Abstract:
The present invention provides a simple means of demodulating optical signals, e.g. wideband M-ary orthogonal. The demodulator comprises an optical processor and a comparison module. The optical processor transforms M input optical signals into 2 log 2 (M) intermediary optical signals and the comparison module determines the logical representation of the input data based on log 2 (M) binary comparisons of the optical power of the intermediary signals. Example embodiments may be reconfigurable to receive optical signals using M-FSK, M-PPM, M-PolSK, and hybrid M-ary orthogonal modulation formats. Example embodiments also offer small size, weight and power consumption for both free-space and fiber optic environments as well as improved receiver sensitivity and reduced electron bandwidth requirements.

Description:
RELATED APPLICATION 
       [0001]    This application claims the benefit of U.S. Provisional Application No. 61/481,360, filed on May 2, 2011. 
         [0002]    The entire teachings of the above application(s) are incorporated herein by reference. 
     
    
     GOVERNMENT SUPPORT 
       [0003]    This invention was made with government support under FA821-05-C-002 awarded by the United States Air Force. The government has certain rights in the invention. 
     
    
     BACKGROUND OF THE INVENTION 
       [0004]    The parallelization of optical communications using wavelength division multiplexing (WDM) has led to tremendous increases in fiber-optic channel capacity over the past decade. The use of numerous WDM channels to transmit information leverages the vast available spectrum of the optical channel (such as a guided, e.g., fiber-optic, or unguided, e.g., free space, optical channel) which exceeds many THz, with each channel preferably using a manageable amount of bandwidth (e.g., GHz-class) that may, in practice, be generated with available electronics. 
         [0005]    Many applications of this technology require implementations that have small size, low weight, and low power consumption (SWAP). For example, space-based communications, especially those over the distances that exceed a typical Earth orbit, are usually power-starved, so simple low-SWAP receiver (RX) implementations with good sensitivity are desirable; improvements in RX sensitivity provide more link margin, extend link distances, and enable lower-power transmitters (TXs), an effect that lowers nonlinear impairments and may provide benefit in both fiber-optic guided and free-space applications. The need exists for a wide-band parallel optical communication receiver, with good receiver sensitivity, reduced electrical bandwidth, simplified implementation, and lower size, weight, and power (SWAP). 
       SUMMARY OF THE INVENTION 
       [0006]    In one embodiment, the present invention is an optical demodulator. The optical demodulator comprises an optical processor and a comparison module. The optical processor is configured to transform M parallel input optical signals into 2×log 2  M intermediary optical signals. In example embodiments, the M parallel input optical signals represent input data encoded in an M-ary orthogonal modulation format, M being an integer greater than 2. The comparison module is optically connected to the optical processor and is configured to compare optical power of the intermediary optical signals to determine logical representation of the input data. 
         [0007]    In another embodiment, the present invention is a method of optically demodulating input data. The method comprises transforming M parallel input optical signals into 2×log 2  M intermediary optical signals. In example embodiments, the M parallel input optical signals represent input data encoded in an M-ary orthogonal modulation format, M being greater than 2; and comparing optical power of the intermediary optical signals to determine a logical representation of the input data. 
         [0008]    Embodiments of the invention advantageously enable a variety of wide-band parallel optical communication receivers, with good receiver sensitivity, reduced electrical bandwidth, simplified implementation, and lower size, weight, and power (SWAP). Reconfigurable optical elements enable the receiver to accommodate a variety of modulation formats, such as M-ary frequency shift keying (M-FSK), wavelength division multiplexed (WDM)-based modulations including WDM M-ary pulse position modulation (M-PPM), on-off-keying (WDM-OOK), polarization shift keying (PolSK), polarization diversity, and hybrid formats (e.g., M-FSK/PPM) with improved performance and scalability to high data rates, and modulation bandwidths that may exceed 40 Gsym/sec with aggregate bandwidths that may occupy many THz of spectrum. 
         [0009]    Example embodiments of the invention disclosed herein provide advantages over the conventional methods of demodulating data encoded in orthogonal modulation formats. Conventional M-FSK receivers use M separate detectors followed by M-to-1 winner-take-all analog comparison circuitry that picks the maximum signal (difficult to implement at high rates, e.g., more than a few GHz-class rates) or employ M analog-to digital converters (ADC), where the digital outputs are digitally compared to determine which received frequency signal is the largest. While conceptually straightforward, the ADC-based approach requires M=2 k  detectors and ADCs, where k is the number of bits per symbol, and high-speed ADCs are power-hungry and expensive, especially at high symbol bandwidths. 
         [0010]    Due to the relationship between frequency (f) and wavelength (λ) for electro-magnetic waves, i.e., c=λf, where c is the speed of light in vacuum, the frequencies that make up an M-FSK symbol set have a corresponding set of wavelengths. Consequently, the terms “frequency” and “wavelength” may be used interchangeably. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0011]    The foregoing will be apparent from the following more particular description of example embodiments of the invention, as illustrated in the accompanying drawings in which like reference characters refer to the same parts throughout the different views. The drawings are not necessarily to scale, emphasis instead being placed upon illustrating embodiments of the present invention. 
