Abstract:
A photonic arbitrary waveform modem utilizes a bipolar coding scheme. The bipolar coding scheme includes an arbitrary waveform modem which includes a plurality of tapped delay lines and is implemented by partitioning each optical frequency chip into positive and negative segments. Signals are decoded by effectively multiplying the transmit and receive code vectors and individually summing the positive and negative tap weights. The positive and negative tap weights are differenced to recreate the transmitted signal. The bipolar coding scheme allows for the use of truly orthogonal codes which decreases the interference and reduces the probability of detection.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is related to commonly-owned copending patent application entitled “Arbitrary Waveform Modem”, Ser. No. 09/120,851, filed on Jul. 22, 1998, now U.S. Pat. No. 6,396,801. 
    
    
     This invention was made with Government support under U.S. Government Contract No. N66001-99-C-8607, awarded by the United States Navy. The Government has certain rights in this invention. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a communication system and more particularly to a photonic arbitrary waveform modem for use in various applications including secure multiple access communication systems which utilizes bipolar encoding to provide true orthogonal coding to reduce co-channel interference. 
     2. Description of the Prior Art 
     Multiple access communication systems are generally known in the art and are used in various applications, such as cellular telephone communication systems. Various multiple access communication systems are known, for example, frequency division multiple access (FDMA), time division multiple access (TDMA) and code division multiple access (CDMA) systems are known. In FDMA communication systems, the frequency band is partitioned into a number of channels. Each user is temporarily assigned a channel, for example, for the duration of a call. In TDMA communication systems, each user is assigned a time slot in a frame and each call is time division multiplexed according to the user&#39;s assigned time slot. 
     In order to further improve the system capacity, CDMA communication systems have been developed. Examples of CDMA communication systems are disclosed in U.S. Pat. Nos. 4,494,228; 4,901,307; 5,103,459; 6,185,246; and commonly-owned U.S. Pat. No. 6,167,024. Such CDMA communication systems are also disclosed in “Synthesis and Demonstration of High Speed, Bandwidth Efficient Optical Code Division Multiple Access (CDMA) Tested at 1 Gb/s Throughput” by Mendez, et al.  IEEE Photonics Technology Letters , Vol. 6, No. 9, September 1994, pages 1146-1149, all hereby incorporated by reference. 
     In such CDMA communication systems, a code, known as a Walsh code, is assigned to a user at the beginning of each communication and multiplied by each databit in the signal to be transmitted (i.e. digital bit stream), effectively spreading the signal over a wider frequency band, thus forming a direct sequence spread spectrum communication system. In such CDMA communication systems, all users effectively use the same timeslot and frequency band. Interference between users is prevented by selection of orthogonal Walsh codes. An advantage of spread spectrum communication techniques, such as CDMA, is the relatively low probability that the communication signals will be intercepted and detected. 
     In order to further increase the security in military communication systems, an arbitrary waveform modem has been developed that is characterized by non-periodic or chaotic waveforms. The arbitrary waveform modem is described in detail in commonly-owned copending U.S. patent application Ser. No. 09/120,851, filed on Jul. 22, 1998, hereby incorporated by reference and illustrated in  FIGS. 1 and 2 . In particular,  FIG. 1  illustrates an arbitrary waveform modem transmitter, while  FIG. 2  illustrates an arbitrary waveform receiver. As will be discussed in more detail below, the arbitrary waveform modem provides the ability to select infinitely variable tap spacings through the use of fiber optic Bragg gratings. It also enables the generation of an arbitrary waveform with relatively long symbol times, large bandwidths and non-uniform tap spacing which allows the modulated waveform to be any shape necessary. Since the modem can generate non-uniform tap spacings, the phasing of the chip, baud or symbol can be arbitrarily set to any value to produce a waveform characteristic that degenerates the rate line spectral components making interception improbable. Additionally, co-channel interference is reduced because the cross-correlation between orthogonally selected waveforms diminishes. 
     In general, the photonic arbitrary waveform modem modulates a signal waveform (e.g. digital bit stream) onto an optical carrier that is derived from a broadband source, for example, a super-luminescent diode (SLD). The various optical frequency components or chips are time delayed by differing amounts by a set of narrow band Bragg grating filters before being transmitted. At the receiver, another set of Bragg grating filters temporally realigns all of the frequency chips providing an increase in the signal-to-noise ratio that is equal to the number of chips in the code which enables recovery of the signals. 
