FIELD OF THE INVENTION  
         [0001]    This invention relates to tunable optical filters, and more particularly to filters that have variable spectral reflectance and transmittance functions, and even more particularly to multi-wavelength optical communication systems and high-density wavelength-division multiplexed network systems.  
         BACKGROUND  
         [0002]    It is known that tunable optical filters can be constructed from liquid crystals. For example, Patel U.S. Pat. No. 5,111,321 (hereinafter, “Patel”) shows a dual-polarization liquid crystal etalon filter that includes a nematic liquid crystal in a Fabry-Perot cavity. The crystal is divided into two portions that are buffed in orthogonal directions so that they align the liquid crystal parallel to their surfaces. Using a polarization beam diversity scheme, an input beam is split into its orthogonal polarization components and both portions of the Fabry-Perot cavity operate in equal amounts upon the components to induce a polarization independent filter. The spectral location of the transmittance peak maximum is tunable by varying the voltage applied to the etalon. Patel uses a single voltage generator to apply a potential difference across both portions of the cavity, which disadvantageously limits the tunability of the filter.  
           [0003]    Kershaw U.S. Pat. No. 6,154,591 (hereinafter, “Kershaw”) also shows a tunable optical device. The device shown by Kershaw includes multiple optical waveguides separated by a space filled with a liquid crystal that is oriented by an alignment layer or grating to form a Fabry-Perot resonant cavity.  
           [0004]    During operation, applying a voltage across the cavity alters the refractive index of the liquid crystal. Kershaw shows an array of filters that can be constructed using optical fibers positioned between a substrate and a superstrate enabling independent tuning of each filter. Each of the filters is used to filter a separate optical signal and those signals do not mix, limiting tunability.  
           [0005]    Dingel et al. U.S. Pat. No. 6,304,689 (hereinafter, “Dingle et al.”) shows a general multi-function filter that uses a Michelson-Gires-Tournois resonator. The filter shown by Dingle et al. can allegedly function as a channel passing filter, a channel dropping filter, and a bandpass filter, depending on the interferometer arm length difference and reflectance. In the resonator used by Dingle et al., one of the reflecting mirrors of a Michelson interferometer or a Tynman-Green interferometer is substituted with a Gires-Tornouis resonator, which allegedly makes the line width narrower and contrast greater for the channel passing filter. The device shown by Dingel et al. is bulky and relatively expensive to manufacture.  
           [0006]    Additional tunable filters are described, for example, in Diemeer U.S. Pat. No. 6,285,504 and Cheng et al. U.S. Pat. No. 5,481,402.  
           [0007]    It is also known that liquid crystals can be used to form Fabry-Perot interferometer-based electro-optic modulators. For example, Saunders U.S. Pat. No. 4,779,959 (hereinafter, “Saunders”) shows such an electro-optic modulator in which a liquid crystal is placed between mirror layers, each of which bears a respective rubbed polyimide layer that provides homogeneous alignment of the liquid crystal molecules. The mirrors are connected to an electrical bias that can be varied between two values: above and below a threshold for refractive index sensitivity. Saunders uses a single liquid crystal modulator to modulate an optical signal. Saunders, however, does not show how to construct an arbitrary tunable modulator.  
           [0008]    It is further known that liquid crystals can be used to form variable optical attenuators. For example, Sinclair et al. U.S. Pat. No. 4,364,639 (hereinafter, “Sinclair et al.”) shows a variable attenuation electro-optic device that has passes light through a dynamic scattering liquid crystal cell whose optical transmittance can be varied by varying an AC electric field applied across it. Sinclair et al. describes reflective and transmissive embodiments using Selfoc type lenses. By adjusting the length of such a lens, it can be used to focus, diverge, invert, or collimate a light beam, performing the same functions as regular spherical optics with the added benefit that the end-surfaces are flat. The attenuators shown by Sinclair, however, are relatively chromatically inflexible.  
           [0009]    It is also known that liquid crystals can be used to form optical fiber-based attenuators. For example, Rumbaugh et al. U.S. Pat. No. 5,015,057 (hereinafter, “Rumbaugh et al.”) describes a polarization insensitive optical attenuator that uses a polymer-dispersed liquid crystal film to provide attenuation over a range of attenuation values. Rumbaugh et al. shows a liquid crystal film between adjacent sections of an optical fiber, a tubular housing for retaining the liquid crystal between the adjacent sections, and a voltage source for applying an electric field across the liquid crystal. The device shown by Rumbaugh et al. always uses a single liquid crystal cell between sections of an optical fiber.  
           [0010]    Hanson U.S. Pat. No. 4,410,238 (hereinafter, “Hanson”) shows an optical switch attenuator that includes two slabs of birefringent material having a liquid crystal polarization rotator as a control element between the slabs. By controlling the rotator electrically, Hanson selects a variable ratio of transmitted-to-displaced output optical power. Hanson does not show a broadly tunable optical switch.  
           [0011]    Other types of attenuators are known, such as attenuators that use neutral density filters or circularly graded half-slivered mirrors that are moveable or rotatable into and out of the beam path. These mechanical attenuators, however, are generally costly, unreliable, and bulky.  
           [0012]    Madsen U.S. Pat. No. 5,953,467 (hereinafter, “Madsen”) shows a switchable optical filter that includes an optical splitter coupled to an input waveguide, one or more output waveguides, and multiple interferometer waveguides. During operation, a multi-wavelength signal is split into the interferometer waveguides. Then, using a sequence of controllable phase shifters and reflective filters, specific wavelength signals are reflected from a respective interferometer waveguide into the splitter and then to a respective output waveguide. In one embodiment, Madsen changes the relative phase difference for the reflected light in each waveguide to vary the output port. Unfortunately, Madsen requires complex interferometric waveguides and phase-shifters.  
           [0013]    Finally, Grasis et al. U.S. Pat. No. 6,198,857 shows an add/drop optical multiplexing device. The device includes a filter assembly defining a light path that extends from a common port, serially through a first channel port and a second channel port, and finally a pass-through port. The first and second ports each have substantially the same transmittance and reflectance properties. The device shown by Grasis et al. includes filter elements, but these elements are not necessarily tunable.  
           [0014]    It would therefore be desirable to provide reliable, compact, and inexpensive methods and apparatus for tunable spectral filtering.  
           [0015]    It would also be desirable to provide methods and apparatus for polarization independent tunable filtering.  
           [0016]    It would be further desirable to provide methods and apparatus for multiplexing and demultiplexing optical channels.  
           [0017]    It would be more desirable to provide methods and apparatus for dynamic gain and spectral equalization.  
           [0018]    It would be still more desirable to provide methods and apparatus for tunable optical blocking, switching, and modulation.  
         SUMMARY OF THE INVENTION  
         [0019]    It is therefore an object of this invention to provide methods and apparatus for reliable, compact, and inexpensive tunable spectral filtering.  
           [0020]    It also an object of this invention to provide methods and apparatus for polarization independent tunable filtering.  
           [0021]    It is a further object of this invention to provide methods and apparatus for multiplexing and demultiplexing optical channels.  
           [0022]    It is another object of this invention to provide methods and apparatus for dynamic gain and spectral equalization.  
           [0023]    It is yet another object of this invention to provide methods and apparatus for tunable optical blocking, switching, and modulation.  
           [0024]    In accordance with this invention, a tunable optical filter is provided. The filter can include an optical assembly for receiving incident light, an optical assembly for providing a filtered light, and a plurality of independently tunable filter elements. Each of the elements is located along a different optical path, although these paths all pass through the assemblies. Also, each of the filter elements filters a different component of the incident optical signal such that, when the components are combined, a filtered optical signal is formed.  
           [0025]    It will be appreciated that in its most simple form, a filter consistent with this invention only needs to include multiple independently tunable filter elements that are appropriately positioned to receive an incident signal and reflect and/or transmit a filtered one. Thus, a filter consistent with this invention can operate in reflection mode, a transmission mode, and a simultaneous combination thereof.  
