahigh-order modes with parameters *ε2* =−19 + 0.5i , *ε1* = 2.89, and *d* = 2 mm.

Optical Devices Based on Symmetrical Metal Cladding Waveguides 151

*Engineering Research Center of Optical Instrument and System, Ministry of Education,*

The author thanks Ning Yang and YinQi Bao, students from the University of Shanghai for Science and Technology, for editing the manuscript of this chapter. This work is partly supported by the Leading Academic Discipline Project of Shanghai Municipal Government (S30502), "Chen Guang" Research Fund from Shanghai Municipal Education Commission and Shanghai Education Development Foundation (09CG49), and the Basic Research Program of Shanghai from Shanghai Committee of Science and Technology

[1] O. Solgaard, F. Ho, J. I. Thackara, and D. M. Bloom, High frequency attenuated total internal reflection light modulator, *Appl. Phys. Lett*., Vol. 61, No. 21, pp. 2500-2502

[2] B. Yu, G. Pickrell, and A. Wang, Thermally tunable extrinsic Fabry-Perot filter, *IEEE*

[3] R. Horvath, H. C. Pedersen, and N. B. Larsen, Demonstration of reverse symmetry waveguide sensing in aqueous solutions, *Appl. Phys. Lett.*, Vol. 81, No. 12, pp. 2166-2168

[4] H. Shin and S. Fan, All-Angle Negative refraction for surface plasmon waves using a metal-dielectric-metal structure, *Phys. Rev. Lett.*, Vol. 96, No. 7, pp. 3907-3910 (2006). [5] H. F. Lu, Z. Q. Cao, H. G. Li and Q. S. Shen, Study of ultrahigh-order modes in a symmetrical metal-cladding optical waveguide, *Appl. Phys. Lett.*, Vol. 85, No. 20, pp.

[6] H. G. Li, Z. Q. Cao, H. F. Lu, and Q. S. Shen, Free-space coupling of a light beam into a symmetrical metal-cladding optical waveguide, *Appl. Phys. Lett.*, Vol. 83, No. 14, pp.

[7] X. M. Liu, P. F. Zhu, Z. Q. Cao, Q. S. Shen, and J. L. Chen, Prism coupling of ultrashort light pulses into waveguides, *J. Opt. Soc. Am. B*, Vol. 23, No. 2, pp. 353-357 (2006). [8] L. Chen, Y. M. Zhu, D. W. Zhang, Z. Q. Cao and S. L. Zhuang, Investigation of the limit of lateral beam shifts on a symmetrical metal-cladding waveguide, *Chin. Phys. B*, Vol.

[9] X. B. Liu, Z. Q. Cao, P. F. Zhu, Q. S. Shen, and X. M. Liu, Large positive and negative lateral optical beam shift in prism-waveguide coupling system, *Phys. Rev. E*, Vol. 73,

*Photon, Technol. Lett*., Vol. 16, No. 10, pp. 2296-2298 (2004).

**Author details**

**Acknowledgement**

(11ZR1425000).

**5. References**

(1992).

(2002).

4579-4581 (2004).

2757-2759 (2003).

18, No. 11, pp. 4875-4880 (2009).

No. 5, pp. 6617-6621 (2006).

*Shanghai Key Lab of Modern Optical System,*

*University of Shanghai for Science and Technology, China*

Lin Chen

**Figure 23.** Delay tuning of slow light in an SMCW structure by adjusting the incident angle.

#### **4. Conclusion**

The properties of UHM in a SMCW and its applications on optical devices have been demonstrated in this chapter. It is found that the effective refractive index of UHM is sensitive to the refractive index, the thickness of the waveguide layer and the incident wavelength. UHM has also shown strong dispersion and polarization independent effects. Then, a polarization independent and tunable comb filter based on SMCW has been introduced, which has greater than 12 dB channel isolation, less than 0.2 dB insertion loss, and accurate 0.8 nm channel spacing in optical communication range. Taking the reflectivity and GH shift as the sensing probe, a new oscillating wave sensor is investigated to measure minute changes in various parameters such as the refractive index of the guiding layer, the thickness of the waveguide layer and the incident wavelength. It is demonstrated both theoretically and experimentally that its sensitivity is enhanced by one order of magnitude than that of evanescent wave sensor. Furthermore, an EO polymer modulator employing an SMCW is presented. The fabricated modulator achieves an 8.2% modulation depth with 10Vp-p driving voltage at 1 MHz. Finally, a new mechanism for slow light assisted by UHMs excited in the SMCW is introduced. A delay bandwidth product greater than 2 is demonstrated in the experiment with a signal of 1.0 GHz sinusoidal pulse train. Without use of any coherent or material resonance, this scheme is not subject to limitations of the delay bandwidth product and can generate arbitrarily small group velocities over an unusually large frequency bandwidth. We think such SMCWs possess unique and advantageous properties over the state-of-the-art and may have great potential for next generation optical devices.

