Abstract:
A filter and a method of filtering a high frequency electrical signal using photonic components is disclosed. The filter has a serially fiber-coupled laser source, a modulator, a filter, and a photodetector. The electrical signal is applied to the modulator. The modulated light propagates through the filter which is constructed to pass not only a modulated sideband, but also at least a fraction of light at the carrier frequency of the laser. The photodetector detects a signal at the beat frequency between the carrier and sideband signals, after both signals have propagated through the filter. As a result, a separate optical branch for light at the carrier frequency is not required, which considerably simplifies the filter construction and makes it more stable and reliable.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    The present invention claims priority from U.S. provisional patent application No. 61/158,792, filed Mar. 10, 2009, which is incorporated herein by reference. 
     
    
     TECHNICAL FIELD 
       [0002]    The present invention relates to signal filtering, and in particular to photonic filtering of electrical signals. 
       BACKGROUND OF THE INVENTION 
       [0003]    Communication satellites operating in the Ka-band frequency range often use a large number of microwave communication beams. The satellites typically have a lifetime of over 15 years. It is rather difficult to predict the information carrying capacity of individual beams during such a long period of time. Accordingly, dynamic allocation of the bandwidth among the microwave communication beams is highly desirable. 
         [0004]    The dynamic bandwidth allocation can be provided by tunable microwave filters having a tunable central frequency and a variable width of the passband. Such tunable microwave filters can be installed in both the ground stations and onboard the satellites. To be practically usable, the tunable filters must possess a high stability of the spectral response, strong out-of-band rejection, and small group delay variation. Furthermore, tunable filters placed on satellites must be lightweight and meet stringent space-launch qualification requirements. 
         [0005]    Electronic filters are ubiquitous in circuit design. Many types of electronic filters are presently available. The most common filters use bulk elements, such as capacitors, inductors, and so on, to form single- or multi-pole filters at appropriate frequencies of interest. It is possible to build tunable filters using switching banks or variable components. Although these filters can operate up to several gigahertz in frequency, they are mostly used for lower frequencies, where the physical dimensions of the components are still small compared to the wavelength of operation. 
         [0006]    Circuits operating at microwave frequencies typically use planar or coaxial waveguide structures. These filters utilize distributed capacitance and inductance created by a particular geometry of the waveguide structure, in conjunction with the abrupt variations in impedance created by stubs and slots, to form resonant cavities. Using ceramic materials or high-temperature superconductors to form very low loss substrates can result in very high finesse (high-Q) filters. Planar structures are reasonably easy to fabricate using conventional circuit board techniques. However, the circuit board based planar structures tend to be lossy at higher frequencies due to radiative loss. Coaxial structures are superior in this regard because the outer conductor shields the structure, but these tend to be bulky and heavy. 
         [0007]    Millimeter-wave filters can be formed using dielectric resonators and cavity structures, but they are difficult to fabricate, and the resulting filter characteristics can be very sensitive to fabrication errors, particularly when the filters contain multiple coupled resonators. Both the microwave and the millimeter-wave filters are difficult to tune and have a limited tuning range. Furthermore, it is difficult to change the finesse of a particular filter or to generate a variable bandwidth filter. 
         [0008]    In a satellite, a bank of filters is switched in and out of a signal path to change the channel bandwidth, and a programmable frequency converter is used to change the center frequency. There are two major difficulties associated with this approach. First, a very limited number of filters can be practically used due to a large number of communication beams, and even these few filters per beam result in a very heavy and bulky overall structure. Second, once the set of filters is determined, it remains fixed for the lifetime of the satellite. Because of these intrinsic difficulties, other approaches have been investigated. 
         [0009]    One such approach, presented by Ming Yu el al. in a paper entitled “A Ka Band Tunable Filter for Reconfigurable Payload”, 15 th Ka and Broadband Communications, Navigation and Earth Observation Conference, Sep.  23-25, 2009, which is incorporated herein by reference, consists of having a mechanically tunable cavity filter. However, any mechanically controlled devices or subsystems in a satellite raise substantial reliability issues. 