           [0012]      FIG. 1A  is a power vs. time plot providing a schematic representation of the On-Off-Keying (OOK) modulation format. 
           [0013]      FIG. 1B  is a power vs. time plot providing a schematic representation of Phase-Shift Keying (PSK) modulation format. 
           [0014]      FIG. 1C  is a power vs. time plot providing a schematic representation of M-ary Pulse Position Modulation (M-PPM) format, where the symbol set size M=4. 
           [0015]      FIG. 1D  is a power vs. time plot providing a schematic representation of M-ary frequency-shift keying modulation (M-FSK) format, where the symbol set size M=4. 
           [0016]      FIG. 2A  is a schematic representation of an M-FSK symbol set of M=8 different symbols (frequencies). 
           [0017]      FIG. 2B  is a schematic representation of a M-FSK waveform vs. time, showing four different symbols (frequencies) of the M-symbol set, each symbol being represented by a non-return-to-zero (NRZ) waveform. 
           [0018]      FIG. 2C  is a schematic representation of a M-FSK waveform vs. time, showing four different symbols (frequencies) of the M-symbol set, each symbol being represented by return-to-zero (RZ) pulse which has a Gaussian shape. 
           [0019]      FIG. 3A  is a schematic diagram of a parallel transmitter that may be used to transmit the data using a variety of modulation formats such as WDM-OOK, orthogonal modulations such as M-FSK, M-PPM, and PoLSK, and hybrid modulation formats. 
           [0020]      FIG. 3B  is a superposition of two power vs. time plots providing schematic representations of 8-ary PPM and 8-ary FSK modulation waveforms, where the different frequencies (wavelengths) are indicated by where i={1, 2, . . . 8} . 
           [0021]      FIG. 4  is a superposition of two power vs. time plots providing schematic representations of 8-ary PPM, and 8-ary PPM wavelength-multiplexed over four wavelengths (4-WDM/8-PPM). 
           [0022]      FIG. 5  is a schematic diagram of a conventional demodulator of data encoded by the above-described orthogonal modulation formats. 
           [0023]      FIG. 6A  is a schematic diagram of an example embodiment of an optical demodulator of the present invention suitable for demodulating data encoded in a 4-ary FSK format. 
           [0024]      FIG. 6B  is a photograph of an example embodiment shown in  FIG. 6A . 
           [0025]      FIG. 6C  is a schematic diagram of an example embodiment of an optical demodulator of the present invention suitable for demodulating data encoded in a 4-ary FSK format that employs variable optical attenuators. 
           [0026]      FIG. 7A  is a schematic diagram of an example embodiment of an optical demodulator of the present invention suitable for demodulating data encoded in a 8-ary FSK format. 
           [0027]      FIG. 7B  is a photograph of an example embodiment shown in  FIG. 7A . 
           [0028]      FIG. 8  is a schematic diagram of an example embodiment of an optical demodulator of the present invention suitable for demodulating data encoded in a 16-ary FSK format. 
           [0029]      FIG. 9A  is a schematic diagram of an example embodiment of an optical demodulator of the present invention suitable for demodulating data encoded in a 8-ary FSK format and hybrid formats such as 8-ary FSK/M-PPM, and providing soft-information for use in decoding. 
           [0030]      FIG. 9B  is a schematic diagram of an another example embodiment of an optical demodulator of the present invention suitable for demodulating data encoded in a 8-ary FSK format and hybrid formats such as 8-ary FSK/M-PPM, and providing soft-information for use in decoding, wherein the soft information is obtained from alternative locations. 
           [0031]      FIG. 10  is a schematic diagram of an example embodiment of an optical demodulator of the present invention suitable for demodulating data encoded in a 4-ary FSK format. 
           [0032]      FIG. 11A  is a block diagram of an experimental setup for measuring the communication performance of an example embodiment of a receiver of the present invention. 
           [0033]      FIG. 11B  is a plot showing bit error rate as a function of received power. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0034]    A description of example embodiments of the invention follows. 
         [0035]    The orthogonal modulation formats are explained with reference to  FIGS. 1A-1D . The term “orthogonal,” as used herein with reference to a modulation format Refers to the property that any two symbols of an orthogonal symbol set, s i (t) and s j (t) have the following well known mathematical relationship 
         [0000]      ∫ s   i ( t ) s   j ( t ) dt=E   s δ ij  
 
         [0000]    where E s  is the energy per symbol and δ ij  is the Kronecher delta function: 
         [0000]    
       
         
           
             
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                           i 
                         
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         [0000]    In other words, different symbols within an orthogonal symbol set have the same energy (E s ) but no joint energy, meaning filters may be employed to separate orthogonal symbols without any crosstalk. 