           [0026]    According to yet another aspect of this invention, a method of tunable optical filtering is provided. The method includes dividing an incident optical beam into a plurality of beam components, filtering each of the components with at least one independently tunable filter elements, and combining the components after filtering to form a filtered optical beam. 
       
    
    
     BRIEF DESCRIPTION OF DRAWINGS  
       [0027]    The above and other objects and advantages of the invention will be apparent upon consideration of the following detailed description, taken in conjunction with the accompanying drawings, in which like reference characters refer to like parts throughout, and in which:  
         [0028]    [0028]FIG. 1 shows simulated reflectance spectra for a pixelated Fabry-Perot etalon and a pixelated Gires-Tornouis etalon with all of the filter elements tuned to 1.5 microns, consistent with this invention;  
         [0029]    [0029]FIG. 2 shows simulated reflectance spectra for the same Fabry-Perot and Gires-Tornouis etalons used in FIG. 1, except that four of the ten filters have been tuned to 1.52, 1.53, 1.54, and 1.55 microns, consistent with this invention;  
         [0030]    [0030]FIG. 3 shows simulated reflectance spectra for the same Fabry-Perot and Gires-Tornouis etalons used in FIGS. 1 and 2, except that two of the filter elements are tuned to 1.52 microns and two of the filter elements are tuned 1.53 microns, consistent with this invention;  
         [0031]    [0031]FIG. 4 shows additional simulated reflectance spectra for a pixelated Fabry-Perot etalon and a pixelated Gires-Tornouis etalon using twenty filter elements, four of which were tuned to 1.52, 1.53, 1.54, and 1.55 microns, and sixteen of which were tuned to 1.50 microns, consistent with this invention;  
         [0032]    [0032]FIG. 5 shows more simulated reflectance spectra for a pixelated Fabry-Perot etalon and a pixelated Gires-Tornouis etalon using 2 filter elements having reflection coefficients of 0.98, with one tuned to 1.50 microns and the other tuned to 1.53 microns, consistent with this invention;  
         [0033]    [0033]FIGS. 6 and 7 show simulated reflectance spectra that are similar to FIG. 5, except that the reflectance of the filter element reflectors were 0.8 and 0.64, respectively, consistent with this invention;  
         [0034]    [0034]FIG. 8 shows the same Fabry-Perot reflectance spectrum shown in FIG. 2, plus a corresponding transmittance spectrum (assuming no absorption), consistent with this invention;  
         [0035]    [0035]FIG. 9 shows simulated reflectance spectrum for a single Fabry-Perot filter element that has a reflection coefficient of about 0.99 and that is tuned to 1.5200 microns, consistent with this invention;  
         [0036]    [0036]FIG. 10 shows simulated reflectance spectrum for two Fabry-Perot filter elements that each have a reflection coefficient of about 0.99, with one filter element tuned to 1.52000 microns and the other filter element is tuned to 1.52025 microns, consistent with this invention;  
         [0037]    [0037]FIG. 11 shows simulated reflectance spectrum for two Fabry-Perot filter elements that each have a reflection coefficient of about 0.98 and a free spectral range of 0.1 micron, with one filter element tuned to 1.52000 microns and the other filter element tuned to 1.52025 microns, consistent with this invention;  
         [0038]    [0038]FIG. 12 shows a top planar view of an illustrative filter that includes two filter elements, consistent with this invention;  
         [0039]    [0039]FIG. 13 shows a longitudinal elevational view of the filter shown in FIG. 12, taken from line  13 - 13  of FIG. 12, consistent with this invention;  
         [0040]    [0040]FIG. 14 shows a top planar view of another illustrative filter, consistent with this invention;  
         [0041]    [0041]FIG. 15 shows yet another illustrative filter consistent with this invention that can operate in both reflection mode and transmission mode simultaneously;  
         [0042]    [0042]FIG. 16 shows a top planar view of another illustrative filter that is similar to the shown in FIG. 12 except that it includes two lenses for either converging or diverging a beam light in transmission mode, consistent with this invention;  
         [0043]    [0043]FIG. 17 shows still another filter, which is similar to the filter shown in FIG. 16, except that the filter operates in reflection mode, consistent with this invention;  
         [0044]    [0044]FIG. 18 shows another illustrative filter that includes a dual fiber collimator, consistent with this invention;  
         [0045]    [0045]FIG. 19 shows still another illustrative filter that can operate in both reflection mode and transmission mode simultaneously, consistent with this invention;  
         [0046]    [0046]FIG. 20 shows still another illustrative filter that includes beam walk-off crystals for splitting and reuniting a beam&#39;s orthogonal polarization components, consistent with this invention;  
         [0047]    [0047]FIG. 21 shows a further illustrative filter that operates in reflection mode and leverages a polarization diversity scheme, consistent with this invention;  
         [0048]    [0048]FIG. 22 shows another illustrative filter that includes a beam walk-off crystal, operates in reflection mode, and only uses one set of filter elements, consistent with this invention;  
         [0049]    [0049]FIG. 23 shows another illustrative filter that is nearly identical to the filter shown in FIG. 22, except that the prisms of FIG. 22 have been substituted for lenses, consistent with this invention;  
         [0050]    [0050]FIG. 24 shows illustrative add/drop optical multiplexing device, consistent with this invention;  
         [0051]    [0051]FIG. 25 shows an optical branch filter, consistent with this invention;  
         [0052]    [0052]FIG. 26 shows another illustrative optical multiplexing device, consistent with this invention;  
         [0053]    [0053]FIG. 27 shows yet another illustrative multiplexing device, consistent with this invention;  
         [0054]    [0054]FIG. 28 shows an illustrative device that includes a circulator, consistent with this invention;  
         [0055]    [0055]FIG. 29 shows another illustrative device that includes two circulators, consistent with this invention; and  
         [0056]    [0056]FIG. 30 shows a simplified, exploded, perspective view of a micro-electromechanical (hereinafter, “MEMS”) type device consistent with this invention. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0057]    A filter consistent with this invention includes an optical assembly for receiving an incident optical signal, an optical assembly for providing a filtered optical signal, and a plurality of independently tunable filter elements. Each of the elements is located along a different optical path, although each of the paths intersects at least at the assemblies. Also, each of the filter elements filters a different component of the incident optical signal such that, when the components are combined, a filtered optical signal is formed.  
         [0058]    During operation, a beam is spatially divided into at least two different components that are separately directed to at least two of the filter elements (i.e., pixels). As used herein, a pixel is the smallest independently controllable element of a filter. Each of the pixels acts like a tunable filter that can be tuned to reject a particular band of frequencies. When the pixels simultaneously filter different components of the beam, a composite filtered beam is formed from the individual filtered components.  
         [0059]    In one embodiment of this invention, the filter can include two or more Fabry-Perot etalons. A Fabry-Perot etalon is, generally, a nonabsorbing, multireflecting device that serves as a multi-layer, narrow-band pass filter. A Fabry-Perot etalon can be formed from two substantially parallel planar reflectors separated by a gap, which can be filled with an optically active material (e.g., electro-optic material, such as a liquid crystal layer, a thermo-optic material, such as glass or a polymer, etc.). In the case of a Fabry-Perot etalon, the two planar reflectors have substantially the same reflectance and can operate in either reflection mode or transmission mode. It will be appreciated that the physical distance, and thus the optical path, between the reflectors can be varied using MEMS, or any other mechanical device capable of actuating the position of at least one of the reflectors.  
         [0060]    When an optically active layer is used, such as a liquid crystal, the index of refraction of the layer can be varied by applying a voltage between electrodes disposed on each of the reflectors. It will be appreciated that the reflector can be electrically conductive, in which case the reflector itself can act as the electrode.  
         [0061]    A filter can be formed from a single Fabry-Perot etalon structure that is pixelated to form an array of active pixel areas (i.e., filter elements). The array can be a one-dimensional, two-dimensional, or three-dimensional (i.e., if cascaded). The filter can be constructed so that each of the filter elements has a free spectral range (hereinafter, “FSR”) that is wider than a predetermined spectral band (i.e., the band that needs to be controlled). For example, an acceptable FSR is about 150 nm centered on 1575 nm. When the FSR is sufficiently wide, the default reflectance or transmittance spectrum of the element can be made substantially flat. This flat default spectrum can be especially useful to protect against catastrophic optical events, such as when a controlling voltage source fails.  