         [0010]    Another approach, exemplified in a paper by Glyn Thomas et al. entitled “Agile Equipment for an Advanced Ku/Ka Satellite”,  ESA Workshop on Advanced Flexible Telecom Payloads,  18-20  Nov.  2008,  ESA/ESTEC, Noordwijk The Netherlands,  which is incorporated herein by reference, uses an electrical heterodyne principle. The signal is frequency down-converted to a given intermediate frequency (IF) using a programmable synthesizer, two cascaded bandpass filters are used to achieve the required filtering, and then another programmable synthesizer is used to bring the signal to the desired channel frequency. The main drawbacks of this circuit are the power consumption, and large volume and mass, which are all very detrimental for a space application. 
         [0011]    Electrical filters based on photonic circuits have been reported numerous times, primarily in the academic literature. These are generally based on: tapped delay lines to emulate a finite impulse response (FIR) filter, delay line interferometers, fiber Bragg grating (FBG) delay lines, dispersive fiber delays, and acousto-optic modulators. In general, these techniques are better suited towards forming notch filters, not bandpass filters required for a satellite bandwidth allocation and tuning applications. 
         [0012]    Ilchenko et al. disclose in United States Patent Application US2005/0175358, which is incorporated herein by reference, a tunable radio frequency and microwave photonic filter using an optical heterodyne principle. Referring to  FIG. 1 , a filter  100  of Ilchenko et al. is shown having a laser  101 , an electro-optical modulator (EOM)  102 , a whispering-gallery mode (WGM) filter  103 , a photodetector  104 , beamsplitters  105 , and mirrors  106 . The WGM filter  103  has evanescent field couplers  107  and cascaded WGM resonators  108 . In operation, the laser  101  emits a beam at a carrier frequency that is modulated by the EOM  102  with a radio frequency input signal  110  to create sidelobes in a spectrum of the optical signal. The WGM filter  103  selects one such sidelobe. A fraction of the laser beam is split by the beamsplitter  105  before the EOM  102  to propagate through a path  109  defined by the beamsplitters  105  and the mirrors  106 . The photodetector  104  receives the combined modulated and the split laser beam and provides an output electrical signal  111  at a differential frequency between the passband frequency of the filter  103  and the carrier frequency. By tuning the WGM filter  103 , the passband central frequency of the filter  100  can be tuned. 
         [0013]    The filter of Ilchenko et al. suffers from the drawbacks of overall complexity and lack of stability due to presence of multiple optical elements and optical paths. 
         [0014]    Accordingly, it is a goal of the present invention to provide a filter of a millimeter-wave or microwave signal, which would be lightweight, simple, reliable, and tunable in both central frequency and bandwidth. 
       SUMMARY OF THE INVENTION 
       [0015]    Advantageously, the present invention does not require multiple optical paths for downshifting the carrier frequency back into the electrical domain, resulting in a reliable, simple, widely tunable filter of electrical signals using optical filtering elements. 
         [0016]    In accordance with the invention there is provided a filter for filtering an electrical signal, comprising:
       an optical modulator for receiving light at a carrier frequency and for modulating light at a frequency of the electrical signal;   an optical filter coupled to the optical modulator, for receiving the modulated light and for selecting light at a first frequency to propagate therethrough with at least a fraction of light at the carrier frequency; and   a photodetector coupled to the optical filter, for detecting a signal at a beat frequency between the first frequency and the carrier frequency,   wherein the detected signal at the beat frequency comprises an output signal of the filter.       
 
         [0021]    Preferably, the electrical filter is tunable by tuning at least one of the first frequency of the optical filter or the carrier frequency of light. In one embodiment, the optical filter includes a dual-band optical filter having a first passband for light at the first frequency and a second passband for light at the carrier frequency. 
         [0022]    In one embodiment, the dual-band optical filter has first and second optical sub-filters connected in series, the first and the second optical sub-filters each having first and second passbands. The first passband of the dual-band optical filter comprises an overlap region between the first passbands of the first and the second optical sub-filters, and the second passband of the dual-band optical filter comprises an overlap region between the second passbands of the first and the second optical sub-filters. As a result, a central frequency and/or a bandwidth of the first passband of the optical filter is tunable by tuning a central frequency of the first passband of the first optical sub-filter, of the second optical sub-filter, or of both the first and the second optical sub-filters, whereby the filter for filtering the electrical signal is tunable in frequency and/or bandwidth. 
         [0023]    Preferably, the electrical filter also includes a light source for providing light at the carrier frequency. The light source can be directly modulated, in which case a separate optical modulator will not be required. 