         [0036]    To better understand the benefits afforded by embodiments of this invention, it is instructive to understand the properties of commonly used modulation formats.  FIG. 1A  is a schematic representation of the On-Off-Keying (OK) modulation format imlementented with NRZ signaling. This is one of the simplest modulation formats, employing intensity modulation and a symbol set of two symbols (0 and 1) indicated by the presence or absence of optical power within the symbol to transmit encoded data. For an equal likelihood of 1s and 0s, OOK has a 50% duty cycle and the peak power is twice the average. As with all binary formats, OOK conveys log 2 (2) or 1 bit per symbol.  FIG. 1B  is a schematic representation of Phase-Shift Keying (PSK) modulation format or Differentially encoded Phase-Shift Keying (DPSK). In phase modulation formats, data is encoded in phase or phase difference.  FIG. 1B  shows a binary PSK format, employing only two symbols (with phase 0 and π) or a binary DPSK format employing only two symbols (with 0 and π phase difference). 
         [0037]    Additional example orthogonal modulation formats are M-ary Pulse Position Modulation (M-PPM, often considered for high-sensitivity applications), and M-ary Frequency Shift Keying (M-FSK). M-FSK has advantages over M-PPM because it has the same theoretical sensitivity benefit over binary formats but has lower peak power and electronic bandwidth (for a given M and data rate), compatibility with high-power semiconductor and Erbium-doped optical amplifiers. Further, M-FSK, unlike M-PPM, is well suited for use over long-haul fiber-optic links, where high-peak-power optical nonlinearities are often prohibitive. On the other hand, a drawback of M-FSK is the complexity of demodulation compared to M-PPM. M-PPM demodulators may be implemented with a single receiver and ADC, whereas conventional M-FSK demodulators, such as an example illustrated in  FIG. 5 , are implemented with M parallel receivers. 
         [0038]      FIG. 1C  is a schematic representation of M-ary (here, 4-ary) Pulse Position Modulation (M-PPM) format. In this format, data is encoded by the position of each pulse. In  FIG. 1C , there are 4 symbols (corresponding to pulse positions) in a set.  FIG. 1D  is a schematic representation of M-ary (here, 4-ary) frequency-shift keying modulation (M-FSK) format. In this format, data is encoded by the frequency (represented by color) of each pulse. There are 4 symbols in a set, each symbol corresponding to one of selected colors (out of four, as shown in the example). 
         [0039]    Common to all the  FIGS. 1A-1D  is the average power (equal to 1 unit) and the data rate, (e.g., bits/time). 
         [0040]    Modulation bandwidth (BW) is the bandwidth needed to generate a symbol, e.g., how fast the signal needs to be turned on or off in OOK. Since typical modulation is usually driven by electronics, the modulation bandwidth generally analogous to the electrical bandwidth, and this may often pose a practical limit in high-speed wide band communication systems. Modulation bandwidth of an M-PPM method is given by 
         [0000]      BW= M/ log 2 ( M ), 
         [0000]    whereas modulation bandwidth of an M-FSK method is given by 
         [0000]      BW=1/log 2 ( M ). 
         [0000]    Thus, for a given M, M-PPM requires M-times more modulation bandwidth than M-FSK, though they both may occupy the same net signaling (e.g. optical) bandwidth. In M-FSK, the net signaling bandwidth is increased directly in the frequency domain by the superposition of M spectrally distinct frequencies, whereas in M-PPM, the net signaling bandwidth increases in the time domain, with shorter pulses requiring fast modulation and wider bandwidth for each symbol. M-PPM and M-FSK formats are especially useful orthogonal modulation formats. These formats permit transmission of more information-per-symbol (bits/symbol), defined as 
         [0000]        k =log 2 ( M ), 
         [0000]    where k is the number of bits per symbol. Furthermore, receiver sensitivity generally improves with information-per-symbol k. It should be noted that a modulation rate (electrical bandwidth) of the M-PPM method is given by M/k, while a modulation rate of an M-FSK method is given by 1/k. M-FSK method has an additional advantage over M-PPM in that it requires lower peak power. 
         [0041]    It should be noted that for hybrid orthogonal modulation formats such as p-PPM/f-FSK/L-PoLSK, the equation above for the bits/symbol becomes 
         [0000]        k   eff =log 2 ( M   eff ), 
         [0000]    where M eff =p·f·L, where p is the number of PPM position, f is the number of FSK requencies, and L is the number of polarizations (each ≧1) in the hybrid-orthogongal symbol set. 
         [0042]      FIG. 2A ,  FIG. 2B , and  FIG. 2C  further illustrate the M-FSK method of encoding.  FIG. 2A  is a schematic representation of an 8-FSK symbol set of 8 different symbols (frequencies).  FIG. 2B  is a schematic representation of a 4-FSK symbol set, having four different symbols (frequencies), each symbol being represented by an non-return-to-zero (NRZ) or square-shaped waveform, with 100% duty cycle the peak power equal to the average. Alternatively,  FIG. 2C  illustrates the M-FSK method of encoding with a Gaussian-shaped return-to-zero (RZ) waveform with approximately 33% duty cycle. In this case, the peak power is approximately three times the average. 