     One major shortcoming of the photonic arbitrary waveform modem is that it relies on the direct summation of optical intensities which restricts the system to a set of unipolar codes (i.e. each tap weight can take on a value of 0 or 1). For a given number of wavelength taps, this places a limitation on the number of codes that can be generated that offer a high degree of orthogonality while providing reasonable processing gain. For example, for a case for which there are 16 taps, the Mendez article, discussed above, indicates that an optimum set of 16 pseudo-orthogonal code words can be constructed by utilizing various combinations of 5 taps. These codes produce an autocorrelation value of 5 and cross correlation values of either 1 or 2. Thus, there is a need for a photonic arbitrary waveform modem which increases the number of codes that can be generated to provide optimum efficiency of spectral occupancy while at the same time provide low co-channel interference modulation characteristics. 
     SUMMARY OF THE INVENTION 
     Briefly, the present invention relates to a photonic arbitrary waveform modem that utilizes a bipolar coding scheme. The bipolar coding scheme includes an arbitrary waveform modem which includes a plurality of tapped delay lines and is implemented by partitioning each optical frequency chip into positive and negative segments. Signals are decoded by effectively multiplying the transmit and receive code vectors and individually summing the positive and negative tap weights. The positive and negative tap weights are differenced to recreate the transmitted signal. The bipolar coding scheme allows for the use of truly orthogonal codes, which decreases the interference and reduces the probability of detection. 
    
    
     
       DESCRIPTION OF THE DRAWINGS 
       These and other advantages of the present invention will be readily understood with reference to the following specification and attached drawing wherein: 
         FIG. 1  is a simplified diagram of a known arbitrary waveform modem transmitter for use with the present invention. 
         FIG. 2  is a simplified diagram of a known arbitrary waveform modem receiver for use with the present invention. 
         FIG. 3  is a more detailed block diagram of the known arbitrary waveform modem for use with the present invention. 
         FIG. 4  is a block diagram of a bipolar arbitrary waveform transmitter in accordance with the present invention. 
         FIG. 5  is a block diagram of a bipolar arbitrary waveform receiver in accordance with the present invention shown implemented with matched transmit/receive codes. 
         FIG. 6  is similar to  FIG. 5  except with unmatched transmit/receive codes. 
         FIGS. 7A and 7B  are exemplary six (6) chip bipolar codes obtained by partitioning the optical spectrum of a super-luminescent diode. 
         FIG. 8A  is an elevational view of a basic waveguide structure for use with the present invention illustrating the mode profiles. 
         FIG. 8B  is a dispersion diagram of the optical propagation constant β for the structure illustrated in FIG.  8 A. 
         FIG. 9A  is a further development of  FIG. 8A  the structure shown illustrated shown with an electro-optic overlay. 
         FIG. 9B  is a dispersion diagram for the structure illustrated in FIG.  9 A. 
         FIG. 10A  is a further development of the structure illustrated in  8 B but with Bragg gratings formed thereon. 
         FIG. 10B  is a dispersion diagram for the structure illustrated in FIG.  10 A. 
     
    
    
     DETAILED DESCRIPTION 
     The present invention relates to a bipolar coding scheme for an arbitrary waveform modem as described in detail in commonly-owned co-pending U.S. patent application Ser. No. 09/120,851, filed on Jul. 22, 1998. In order to prevent drift of the tap weights due to temperature drifts of the tapped delay lines and other factors, a closed servo loop may be provided for each tap weight. The closed servo loop is described in detail in commonly-owned U.S. Pat. No. 6,167,024, hereby incorporated by reference. 
     In order to fully understand the invention, a detailed description of the unipolar arbitrary waveform modem is described and illustrated in connection with FIG.  3 . The bipolar arbitrary waveform modem in accordance with the present invention is described and illustrated in connection with  FIGS. 4-6 . Exemplary bipolar codes for the bipolar arbitrary waveform modem are illustrated in  FIGS. 7A and 7B . Finally,  FIGS. 8A-10B  illustrate a waveguide for use with the bipolar arbitrary waveform modem illustrated in  FIGS. 4-6 . 