         [0024]    In accordance with another aspect of the invention there is further provided a filter for filtering an electrical signal, comprising:
       a first source of light at a carrier frequency modulated at a frequency of the electrical signal; and   an optical filter coupled to the first source of light, for receiving the modulated light and for selecting light at a first frequency to propagate thcrethrough with at least a fraction of light at the carrier frequency, for subsequent conversion into an output electrical signal at a beat frequency between the first frequency and the carrier frequency.       
 
         [0027]    The first source of light can be a directly modulated light source, such as a directly modulated laser source, for emitting light at the carrier frequency modulated at the frequency of the electrical signal. Alternatively, the first source of light can be an optical modulator for receiving light at the carrier frequency from an external laser source and for modulating light from that source at the frequency of the electrical signal. 
         [0028]    In accordance with yet another aspect of the invention there is provided a method of filtering an electrical signal, comprising:
       (a) providing an optical signal at a carrier frequency;   (b) modulating the optical signal of step (a) at a frequency of the electrical signal, so as to generate a modulated optical signal having a sidelobe frequency band;   (c) filtering the optical signal modulated in step (b) using an optical filter having a first passband for passing light at a first frequency within the sidelobe frequency band, and a carrier passband for passing light at the carrier frequency; and   (d) detecting a signal at a beat frequency between the optical signals filtered in step (c).       
 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0033]    Exemplary embodiments will now be described in conjunction with the drawings in which: 
           [0034]      FIG. 1  is a schematic view of a prior-art optical filter used for filtering electrical signals; 
           [0035]      FIG. 2  is a diagrammatic view of a filter according to the present invention, illustrating the principle of operation of the filter; 
           [0036]      FIG. 3  is a diagrammatic view of filters of the present invention, showing spectra of signals propagating through the filters; 
           [0037]      FIG. 4  is a transmission spectrum of a fiber Bragg grating (FBG) having two transmission bands; 
           [0038]      FIG. 5  is a schematic view of a compound FBG shown in  FIG. 3 ; 
           [0039]      FIGS. 6A to 6C  are transmission spectra of FBGs of  FIG. 5 , illustrating the principle of tuning bandwidth of the passband of the compound FBG of  FIG. 3 ; 
           [0040]      FIGS. 7A to 7C  are transmission spectra of FBGs of  FIG. 5 , illustrating the principle of tuning central frequency of the passband of the compound FBG of  FIG. 3 ; and 
           [0041]      FIG. 8  is an attenuation spectrum illustrating definition of FBG main parameters. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0042]    While the present teachings are described in conjunction with various embodiments and examples, it is not intended that the present teachings be limited to such embodiments. On the contrary, the present teachings encompass various alternatives, modifications and equivalents, as will be appreciated by those of skill in the art. 
         [0043]    Referring to  FIG. 2 , a diagrammatic view of a filter  200  of the present invention is shown. The filter  200  has an optical modulator  202  for receiving light at a carrier frequency f C  and for modulating the received light with an input electrical signal  201  represented by a spectral band  223  centered at a frequency f 0 ; an optical filter  204  coupled to the optical modulator  202 , for receiving the modulated light and for filtering light at a filtering frequency f F ; and a photodetector  206  coupled to the optical filter  204 , for detecting light at a beat frequency between the filtering and carrier frequencies f F  and f C . 
         [0044]    In operation, an optical signal at the carrier frequency f C  is provided to the modulator  202 . The frequency spectrum of the optical signal is shown at  212 . The modulator  202  modulates the optical signal with the input electrical signal  201 . The frequency spectrum of the input electrical signal  201  is shown at  222 . The input spectrum  222  has the spectral band  223  centered at f 0 . The spectral band  223  has a finite bandwidth. 
         [0045]    The modulated optical spectrum is shown at  214 . It has a signal  213  at the carrier frequency f C  and sidelobe frequency bands  223 ′,  223 ″, which resemble the spectral band  223  of the electrical signal and are centered at f C +f 0  and f C −-f 0 , respectively. Depending on type of modulation, only one sidelobe frequency band  223 ′ may be present in the spectrum  214 . If both sidelobes are present, the frequency band  223 ″ can be suppressed by an appropriate notch filter, not shown, included into the optical filter  204 . Alternatively, the signal at  223 ″ can be retained while the signal at  223 ′ is suppressed. For the sake of the following example, the signal at  223 ′ is retained. 