#### **Author details**

150 Optical Devices in Communication and Computation

**4. Conclusion**

devices.

**Figure 23.** Delay tuning of slow light in an SMCW structure by adjusting the incident angle.

The properties of UHM in a SMCW and its applications on optical devices have been demonstrated in this chapter. It is found that the effective refractive index of UHM is sensitive to the refractive index, the thickness of the waveguide layer and the incident wavelength. UHM has also shown strong dispersion and polarization independent effects. Then, a polarization independent and tunable comb filter based on SMCW has been introduced, which has greater than 12 dB channel isolation, less than 0.2 dB insertion loss, and accurate 0.8 nm channel spacing in optical communication range. Taking the reflectivity and GH shift as the sensing probe, a new oscillating wave sensor is investigated to measure minute changes in various parameters such as the refractive index of the guiding layer, the thickness of the waveguide layer and the incident wavelength. It is demonstrated both theoretically and experimentally that its sensitivity is enhanced by one order of magnitude than that of evanescent wave sensor. Furthermore, an EO polymer modulator employing an SMCW is presented. The fabricated modulator achieves an 8.2% modulation depth with 10Vp-p driving voltage at 1 MHz. Finally, a new mechanism for slow light assisted by UHMs excited in the SMCW is introduced. A delay bandwidth product greater than 2 is demonstrated in the experiment with a signal of 1.0 GHz sinusoidal pulse train. Without use of any coherent or material resonance, this scheme is not subject to limitations of the delay bandwidth product and can generate arbitrarily small group velocities over an unusually large frequency bandwidth. We think such SMCWs possess unique and advantageous properties over the state-of-the-art and may have great potential for next generation optical Lin Chen *Engineering Research Center of Optical Instrument and System, Ministry of Education, Shanghai Key Lab of Modern Optical System, University of Shanghai for Science and Technology, China*

### **Acknowledgement**

The author thanks Ning Yang and YinQi Bao, students from the University of Shanghai for Science and Technology, for editing the manuscript of this chapter. This work is partly supported by the Leading Academic Discipline Project of Shanghai Municipal Government (S30502), "Chen Guang" Research Fund from Shanghai Municipal Education Commission and Shanghai Education Development Foundation (09CG49), and the Basic Research Program of Shanghai from Shanghai Committee of Science and Technology (11ZR1425000).

#### **5. References**

[10] L. Chen, Z. Q. Cao, F. Ou, H. G. Li, Q. S. Shen, and H. C. Qiao, Observation of large positive and negative lateral shifts of a reflected beam from symmetrical metal-cladding waveguides, *Opt. lett.*, Vol. 32, No.11, pp. 1432-1434 (2007).

**Chapter 8**

© 2012 Huang and Tao, licensee InTech. This is an open access chapter 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.

© 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

Surface Plasmon polaritons (SPPs) are electromagnetic waves that propagate along the interface of metal and dielectric. In recent years, plasmonics is called the area of

and reproduction in any medium, provided the original work is properly cited.

**Nano-Plasmonic Filters Based on**

Xu Guang Huang and Jin Tao

nano-scale optical elements integration.

http://dx.doi.org/10.5772/75765

**1. Introduction**

Additional information is available at the end of the chapter

**Tooth-Shaped Waveguide Structures**

Along with development of human society and technology, it becomes more dependable on the miniaturization and integration of semiconductor components, circuits and devices. The performance of integrated circuits, such as micro-processor, is in accordance with the famous Moore's law that the number of transistors placed inexpensively on an integrated circuit doubles approximately every two years. However, the integration of modern electronic components and devices for information communication and processing have been approaching its fundamental speed and bandwidth limitation, because the ultra-intensive electrical interconnects have an increased effective resistor-capacitor (RC) time constant that increases the time of charging and discharging [1, 2]. This has caused an increasing serious problem that hinders further development in many fields of modern science and technology. Using light signals instead of electronic is one of the most promising solutions. The speed of optical signal is on the order of 108 m/s, which is about 3 orders of the saturation velocity of electrons in a semiconductor such as silicon [3]. However, a major problem with using light as information carrier in conventional optical devices is the poor performance of integration and miniaturization. Dielectric waveguides are basic components and cannot allow the localization of electromagnetic waves into subwavelength-scale regions because of diffraction limit λ0/2*n*, here λ0 is the wavelength of the light in the free space and *n* is the refractive index of the dielectric. Photonic crystal (PC) structures and devices have been studied by many researchers since E. Yablonovitch and S. John ' s two milestone published papers in 1987 [4, 5], which confirmed that the light can be confined in the nanoscale. However, the dimensions of the PC system are on the order of the wavelength or even larger, making them less appropriate for