         [0062]    Furthermore, the filter can be constructed such that when no voltage is applied to the individual filter elements, the individual filter elements (as well as the filter as a whole) is tuned to have a transmission wavelength that is outside that spectral band. In this case, all wavelengths inside the band are reflected. The reflected light can then be collected and coupled to an output fiber.  
         [0063]    If a certain wavelength λ in the band needs to be attenuated, an appropriate voltage can be applied to one or more of the pixels and tuned to λ, thereby attenuating the reflectance spectra. It will be appreciated that when just one pixel is used, only a minimum amount of attenuation can be applied. Hence, attenuation can be controlled in finer increments by dividing the beam into many components, and directing each of those components to an independently tunable pixel. The shape of the attenuated region of the spectrum depends on the finesse of the filter, which is determined by the reflection coefficients of the pair of reflectors as well as the thickness of the etalon cavity. The finesse and the number of pixels can be chosen to construct a desirably smooth tunable filter.  
         [0064]    The exact number and precise dimensions of the individual filter elements largely depends on the filter application. It has been found, for example, that when building a gain equalizer, 10 or more filter elements can be used, however, less than fifty filter elements, and in particular about 20 filter elements, has been found to be satisfactory. In the case of a wavelength division multiplexing (hereinafter, “WDM”) filter, an effective number of filter elements has been found to range anywhere between 2 and about 20.  
         [0065]    When a Fabry-Perot filter element is used, the reflection coefficient of the element&#39;s reflectors can be between 0.3 and somewhat less than 1.0. For WDM filter applications, reflection coefficients are generally large to form narrow passbands (or “dips”) in the filtered spectra, and can be between about 0.7 and about 1.0, preferably between about 0.9 and about 1.0, and most preferably between about 0.98 and about 1.0. For example, when 2 filter elements are tuned 0.25nm away each other, a reflection coefficient of 0.99 will generate about 0.5 nm of a full-width-half-maximum (“FWHM”) passband at a selected wavelength, while a 0.98 reflection coefficient will only generate about 0.75 nm passband.  
         [0066]    Also, with a multi-element filter consistent with this invention, a filter profile with a substantially flat top can be generated while minimally sacrificing peak transmittance. Thus, a filter consistent with this invention provides a flexible method for tailoring filter profiles, such as for WDM filter applications.  
         [0067]    Although not wishing to be bound by any particularly theory, it will be appreciated that the phase and amplitude of a Fabry-Perot etalon are normally effected during operation in reflection mode:  
       A   =     r            exp                 θ     -   1       1   -       r   2        exp                 θ                                 
 
         [0068]    where A is the amplitude of a reflected optical signal, r is the reflection coefficient of each of the reflectors, and θ is the round-trip phase delay between the beams reflected from the reflectors (i.e., θ=2d/λ).  
         [0069]    In a Fabry-Perot etalon, maximum transmittance is achieved when all filter elements are tuned to have resonance outside the desired band. To induce loss at a particular wavelength or band, one or more filter elements can be tuned to reflect at that wavelength or narrow band, accordingly. For each filter element added, the reflectance or transmittance of the filter as a whole can be decreased or increased. By tuning just one filter element to a particular wavelength, transmittance can be reduced to (1−1/N) 2 ˜1−2/N.  
         [0070]    A simple numerical model can be used to estimate the performance of a tunable multi-element filter consistent with this invention. Assume that the modal field of a single mode fiber, after being imaged backwards by a lens on the element, is F(x,y). Also assume that the input field after the element is A(x,y). Then, the transmittance into the fiber can be written substantially as:  
       T   =         |     ∫       A        (     x   ,              y     )              F   *          (     x   ,              y     )               x             y              |   2         ∫       AA   *             x             y          ∫       FF   *                        x             y               .                           
 
         [0071]    It will be appreciated that this expression is simply the overlap of the input field with the modal field, normalized by the product of the two fields. If the fields are identical and overlap is maximized, perfect transmittance (T=1) occurs. In contrast, when overlap is minimized (i.e., zero), essentially no transmission occurs.  
         [0072]    If the input field to the element perfectly matches the fiber field, then the element has no amplitude or phase modulation and transmittance is maximized (e.g., T=1). We can simplify the calculation by further assuming that field F is uniform over the aperture of area S. It will be appreciated, however, that more exact calculations can be made by including Gaussian profiles. The filter can be divided into N sections of equal area S/N, where S is the total filter area on which the input field is incident. Then, each filter element modifies the input field incident on the element to be A n .  
         [0073]    Under these assumptions, transmittance T of the filter is substantially equal to:  
       T   =     |       1   N        Σ                   A   n            |   2     .                           
 
         [0074]    As described above, and according to one embodiment of this invention, each of the filter elements can be a separately tunable liquid crystal Fabry-Perot resonator. In this case, tuning can be performed by varying the amplitude of the input field of each element, the phase of each element, or a combination of amplitude and phase.  
         [0075]    In another embodiment consistent with this invention, the filter elements can be Gires-Tornouis etalons. Like the Fabry-Perot etalon, a Gires-Tornouis etalon is a substantially nonabsorbing, multireflecting device that serves as a multi-layer, narrow band pass filter. Unlike a Fabry-Perot etalon, the two planar reflectors have different reflection coefficients, one of which has a reflection coefficient of about 1.0. For this reason, a Gires-Tornouis etalon can only operate in reflection mode. In order to vary the index of refraction of the optically active layer (e.g., liquid crystal layer), an electrode can be disposed on each of the reflectors or, when the reflector is electrically conductive, the reflector itself can act as the electrode.  
         [0076]    When a Gires-Tornouis etalon is tuned, only the phase of the light, not its amplitude reflectance (which is always about 1), changes. Attenuation can be induced, however, by controllably interfering light reflected by two or more different filter elements.  
         [0077]    Thus, amplitude reflectance is always about 1, but the phase will be wavelength dependent as follows:  
       A   =           exp                 θ     -   r       1   -     r                 exp                                  θ         .                           
 
         [0078]    The phase at resonance (i.e., A=1) is inverted with respect to anti-resonance (i.e., A=−1). As in the case of a Fabry-Perot etalon, etalons can be designed so that resonances can be tuned beyond a desirable predetermined band.  
         [0079]    However, unlike the case of a Fabry-Perot etalon, a Gires-Tornouis etalon has no loss at those resonant wavelengths because the phase is uniform. By tuning a filter element to a different wavelength, a change in transmittance can be induced both at that wavelength and at the original resonance wavelength because both wavelengths see a non-uniform phase front. This tuned filter element now interferes destructively with the background field, leading to a transmittance substantially equally to about (1−2/N) 2 ˜1−4/N.  
         [0080]    FIGS.  1 - 3  show the effect of tuning individual filter elements consistent with this invention.  
         [0081]    [0081]FIG. 1 shows simulated reflectance spectra  5  and  7  for a pixelated Fabry-Perot etalon and a pixelated Gires-Tornouis etalon, respectively. Both spectra were simulated using ten filter elements and a gap thickness of 7 microns. In the case of the Fabry-Perot etalon, both reflectors have a reflection coefficient equal to 0.8. In the case of the Gires-Tournouis etalon, however, only the front reflector has a reflection coefficient equal to 0.8; the back reflector has a reflection coefficient of about 1.0. In both cases, all ten of the filter elements were tuned to 1.50 microns. Thus, Fabry-Perot spectrum  5  has reflectance dip  6  (i.e., a transmittance that peaks) at 1.5 microns. It will be appreciated that a similar peak occurs at 1.6 microns, so that the FSR of spectrum  5  is about 0.1 microns. In contrast to the Fabry-Perot spectrum  5 , Gires-Tornouis spectrum  7  is flat across the entire spectrum because all filter elements are in phase with one another.  