         [0043]      FIG. 3A  illustrates a flexible h-channel parallel transmitter  100 . It is a schematic diagram of a parallel transmitter that may be used to transmit the data modulated by a variety of modulation methods. Here, h laser sources  102   a  through  102   h  generate optical signals, modulated by modulators  104   a  through  104   h.  The signals are then combined by a wavelength division multiplexing module  106 , and amplified by an amplifier  108 . This transmitter, for example, may generate h-WDM signals in which each of the modulators imparts independent data onto wavelengths a-h. In this case, each modulator could, for example, impart OOK or M-PPM as shown in  FIG. 4 . Alternatively, the h-modulators may impart data that is dependent, and generate, for example, h-ary FSK modulation, in which only one wavelength is transmitted within a given symbol time as shown in  FIG. 3B , for the case of h=8. As may be seen, the data comprises eight optical signals, each signal carrying orthogonal symbols encoded by the presence, during a certain time frame, of a signal of certain frequency. The equivalent M-PPM format for the case of M=8 is shown in  FIG. 3B , with the same average power, net data rate, and theoretical sensitivity, but with 8 times the peak power and ⅛ th  the signal duration, thus requiring 8 times the modulation bandwidth and 8 times the electrical bandwidith in both the TX and RX electronics. 
         [0044]      FIG. 4  illustrates another example of the how the modulation may be adapted, in this case without changing the average power, the information per symbol, or the sensitivity. Here, the M-PPM format (again using an example of M=8) is reconfigured, so that the data is conveyed by four-fold wavelength division multiplexing (4-WDM/8-PPM), which reduces the peak power and required modulation by a factor of 4 (the number of wavelengths), at the cost of the 4× increase in parallelization in the TX and RX. This signal may be wavelength multiplexed using, for example, a transmitter similar to transmitter 100 shown in  FIG. 3A . As may be seen, the received signal (carrying the data) comprises four optical signals, each signal carrying orthogonal 8-ary PPM symbols encoded by the presence of a signal at a certain position within any given time frame. 
         [0045]    In addition to time-domain position and frequency, other properties of optical signals (generically electro-magnetic signals) such as polarization may be traded to achieve the desired aggregate characteristics, such as sensitivity, modulation and electrical bandwidth, peak power, etc., as is known in the art. For example, a second orthogonal polarization may be added to the orthogonal symbol constellation in exchange for reducing the number of PPM positions by a factor of two. This would reduce the peak power and the modulation bandwidth by a factor of two, without impacting the bits per symbol or the data rate. A similar effect may be achieved by doubling the number of orthogonal FSK frequencies in exchange for halving the number of PPM positions in the symbol constellation. 
         [0046]    A conventional demodulator  300  of data encoded by the above-described orthogonal modulation formats is illustrated with reference to  FIG. 5 . The wavelength division multiplexed data is separated into M optical input signals by a wavelength division multiplexing (WDM) module  302 . Each one of the M optical input signals is converted into a corresponding electric input signal by diodes  304 . The electrical input signals are then converted into digital signals by analog-to-digital converters (ADCs)  306 , and the resulting digital signals are compared by a comparator  308 , thus permitting setting the bits encoded in the received data. 
       Optical Processor of the Present Invention 
       [0047]    Example embodiments of the present invention include an optical processor configured to demodulate data encoded by an orthogonal modulation format. As used herein, the term “optical processor” means that the processor that converts its input optical signal into its output optical signal without any digital processing of the optical signal or an electrical signal into which the optical signal is converted. 
         [0048]    An example embodiment of the present invention is illustrated in  FIG. 6A  and is further shown in  FIG. 6B , which is a photograph of an example embodiment shown in  FIG. 6A . Referring to  FIG. 6A , an optical demodulator  400  is shown. The optical demodulator  400  includes an optical processor  410 , with inputs  409  and outputs  425 , and a comparison module  412 . The optical demodulator  400  may optionally include a preprocessor  402 , with outputs  409 . The preprocessor  402  may include a processing elements  404  configured to separate the data into M optical signals. In an example embodiment, processing element  404  may be a wavelength division multiplexing (WDM) module configured to separate the data into M optical signals, with each signal being a distinct wavelength (or frequency). The processing element  404  may include a plurality of WDMs, temporal switches, polarization splitters, and VOAs so that the M optical signals  409  that may be reconfigured to represent different orthogonal bases, (e.g, frequency, polarization, position, or some combination thereof). The preprocessor  402  may further include an amplifier  406  and periodic filter  408  or a polarization filter/splitter  407 . The periodic filter  404  may be matched to the optical waveform of the symbols of the orthogonal modulation format. 
