Abstract:
In one embodiment, the optical transport system has an optical transmitter, an optical receiver, and one or more phase-sensitive amplifiers (PSAs) disposed within an optical link that connects the optical transmitter and receiver. The optical transmitter employs a first nonlinear optical process to generate a two-carrier signal in a manner that makes this signal suitable for phase-sensitive amplification. The PSAs employ a second nonlinear optical process to optically amplify the two-carrier signal in a phase-sensitive manner to counteract the attenuation imposed onto the two-carrier signal by lossy components of the optical link. The optical receiver employs a third nonlinear optical process in a manner that enables the receiver to beneficially use redundancies in the two-carrier signal, e.g., for an SNR gain. The optical transport system can advantageously be implemented to have better noise properties than a comparable conventional system, which enables a commensurate increase in the data-transport capacity.

Description:
BACKGROUND 
       [0001]    1. Field of the Invention 
         [0002]    The invention relates to optical communication equipment and, more specifically but not exclusively, to the generation, transmission, and detection of an optical communication signal having two carrier frequencies, such as that suitable for optical phase-sensitive amplification. 
         [0003]    2. Description of the Related Art 
         [0004]    This section introduces aspects that may help facilitate a better understanding of the invention(s). Accordingly, the statements of this section are to be read in this light and are not to be understood as admissions about what is in the prior art or what is not in the prior art. 
         [0005]    A phase-sensitive amplifier (PSA) provides optical-signal amplification while adding very little noise to the signal, with a noise figure of 0 dB (decibels) theoretically shown to be possible. A PSA is also a useful tool for regenerating optical signals and cleaning up signal distortions accumulated in the optical link. A PSA is compatible with various modulation formats and can produce optical gain over a relatively wide spectral range sufficient for WDM (wavelength-division multiplexing) applications. Optical transport systems that can realize in practice these and other benefits of phase-sensitive amplification are being currently developed. 
       SUMMARY 
       [0006]    Disclosed herein are various embodiments of an optical transport system that can leverage optical phase-sensitive amplification of a modulated two-carrier signal to advantageously support a higher information-transmission capacity than that achievable with a comparable conventional optical transport system by up to two bits per second per Hertz. In one embodiment, the optical transport system has an optical transmitter, an optical receiver, and one or more phase-sensitive amplifiers (PSAs) disposed within an optical link that connects the optical transmitter and receiver. The optical transmitter employs a first nonlinear optical process to generate the two-carrier signal in a manner that makes this signal suitable for phase-sensitive amplification. The PSAs employ a second nonlinear optical process to optically amplify the two-carrier signal in a phase-sensitive manner to counteract the attenuation imposed onto the two-carrier signal by lossy components of the optical link. The optical receiver employs a third nonlinear optical process in a manner that enables the receiver to beneficially use redundancies in the two-carrier signal, e.g., for a signal-to-noise ratio (SNR) gain. 
         [0007]    According to one embodiment, provided is an apparatus having a nonlinear optical device configured to optically mix, via a first nonlinear optical process, a first modulated optical signal and a second modulated optical signal to generate a first mixed signal and a second mixed signal; and an optical detector configured to generate a first measure and a second measure, said first measure being a measure of the first mixed signal and said second measure being a measure of the second mixed signal. The apparatus further has a signal processor configured to determine a constellation symbol based on the first and second measures; and decode the constellation symbol to determine a corresponding bit word carried by the first and second modulated optical signals. 
         [0008]    According to another embodiment, provided is an apparatus comprising an optical transmitter. The optical transmitter comprises an optical modulator configured to modulate an optical carrier with data to generate a first modulated optical signal; and a nonlinear optical device configured to optically mix, via a phase-conjugation (PC) process, the first modulated optical signal, a first optical-pump signal, and a second optical-pump signal to generate a second modulated optical signal. The nonlinear optical device comprises an optical filter configured to optionally separate the first and second modulated optical signals from the first and second optical-pump signals and apply the first and second modulated optical signals to an output port of the optical transmitter. 
         [0009]    According to yet another embodiment, provided is an apparatus comprising an optical transmitter. The optical transmitter comprises an optical source configured to generate a first optical carrier and a second optical carrier so that the two optical carriers are phase-locked to one another. The optical transmitter further comprises a first optical modulator and a second optical modulator. The first optical modulator is configured to modulate the first optical carrier with data to generate a first modulated optical signal. The second optical modulator is configured to modulate the second optical carrier with the data to generate a second modulated optical signal in a manner that causes the second modulated optical signal to carry optical symbols that are conjugates of the corresponding optical signals carried by the first modulated optical signal. The optical transmitter further comprises an optical coupler configured to apply the first and second modulated optical signals to an output port of the optical transmitter. In one implementation, the optical source comprises a first laser configured to generate the first optical carrier, a second laser configured to generate the second optical carrier, and a phase-lock circuit configured to cause the first and second lasers to lock the phases of the first and second optical carriers with respect to one another. In another implementation, the optical source comprises an optical fiber amplifier configured to generate the second optical carrier, via a Bragg-scattering (BS) process, using a portion of the optical power of the first optical carrier. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0010]    Other aspects, features, and benefits of various embodiments of the invention will become more fully apparent, by way of example, from the following detailed description and the accompanying drawings, in which: 
           [0011]      FIG. 1  shows a block diagram of an optical transport system according to one embodiment of the invention; 
           [0012]      FIGS. 2A-2D  show frequency diagrams corresponding to representative nonlinear optical processes that can be used in a phase-sensitive amplifier (PSA) of the optical transport system shown in  FIG. 1  according to various embodiments of the invention; 
           [0013]      FIG. 3  shows a block diagram of an optical receiver that can be used in the optical transport system of  FIG. 1  according to one embodiment of the invention; 
           [0014]      FIGS. 4A-4B  show frequency diagrams corresponding to a Bragg-scattering process that can be used in an optical frequency converter of the optical receiver of  FIG. 3  according to one embodiment of the invention; and 
           [0015]      FIG. 5  shows a block diagram of an optical transmitter that can be used in the optical transport system of  FIG. 1  according to one embodiment of the invention. 
       