     Unipolar Arbitrary Waveform Modem 
     An arbitrary or chaotic waveform modem as described and illustrated in co-pending commonly owned patent application Ser. No. 09/120,851, filed on Jul. 22, 1998, is illustrated in FIG.  3  and generally identified with the reference numeral  200 . The arbitrary waveform modem  200  includes an arbitrary or chaotic waveform generator or modulator portion  202  and a chaotic waveform receiver or demodulator portion  204 , configured as a sliding window correlator. The modulator portion  202  and the demodulator portion may be identical and may be operated in a half duplex made in order to reduce hardware. As will be discussed below, the modulator portion  202  can be configured to generate an RF or an optical output, generally indicated with the reference numeral  206 . On the same token, the receiver or modulator portion  204  is adapted to receive either a modulated optical or an RF modulated waveform  206 . The modulator portion  202  is configured as an arbitrary waveform generator and is adapted to generate any waveform including a non-periodic or arbitrary waveform as illustrated with the reference  206  and even periodic waveform. As shown, the modulator portion  202  may include a finite impulse response (FIR) filter  208  with a plurality of variable time delay tapped delay lines, generally indicated with the reference numeral  210 . The shape of the waveform generated by the arbitrary waveform modem  200  is a function of the tap weights W 1  . . . WN applied to the tapped delay lines  210  which, in turn, allows a modulator portion  202  to generate arbitrary or chaotic waveforms, such as the waveform illustrated with the reference numeral  206 . Depending on the tap weights, the modulator portion  202  may also be used to generate periodic waveforms. As shown, the tapped delay lines  210  are formed from fiber optics with non-uniform spaced Bragg gratings. As discussed above, such Bragg gratings may be formed from a series of photo induced refractive index perturbations in an optical fiber which causes the reflection of optical signals within a selective wavelength band. The grating wavelength of maximal reflectivity is selected for each one of the incident optical inputs from a plurality of different lengths which enable the modulator portion  202  to generate virtually any waveform including a chaotic or arbitrary waveform as indicated with the reference numeral  206 . In order to control drifting of the tap weights, W 1  . . . WN, for example, due to temperature drift, the tap weights W 1  . . . WN may be controlled by the servo control loop as discussed in commonly owned U.S. Pat. No. 6,167,024, hereby incorporated by reference. By preventing the tap weights W 1  . . . WN from drifting, the modem  200  is able to generate any arbitrary or chaotic waveform  206 , while minimizing if not eliminating any phase noise resulting from temperature drift of the tapped delay lines. 
     The modulator portion  202  and the demodulator portion  204  are configured as a sliding window correlator. The demodulator portion includes a matched filter portion  212 . The matched filter portion  212  may be a FIR filter which includes a plurality of tapped delay lines  212  formed from fiber optics with non-uniform spaced Bragg gratings. In order to form a matched filter, the tapped delay lines  212  are formed as a mirror image of the tapped delay lines  210  which form part of the FIR filter  208  in the modulator portion  202 . The tapped delay lines in both the modulator portion  202  and the demodulator portion  204  are generally identical. The mirrored or reflexive tap assignment of the demodulator portion  204  provides for proper timing of the signals from the modulator portion  202  to the demodulator portion  204 . In particular, the first and shortest signal from the modulator portion  202  from the tapped delay line corresponding to the weight W 1  is correlated with the longest tapped delay line in the demodulator portion  204 , and assigned the same tap weight W 1 . The rest of the tapped lines in the modulator portion  202  are similarly correlated to the tapped delay lines in the demodulator portion  204 , so that the signals generated by the demodulator portion  202  are in the proper time sequence. 
     The data input signal is applied to the modulator portion  202 . The data input may be a digital data word, for example, in the form of a mark space modulated signal. The data input is applied to a symbol encoder  214  in which the data input is translated to set of tap weights, W 1 -W 1   c . As discussed in commonly owned U.S. Pat. No. 6,167,024, these tap weights may be tracked by a servo control loop as discussed and illustrated in FIGS. 1-5 of the &#39;024 patent. In particular, each of the tap weights W 1  . . . W 1   c  may be applied to individual servo control loops as illustrated in FIG. 1 of the &#39;024 patent. As discussed above, each of the servo loops generates a servoed tap weight signal, identified with the reference numeral  36  in FIG. 1 in the &#39;024 patent, which compensates for temperature drift in the tapped delay lines. This signal  36  may then be applied as the tap weight signals W 1  . . . W 1   c  in the modulator portion  202  as well as the demodulator portion  204 . 