         [0082]    [0082]FIG. 2 shows simulated reflectance spectra  9  and  11  for the same Fabry-Perot and Gires-Tornouis etalons used in FIG. 1, except that four of the ten filters have been tuned to 1.52, 1.53, 1.54, and 1.55 microns. Now, both reflectance spectra  9  and  11  have a large dip at 1.5 microns as well as four smaller dips at 1.52, 1.53, 1.54, and 1.55 microns.  
         [0083]    In the case of the Fabry-Perot etalon, the effect of tuning four of the ten filter elements is that dip  13  (shown in FIG. 2) is shallower (i.e., reflects more) than corresponding dip  6  (shown in FIG. 1) at 1.50 microns. Also, the four smaller dips at 1.52, 1.53, 1.54, and 1.55 microns have appeared for the first time and have reflectance minima of approximately 0.75.  
         [0084]    In the case of the Gires-Tornouis etalon, the effect of tuning four of the ten filter elements is that large dip  14  and four smaller dips at 1.52, 1.53, 1.54, and 1.55 microns appear for the first time. It will be appreciated that the dips in Gires-Tornouis spectrum  11  are narrower and deeper and exhibit lower insertion loss that the respective dips in Fabry-Perot spectrum  9 .  
         [0085]    [0085]FIG. 3 shows simulated reflectance spectra  15  and  17  for the same Fabry-Perot and Gires-Tornouis etalons used in FIGS. 1 and 2, except that two of the filter elements are tuned to 1.52 microns and two of the filter elements are tuned 1.53 microns. Now, both reflectance spectra  15  and  17  have a relatively large dip at 1.5 microns as well as two smaller dips at 1.52 and 1.53 microns. Like the spectra shown in FIG. 2, the reflectance minima in Gires-Tornouis spectrum  17  are narrower and deeper and exhibit lower insertion loss than the respective dips in the Fabry-Perot spectrum  15 .  
         [0086]    A comparison between FIGS. 2 and 4 shows how the number of filter elements affects the reflectance spectra consistent with this invention.  
         [0087]    [0087]FIG. 4 shows simulated reflectance spectra  20  and  22  for a pixelated Fabry-Perot etalon and a pixelated Gires-Tornouis etalon, respectively. In contrast to FIG. 2, which only includes reflectance spectra for ten filter elements, spectra  20  and  22  of FIG. 4 were simulated using twenty filter elements, four of which were tuned to 1.52, 1.53, 1.54, and 1.55 microns, and sixteen of which were tuned to 1.50 microns. Thus, the etalons used to simulate the spectra shown in FIG. 4 have a smaller percentage of surface area that is tuned to wavelengths that are different from 1.50 microns when compared to the etalons used to simulate the spectra shown in FIG. 2. A comparison of the spectra shown in FIGS. 2 and 4 reveals that this smaller surface area causes the small dips at 1.52, 1.53, 1.54, and 1.55 microns to be less deep and the large dip at 1.50 microns to be more deep.  
         [0088]    FIGS.  5 - 7  show the effect of the reflection coefficients of individual filter element reflectors consistent with this invention.  
         [0089]    [0089]FIG. 5 shows simulated reflectance spectra  25  and  27  for a pixelated Fabry-Perot etalon and a pixelated Gires-Tornouis etalon, respectively.  
         [0090]    Both spectra were simulated using 2 filter elements and a gap thickness of 7 microns. For each etalon structure, one filter element was tuned to 1.50 microns and the other filter element was tuned to 1.53 microns. In the case of the Fabry-Perot etalon, both reflectors have a reflection coefficient equal to about 0.98. In the case of the Gires-Tournouis etalon, however, only the front reflector has a reflection coefficient equal to 0.98; the back reflector has a reflection coefficient of about 1.0.  
         [0091]    [0091]FIGS. 6 and 7 are similar to FIG. 5, except that the reflection coefficients of the individual filter elements are less. In FIG. 6, the etalons used to simulate the reflectance spectra had coefficients that were 0.8 (although the back reflector of the Gires-Tournouis etalon has a reflection coefficient of about 1.0). Similarly, in FIG. 7, the etalons used to simulate the reflectance spectra had a reflection coefficient of 0.64 (although, again, the back reflector of the Gires-Tournouis etalon has a reflection coefficient of about 1.0). Inspection of FIGS.  5 - 7  reveals that as the reflection coefficient of the reflectors decreases, the width of the dips in the spectra become less deep, yet broader.  
         [0092]    It will be appreciated that for a Fabry-Perot filter element, or for a Fabry-Perot etalon that includes multiple filter elements, the sum of the reflectance and the transmittance, for any particular wavelength, is equal to one, assuming no absorption. Thus, as shown in FIG. 8, reflectance spectrum  40  (which is the same as spectrum  9  of FIG. 2) plus transmittance spectra  45  equals one. In a Gires-Tornoius etalon, however, transmittance of any individual filter element and of a filter made from such elements, is always essentially zero.  
         [0093]    FIGS.  9 - 11  show how a filter constructed from Fabry-Perot filter elements can be tuned to achieve a desirable transmittance spectrum that could be used, for example, in a WDM filter application. FIG. 9 shows simulated reflectance spectrum  50  for a single Fabry-Perot filter element that has a reflection coefficient of about 0.99, a FSR of 0.1 micron, and which is tuned to 1.5200 microns. FIG. 10 shows simulated reflectance spectrum  55  for two Fabry-Perot filter elements that each have a reflection coefficient of about 0.99 and a FSR of 0.1 micron. One of the filter elements is tuned to 1.52000 microns and the other filter element is tuned to 1.52025 microns. The spectra of the individual filter elements are not shown separately, but are apparent as dip  53  in the peak of spectrum  55 .  
         [0094]    [0094]FIG. 11 shows simulated reflectance spectrum  60  for two Fabry-Perot filter elements that each have a reflection coefficient of about 0.98 and a FSR of 0.1 micron. Like in FIG. 10, one of the filter elements is tuned to 1.52000 microns and the other filter element is tuned to 1.52025 microns. In FIG. 11, however, no dip appears at the peak of spectrum  60  because the component spectra are somewhat broader due to the lower reflection coefficient value.  
         [0095]    FIGS.  12 - 26  show various illustrative tunable optical filters, and devices constructed with the filters, consistent with this invention.  
         [0096]    [0096]FIG. 12 shows a top planar view of illustrative filter  100  consistent with this invention. As shown in FIG. 12, filter  100  filters incident optical beam  102 , which is provided by input fiber  104 , in transmission mode. Beam  102  is capable of being divided into two or more optical components  106  and  108  that can be directed to travel along different optical paths  110  and  112 , respectively. Each path starts at tip  105  of input fiber  104  and ends at tip  114  of output fiber  116 .  
         [0097]    In one embodiment, filter  100  can be an etalon that includes a two-dimensional array of independently tunable filter elements. FIG. 13 shows a longitudinal elevational view of filter  100 , taken from line  13 - 13  of FIG. 12, which includes at least filter elements  101  and  103 . As best shown in FIG. 12, elements  101  and  103  are located along optical paths  110  and  112 , respectively. After optical components  106  and  108  are transmitted through filter  100 , those components (or portions thereof) follow optical paths  106  and  108  and combine at tip  114  to form filtered optical signal  119 .  
         [0098]    It will be appreciated that before optical components  106  and  108  enter filter  100 , they are effectively part of the same beam. The boundary between these components is defined only by the boundary that exists between filter elements  101  and  103 . However, one or more optical elements, such as a lens, a micro-lens, a prism, diffractive optics, or a polarization beam splitter, can be used to collimate, diffract, deflect, separate, or polarize the incident light before entering filter  100 , if desired.  
         [0099]    It will be further appreciated that filter  100  has thickness  118 , across which optical components  106  and  108  propagate. As components  106  and  108  propagate through filter  100 , these components diverge reducing the amount of light that can be collected by fiber tip  114 . Thus, when thickness  118  is large, the amount of light that can be collected (without, for example, a lens) by fiber tip  114  is small. Thus, in an embodiment that does not include a converging optical element between filter  100  and fiber tip  114 , filter  100  is preferably relatively thin. Of course, if a converging optical element were used between filter  100  and fiber tip  114 , the amount of light that could be collected, after transmission through the elements would increase.  