## **Nano-Plasmonic Filters Based on Tooth-Shaped Waveguide Structures**

Xu Guang Huang and Jin Tao

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/75765

#### **1. Introduction**

152 Optical Devices in Communication and Computation

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Along with development of human society and technology, it becomes more dependable on the miniaturization and integration of semiconductor components, circuits and devices. The performance of integrated circuits, such as micro-processor, is in accordance with the famous Moore's law that the number of transistors placed inexpensively on an integrated circuit doubles approximately every two years. However, the integration of modern electronic components and devices for information communication and processing have been approaching its fundamental speed and bandwidth limitation, because the ultra-intensive electrical interconnects have an increased effective resistor-capacitor (RC) time constant that increases the time of charging and discharging [1, 2]. This has caused an increasing serious problem that hinders further development in many fields of modern science and technology. Using light signals instead of electronic is one of the most promising solutions. The speed of optical signal is on the order of 108 m/s, which is about 3 orders of the saturation velocity of electrons in a semiconductor such as silicon [3]. However, a major problem with using light as information carrier in conventional optical devices is the poor performance of integration and miniaturization. Dielectric waveguides are basic components and cannot allow the localization of electromagnetic waves into subwavelength-scale regions because of diffraction limit λ0/2*n*, here λ0 is the wavelength of the light in the free space and *n* is the refractive index of the dielectric. Photonic crystal (PC) structures and devices have been studied by many researchers since E. Yablonovitch and S. John ' s two milestone published papers in 1987 [4, 5], which confirmed that the light can be confined in the nanoscale. However, the dimensions of the PC system are on the order of the wavelength or even larger, making them less appropriate for nano-scale optical elements integration.

Surface Plasmon polaritons (SPPs) are electromagnetic waves that propagate along the interface of metal and dielectric. In recent years, plasmonics is called the area of

© 2012 Huang and Tao, licensee InTech. This is an open access chapter 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. © 2012 The Author(s). Licensee InTech. This chapter is 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.

nanophotonics under the light diffraction limit that studies the transmission characteristics, localization, guiding of the SPP mode using metallic nanosturctures. The plasmonic waveguides are the most basic components and have been given much attention. Various kinds of metallic nanostructures have been proposed for SPP guiding. Generally these structures could be classified into three big categories: 1) chains of metal nanoparticles [6] and cylindrical metallic nanorods with various geometries [7]. 2) Metaldielectirc-metal (MDM) or Metal-insulator-metal (MIM) plasmonic waveguides, including groove channel structures in metallic substrates [8], slot waveguide [9]. 3) Dielectricmetal-dielectric (DMD)/ Insulator-metal-Insulator (IMI) waveguide [10]. It should be noted that not all these plasmonic structures can be used for guiding SPP mode to achieve subwavelength localization. Among them, MDM/MIM plasmonic waveguide can propagate SPP mode in the subwavelength scale with relatively low dissipation and large propagation distance. Our following proposed structures are mainly based on the MDM/MIM structures.

Nano-Plasmonic Filters Based on Tooth-Shaped Waveguide Structures 155

(2)

*p Hz* is the bulk plasma

stands for the dielectric constant at

),

is the angular

with *k*z1 and *k*z2 defined by momentum conservations:

Drude model: 2 ( ) / ( ). *m p i* Here 16 1.38 10

frequency of the incident electromagnetic radiation,

infinite angular frequency with the value of 3.7 [16]

electrons. 13

Where *in* and *m*

2 22 2 22 10 20 , . *z in z m kk kk*

*k0*=2π/*λ0* is the free-space wave vector. The propagation constant *β* is represented as the effective index *neff* =*β/k0* of the waveguide for SPPs. The real part of *neff* of the slit waveguide as a function of the slit width at different wavelengths is shown in Fig. 1. It should be noted that the dependence of *neff* on waveguide width is also suitable to the region of the tooth waveguide with the tooth width of *wt* shown in Fig. 2. The imaginary part of *neff* is referred to the propagation length which is defined as the length over which the power carried by the wave decays to 1/e of its initial value: *Lspps*=*λ0*/[4π·Im(*neff*)]. In the calculation above and the following simulations, the insulator in all of the structures is assumed to be air ( 1 *in*

and the frequency-dependent complex relative permittivity of silver is characterized by

frequency, which represents the natural frequency of the oscillations of free conduction