     Upon receipt of the data input, the symbol encoder  214  triggers an impulse generator  216  which modulates light from an optical source  218 , such as a semiconductor laser or fiber optic laser through an optical modulator  220 . In other words, an optical impulse is created at the output of the optical modulator  220 . 
     The impulse generator  216  may be, for example, a Schmidt trigger, which generates a pulse when triggered by the symbol encoder  214  upon receipt of a data input signal. The optical modulator  220  may be a Mach-Zehnder optical modulator, which are well known in the art. The optical source  218  may be virtually any optical source including a laser, for example, a fiber optic or semiconductor laser which generates either single or multiple wavelength components as discussed below. 
     The light impulse at the output of the optical modulator  220  is applied to an optical circulator  222  which initially directs the light impulse to a splitter/summer  224 . The splitter/summer  224  splits the light signal into a number of channels corresponding to the number of tapped delay lines W 1  . . . WN. The channelized signals are directed to the various tapped delay lines  210  and reflected back to the splitter/summer  224  after the appropriate time delay by the tapped delay lines  210 . The reflected signals from the splitter/summer  224  are reflected back to the optical circulator  222  to form the arbitrary waveform  206 . Suitable splitter/summers and optical circulators are well known in the art. 
     The waveform  206  may be transmitted as either an optical or an RF waveform. In embodiments where the waveform  206  is transmitted as an RF waveform, the output from the optical circulator  222  is applied to an optical demodulator  225  which demodulates the RF signal from the optical signal. In such an application, the RF signal is transmitted to the demodulator portion  212 , where it is received by an optical remodulator or modulator  226 . The remodulator or modulator  226  may be similar to the optical modulator  220  and formed from a Mach-Zehnder type modulator as discussed above. The optical demodulator  225  may be a commonly known optical detector, such a photodetector or photodiode. 
     As discussed above, the demodulator portion  204  includes a matched filter  212 , such as a FIR filter, which includes a plurality of tapped delay lines  213 . The tapped delay lines  213  in the demodulator portion  204  are identical to the tapped delay lines  210  in the modulator portion  202 ; the only difference being is that the weights W 1 -WN are applied in the opposite order as discussed above. 
     The modulated waveform  206  is received by an optical circulator  228 . The optical circulator  206  directs the modulated waveform  206  to a splitter summer  229 . The splitter/summer  229 , the same as the splitter summer  224 , is coupled to a plurality tapped delay lines  213  having the weights assigned in the opposite order than the filter  208 , as discussed above. The splitter/summer  229  splits the modulated signal up into a plurality of channels which are, in turn, directed to each of the tapped delay lines  213  and reflected back to the splitter/summer  229  and, in turn, to the optical circulator  228 . As discussed above, this configuration forms a sliding window correlator. The signals reflected back to the splitter summer  228  are directed to an optical detector  230  which, as discussed above, may be a photodiode. The output from the photodiode is the recovered data output signal  232 . The output of the optical detector  230  is also directed to a symbol recovery block  232  which may be a phase locked loop and directed to a symbol encoder  234 , similar to the symbol encoder  214 . As discussed above, the symbol encoder  234  is used to provide the tap weights W 1  . . . WN to the tapped delay lines  213  as discussed above. The symbol recovery block  232  recovers the tap weights in digital form, which, in turn, are applied to the symbol encoder  234  for assigning the various tap weights W 1  . . . WN to the tap delay lines  213 . 
     Bipolar Photonic Arbitrary Waveform Modem 
     The bipolar arbitrary waveform modem in accordance with the present invention is illustrated in  FIGS. 4-6  and includes a bipolar arbitrary waveform modem transmitter  300  and a bipolar arbitrary waveform modem receiver  302 .  FIG. 5  illustrates a receiver application where the transmit and receive codes are matched while  FIG. 6  illustrates a receiver application where the transmit and receive codes are unmatched. None of the embodiments utilize a splitter/summer as in unipolar embodiment to eliminate the losses associated therewith to improve the performance of the device, and specifically the signal-to-noise ratio at the output. 