         [0049]    A further example embodiment of parallel receiver  400  is shown in  FIG. 6C . In this example embodiment, preprocessor  402  may further include optional variable optical attenuators (VOAs)  405  that may be used to select or balance the preprocessor outputs  409  s 1 , s 2 , s 4  in this example prior to the optical processor  410 . The VOAs  405 , with individual elements  405   a,    405   b,  . . .  405   d  may serve to compensate for biases in other elements of the preprocessor  402  or the processor  410  to optimize performance (e.g., by correcting for insertion loss variations in WDM outputs), or configure the operation of the preprocessor though selection of the preprocessor outputs  409  that pass though to the optical processor  410 . Similarly, VOAs  415  may be included in the optical processor  410  to compensate for biases in the split ratios (e.g., biases that may be due to manufacturing errors or tolerances, or wavelength or polarization dependent losses). 
         [0050]    Referring to  FIG. 6C , the optical processor  410  may be configured to transform M parallel input optical signals into 2×log 2  M intermediary optical signals  425 . The M input optical signals can, in example embodiments, represent input data encoded in an M-ary orthogonal modulation format. In example embodiments, M is greater than 2. The intermediary optical signals  425  are weighted superposition of optical input signal powers  409 . The weighting is determined by the fixed optical coupling elements  422  and the reconfigurable VOAs  415 . In an example embodiment, the intermediary optical signals  425  are: 
         [0000]        A+=w 1· s 3+ w 2· s 4
 
         [0000]        A−=w 3· s 1+ w 4· s 2
 
         [0000]        B+=w 5· s 2+ w 6· s 4
 
         [0000]        B−=w 7· s 1+ w 8· s 3,
 
         [0000]    where the weighting factors w 1 -w 8  may be reconfigured by adjusting the transmission of VOAs  415 . 
         [0051]    Referring again to  FIG. 6A  and  FIG. 6C , the comparison module  412  is optically connected to the optical processor  410 . The comparison module  412  is configured to compare optical power of the intermediary optical signals  425  (shown in  FIG. 6C ), which are output by the optical processor  410  and presented to the comparison module  412 , to determine a logical representation of the input data. 
         [0052]    As explained above, the logical representation of the input data includes a set of k bits, k being equal to log 2  M. In an example embodiment, the k logical bits are determined by comparing the power of intermediary optical signals A+ to A− and B+ to B− as shown in  FIG. 6C . In this case, [% Mark: Is this an acceptable notation?] 
         [0000]      Bit0= A+&lt; &gt;A−   
         [0000]      Bit1= B+&lt; &gt;B−   
         [0000]    where &lt; &gt; is represents the comparison (greater than or less than): if A+ is greater than A−, the Bit 0  is a logical 1 and if A+ is less than A−, Bit 0  is a 1, and so forth. For the example embodiment where the output of preprocessor  409  represents M-ary orthogonal symbols (e.g., 4-FSK symbols), Bit 0  and Bit 1  are the logical representation of this M-ary input data. In this case, M=4, with 2 bits of logical data. In general, this approach scales to larger M, will be shown in  FIG. 7A  and  FIG. 8 . 
         [0053]    Referring again to  FIG. 6C , the weighting factors imparted by VOAs  415  are reconfigured to enable the demodulator to demodulate other modulation formats. For example, by making weighing elements w 1 =1 and w 2 , w 3 , w 4 =0; and w 6 =1 and w 5 , w 7 , w 8 =0; Bit  0  represents the OOK demodulation of symbol s 3  and Bit  1  represents the OOK demodulation of symbol s 4 . By making weighing elements w 2 , w 4 =1 and w 1 , w 3 =0; and w 6 =1 and w 5 , w 7 , w 8 =0; Bit  0  represents the 2-orthogonal (e.g, 2-FSK) demodulation of symbols s 4  and s 2 . Thus, adjustment of VOA transmission and the corresponding weighting functions enables the demodulator to reconfigure so that it may demodulate other modulation formats, thereby increasing flexibility. 
         [0054]    Referring now to  FIG. 6A , comparison module  412  includes optical detectors  414   a  through  414   d,  converting intermediary optical signal into intermediary electrical signals, and is configured to perform k binary comparisons of optical powers of the intermediary optical signals using comparators  416   a  and  416   b.    
         [0055]    Referring again to  FIG. 6A , optical processor  410  includes an optical distribution matrix  418  configured to, in this example embodiment, to pairwise add the M parallel input optical signals. Generally, the addition of the optical signals may be achieved by combining the powers of the signal in two at time (e.g., pairwise), three at a time, and in general N at a time, where N is positive integer. The optical distribution matrix  418  comprises at least M waveguides  420  and at least M optical couplers  422 . The optical couplers  422  may be single mode couplers or multi-mode N×1 couplers that may efficiently combine N single-mode inputs into 1 multimode output. When used in the last column of the optical distribution matrix  418  prior to the optical detectors  414  and the optical detectors are configured to efficiently accept such multimode inputs, this may provide reduced insertion loss through the distribution matrix  418  with little or no performance penalty. For example, 50/50 single mode couplers have a minimum of 3 dB insertion loss, whereas a 2×1 single-mode to multimode coupler/combiner may have near zero insertion loss. 