**Figure 1.** Real part of the effective of refraction index versus the width of a MIM slit waveguide structure.

The tooth-shaped waveguide filter is shown in Fig. 2. In the following FDTD simulations, the grid sizes in the *x* and *z* directions are chosen to be 5nm×5nm. Since the width of the waveguide is much smaller than the operating wavelength in the structure, only fundamental waveguide mode is supported. Two power monitors are respectively set at the

2.73 10 *Hz* is the damping frequency of the oscillations,

are respectively dielectric constants of the insulator and the metal,

Wavelength selection is one of key technologies in fields of optical communication and computing. To achieve wavelength filtering characteristics, plasmonic Bragg reflectors and nanocavities have been proposed. They include the metal hetero-structures constructed with several periodic slots vertically along a metal-dielectric-metal (MDM) waveguide [11], the Bragg grating fabricated by periodic modulating the thickness of thin metal stripes embedded in an insulator [12] and the periodic structure formed by changing alternately two kinds of the insulators [13,14]. Lately, a high-order plasmonic Bragg reflector with a periodic modulation of the core index of the insulators [15], and a structure with periodic variation of the width of the dielectric in MDM waveguide [16] have been proposed. Most of the periodic structures mentioned above, however, have total length of micrometers and relatively high propagation loss of several decibels.

In this chapter, we present our recent work on compact nano-plasmonic waveguide filters based on T-series and nano-capillary structures. In section 2, we introduce the novel nanometeric plasmonic filter in a tooth-shaped MIM waveguide and give an analytic model based on the scattering matrix method. In section 3, we investigate the characteristics of double-side teeth-shaped nano-plasmonic waveguide. In section 4 and section 5, we introduce the multiple multiple-teeth-shaped plasmonic filters and asymmetrical multiple teeth-shaped narrow pass band subwavelength filter. In section 6, we introduce a wavelength demultiplexing structure based on metal-dielectric-metal plasmonic nanocapillary resonators. Finally, we make a conclusion.

#### **2. Single-tooth shaped plasmonic waveguide filter [17]**

To begin with the dispersion relation of the fundamental TM mode in a MIM waveguide (shown in the inset of Fig. 1) is given by [18]:

$$
\varepsilon\_{in} k\_{z2} + \varepsilon\_m k\_{z1} \coth(-\frac{ik\_{z1}}{2}w) = 0,\tag{1}
$$

with *k*z1 and *k*z2 defined by momentum conservations:

154 Optical Devices in Communication and Computation

MDM/MIM structures.

relatively high propagation loss of several decibels.

capillary resonators. Finally, we make a conclusion.

(shown in the inset of Fig. 1) is given by [18]:

**2. Single-tooth shaped plasmonic waveguide filter [17]**

*in z m z*

nanophotonics under the light diffraction limit that studies the transmission characteristics, localization, guiding of the SPP mode using metallic nanosturctures. The plasmonic waveguides are the most basic components and have been given much attention. Various kinds of metallic nanostructures have been proposed for SPP guiding. Generally these structures could be classified into three big categories: 1) chains of metal nanoparticles [6] and cylindrical metallic nanorods with various geometries [7]. 2) Metaldielectirc-metal (MDM) or Metal-insulator-metal (MIM) plasmonic waveguides, including groove channel structures in metallic substrates [8], slot waveguide [9]. 3) Dielectricmetal-dielectric (DMD)/ Insulator-metal-Insulator (IMI) waveguide [10]. It should be noted that not all these plasmonic structures can be used for guiding SPP mode to achieve subwavelength localization. Among them, MDM/MIM plasmonic waveguide can propagate SPP mode in the subwavelength scale with relatively low dissipation and large propagation distance. Our following proposed structures are mainly based on the

Wavelength selection is one of key technologies in fields of optical communication and computing. To achieve wavelength filtering characteristics, plasmonic Bragg reflectors and nanocavities have been proposed. They include the metal hetero-structures constructed with several periodic slots vertically along a metal-dielectric-metal (MDM) waveguide [11], the Bragg grating fabricated by periodic modulating the thickness of thin metal stripes embedded in an insulator [12] and the periodic structure formed by changing alternately two kinds of the insulators [13,14]. Lately, a high-order plasmonic Bragg reflector with a periodic modulation of the core index of the insulators [15], and a structure with periodic variation of the width of the dielectric in MDM waveguide [16] have been proposed. Most of the periodic structures mentioned above, however, have total length of micrometers and