         [0100]    [0100]FIG. 14 shows a top planar view of illustrative filter  120  consistent with this invention. In contrast to filter  100 , which was designed to operate in a transmission mode, filter  120  filters incident optical beam  122  provided by input fiber  124  in a reflection mode. Like beam  102 , beam  122  is divided into two or more optical components  126  and  128  that can be directed to travel along different optical paths  130  and  132 , respectively. Each path starts at tip  125  of input fiber  124  and ends at tip  134  of output fiber  136  such that, when combined, components  126  and  128  form output beam  139 .  
         [0101]    Like filter  100 , filter  120  can be an etalon that includes a one-dimensional or multi-dimensional array of independently tunable filter elements. Although FIG. 14 only shows two filter elements  121  and  123 , it will be appreciated that a filter consistent with this invention can include any number of elements that may be necessary to achieve a desirable level of filter tunability.  
         [0102]    A filter consistent with this invention can also operate in both the reflection and transmission modes simultaneously. Such a filter can be constructed by placing a reflection output fiber on the input side of the filter (as shown in FIG. 14) and a transmission output fiber on the side opposite the input side of the filter (as shown in FIG. 12). As described more fully below, additional input and output ports (e.g., fibers) can be added to a filter consistent with this invention.  
         [0103]    For example, FIG. 15 shows illustrative filter  160  consistent with this invention that can operate in both reflection mode and transmission mode simultaneously. Filter  160  includes a plurality of independently tunable filter elements  161  and  162 . Elements  161  and  162  are located along different optical paths  163  and  164 , respectively, although both paths intersect near the tips of fibers  165  and  191 . As described above, each filter element filters a different component of incident optical signal  167  such that, when the components are combined, filtered optical signal  168  is formed in reflection mode and filtered optical signal  169  is formed in transmission mode.  
         [0104]    It can be seen from FIG. 15, then, that a first component of incident beam  167  travels along path  163  during which time a portion of that beam can be reflected by filter element  161  and redirected to fiber  191  to partially form filtered beam  168 . Similarly, a different portion of the first component can travel through element  161  and be transmitted along path  193  to output fiber  192  to partially form filtered beam  169 .  
         [0105]    In an identical fashion, a second component of incident beam  167  travels along path  164  during which time a portion of that beam may be reflected by filter element  162  and redirected to fiber  191  to partially form filtered beam  168 . A different portion of the second component can, depending on the state of the filter, travel through element  162  and be transmitted along path  194  to output fiber  192  to partially form filtered beam  169 .  
         [0106]    [0106]FIG. 16 shows illustrative filter  140 . Filter  140  includes optical assembly  142  that receives incident optical signal  141  from input fiber  143 , optical assembly  144  for providing filtered optical signal  146  to fiber  148 , and plurality  150  of independently tunable filter elements  151  and  153 . Elements  151  and  153  are located along different optical paths  155  and  157 , respectively, although both paths intersect near the tips of fibers  143  and  148 , which can be parts of the assemblies. As described above, each of the filter elements filters a different component of incident optical signal  141  such that, when the components are combined, filtered optical signal  146  is formed.  
         [0107]    Thus, consistent with this invention, an optical assembly can include one or more beam shaping or directional elements (i.e., lenses, prisms, diffractive optics, etc.) that direct optical signals between an input or output fiber and filter elements. It will be appreciated, however, that lenses can be used generally to direct, redirect, converge, diverge, or collimate any optical beam or portion thereof, even between a cascade of filter elements.  
         [0108]    Thus, during operation consistent with this invention, a beam can be spatially dispersed into at least two different components and directed to at least two respective filter elements (e.g., pixels). Each of the pixels acts like a tunable filter that can be tuned to reject a particular band of frequencies.  
         [0109]    [0109]FIG. 17 shows another illustrative filter  170 . Filter  170  is similar to filter  140 , except that filter  170  operates in reflection mode while filter  140  operates in transmission mode. Filter  170  includes optical assembly  172  that receives incident optical signal  171  from input fiber  173 , optical assembly  174  for providing filtered optical signal  176  to fiber  178 , and plurality  180  of independently tunable filter elements  181  and  182 . Elements  181  and  183  are located along different optical paths  185  and  187 , respectively, although both paths intersect near the tips of fibers  173  and  178 . It will be appreciated that fibers  173  and  178  can form parts of the assemblies. As described above, each of the filter elements filters a different component of incident optical signal  171  such that, when the components are combined, filtered optical signal  176  is formed at the tip of fiber  178 .  
         [0110]    [0110]FIG. 18 shows another illustrative filter  200  consistent with this invention. Filter  200  includes dual fiber collimator  210  that receives incident optical signal  202  from input fiber  204  and that provides filtered optical signal  206  to fiber  208 , and plurality  211  of independently tunable filter elements  212  and  214 . Elements  212  and  214  are located along different optical paths  216  and  218 , respectively, although both paths intersect near fiber tips  220  and  222 . As described above, each of filter elements  212  and  214  filters a different component of incident optical signal  202  such that, when the components are combined, filtered optical signal  206  is formed, in this case, at fiber tip  222 .  
         [0111]    [0111]FIG. 19 shows another illustrative filter  240  consistent with this invention that can operate in both reflection mode and transmission mode simultaneously. Filter  240  includes optical assembly  242  (e.g., a lens) that receives incident optical signal  241  from input fiber  243 , optical assembly  244  (e.g., another lens) that provides filtered optical signal  246  to fiber  248 , and plurality  250  of independently tunable filter elements  251  and  252 . Elements  251  and  252  are located along different optical paths  255  and  257 , respectively, although both paths intersect near the tips of fibers  243  and  248 . As described above, each of the filter elements filters a different component of incident optical signal  241  such that, when the components are combined, filtered optical signal  246  is formed. As described more fully below with respect to other embodiments, additional input and output ports (e.g., fibers) can be added to a filter consistent with this invention.  
         [0112]    According to another aspect of this invention, polarization diversity can be used to perform polarization-independent spectral filtering. FIGS.  20 - 23  shows four illustrative embodiments of polarization diversity-based spectral filters consistent with this invention.  
         [0113]    [0113]FIG. 20 shows illustrative filter  300 . Filter  300  includes optical assembly  310  that receives incident optical signal  315  from input fiber  320 , optical assembly  325  that collects and provides filtered optical signal  330  to fiber  335 , and plurality  340  of independently tunable filter elements  341 - 344 . Each of filter elements  341 - 344  is located along a different optical path, although all paths share a common starting point and a common ending point—they all diverge from and converge toward fibers  320  and  335 , respectively.  
         [0114]    Optical assembly  310  can include a polarization beam splitting component, such as beam walk-off crystal  312 , for dividing incident signal  315  into orthogonal polarization components  313  and  314 . Within crystal  312 , component  313  has polarization direction  317  pointing in and out of FIG. 20 and component  314  has polarization direction  318  that lies within the plane of FIG. 20. Although beam walk-off crystal  312  can simply be a birefringent crystal, other types of polarization beam splitting components that can be used consistent with this invention include Brewter angle, Rochon, and Wollaston prisms, etc.  
         [0115]    When component  314  reaches end  321  of crystal  312 , component  314  is directed toward and incident upon filter set  347 , which includes filter elements  343  and  344 . If filter elements  343  and  344  are filled with a liquid crystal, for example, then the directors of the liquid crystals are preferably aligned with the polarization direction of the beam being filtered. It is known that such alignment will maximize tunability of the beam as it propagates through the liquid crystal without changing the polarization of the light. It will be appreciated that when component  314  exits crystal  312 , the polarization direction remains within the plane of FIG. 18.  