     The bipolar arbitrary waveform  300  transmitter and receiver  302  provide the ability to select infinitely variable tap spacings through the use of fiber optics and Bragg grating reflection filters. The generation of an arbitrary waveform with relatively long symbol times, relatively large bandwidths and non-uniform tap spacing is possible. Therefore, the waveform can be any shape necessary. Because the bipolar arbitrary waveform modem can generate non-uniform tap spacing, the phasing of the chip, baud or symbol can be arbitrarily set to any value to produce a waveform characteristic that degenerates the rate line spectral components making interception improbable if not impossible. Additional, co-channel interference is also reduced because the cross-correlation between orthogonally selected waveforms diminishes. 
     The overall effectiveness of the arbitrary waveform modem is enhanced using a bipolar coding scheme. In such a scheme, the tap weights take on the values of +1 or −1 making it possible to construct truly orthogonal codes. As the number of taps increases, code words become random, noise-like sequences with auto correlation values equal to the number of taps and cross-correlation values that approach zero. The bipolar coding scheme is implemented by impressing a polarity (i.e. sign) on each frequency chip, either positive or negative, which is representative of the tap weight. 
     Referring to  FIG. 4 , the bipolar arbitrary waveform modem transmitter  300  includes an optical source  304 , for example, a broadband super-luminescent diode (SLD) source  304 , which generates a broadband optical carrier signal  306 . The broadband optical carrier signal  306  is modulated with a signal waveform  308  by way of an optical modulator  310 . The optical modulator  310  may be, for example, a Mach-Zehnder modulator, and produces an optically modulated signal  312 , which, in turn, is applied to an optical circulator  314 . Such devices are well known in the art. 
     A symbol encoder  316  encodes the signal waveform  308  with a bipolar encoding scheme in accordance with the present invention. The symbol encoder  316  may include an encoder, pseudo-random sequence generator, Walsh generator and a pair of exclusive OR gates for generating orthogonal Walsh codes, as generally described in U.S. Pat. No. 6,185,246, hereby incorporated by reference. The symbol encoder generates a transmit code vector comprising the set of tap weights w i   n , where i indicates a particular code vector that is a member of a code set and n indicates the number of the optical frequency chips in the particular code set. As described and illustrated only six (6) optical frequency chips are illustrated but in practice the number of optical frequency chips can be in the order of 100. The optical frequency assignments for an exemplary code is illustrated in FIG.  7 A and generally identified with the reference numeral  318 . The code  318  is divided into a number of segments  320  equal to the number of optical frequency chips employed in the particular code set. As mentioned above, for illustration and discussion purposes, a fixed bit code set is illustrated and thus the exemplary code  318  is divided into six segments  320 . In accordance with an important aspect of the invention, each of the segments  320  is subdivided into two subsegments corresponding to ν −   n  and ν +   n . 
     The transmit code vector comprising tap weights w i   1  through w i   6  is applied to a filter  322  which includes a plurality of optical delay lines, generally indicated by the reference  324 , formed from a combination of fiber optics and non-uniform spaced Bragg reflection gratings to provide a plurality of non-uniform delays illustrated as τ 1 -τ 6 . Assuming the tap weights are either +1 or −1, the transmit code vector illustrated in  FIG. 4  is simply (−, +, −, −, + and −), which results in the reflection of optical frequencies ν −   1 , ν +   2 , ν −   3 , ν −   4 , ν +   5 , ν −   6 . 