In this chapter, we present our recent work on compact nano-plasmonic waveguide filters based on T-series and nano-capillary structures. In section 2, we introduce the novel nanometeric plasmonic filter in a tooth-shaped MIM waveguide and give an analytic model based on the scattering matrix method. In section 3, we investigate the characteristics of double-side teeth-shaped nano-plasmonic waveguide. In section 4 and section 5, we introduce the multiple multiple-teeth-shaped plasmonic filters and asymmetrical multiple teeth-shaped narrow pass band subwavelength filter. In section 6, we introduce a wavelength demultiplexing structure based on metal-dielectric-metal plasmonic nano-

To begin with the dispersion relation of the fundamental TM mode in a MIM waveguide

2 1 coth( ) 0, 2

1

*kk w* (1)

*z*

*ik*

$$k\_{z1}^2 = \varepsilon\_{in} k\_0^2 - \beta^2 \quad , \quad k\_{z2}^2 = \varepsilon\_m k\_0^2 - \beta^2 \,. \tag{2}$$

Where *in* and *m* are respectively dielectric constants of the insulator and the metal, *k0*=2π/*λ0* is the free-space wave vector. The propagation constant *β* is represented as the effective index *neff* =*β/k0* of the waveguide for SPPs. The real part of *neff* of the slit waveguide as a function of the slit width at different wavelengths is shown in Fig. 1. It should be noted that the dependence of *neff* on waveguide width is also suitable to the region of the tooth waveguide with the tooth width of *wt* shown in Fig. 2. The imaginary part of *neff* is referred to the propagation length which is defined as the length over which the power carried by the wave decays to 1/e of its initial value: *Lspps*=*λ0*/[4π·Im(*neff*)]. In the calculation above and the following simulations, the insulator in all of the structures is assumed to be air ( 1 *in* ), and the frequency-dependent complex relative permittivity of silver is characterized by Drude model: 2 ( ) / ( ). *m p i* Here 16 1.38 10 *p Hz* is the bulk plasma frequency, which represents the natural frequency of the oscillations of free conduction electrons. 13 2.73 10 *Hz* is the damping frequency of the oscillations, is the angular frequency of the incident electromagnetic radiation, stands for the dielectric constant at infinite angular frequency with the value of 3.7 [16]

**Figure 1.** Real part of the effective of refraction index versus the width of a MIM slit waveguide structure.

The tooth-shaped waveguide filter is shown in Fig. 2. In the following FDTD simulations, the grid sizes in the *x* and *z* directions are chosen to be 5nm×5nm. Since the width of the waveguide is much smaller than the operating wavelength in the structure, only fundamental waveguide mode is supported. Two power monitors are respectively set at the

positions of *P* and *Q* to detect the incident and transmission fields for calculating the incident power of *Pin* and the transmitted power of *Pout*. The transmittance is defined to be *T*=*Pout/Pin*. The length of *L* is fixed to be 300nm, while the tooth width and depth are respectively *wt*=50nm and *d*=100nm. The tabulation of the optical constants of silver [19] is used in the simulation. As shown in Fig. 3(a), the tooth-shaped waveguide is of a filtering function: A transmission dip occurs at the free space wavelength nearly 784nm with the transmittance of ~0%. The maximum transmittance at the wavelengths longer than 1700nm is over 90%. The contour profiles of the field distributions around the tooth-shaped area at different wavelengths are shown in Figs. 3(b)-3(d). The filtering structure is distinguished from the Bragg reflectors based on periodical heterostructure.

Nano-Plasmonic Filters Based on Tooth-Shaped Waveguide Structures 157

, (3)

i *E* and

The phenomenon above can be physically explained in the scattering matrix theory [20] as

out in 1 1 out in 2 2 out in 3 3

splitting coefficients of a incident beam from Port *i* (*i*=1,2,3), caused by the structure. in

2 2

in in 2 1 1

out in 13 1

2 1 3

*E s s T t i E r i*

2 11

Therefore, the transmittance *T* from Port 1 to Port 2 is given by:

It can be seen from Eq. (8) that, if the phase satisfies

in 1 1 3

*s E E sE i r i r i i*

3

*ssE E tE i r i*

reflection on the air-silver surface. Combined Eq. (5) and Eq. (6), the output field at Port 2 is

in

2 2 out

terms inside the absolute value sign on the right of the equation will cancel each other (as it

exp( ( )) 1 exp( ( ))

exp( ( )) 1 exp( ( ))

, and

i *E* stand for the fields of incident and output beams at Port *i*, respectively. Using the fact

out in in

exp( ( ))(1 exp( ( )) exp(2 ( )) ...) exp( ( )) 1 exp( ( ))