         [0046]    The optical filter  204  passes light at the filtering frequency f F . Furthermore, according to the invention, the optical filter  204  also passes at least a fraction of light at the carrier frequency f C  to propagate therethrough together with light at the filtering frequency f F , obviating a general requirement of the prior art to have a separate optical branch for light at the carrier frequency f C . It is to be understood that the bandwidth of the filter  204 , although narrow, is a finite bandwidth. 
         [0047]    The optical spectrum of the signal after the optical filter  204  is shown at  216 . It has a signal  215  at the filtering frequency f F  and a signal  213 A at the carrier frequency f C . The rest of the spectral shape represented by the sidelobe  223 ′ is filtered out, or suppressed. It is to be understood that the signal  215  at the filtering frequency f F  is of a finite, although narrow, bandwidth. 
         [0048]    The optical signal represented by the spectrum  216  is detected by the photodetector  206 . The electric fields of the signals at frequencies f C  and f F  will interfere at a photosensitive surface of the photodetector  206 , resulting in an electrical signal  225  at a beat frequency f F −f C  appearing at an output  209  of the filter  200 . As is known to one of skill in the art, the beat frequency signal appears because a photodetector signal is proportional to light intensity, which is proportional to square of the electric field. The detected signal at the beat frequency comprises an output signal of the filter. 
         [0049]    By tuning the differential frequency f F −f C , the filter  200  may be tuned in frequency. From a practical standpoint, at least one of the filter frequency f F  of the optical filter or the carrier frequency of light f C  needs to be tuned relative to the other frequency for the filter  200  to be tuned. 
         [0050]    Referring now to  FIG. 3 , a diagrammatic view of filters  300 A and  300 B of the present invention is shown. The filters  300 A and  300 B are particular implementations of the filter  200  of  FIG. 2 . Similar numerals in  FIGS. 2 and 3  refer to similar elements. The filter  300 A uses a fiber Bragg grating (FBG)  304 A in transmission, while the filter  300 B uses an FBG  304 B in reflection. An optical circulator  308  is incorporated into the optical path of the filter  300 B having the reflection FBG  304 B. A beamsplitter, not shown, can be used instead of the optical circulator  308 . 
         [0051]    The filters  300 A and  300 B of  FIG. 3  have a laser diode  310  for emitting light at the carrier frequency f C , an optical modulator  302  for receiving light from the laser  310  and for modulating light with an input electrical signal, the FBGs  304 A and  304 B, respectively, coupled to the optical modulator  302 , for receiving the modulated light and for filtering light, and a photodetector  306  coupled to the FBGs  304 A and  304 B, respectively, for detecting a signal at a beat frequency between the frequencies of the filtered light. The signal detected by the photodetector  306  is the output electrical signal of the filters  300 A and  300 B. 
         [0052]    The FBGs  304 A and  304 B have an optical response function  320 . In the transmission FBG  304 A this response function  320  is the transmitted response, and in the reflection FBG  304 B this response function  320  is the reflected response. The laser diode  310 , the optical modulator  302 , the FBGs  304 A and  304 B, and the photodetector  306  are optically coupled with an optical fiber  311  as shown in  FIG. 3 . 
         [0053]    In general, to characterize a spectral response of an electrical filter, a frequency-swept electrical signal is applied to the filter input, and an output electrical signal is measured. The output electrical signal plotted against the frequency of the swept signal represents the response function of the filter being characterized. Accordingly, to obtain a spectral response of the filters  300 A or  300 B, a frequency-swept electrical signal can be applied to the modulator  302 . As a result of modulation, a component  323 ′ appears in the optical spectrum of the signal at the output of the modulator  302 . The separation between the component  323 ′ and a signal  313  at the carrier frequency f C  corresponds to the frequency of modulation by the modulator  302 . 
         [0054]    The signal is filtered by the FBGs  304 A or  304 B having the spectral response  320 . Both signals  313  and  323 ′ co-propagate through the FBGs  304 A or  304 B. As mentioned previously, the other sideband  223 ″ is suppressed. At the detector  306 , the optical signals interfere with each other to generate an signal at a beat frequency therebetween. As the electrical signal is swept in frequency, the component  323 ′ is shifted relative to the carrier frequency component  313 , resulting in attenuation of the component  323 ′ by the FBGs  304 A or  304 B when the component  323 ′ shifts beyond the passband of the optical attenuation spectrum  320  of the FBGs  304 A or  304 B. The output electrical signal at the photodetector plotted against the frequency of the swept signal will form a spectral response  330  corresponding to the optical attenuation spectrum  320  of the FBGs  304 A or  3048 . Therefore, by adjusting the optical attenuation spectrum  320 , one can adjust the electrical response function  330  of the filters  300 A or  300 B. 