     The signal-modulated optical energy  312  is applied to the optical delay lines  322  by way of the optical circulator  314  and reflected back to the optical circulator  314  after the appropriate time delay and an output port  326  to form an arbitrary waveform transmission signal  328 . As mentioned above, the optical frequency chips are partitioned into subsegments identified to ν −   n  and ν +   n . The transmitter  300  is configured to select the minus ν −   n  or plus ν +   n  frequency for each chip by simply tuning the reflection band for that chip&#39;s Bragg grating. This can accomplished in a number of different ways. For example, a Bragg filter can be fabricated as a fixed period grating on a channel waveguide on an electro-optic substrate or on an amorphous substrate with a deposited electro-optic overlay, for example, as disclosed in U.S. Pat. Nos. 5,717,798 and 5,740,292 and “Tuneable Electro-Optic Waveguide TE-TM Converter/Wavelength Filter”, by Alferness et al.,  Appl. Phys. Lett , 40, pages 861-862, May 15, 1982, all hereby incorporated by reference. The present invention is unique in the use of electro-optic effect to invert the waveguide mode structure, thereby directing or switching, light of a particular wavelength or optical frequency that is initially in an input waveguide to a preselected one of two possible output waveguides. By applying an appropriate electrical field, the optical propagation constant in the area of the grating is altered thus changing the center frequency of the reflection band. 
     A receiver for detecting for demodulating the arbitrary waveforms  328  is illustrated in  FIG. 5  for matched transmit and receive codes. An illustration of an arbitrary waveform modem receiver for unmatched transmit and receive codes is illustrated in FIG.  6 . In both cases the tap weights for the transmitted chips are multiplied by the corresponding tap weights for the receive code. Referring to  FIGS. 5 and 6 , the optical receiver  302  includes a waveguide  330  for receiving the arbitrary waveform  328  from the arbitrary waveform transmitter  300 . The arbitrary waveform receiver  302  includes a symbol encoder  332  for encoding a receive code and a set of appropriate optical delay lines that are complementary to the transmitter optical delay lines. That is to say that the sum of the delays experienced by each of the chips in the transmitter and receiver is made to be identical for all of the chips. 
     The tap weights for each of the chips of the transmit code are multiplied by the corresponding tap weights of the receive code. If the result is +1, the optical energy is routed to a (+) detector  334 , where all time coincident +1 chips are summed. If the result is −1, the optical energy is routed to a (−) detector  226 , where all time coincident −1 chips are summed. The outputs of the detectors  334  and  336  are differenced by way of a difference amplifier  338  which generates an output signal  340 , which is a replica of the transmitted signal  308  whose amplitude is proportional to the correlation between the transmit code vector w i  and receive code w j  as generally illustrated by equation (1) below. 
               Sig   out     =         Sig   in     ⁢       ∑   k     ⁢       w   k   i     ⁢     w   k   j           +   noise             (   1   )             
 
     As shown in  FIG. 5 , for the case where the transmit code vector w i  and receive code vector w j  are identical as shown, the products of each of the chips is positive. Thus, all of the chips are directed to the (+) detector  334 . On the other hand, if an orthogonal code, for example, the code  342  as illustrated in  FIG. 7B , is utilized for the receive code vector w j , the result is as shown in FIG.  6 . In this application, the result of the multiplication of the chips for some of the tap weights is minus, therefore, these chips are applied to the (−) detector  336  and differenced by the difference amplifier  338  to provide an output signal  342  which is essentially zero. 
     The receiver  302  is relatively more complicated than the transmitter  300  since it must direct the − or + frequency to one of two identical receive optical delay lines, depending on the receive tap weight. This function may be implemented by a three waveguide structure, as generally illustrated in FIG.  8 A and identified with the reference numeral  330 . The waveguide  330  is configured with three waveguide layers  334 ,  346  and  348  forming waveguides  1 ,  2  and  3 , respectively, on a substrate  350 , for example a silicon dioxide layer formed on the surface of a silicon substrate by an oxidation process that is common in the semiconductor industry. The substrate  350  is selected with an index of refraction is of n 0 , while waveguide  1  ( 344 ) is formed with a index of refraction of n 1 . The waveguides  2  and  3  ( 346  and  348 ) are formed with an index of refraction of the n 2 . The three waveguide structure  330  is formed such that it follows a relationship where n 1 &gt;n 2 &gt;n 0 . 