( )

>

, (7)

( ) (2 1)

*m* (*m=*0,1,2…), the two

. (8)

, (6)

, *ri, ti* and *si* (*i*=1,2,3) are respectively the reflection, transmission and

3

1 3 113 113 1 *r r tss rss t r* 22 1 . (4)

2 11 33 *E tE sE* , (5)

3

*r i*

in

is the phase-shift caused by the

*E E E SE E E*

follows:

where

out

113 11 3 113

*rts S trs ssr*

that *S* 1 , one can obtain:

2 *E* 0 , one has

3 *E* is given as follows:

3 11 3 3

where the phase delay 4 ( ) ( ) *eff n d*

For the case of in

in which in

derived as:

**Figure 2.** The structure schematic of a single tooth-shaped waveguide filter, with the slit width of *w*, the tooth width of *wt*, and the tooth depth of *d*.

**Figure 3.** (a) Transmission of the single tooth-shaped MIM waveguide compared with a straight MIM slit waveguide. The width of the waveguide is *w*=50nm, and the tooth width and depth are respectively *wt*=50nm and *d*=100nm. The contour profiles of field *Hy* of the tooth-shaped waveguide at different wavelengths of (b) λ=510nm, (c) λ=783nm, and (d) λ=1550nm.

The phenomenon above can be physically explained in the scattering matrix theory [20] as follows:

$$
\begin{pmatrix} E\_1^{\text{out}} \\ E\_2^{\text{out}} \\ E\_3^{\text{out}} \end{pmatrix} = \mathbf{S} \cdot \begin{pmatrix} E\_1^{\text{in}} \\ E\_2^{\text{in}} \\ E\_3^{\text{in}} \end{pmatrix}' \tag{3}
$$

where 113 11 3 113 *rts S trs ssr* , *ri, ti* and *si* (*i*=1,2,3) are respectively the reflection, transmission and

splitting coefficients of a incident beam from Port *i* (*i*=1,2,3), caused by the structure. in i *E* and out i *E* stand for the fields of incident and output beams at Port *i*, respectively. Using the fact that *S* 1 , one can obtain:

$$2r\_1^2r\_3 + 2t\_1s\_1s\_3 - 2r\_1s\_1s\_3 - t\_1^2r\_{\phantom{e}3} = 1\,\text{.}\tag{4}$$

For the case of in 2 *E* 0 , one has

156 Optical Devices in Communication and Computation

tooth width of *wt*, and the tooth depth of *d*.

from the Bragg reflectors based on periodical heterostructure.

positions of *P* and *Q* to detect the incident and transmission fields for calculating the incident power of *Pin* and the transmitted power of *Pout*. The transmittance is defined to be *T*=*Pout/Pin*. The length of *L* is fixed to be 300nm, while the tooth width and depth are respectively *wt*=50nm and *d*=100nm. The tabulation of the optical constants of silver [19] is used in the simulation. As shown in Fig. 3(a), the tooth-shaped waveguide is of a filtering function: A transmission dip occurs at the free space wavelength nearly 784nm with the transmittance of ~0%. The maximum transmittance at the wavelengths longer than 1700nm is over 90%. The contour profiles of the field distributions around the tooth-shaped area at different wavelengths are shown in Figs. 3(b)-3(d). The filtering structure is distinguished

**Figure 2.** The structure schematic of a single tooth-shaped waveguide filter, with the slit width of *w*, the

**Figure 3.** (a) Transmission of the single tooth-shaped MIM waveguide compared with a straight MIM slit waveguide. The width of the waveguide is *w*=50nm, and the tooth width and depth are respectively *wt*=50nm and *d*=100nm. The contour profiles of field *Hy* of the tooth-shaped waveguide at different

wavelengths of (b) λ=510nm, (c) λ=783nm, and (d) λ=1550nm.

$$E\_2^{\text{out}} = t\_1 E\_1^{\text{in}} + s\_3 E\_3^{\text{in}} \, \text{ \, \, \tag{5}$$

in which in 3 *E* is given as follows:

$$E\_3^{\text{in}} = \text{s}\_1 E\_1^{\text{in}} \exp(i\phi(\lambda))(1 + r\_3 \exp(i\phi(\lambda)) + r\_3^2 \exp(2i\phi(\lambda)) + \dots) = \frac{\text{s}\_1 E\_1^{\text{in}}}{1 - r\_3 \exp(i\phi(\lambda))} \exp(i\phi(\lambda)) \tag{6}$$

where the phase delay 4 ( ) ( ) *eff n d* , and ( ) is the phase-shift caused by the reflection on the air-silver surface. Combined Eq. (5) and Eq. (6), the output field at Port 2 is derived as:

$$E\_2^{\text{out}} = t\_1 E\_1^{\text{in}} + \frac{s\_1 s\_3 E\_1^{\text{in}}}{1 - r\_3 \exp(i \phi(\mathcal{A}))} \exp(i \phi(\mathcal{A})) \,, \tag{7}$$