         [0116]    The length of a crystal  312  is preferably sufficiently long such that the two polarization components do not overlap when they reach the end of the crystal. When a walk-off crystal is made from YVO 4 , for example, the two components will separate by a maximum distance that is approximately one tenth of the crystal&#39;s length. Thus, if the incident beam diameter is 1 mm and the length of the crystal is 15 mm, two polarization beam components will have their centers separated by 1.5 mm, which is sufficient to avoid overlap of the polarization components.  
         [0117]    In contrast, when component  313  reaches end  321  of crystal  312 , beam  313  passes through half-wave wave plate  319 . Wave plate  319  rotates polarization direction  317  so that it has a polarization direction that is essentially the same as component  314 . It will be appreciated that half-wave wave plate  319  is optional. When wave plate  319  is present in filter  300 , both sets  346  and  347  of filter elements can have liquid crystal directors pointed in the same direction, which simplifies the manufacture of the constituent filter elements.  
         [0118]    Once portions of components  313  and  314  have been transmitted through sets  346  and  347 , respectively, those components have been individually filtered and can now be combined to form a composite filtered optical signal. Combining, or merging, these components can be achieved in the same way that the components were originally divided—namely, with another beam walk-off crystal  350  and half-wave wave plate  360 . Once again, components  313  and  314  have orthogonal polarization components while traveling through beam walk-off crystal  350  and, hence, do not interfere with one another at the convergence point.  
         [0119]    It will be appreciated that input beam  315  could be collimated with lens  322  before entering crystal  312 . Alternatively, beam  315  can be collimated by fiber  315  itself, if its tip is appropriately shaped. If input beam  315  is so collimated, filtered beam  330  will also be collimated when it emerges from crystal  350 . Thus, lens  334  can be added after crystal  350  (or fiber  335  tip can be shaped) to focus beam  330  into fiber  335 .  
         [0120]    It will be further appreciated that sets  346  and  347  preferably perform the same spectral filtering function. In this way, both polarization components are filtered in the same way, making the filter polarization independent.  
         [0121]    As explained above, transmitted portions of polarization components  313  and  314  are ultimately collected by fiber  335 . Reflected portions of these components can also be collected and directed to an additional output fiber. In a geometry similar to FIG. 17, two physically separate fibers can be used, or in a geometry similar to FIG. 18, a dual fiber collimator can be used.  
         [0122]    For example, FIG. 21 shows another illustrative filter  400  consistent with this invention that operates in reflection mode and leverages a polarization diversity scheme. Filter  400  is similar to filter  170  of FIG. 17, except that filter  400  includes beam walk-off crystal  405  that divides input beam  410  into orthogonal polarization components  415  and  420  and merges the components after they are each filtered in reflection mode by at least two sets of filter elements  450  and  460 .  
         [0123]    Thus, filter  400  includes optical assembly  425  and plurality  445  of filter elements. Optical assembly  425  receives incident optical signal  410  from input fiber  430  (via optional lens  412 ) and provides filtered beam  435  to output fiber  440  (via optional lens  437 , which may be the same as lens  412 ). Set  450  includes at least two independently tunable filter elements  452  and  454 . Similarly, set  460  includes at least two independently tunable filter elements  462  and  464 . If each of elements  452 ,  454 ,  462 , and  464  is filled with liquid crystal, then it will be appreciated that the directors of those liquid crystals are preferably aligned with the polarization directions of the respective incident beams. In this way, each of the filter elements can be tuned over the broadest possible range when a voltage is applied to the element. It will be further appreciated, however, that the filter elements need not include liquid crystals and could be, for example, MEMS devices, which are generally not polarization sensitive and need not use polarization diversity schemes.  
         [0124]    Also, for illustrative simplicity, although components  415  and  420  only appear to be incident on a respective boundary between a pair of filter elements, it will be appreciated that component  415  is incident on at least filter elements  452  and  454  and component  420  is incident on at least elements  462  and  464 . This illustrative simplification was also applied to FIGS. 20 and 21.  
         [0125]    Moreover, although polarization components  415  and  420  are directed to two different sets of filter elements, two half-wave rotators (e.g., half-wave wave plates) can be placed between the walk-off crystal and the filter elements in a manner shown in FIGS. 20, 22, and  23 . A single set of filter elements can be used to filter both polarization components. This “single set” technique is illustrated in FIG. 22. This technique simultaneously filters two polarization components that have been changed from orthogonal to parallel before they are filtered, and then made orthogonal once more after they are filtered.  
         [0126]    [0126]FIG. 22 shows filter  500 , which includes optical assembly  510  for receiving incident optical signal  515  from input fiber  520 , optical assembly  525  that provides filtered optical signal  530  to fiber  535 , and at least two independently tunable filter elements  541  and  542 .  
         [0127]    Optical assembly  510  includes beam walk-off crystal  512  for dividing an incident beam into orthogonal polarization components  513  and  514 . As shown in FIG. 22, components  513  and  514  have polarization directions  517  and  518 , respectively, that are orthogonal within beam walk-off crystal  512 .  
         [0128]    Like in filter  300  shown in FIG. 20, when component  513  reaches end  521  of crystal  512 , beam  513  passes through half-wave wave plate  519 , which rotates the polarization direction of component  513 —causing it to have the same polarization direction as component  514 . When wave plate  519  is present in filter  500 , filter elements  541  and  542  can each have liquid crystal directors that are pointed in the same direction, which simplifies the manufacture of the constituent filter elements.  
         [0129]    Assembly  510  can further include lens  570 , which directs polarization components  513  and  514  toward a single set of filter elements (e.g., elements  541  and  542 ). Although lens  570  is optional, its presence along the optical paths of component  513  and  514  directs both components  513  and  514  toward the single set of filter elements.  
         [0130]    The use of a single set of filter elements is possible because both components  513  and  514  have essentially the same polarization direction (e.g., parallel to the plane of FIG. 22) when they enter the set of filter elements. As mentioned above, when filter elements consistent with this invention include liquid crystals, those liquid crystals should have directors that are substantially parallel to the polarization direction of the incident beam. When two more beams pass through the same set of filter elements, the directors of those filter elements should be substantially parallel to the polarization directions of the incident beams. Thus, it will be appreciated that by rotating beam  513  by half-wave wave plate  519  (or alternatively beam  514 ), beams  513  and  514  have polarization directions that are substantially parallel to the directors (not shown) of filter elements  541  and  542 . Also, by using a single set of filter elements for both polarization components, fewer filter elements are required to perform the same filtering function.  
         [0131]    Polarization independent filtering can also be achieved using a method shown by Patel, which is hereby incorporated by reference in its entirety. As discussed above, Patel&#39;s dual-polarization liquid crystal etalon filter includes a nematic liquid crystal in a Fabry-Perot cavity. The crystal is divided into two portions that are buffed in orthogonal directions so that they align the liquid crystal parallel to their surfaces. Using a polarization beam diversity scheme, an input beam is split into its orthogonal polarization components and both portions of the Fabry-Perot cavity operate in equal amounts upon the components to induce a polarization independent filter.  
         [0132]    Thus, according to another aspect of this invention, a dual-polarization liquid crystal etalon, as shown by Patel, can be used to perform polarization-independent filtering, if desired. In this case, each filter element consistent with this invention (e.g., elements  101  and  103  of FIG. 12, elements  121  and  123  of FIG. 14, elements  151  and  513  of FIG. 16, etc.) can each have a polarization beam splitter and two liquid crystal portions buffed in orthogonal directions.  
         [0133]    Returning to FIG. 22, once portions of components  513  and  514  have been filtered by elements  541  and  542 , those portions can be made parallel by lens  573  and then combined to form composite filtered beam  530 . Combining these components can be achieved in the same way that the components were originally divided—namely, with another beam walk-off crystal  550  and half-wave wave plate  560 . FIG. 23 shows another filter, which is nearly identical to filter  500  of FIG. 22, except that prisms  577  and  578  have been substituted for lenses  570  and  573 . Operationally, both filters are identical.  