         [0056]    In the example embodiment shown schematically in  FIG. 6A  (and photographically in  FIG. 6B ), the 4-ary FSK format is used, and optical distribution matrix  418  is configured to pairwise add the M input optical signals to produce the 2×log 2  M intermediary optical signals. In this example with the optical distribution matrix  418  configured with 4 inputs and 4 outputs, it may also be referred to as a quad or a quad demodulator block. With a proper optical preprocessor  402 , which separates M-ary orthogonal optical symbols prior to the distribution matrix  415 , this method may be used to demodulate the orthogonal symbol and determine the k-bits with k pairwise comparisions. For the example of M-FSK, the preprosessor may be implemented with a WDM, which separates the orthogonal frequencies. For M-PPM, the preprocess may be implemented with a circulating 1×M optical switch, which separates the orthogonal positions and delays them so that they are time-aligned at the input of the distribution matrix. As will be explained below, it is possible to configure the optical distribution matrix  418  for M greater than 4, in which case the optical distribution matrix  418  will be configured to pairwise add the M input optical signals to produce auxiliary optical signals and to further pairwise add the auxiliary optical signals to produce 2×log 2  M comparable signals (see  FIGS. 7A and 7B ). 
         [0057]    Another example embodiment of the present invention is illustrated schematically in  FIG. 7A  and is further shown in  FIG. 7B , which is a photograph of the example embodiment shown in  FIG. 7A . The embodiment shown in  FIG. 7A  is an optical demodulator  500  is configured to perform demodulation of data encoded in 8-FSK format. An optical processor  510  of the optical demodulator  500  comprises an optical distribution matrix  518  configured to pairwise add the M input optical signals to produce auxiliary optical signals and further to pairwise add the auxiliary optical signals to produce 2×log 2  M comparable signals. 
         [0058]    Another example embodiment of the present invention is illustrated in  FIG. 8 . In this example, an optical demodulator  600  is configured to perform demodulation of data encoded in 16-FSK format. An optical processor  610  of the optical demodulator  600  comprises an optical distribution matrix  618  configured to pairwise add the M input optical signals to produce auxiliary optical signals and further to pairwise add the auxiliary optical signals to produce 2×log 2  M comparable signals. Although not shown in  FIG. 8 , the optical demodulator  600  further includes a comparison module configured to perform eighth binary comparisons of optical powers of the intermediary optical signals and to set four bits encoded by the 16-FSK modulated input data. As in the case of the 4-ary distribution matrix  418 , the insertion loss and component count in 16-ary distribution matrix  618  may be reduced by substituting multi-mode N×1 couplers that may efficiently combine N single-mode inputs into 1 multimode output. When used in the last columns of the optical distribution matrix  618  prior to the optical detectors, and the optical detectors are configured to efficiently accept such multimode inputs, this may provide reduced insertion loss of up to 3 dB per 50/50 single-mode coupler replaced. For example, if the optical combining of the last two columns of couplers were implemented with 4×1 single-mode to multimode combiners, the loss through the distribution matrix  618  may be reduced by as much as  6  dB and the coupler count reduced by as much as 12 couplers. 
         [0059]    In example embodiments, any of the optical demodulators described above may further include a level estimator employing an Analog-to-Digital Converter (ADC).  FIG. 9A  is a schematic diagram of such an example embodiment, here, an 8-FSK optical demodulator  700 . The optical demodulator  700  includes a level estimator  730  that employs an ADC  732 . The input signal  737  to the ADC  732  is obtained from a portion of the input signal from an optical splitter  735  prior to optical preprocessing. The level estimator  730  may be configured to determine a confidence level of logical representations of the input data. In further example embodiments, the optical demodulator  700  may include a forward error correction module  734  to correct the logical representation of the input data as a function of the confidence level.  FIG. 9B  is a schematic diagram of a similar embodiment, illustrating that an equivalent input  737  to the level estimator  730  may be obtained from other locations within the demodulator  700 . In this example, the input  737  is obtained by adding the power from couplers providing the A+ and A− inputs to the comparison module. Altnernatively, the input signal may be derived from the B+ and B−, or C+ and C− inputs to the comparison module, since the addition of comparison inputs is largely equivalent to the power incident to the optical preprocessor. 
         [0060]    The level estimator may also be configured in an example embodiment to enable hybrid M-ary orthogonal demodulation of f-FSK/p-PPM symbols, where M=f·p. In this case, the optical processor  510  may determine the FSK portion of each orthogonal symbol (e.g, determine which frequency was the largest) and the level estimator may determine the PPM portion of each orthogonal symbol (e.g., determine which time-position was the largest). The hybrid M-ary orthogonal symbols may be envisioned as a two dimensional symbol constellation, with f-frequencies on one axis, and p-positions on the other axis, with a total of f·p symbols and log 2 (f·p) bits per symbol. For example, hybrid 8-FSK/4-PPM is equivalent to 32-ary orthogonal and conveys 5-bits/symbol, with peak power only four times greater than the average and a modulation/electronic bandwidth 20% less than data rate. 