Therefore, the transmittance *T* from Port 1 to Port 2 is given by:

$$T = \left| \frac{E\_2^{\text{out}}}{E\_1^{\text{in}}} \right|^2 = \left| t\_1 + \frac{s\_1 s\_3}{1 - r\_3 \exp(i\phi(\mathcal{L}))} \exp(i\phi(\mathcal{L})) \right|^2. \tag{8}$$

It can be seen from Eq. (8) that, if the phase satisfies ( ) (2 1) *m* (*m=*0,1,2…), the two terms inside the absolute value sign on the right of the equation will cancel each other (as it can be seen in Fig. 3(c)), so that the transmittance *T* will become minimum. Therefore, the wavelength *λm* of the transmission dip is determined as follows:

$$\lambda\_m = \frac{4 \cdot n\_{eff} \cdot d}{(2m+1) - \frac{\Delta \rho(\lambda)}{\pi}} \cdot \tag{9}$$

Nano-Plasmonic Filters Based on Tooth-Shaped Waveguide Structures 159

**Figure 5.** (a) Transmission spectra of the waveguide filters with different tooth depths of *d*, and with a given tooth width of *wt*=50nm and the slit width of *w*=50nm. (b) The wavelength of the transmission dip

Figure 6(a) shows the structure of a proposed double-side teeth-shaped waveguide filter. The waveguide width *w* and the distance *L* are fixed to be 50nm and 300 nm. *d*1 and *d*2 are the depths of the teeth on each side of a MIM waveguide. The transmission spectra of the double-side teeth-shaped waveguide filter and the single-side tooth-shaped waveguide filter are shown in Fig. 6(b), which is obtained with the FDTD method. One can see that there is one dip at the free-space wavelength of nearly 1550nm with the transmittance of ~0%. An analytic model to explain the filtering function of single-side tooth-shaped waveguide structure based on multiple-beam-interference and scattering matrix has been

It can be seen that the wavelength λm is linear to the tooth depth *d* and depends on tooth width *w* through the somewhat inverse-proportionlike relationship between *n*eff and *w* shown in Fig. 1. The dip width of the double-side structure is wider compared with that of the single-side tooth-shaped structure. For better understanding the characteristics of double-side teeth structure, we next discuss the dependence of its filtering spectrum on the

Figure 7 shows the transmission spectra of the double-side teeth-shaped waveguide filters with different teeth depths of *d*1 and *d*2. From Fig. 7(a), one can see that there are two transmission dips at the free-space wavelengths of nearly 790nm and 1230nm with *d*1=100nm and *d*2=180nm. It is found that the wavelength of the second dip shifts to a long wavelength with the increasing of *d*2 while the first trough keeps unchanged due to a fixed value of *d*1=100nm. From Fig. 7(b), we can see that the first dip shifts to a long wavelength with the increasing of *d*1 while the position of the second dip is fixed due to a given

**3. Double-side teeth-shaped nano-plasmonic waveguide filters [21]**

vs. the tooth depth of *d* with *wt*=15nm, *wt*=30nm and *wt*=50nm.

given in the section 1

symmetry of teeth depth.

*d*2=180nm.

It can be seen that the wavelength *λm* is linear to the tooth depth *d*, and depends on tooth width *wt*, through the somewhat inverse-proportion-like relationship between *neff* and *wt* shown in Fig. 1.

Figure 4(a) shows the transmission spectra of the waveguide filters with various tooth widths of *wt*. The maximum transmittance can reach 97%. Figure 4(b) shows the wavelength of the trough vs. the tooth width of *wt*. The primary dip of the transmission moves very significantly to short wavelength (blue-shift) with the increase of *wt* for *wt<*20nm. The shift rate rapidly becomes small after *wt>*20nm, and tends to be saturated when *wt>*200nm. As revealed in the Eq. (9), the above relationship between the dip position and *wt* mainly results from the contribution of the inverse-proportion-like dependence of *neff* on *wt*. The change rate of Δ*neff /*Δ*wt* within the tooth width of 20nm is much higher than that of Δ*neff /*Δ*wt* after *wt>*20nm, as shown in Fig. 1, and becomes finally saturated after *wt>*200nm. Obviously, tooth width *wt* should be chosen within the range of 20-200nm to avoid the critical behavior and the difficulty in fabrication process.