         [0134]    [0134]FIG. 24 shows illustrative add/drop optical multiplexing device  600 . Such a device is often the primary component device of a SONET network, and is often used to drop individual wavelengths onto a first fiber and pass through remaining wavelengths to a different fiber. Such a device can also add certain wavelengths, which are usually the same as the dropped wavelengths, but carry local traffic. Moreover, such a device can also be complemented by a digital cross connect, which mediates between SONET channels as they traverse the network, and in some cases can groom traffic down to the DS-1/DS-3 level.  
         [0135]    Device  600  includes at least one set  610  of filter elements  611 - 620 . The number of filter elements consistent with this invention can be greater or less than the number shown, but must be at least two. Also, although the filter elements are shown as a one-dimensional array, it will be appreciated that two or more one-dimensional arrays can be combined to form a two-dimensional array or combined to form a cascade of arrays. Device  600  also includes multiple optical ports, such as input port  620 , output port  630 , add port  640 , and drop port  650 .  
         [0136]    During operation, optical input signal  621  is provided via port  620  to side  602  of set  610  of filter elements  611 - 620 . Input signal  621  can include, for example, one or more optical channels λ 1 , λ 2 , λ 3 , and λ 4 . Each of these channels can be a discrete wavelength or a band of wavelengths. Also, optical add signal  641  is provided via port  640  to side  604  of set  610 . Signal  641  can include, for example, optical channel λ 1 ′. In accordance with this invention, filter elements  611 - 620  can be individually tuned such that they substantially transmit λ 1  and λ 1 ′, yet reflect λ 2 , λ 3 , and λ 4 . As shown in FIG. 24, this causes optical channels λ 1 ′, λ 2 , λ 3 , and λ 4  to be transmitted to output port  630  and optical channel λ 1  to be transmitted (i.e., dropped from signal  621 ) to output port  650 . It will be appreciated that by tuning each of elements  611 - 620  to perform a predetermined spectral filtering function consistent with this invention, device  600  can be used to selectively add or drop one or more optical channels. Further add and drop ports can be added to device  600 , if desired.  
         [0137]    It will be appreciated that optional lenses  603  and  605  have been added to appropriately direct the incident, transmitted, and reflected beams. It will also be appreciated that the exact location and orientation of the ports depends on whether the device is operated in transmission or reflection mode and whether additional optical components, such as lenses, prisms, and/or mirrors are used. Polarization diversity can also be applied to device  600  to make such a device polarization insensitive, such as by including a beam walk-off crystal.  
         [0138]    Multiple filters constructed consistent with this invention can also be combined and used to construct optical branch filters. FIG. 25, for example, shows optical branch filter  651 , which includes filters  655 ,  660 ,  665 , and  670 , and structure  680  on which the filters are mounted. During operation a wavelength multiplexed optical beam, which may contain a number of optical channels (e.g., at wavelengths λ 1 , λ 2 , λ 3 , and λ 4 ), is directed to filter  655 . If filter  655  is tuned to transmit wavelengths λ 2 , λ 3 , and λ 4  and reflect wavelength λ 1 , only optical channels at wavelengths λ 2 , λ 3 , and λ 4  will reach filter  660 . If filter  660  is tuned to transmit wavelength λ 2  and reflect wavelengths λ 3  and λ 4 , only optical channels at wavelengths λ 3  and λ 4  will reach filter  665 . Finally, if filter  665  is tuned to transmit wavelength λ 3  and reflect wavelength λ 4 , only one optical channel at wavelengths λ 4  will reach filter  670 .  
         [0139]    It will be appreciated that each of filters  655 ,  660 ,  665 , and  670  can be tuned consistent with this invention to filter one or more wavelengths and that the number of filters can be any number greater than one. Finally, structure  680  can be empty or solid, as long as light beams pass through it with relatively low loss.  
         [0140]    [0140]FIG. 26 shows another simplified multiplexing/demultiplexing device  681  consistent with this invention. Device  681  includes a cascade filters in which the main part of an optical beam is transmitted from stage to stage. Device  681  includes multiple sets of filter elements  682 ,  683 , and  684 . The number of filter elements in each set consistent with this invention can be greater or less than the number shown (i.e., four), but must be at least two and can be arranged in a multi-dimensional array. Like device  600 , device  681  also includes multiple optical ports, including input port  686 , output port  687 , and multiple drop ports  688 .  
         [0141]    During operation, a wavelength multiplexed optical beam, which may contain a number of optical channels (e.g., at wavelengths λ 1 , λ 2 , λ 3 , and λ 4 ), is directed to filter  682 . If filter  682  is tuned to transmit wavelengths λ 2 , λ 3 , and λ 4  and reflect wavelength λ 1 , only optical channels at wavelengths λ 2 , λ 3 , and λ 4  will reach filter  683 . If filter  683  is tuned to reflect wavelength λ 2  and transmit wavelengths λ 3  and λ 4 , only optical channels at wavelengths λ 3  and λ 4  will reach filter  684 . Finally, if filter  684  is tuned to reflect wavelength λ 3  and transmit wavelength λ 4 , only one optical channel at wavelengths λ 4  will reach output port  687 .  
         [0142]    [0142]FIG. 27 shows yet another simplified illustrative multiplexing device  691  consistent with this invention. Device  691  includes a cascade filters in which the main part of an optical beam is reflected from stage to stage. Device  691  includes multiple sets of filter elements  692 ,  693 , and  694 . Like devices  600  and  681 , device  691  also includes multiple optical ports, including input port  696 , output port  697 , and multiple drop ports  698 . During operation, a wavelength multiplexed optical beam, which may contain a number of optical channels (e.g., at wavelengths λ 1 , λ 2 , λ 3 , and λ 4 ), is directed to filter  692 . If filter  692  is tuned to reflect wavelengths λ 2 , λ 3 , and λ 4  and transmit wavelength λ 1 , only optical channels at wavelengths λ 2 , λ 3 , and λ 4  will reach filter  693 . If filter  693  is tuned to transmit wavelength λ 2  and reflect wavelengths λ 3  and λ 4 , only optical channels at wavelengths λ 3  and λ 4  will reach filter  694 . Finally, if filter  694  is tuned to reflect wavelength λ 3  and transmit wavelength λ 4 , only one optical channel at wavelengths λ 4  will reach output port  697 .  
         [0143]    The devices shown FIGS. 26 and 27 also include optional lenses  685  and  695 , respectively, to collect and either focus or collimate light. Furthermore, a polarization diversity scheme, such as the ones shown in FIGS.  20 - 23 , can be used with devices  681  and  691  consistent with this invention. Also, it will be appreciated that a hybrid of the devices shown in FIGS. 26 and 27, in which the main part of the beam is reflected by some filters and transmitted by other filters, can be constructed consistent with this invention. Moreover, it will be appreciated that each of the stages shown in FIGS. 26 and 27 can be modified (e.g., as shown in FIG. 24) to add channels to the main beam as well.  
         [0144]    [0144]FIG. 28 shows a simplified schematic of illustrative filtering device  700 . Device  700  includes circulator  705  and set  710  of filter elements consistent with this invention. During operation, input beam  715  is provided to an input of circulator  705 . Circulator  705  receives beam  715  and transmits it to filter element set  710 . Reflected portion R out  of beam  715  reflects from set  710 , reenters circulator  705 , and emerges at output  720 . Also, transmitted portion T out  of beam  715  is transmitted through set  710  and emerges at output  720 . The wavelengths and relative intensities of portions R out  and T out  will depend on the particular reflectance/transmittance spectra of set  710 .  
         [0145]    [0145]FIG. 29 shows another illustrative add/drop multiplexing device  750  that includes multiple circulators consistent with this invention. Device  750  includes circulators  755  and  760 , and set  770  of filter elements. During operation, input beam  775 , which can be wavelength multiplexed (e.g., including optical signals at wavelengths λ 1  and λ 2 ), is provided to input  757  of circulator  755 . Circulator  755  receives beam  775  and transmits it to filter element set  770  via port  758 . If set  770  is tuned to transmit optical signals at wavelength λ 2  and reflect at λ 1 , then optical signal λ 1  will reenter circulator  755  at port  758  and emerge at drop port  759 .  