         [0055]    The compound FBGs  304 A or  304 B are tunable by tuning its temperature, or by stress-tuning, or by tuning any other suitable parameter thereof. The FBGs  304 A and  3048  may be superstructure gratings, multi-phase shift gratings, and/or chirped gratings. These types of gratings are described by Raman Kashyap in a book entitled “Fiber Bragg Gratings”,  Academic Press, ISBN  0-12-400560-8, 1999, which is incorporated herein by reference. In particular, FIGS. 3.24, 6.5 and 7.1 of the above reference show the above stated respective types of the gratings. Other types of gratings can also be used, with or without apodization, including gratings in planar waveguides. 
         [0056]    The laser diode  310  can be a distributed-feedback (DFB) laser. DFB lasers are frequency tuned by tuning the laser temperature using a thermoelectric cooler (TEC), not shown. Thus, by adjusting the temperature of the TEC, the filter  300 A and  300 E can be tuned in frequency. Alternatively, the laser diode  310  can have an external FBG serving as a mirror of the lasing cavity of the laser diode  310 . The laser FBG, not shown, can also be temperature tuned. The laser diode  310  can be modulated directly, in which case no optical modulator  302  will be required. 
         [0057]    Furthermore, the filters  300 A and  300 B, or the filter  200  for that matter, can be implemented using a planar waveguide technology. For example, the optical modulator  202 , the optical filter  204 , and the detector  206  can be implemented on a common planar substrate, coupled by a planar optical waveguide. Integrating the filter  200  of  FIG. 2  using planar waveguide technology may further improve the stability and manufacturability of the filter  200 . 
         [0058]    Turning now to  FIG. 4 , a measured transmission spectrum  400  of the FBG  304 A of  FIG. 3  is shown. The spectrum  400  has two passbands  401  and  402 . The first passband  401  is for filtering light at the sidelobe frequency  323 ′, and the second passband  402  is for passing the carrier component  313  at the carrier frequency f C . When the transmission FBG  304 A is tuned, for example by adjusting the grating temperature, the spectrum  400  shifts towards higher or lower frequencies, as shown at  400 ′ and  400 ″. As the spectrum  400  shifts, the first passband  401  and the second passband  402  shift together. When the first passband shifts, the signal  323 ′at the sidelobe frequency is either passed or attenuated, because the passband  401  is narrow. However, the second passband  402  is wide enough to always pass the carrier component  313 . As a result, mixing of the output signal  323 ′, if any, with a signal at the carrier frequency f C  is always available; and tuning of the transmission FBG  304 A results in tuning the spectral response function  330  of the filter  300 A. Preferably, the passband  401  is tunable by at least 2 GHz, allowing the filter  300 A to operate in a 2 GHz wide frequency band, for example between the frequencies of 18 GHz and 20 GHz. 
         [0059]    Referring to  FIG. 5 , the compound transmission FBG  304 A of  FIG. 3  is shown in  FIG. 5  as consisting of two FBGs  501  and  502  connected in series. Advantageously, having two FBGs  501  and  502  allows both the central frequency and the bandwidth of the filter  300 A to be independently tuned, as explained in more detail below. 
         [0060]    Turning to  FIGS. 6A to 6C , transmission bands  601  and  602  of FBGs  501  and  502  are shown, respectively. The purpose of  FIGS. 6A to 6C  is to illustrate bandwidth tuning of the filter  300 A of  FIG. 3  by tuning FBGs  501  and  502  of  FIG. 5 . FBGs  501  and  502  of  FIG. 5  may be tuned by tuning the grating temperature or any other suitable grating parameter. 
         [0061]    In  FIG. 6A , the transmission bands  601  and  602  do not overlap each other, so that there is no passband. In  FIG. 6B , the transmission bands  601  and  602  are shifted towards each other as shown by arrows  603  and  604 . The transmission bands  601  and  602  form a passband in an overlap region  605  therebetween. The passband is centered at the filter frequency f F  and has a finite bandwidth Δf F1 . In  FIG. 6C , the transmission bands  601  and  602  are shifted towards each other even closer than in  FIG. 6B , forming a passband having a wider bandwidth Δf F2 &gt;Δf F1 . Thus, shifting the transmission bands of the FBGs  501  and  502  towards each other or away from each other results in tuning the bandwidth of the filter  300 A. 