**Figure 4.** (a) Transmission spectra of the waveguide filters with various tooth widths of *wt*, at a fixed tooth depth of *d*=100nm and the slit width of *w*=50nm. (b) The wavelength of the trough versus the tooth width of *wt.*

Figure 5(a) shows the transmission spectra of the filters with different tooth depths of *d*. It is found that the wavelength of the transmission dip shifts to long wavelength with the increasing of *d*. Figure 5(b) reveals that the wavelength of the transmission dip has a linear relationship with the tooth depth, as our expectation in Eq. (9). Therefore, one can realize the filter function in various required wavelength with high performance by changing the width or/and the depth of the tooth. For example, to obtain a filter with a transmission dip at the wavelength of 1550nm, the structural parameters of *wt*=*w*=50nm and *d*=237.5nm can be chosen.

the difficulty in fabrication process.

shown in Fig. 1.

tooth width of *wt.*

wavelength *λm* of the transmission dip is determined as follows:

*m*

can be seen in Fig. 3(c)), so that the transmittance *T* will become minimum. Therefore, the

4

*m*

( ) (2 1) *eff*

It can be seen that the wavelength *λm* is linear to the tooth depth *d*, and depends on tooth width *wt*, through the somewhat inverse-proportion-like relationship between *neff* and *wt*

Figure 4(a) shows the transmission spectra of the waveguide filters with various tooth widths of *wt*. The maximum transmittance can reach 97%. Figure 4(b) shows the wavelength of the trough vs. the tooth width of *wt*. The primary dip of the transmission moves very significantly to short wavelength (blue-shift) with the increase of *wt* for *wt<*20nm. The shift rate rapidly becomes small after *wt>*20nm, and tends to be saturated when *wt>*200nm. As revealed in the Eq. (9), the above relationship between the dip position and *wt* mainly results from the contribution of the inverse-proportion-like dependence of *neff* on *wt*. The change rate of Δ*neff /*Δ*wt* within the tooth width of 20nm is much higher than that of Δ*neff /*Δ*wt* after *wt>*20nm, as shown in Fig. 1, and becomes finally saturated after *wt>*200nm. Obviously, tooth width *wt* should be chosen within the range of 20-200nm to avoid the critical behavior and

**Figure 4.** (a) Transmission spectra of the waveguide filters with various tooth widths of *wt*, at a fixed tooth depth of *d*=100nm and the slit width of *w*=50nm. (b) The wavelength of the trough versus the

Figure 5(a) shows the transmission spectra of the filters with different tooth depths of *d*. It is found that the wavelength of the transmission dip shifts to long wavelength with the increasing of *d*. Figure 5(b) reveals that the wavelength of the transmission dip has a linear relationship with the tooth depth, as our expectation in Eq. (9). Therefore, one can realize the filter function in various required wavelength with high performance by changing the width or/and the depth of the tooth. For example, to obtain a filter with a transmission dip at the wavelength of 1550nm, the structural parameters of *wt*=*w*=50nm and *d*=237.5nm can be chosen.

*n d*

. (9)

**Figure 5.** (a) Transmission spectra of the waveguide filters with different tooth depths of *d*, and with a given tooth width of *wt*=50nm and the slit width of *w*=50nm. (b) The wavelength of the transmission dip vs. the tooth depth of *d* with *wt*=15nm, *wt*=30nm and *wt*=50nm.

#### **3. Double-side teeth-shaped nano-plasmonic waveguide filters [21]**

Figure 6(a) shows the structure of a proposed double-side teeth-shaped waveguide filter. The waveguide width *w* and the distance *L* are fixed to be 50nm and 300 nm. *d*1 and *d*2 are the depths of the teeth on each side of a MIM waveguide. The transmission spectra of the double-side teeth-shaped waveguide filter and the single-side tooth-shaped waveguide filter are shown in Fig. 6(b), which is obtained with the FDTD method. One can see that there is one dip at the free-space wavelength of nearly 1550nm with the transmittance of ~0%. An analytic model to explain the filtering function of single-side tooth-shaped waveguide structure based on multiple-beam-interference and scattering matrix has been given in the section 1

It can be seen that the wavelength λm is linear to the tooth depth *d* and depends on tooth width *w* through the somewhat inverse-proportionlike relationship between *n*eff and *w* shown in Fig. 1. The dip width of the double-side structure is wider compared with that of the single-side tooth-shaped structure. For better understanding the characteristics of double-side teeth structure, we next discuss the dependence of its filtering spectrum on the symmetry of teeth depth.