         [0146]    Transmitted signal λ 2 , however, will pass through to circulator  760  via port  762  and emerge at port  764 . So far, operation of device  750  is similar to device  700 . When another beam  775 , which could include signal λ 1 ′, is provided to port  766  of circulator  760 , circulator  760  transmits it to filter element set  770  via port  762 . Because set  770  is tuned to reflect signals having wavelength λ 1 , optical signal λ 1 ′ will be reflected from filter set  770  and reenter circulator  760  at port  762  and emerge at port  764 , along with transmitted signal λ 2 . In this way, it can be seen that signal λ 1  is dropped and signal λ 1 ′ is added to input beam  775 .  
         [0147]    According to another aspect of the present invention, a dynamic gain equalizer can be constructed. It is known that the intensity level of an optical signal propagating along an optical fiber can depend on the particular optical wavelength, unequalized optical amplification, and other wavelength dependent effects. Thus, an optical signal can strikes a light detector at an intensity level that occasionally saturates the detector or at an intensity level that is below the detector&#39;s optimal threshold level that ensures error-free detection. This fluctuation also limits the number of optical amplifiers that can be used in the optical transmission line, which limits the distance of the link. Thus, a dynamic attenuator consistent with this invention can be used to vary the intensity of a light beam within an acceptable operational range without undesirable variations in the spatial, temporal, spectral, or polarization variation effects.  
         [0148]    Thus, a dynamic gain equalizer can be constructed consistent with this invention that includes a plurality of filter elements (e.g., an etalon that includes an array of independently tunable filter elements), wherein each of the elements is located along a different optical path, although these optical paths may cross one or more times. During operation, light is incident on multiple filter elements and optical transmittances (or alternatively, reflectances) of the elements can be separately varied by varying electric fields (i.e., AC electric fields) applied to the liquid crystals. Of course, any optically, electrically, or mechanically active material can also be used consistent with this invention to vary an individual filter element&#39;s transmittance.  
         [0149]    As mentioned above, a dynamic gain equalizer can be constructed with a Fabry-Perot etalon. The etalon can have any desirable gap thickness, such as between 1 and 10 microns. A gap that is about 5 microns filled with a liquid crystal, for example, has proven to be satisfactory. The etalon can be divided into a sufficient number of pixels to achieve the desired level of smoothness, and preferably has a total surface area that is larger than the incident beam. If, for example, a beam has a diameter of 1 mm, and a pixel has a width of 100 microns, then an array of at least ten pixels are necessary, assuming minimal dead space between pixels. Thus, larger beam diameters will require larger pixel sizes or larger numbers of pixels.  
         [0150]    An equalizer consistent with this invention can be programmed to vary the number of filter elements that either transmit or reflect at a particular wavelength, vary the actual shape of each individual filter element&#39;s wavelength dependent reflectance to design any desirable filter function (or, when the filter element is a Gires-Tornouis etalon, the phase), or a combination of both. This wavelength-agile filter is capable of dynamically equalizing the power of dense WDM (hereinafter, “DWDM”) channels to provide active compensation of inherent optical amplifier gain variations due to weak and strong routed signals. A dynamic equalizer constructed consistent with this invention can be operated in conjunction with an optical spectral power detector, such as in an optical spectrum analyzer.  
         [0151]    Other types of optical devices can be constructed consistent with this invention, including optical cross connects and switchable optical filter.  
         [0152]    A wavelength switchable filter, for example, can be constructed as shown in FIG. 15 or  19 , but it will be appreciated that other multi-port architectures can also be used. For example, FIG. 15 shows filter  160 , which includes a plurality of independently tunable filter elements  161  and  162 . As previously described, each filter element filters a different component of incident optical signal  167  such that, when the components are combined, filtered optical signal  168  is formed in reflection mode and filtered optical signal  169  is formed in transmission mode.  
         [0153]    Filter  160  can be used as a switch by abruptly changing its transmittance at the desired switching wavelength. Thus, when filter  160  has a high transmittance T λ  at wavelength λ, it also has reflectance R λ  at the same wavelength. Because R λ  is equal to T λ −1, one can switch an optical beam&#39;s path between fibers  192  and  191  by simply changing the transmittance between low (i.e., T=0) and high (i.e., T=1) values.  
         [0154]    It can be seen from FIG. 15, then, that a first component of incident beam  167  travels along path  163  during which time a portion of that beam may be reflected by filter element  161  and redirected to fiber  191  to partially form filtered reflected beam  168 . Similarly, a different portion of the first component of incident beam  167  can travel through element  161  and be transmitted along path  193  to output fiber  192  to partially form filtered transmitted beam  169 .  
         [0155]    In an identical fashion, a second component of incident beam  167  travels along path  164  during which time a portion of that beam may be reflected by filter element  162  and redirected to fiber  191  to partially form filtered beam  168 . Similarly, a different portion of the second component of incident beam  167  may travel through element  162  and be transmitted along path  194  to output fiber  192  to partially form filtered beam  169 .  
         [0156]    In addition to the switch described above, a modulator can be constructed consistent with this invention. A modulator is typically a device that is capable of rapidly changing its transmittance or reflectance, sometimes in a polarization dependent way, between high and low values (i.e., 0 and 1) for one or more wavelengths. It will be appreciated, then, that a filter consistent with this invention can be used to modulate an optical signal by modulating one or more filter elements between two states.  
         [0157]    In a similar fashion, a filter consistent with this invention can be used as an optical blocking filter. By selectively increasing or decreasing the reflectance or transmittance, respectively, at one or more wavelengths, one can block wavelengths.  
         [0158]    It will be appreciated that filter elements can also be made from micro-electromechanical and micro-optoelectromechanical (sometimes referred to as MEMS and MOEMS, respectively) devices, which can be controlled to vary the distance between two reflectors. For example, gratings and other wavelength sensitive devices can be made with these micromechanical devices, which could be used to construct filter elements consistent with this invention. It will also be appreciated that bubbles and other hybrid technologies, such as those that integrate MEMS-based optical switches with liquid crystals can also be used to construct dynamic interference filters consistent with this invention.  
         [0159]    [0159]FIG. 30 shows a simplified, exploded, perspective view of MEMS-type device  800  consistent with this invention. Device  800  includes at least a lower array of reflectors  811 - 813 , and an upper array of reflectors  821 - 824 , all of which can be formed using any conventional MEMS construction technique, such as an etching or photolithographic technique. The lower and upper arrays form upper and lower pairs with gaps, and each of the reflectors can be formed monolithically on the same substrate, or separately and then combined to form a hybrid device. For illustrative simplicity, and the large number of possible physical configurations, the upper array of reflectors is not shown as fixed to substrate  805  or anything else. However, both arrays of reflectors are normally fixed to some support structure, such as substrate  805 . Also, although only three pairs of reflectors are shown in FIG. 30, it will be appreciated that a filter consistent with this invention can include any number of reflector pairs, each of which forms a filter element.  
         [0160]    In either case, one or both reflectors of any given pair can be movable such that the distance between the pair is variable. If the reflectors are electrically conductive, they can be used as electrodes that, when charged, causes one or both of the reflectors to move due to an electrostatic force that may form between the reflectors. If the reflectors are not electrically conductive, an electrically conductive layer can be disposed on the reflectors to enable electromechanical gap distance control. Also, because filter elements constructed using MEMS are typically polarization independent, polarization diversity techniques need not be employed.  
         [0161]    One skilled in the art will appreciate that the present invention can be practiced by other than the described embodiments, which are presented for purposes of illustration and not of limitation, and that the present invention is limited only by the claims that follow.
A tunable optical filter is provided that includes an array of independently tunable filter elements. Each of the elements is located along a different optical path that extends between an input and an output port. Optical assemblies for receiving an incident optical signal for providing a filtered optical signal are also provided. In one embodiment, polarization independent spectral filtering can be achieved. Wavelength selectable add/drop multiplexers and demultiplexers, dynamic gain equalizers and attenuators, optical channel blockers and branch filters, switches, and modulators are also provided. Furthermore, methods for constructing and operating filters consistent with this invention are also provided.