         [0061]    In example embodiments, any of the optical demodulators described above may further include a periodic filter matched to the optical waveform of the symbols of the orthogonal modulation format. In other example embodiments, any of the optical demodulators described above may further include at least one variable optical attenuator configured to control pairwise adding of at least two input optical signals. Both such example embodiments are illustrated in  FIG. 10 , which is a schematic diagram of a 4-FSK optical demodulator  800 , but generally scales to the M-ary orthogonal embodiments described herein. In  FIG. 10 , an optical demodulator  800  includes a processor  810  and a comparison module  812 . The optical processor  810  includes an optical distribution matrix  818 . A preprocessor  802  may be comprised of an orthogonal preprocessing filter, such as a wavelength division multiplexing (WDM) module  804  and periodic filter  840 , that filters and separates the orthogonal symbols. In the example embodiment shown in  FIG. 10 , each input signal may further be controlled by a variable optical attenuator  850 .In an example embodiment, the present invention is an optical transceiver comprising any of the optical demodulators described above, configured to demodulate data encoded in an M-ary orthogonal modulation format, and further including a parallel transmitter configured to transmit data encoded in an M-ary orthogonal modulation format. 
         [0062]    In example embodiments, the M-ary modulation format may include an M-ary frequency shift keying (M-FSK) format. In other example embodiments, the M-ary modulation format may include an M-ary pulse-position modulation (M-PPM) format. In further example embodiments, the M-ary modulation format may be a 2-dimensional hybrid f-FSK/p-PPM format or  3 -dimensional f-FSK/p-PPM/L-PSK format. Here, f, p, and L are each positive integer number of orthogonal FSK frequencies, PPM positions, and PolSK polarizations, respectively. 
       Advantages of the Example Embodiments of the Present Invention 
       [0063]    The example embodiments of the present invention provide a straightforward means of demodulating M-FSK optical signals with good sensitivity. These devices and methods disclosed herein may be generalized for M-PPM as well as other hybrid M-orthogonal modulation methods such as those described above. The f-FSK receiver determines which of the f received signal frequencies has the largest energy. Once this determination is made, each demodulated f-FSK symbol generates k bits, where k f =log 2  f. As described herein, f-FSK demodulation may be accomplished with an optical front end comprising simple optical elements, such as optical amplifiers, wavelength division multiplexing (WDM) modules, optical splitters, and variable optical attenuators (VOAs). The elements of the devices described herein may be configured for hard decision decoding (e.g., only digital 0 or 1 logical data is used to perform forward error correction function), with the k-bit M-FSK symbol determined from only k binary comparisons. Graded (non-digital) soft decision information, that is useful for forward error correction (FEC) of the received data, may be attained by the detection and measurement of a single optical output channel containing all M-FSK signals (of which only one of the signals is “on”). The measurement may be achieved via a high-speed photodetector and analog-to-digital converter (ADC). In this case, the k-binary comparisons indicate signal of which frequency has the largest amplitude, and the ADC output indicates the magnitude of that signal. Furthermore, the ADC may also enable the detection of hybrid time-frequency M-ary orthogonal signals, by providing level estimates that may be used to determine which time-position was the largest. 
         [0064]    This is in sharp contrast to conventional M-FSK receivers, which may use M separate detectors followed by M-to-1 winner-take-all analog comparison circuitry (which is difficult to implement at GHz rates) or M-ADCs, where the digital outputs are digitally compared to determine which received signal has the largest amplitude. While conceptually straightforward, the ADC-based approach requires M=2k detectors and ADCs, and high-speed ADCs are power hungry and expensive, and until recently, unavailable at rates of greater than 3 GHz. For 16-FSK, the conventional implementation would require 16 ADCs, whereas only one ADC is needed to obtain soft-decision information using an embodiment of this invention. 
         [0065]    Moreover, in the devices described herein, a single ADC may be used to demodulate hybrid modulation formats, such as a p-PPM/f-FSK hybrid signal, in which symbol information is conveyed in one of f-frequencies and p-time positions. In this case, the M-ary parameter M=f*p, and the number of bits/symbol k=log 2 (M)=log 2 (f·p)=log 2 (f)+log 2 (p). Using an example embodiment of this invention to receive 8-PPM/16-FSK hybrid symbols, 7-bits of (soft) information per symbol may be received with the optical front end followed by one ADC and hardware to support 4-binary comparisons. 
         [0066]    The optical elements in the front end may have wide optical bandwidths, exceeding many THz, and, therefore, capable of accommodating numerous wide-band optical signals that may support ultra-high (GHz-class to 100+ GHz-class) data rates with good sensitivity. The binary comparisons may be achieved using all-optical switching techniques or using more conventional optical-to-electronic (O-E) conversion using high-speed photo-detectors followed by electronic comparators or decision circuitry. Since commercially available photodetectors and comparators have bandwidths exceeding 40 GHz, a 40+ Gsymbol/s 16-FSK receiver using elements of embodiments of this invention may support 160+ Gbps data rates, with the 4-bits from each symbol separated into four 40 GHz data streams. 