         [0062]    Turning to  FIGS. 7A to 7C , transmission bands  701  and  702  of FBGs  501  and  502  are shown, respectively. The purpose of  FIGS. 7A to 7C  is to illustrate central frequency tuning of the filter  300 A of  FIG. 3  by tuning FBGs  501  and  502  of  FIG. 5 . 
         [0063]    In  FIG. 7A , the transmission bands  701  and  702  form a passband in an overlap region  705  therebetween, shifted from the carrier frequency signal  313  by Δ 1 . In  FIG. 7B , the transmission bands  701  and  702  are shifted equally towards higher frequencies as shown by arrows  703  and  704 . The passband is shifted from the carrier frequency signal  313  by Δ 2 &gt;Δ 1 . In  FIG. 7C , the passband is shifted from the carrier frequency signal  313  by Δ 3 &gt;Δ 2 &gt;Δ 1 . Thus, shifting the transmission bands of the FBGs  501  and  502  in the same direction results in tuning the central frequency of the passband of the filter  300 A. It should be noted that both the central frequency and the bandwidth can be tuned together by tuning only one FBG,  501  or  502 . 
         [0064]    The bandwidth of the passband of the FBG  304 A and the roll-off of the passband will strongly affect the filtering characteristics of the filter  300 A. The bandwidth will determine the largest possible bandwidth of the filter  300 A. The largest bandwidth is reached when the central frequencies of the two FBGs  501  and  502  coincide. Making the FBG bandwidth as large as possible would allow a wide range of bandwidth tuning of the filter  300 A. However, a wide passband has the detrimental effect of reducing the filter roll-off of the passband, thus reducing out-of-band attenuation. Increasing the slope of the filter roll-off will limit the narrowest bandwidth of the filter  300 A. Narrow-passband FBGs  501  and  502  will have a steeper spectral slope and attenuate out-of-band information more strongly. Therefore, a trade-off exists between the filter bandwidth and the out-of-band rejection. An optimization of the FBG transmission spectrum is required, depending on particular requirements of a specific radio-frequency filter application. 
         [0065]    It should be noted that an FBG with a properly selected transmission spectrum can also be used to implement a low-pass or a high-pass microwave filter with variable centre frequency and bandwidth. It should also be noted that the above considerations and principles illustrated in  FIGS. 4 ,  5 ,  6 A to  6 C, and  7 A to  7 C having regard to the transmission FBG  304 A used in the filter  300 A are also applicable to the reflection FBG  304 B used in the filter  300 B. In the latter case, proper reflection spectra should be considered instead of the transmission spectra. 
         [0066]    Referring now to  FIG. 8 , an attenuation spectrum  800  of an FBG used in the present invention, for example the FBG  501  or  502 , is shown. The transmission band is defined by a 3 dB bandwidth parameter; a frequency offset at a 20 dB attenuation point relative to a corresponding edge of the 3 dB passband; and a frequency offset at a 35 dB attenuation point relative to a corresponding edge of the 3 dB passband; a ripple value and group delay for the filter passband; and a separation value between carrier and filter passbands. These parameters can be used to specify an FBG suitable for use in a particular radio-frequency filter. The useful ranges of these parameters can be obtained from target specifications of the radio-frequency filter  300 A of  FIG. 3 .  FIG. 8  shows an example of filter passband parameters of such a filter. Other filter passband configurations can be easily realized using this invention. 
         [0067]    A filter with specifications defined in  FIG. 8  can be designed using techniques described by Raman Kashyap in the article entitled “Fiber Bragg Gratings”,  Academic Press, ISBN  0-12-400560-8, 1999, which is incorporated herein by reference. Other techniques known to a person skilled in the art may be used as well. 
         [0068]    A tunable filter of the present invention is usable in space subsystems due to wide tunability, low mass, low volume, and low power consumption. However, it should be understood that a tunable filter of the present invention can also be used in other communication systems requiring flexible bandwidth allocation and center frequency tuning. Furthermore, wide tunability of the filter warrants its application as a “set-and-forget” fixed filter, which is tuned once at the factory and shipped to a customer based on the customer&#39;s frequency specification. 
         [0069]    Further, a filter of the present invention is not intended to only be used for a RF frequency range. For example, a filter using properly selected components can, in principle, be constructed to operate in microwave, mm-wave, terahertz and other frequency ranges.