     Exemplary mode field profiles  352 ,  354  and  356  are shown for the lowest order mode I and the next two higher order modes II and III. A dispersion diagram is illustrated in  FIG. 10B  which illustrates the optical propagation constant for each of the forward propagating (i.e. left to right) modes I + , II +  and III +  and the backward propagating modes I − , II −  and III −  as a function of optical frequencies ν. By placing an electro-optic overlay, generally identified with the reference numeral  358  (or some other means to externally alter the waveguide&#39;s refractive indices) on the waveguides  2  and  3  ( 346  and  348 ) as shown in  FIG. 9A , an asymmetry can be introduced which results in the propagation of the three modes  360 ,  362 ,  364  illustrated in FIG.  9 A. As shown in  FIG. 9A , for the case where a voltage is applied that causes an increase in the refractive index of waveguide  2  ( 346 ), the energy of mode II is predominantly in waveguide  2  ( 346 ) and the energy of mode III is predominantly in waveguide  3  ( 348 ). If a voltage is applied to increase the refractive index of waveguide  3  ( 348 ), the modal distributions are reversed. A dispersion diagram for the optical waveguide illustrated in  FIG. 9A  is shown in FIG.  9 B. 
     If a grating is disposed on the waveguides illustrated in  FIG. 9A , the forward propagating light in mode I can be coupled to backward propagating modes II and III only at those optical frequencies that satisfy the grating in phase matching condition given by equation (2).
 
|β +   I |+|β −   II,III   |=K   G    (2)
 
where β is the propagation constant for a particular mode and K G  is the grating constant given by K G =2π/Λ G , where Λ G  is the grating period.
 
     Referring to  FIG. 10A , the waveguide  1  ( 344 ) corresponds to the main receive waveguide while waveguides  2  and  3  ( 346  and  348 ) correspond to the negative product and positive product waveguides, respectively. The receive tap weight is set to a value of (+) by applying a voltage to the waveguide  2  ( 346 ) as shown in FIG.  10 A. Thus, light incident on the grating at a frequency ν +  corresponding to ν 1-3  will be transferred to mode III predominantly in waveguide  3  and light at a frequency at ν − corresponding to ν 1-2  will be transferred to mode II predominantly in waveguide  2  ( 346 ). In order assign a value of (−) to the tap weight, a voltage is applied to waveguide  3  ( 348 ). In this case, light at the frequency ν +  transfers to mode III which is now predominantly in waveguide  2  and light at ν −  transfers to mode II which is now predominantly in waveguide  3 . 
     The waveguide  330  may be formed as a semiconductor waveguide or as a dielectric waveguide. The fabrication of semiconductor waveguides is relatively well known in the art as set forth in U.S. Pat. Nos. 5,416,884; 5,678,935; 5,841,930; 5,891,748 and 5,917,981, hereby incorporated by reference. Further the fabrication of dielectric waveguides is relatively well known in the art as set forth in U.S. Pat. Nos. 3,659,916; 4,111,523; 4,284,663; 5,613,995 and 6,054,253, hereby incorporated by reference. An example embodiment of the present invention would comprise a highly polished silicon wafer, upon which has been grown a 15 μm thick layer of silicon dioxide (SiO 2 ) by the technique of thermal oxidization. The optical waveguides can be fabricated on the surface of the SiO 2  by using chemical vapor deposition of doped SiO 2  and RF sputtering techniques as set forth in R. L. Davis and S. H. Lee, “Low-loss waveguides on silicon substrates for photonic circuits,”  Optical Technology for Signal Processing Systems , Mark P. Bendett, editor, v. 1474, p. 20, SPIE, Orlando, Fla., 1991. Well-known photolithography processes can be used to define the waveguide patterns on the surface of the substrate. Typical cross-section dimensions for the waveguides may be on the order of 4 μm×4 μm, the actual sizes will depend on the selection of materials. The electro-optic active overlay can be a sputter-deposited film of zinc oxide (ZnO) as set forth in F. S. Hickernell, “DC triode sputtered zinc oxide surface elastic wave transducers,” Journal of Applied Physics, v 44, p. 1061, Mar, 1973. The fixed grating can be etched as a surface relief pattern in the surface of the waveguide structure or it may be generated by introducing a periodic perturbation to the waveguides&#39; refractive indices in a method similar to that used for manufacturing fiber Bragg gratings in optical fibers as set forth in U.S. Pat. No. 4,725,110: “Method for impressing gratings within fiber optics.” 
     Obviously, many modification and variations of the present invention are possible in light of the above teachings. For example, thus, it is to be understood that, within the scope of the appended claims, the invention may be practiced otherwise than as specifically described above.