         [0067]    Another useful aspect of embodiments of this invention is the ability to reconfigure and optimize such an M-FSK. This may enable, for example, a single 16-FSK receiver to leverage common hardware elements to demodulate up to two 8-FSK signals, four 4-FSK signals, eight 2-FSK signals, and sixteen WDM-OOK signals. Such implementation may be achieved with integrated photonics, which may implement all of the needed elements including low-power variable optical attenuators (VOAs) in a small form factor. The VOAs may be used as optical switching elements or as trimming elements, enabling reconfiguration or proper power balancing needed for optimized performance. 
         [0068]    Yet another aspect of embodiments of this invention is the use of multi-mode optics to reduce insertion losses and increase reconfigurable functionality with fewer optical elements. For example, high-speed (greater than 10 GHz-class) photodetectors may be procurred with multi-mode input fiber. 
         [0069]    The example embodiments of the invention described herein enable wide-band M-FSK optical receivers which may support ultra-high-speed optical communications with greatly simplified implementation. Hard decision M-FSK reception may be implemented with only k=log 2 (M) binary comparisons, and may support ultra-high data rates (e.g., greater than 160 Gbps) with good sensitivity. The addition of a single ADC enables soft decision FEC as well as hybrid modulation formats (e.g., PPM/FSK hybrids). Conventional M-FSK receivers, in comparison, would require M-ADCs. Relative to differential phase shift keying (DPSK), which is an established high-speed high-sensitivity modulation format, the sensitivity of an 8-FSK receiver using embodiments of this invention has been demonstrated to be better than DPSK theory, and requires only 1/log 2 (M) or ⅓ the electronic bandwidth. 
         [0070]    Relative to M-PPM, M-FSK in theory provides the same sensitivity but with M-times lower peak power and electronic bandwidth. Thus, for ultra-high-sensitivity applications (including those using photon-counting receivers) that are limited by electronic bandwidths, M-FSK may extend data rates by a factor of M. As a result, this high-speed high-sensitivity receiver facilitates the use of M-FSK waveforms, which are much more suitable than M-PPM waveforms in nonlinear-limited designs such as high-power optical amplifiers and (long-haul) fiber-optic communications. Moreover, with high data rates (R) conveyed at R/log 2 (M) symbol rates, M-FSK waveforms are much more tolerant in dispersion-limited channels (e.g., optical fiber). 
         [0071]    The reconfigurable/adjustable elements of embodiments of this invention allow a single receiver to re-use elements to implement different demodulation functions, e.g., a 16-FSK receiver may be reconfigured to 4-FSK receivers. Moreover, the adjustable elements enable trimming such that the performance of a single receiver may be optimized to compensate for manufacturing variances (thus increasing the yield and reducing cost) and accommodate a wide range of wavelengths and modulation formats. 
         [0072]    The multi-mode aspects of this invention simplify/enhance reconfiguration options while reducing optical insertion loss. 
         [0073]    Lastly, the parallel receiver of embodiments of this invention enables high-sensitivity reception of a variety of modulation formats at high rates using wide-band optical signaling. This combination together with the ability to reconfigure may be used to provide enhanced means of secure communications—which are hard to detect and demodulate. 
       EXEMPLIFICATION 
       [0074]      FIG. 11A  is a block diagram of a transmitter  1100  and a receiver  1110 , setup for measuring the communication performance of an example embodiment of a receiver of the present invention. This setup was used to obtain data presented in  FIG. 11B . Receiver  1110  includes optical distribution matrix  1120  configured for demodulating a signal encoded in 8-ary FSK format. 
         [0075]    In the setup shown in  FIG. 11A , an 8-FSK transmitter  1100  is conveying 3 bits/symbol at a rate of 2.5 Gysmbols/sec (for an aggregate data rate of 7.5 Gbit/s) and an 8-FSK receiver  1110  is configured to experimentally measure the receiver sensitivity. The 8-FSK receiver  1110  includes a single polarization optically-preamplifier, and optical preprocessor that includes a 12.5 GHz WDM implemented with an arrayed waveguide grating router (AWGR) and 12.5 GHz delay-line interferometer (DI) with a net transfer function that is nearly-matched to the 33% RZ waveforms generated by the transmitter. 
         [0076]    The results of the measurement are presented in  FIG. 11B , which is a plot showing bit error rate as a function of received power. The plot shown in  FIG. 11B  demonstrates that measured 8-FSK bit-error-rate (BER) performance is within 1.5 dB from quantum-limited theory corresponding to less than 20 photons/bit at 10 −9  BER. This is better than 2-DP_SK theory. The sensitivity of the receiver employed in this experiment is among the highest reported in the absence of a forward error correction, especially for the data rates of greater than 1 Gbit/s. 
         [0077]    The teachings of all patents, published applications and references cited herein are incorporated by reference in their entirety. 
         [0078]    While this invention has been particularly shown and described with references to example embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the scope of the invention encompassed by the appended claims.