    
    
     DETAILED DESCRIPTION 
       [0016]      FIG. 1  shows a block diagram of an optical transport system  100  according to one embodiment of the invention. System  100  has an optical transmitter  110  and an optical receiver  140  connected to one another via an optical transport link  104 . Link  104  is illustratively shown as having four sections  106   a - 106   d  of optical fiber and two phase-sensitive amplifiers (PSAs)  120   1 - 120   2 . In alternative embodiments, link  104  may have a different number of fiber sections  106  and/or a different number of PSAs  120 . Various additional components, such as optical routing elements, variable optical attenuators, optical splitters, optical filters, and the like, may be incorporated into link  104  as appropriate or necessary. 
         [0017]    Transmitter  110  is configured to receive an input data stream  102  and generate a corresponding optical output signal that is applied to fiber section  106   a  to carry the data of the input data stream, via link  104 , to receiver  140 . Transmitter  110  generates the optical output signal using two different optical carriers. More specifically, transmitter  110  modulates the two optical carriers with the data of data stream  102  in a correlated manner to form a corresponding coherent superposition state that lends itself to phase-sensitive amplification in PSAs  120  of link  104 . As the coherent superposition state generated by transmitter  110  propagates along link  104 , it becomes a coherent-like superposition state rather than a true coherent state due to the increased noise. A representative two-carrier modulation scheme that can be implemented in transmitter  110  is described in more detail below in reference to  FIG. 5 . 
         [0018]    Each of the two modulated optical carriers of the two-carrier signal launched by transmitter  110  into link  104  carries the same data and can, in principle, be individually demodulated and decoded in a conventional manner to fully recover the data of data stream  102 . Therefore, from a conventional point of view, these two modulated optical carriers are redundant. However, the fact that these modulated optical carriers form a superposition quantum state enables system  100  to realize the above-indicated benefits of phase-sensitive amplification. For example, in one embodiment, system  100  can be configured to leverage the beneficial characteristics of the two-carrier signal generated by transmitter  110  and the phase-sensitive amplification provided by PSAs  120  in link  104  to advantageously support a higher information-transmission capacity than that achievable with a comparable conventional optical transport system. More specifically, various embodiments of system  100  can provide an information-transmission-capacity increase of about 1-2 bits per second per Hertz. 
         [0019]      FIGS. 2A-2D  graphically illustrate representative nonlinear optical processes that can be used in a PSA  120  of system  100  to provide phase-sensitive amplification according to various embodiments of the invention. The nomenclature used in  FIGS. 2A-2D  adheres to the nomenclature that is conventionally used in nonlinear optics for the description of various optical parametric processes, where p and q denote the optical-pump signals, and s and i denote the “signal” and the “idler,” respectively. In the context of this description, signal s and idler i represent the two optical carriers of the two-carrier signal generated by transmitter  110  and directed via optical link  104  to receiver  140  (see  FIG. 1 ). 
         [0020]      FIG. 2A  shows a frequency diagram corresponding to a modulation-interaction (MI) process that can be used in PSA  120  ( FIG. 1 ) according to one embodiment of the invention. Modulation interaction is a degenerate four-wave mixing (FWM) process, in which two pump photons are destroyed, and one signal photon and one idler photon are created, e.g., 2π p →π s +π i , where π x  represents a corresponding photon with frequency ω x  (x=p, s, i). 
         [0021]      FIGS. 2B-2C  show frequency diagrams corresponding to phase-conjugation (PC) processes that can be used in PSA  120  according to another embodiment of the invention. Phase conjugation is a non-degenerate FWM process, in which one photon from each of two pumps is destroyed, and one signal photon and one idler photon are created, e.g., π p +π q →π s +π i , where π x  represents a corresponding photon (x=q, p, s, i). In the two flavors of phase conjugation shown in  FIGS. 2B and 2C , respectively, both the signal and the idler frequencies are either outside of the frequency range between the two pumps ( FIG. 2B ) or inside that frequency range ( FIG. 2C ). Additional description of representative two-pump phase-conjugation processes can be found, e.g., in U.S. Pat. No. 7,164,526, which is incorporated herein by reference in its entirety. 
         [0022]      FIG. 2D  shows a frequency diagram corresponding to a non-degenerate down-conversion (DC) process that can be used in PSA  120  according to yet another embodiment of the invention. Down-conversion is a three-wave-mixing (TWM) process, in which one pump photon is destroyed, and one signal photon and one idler photon are created, e.g., π p →π s +π i , where π x  represents a corresponding photon (x=p, s, i). 
         [0023]    Referring back to  FIG. 1 , in operation, PSA  120  receives, from the upstream fiber section  106 , a two-carrier signal, with the two modulated optical carriers of that signal serving as the “signal” and “idler” modes, respectively. PSA  120  then applies the received two-carrier signal, together with one or two optical pumps, to an appropriate nonlinear optical medium to cause energy transfer from the optical pump(s) to the modulated carriers, e.g., via one of the nonlinear optical processes shown in  FIGS. 2A-2D , thereby amplifying the modulated carriers in a phase-sensitive manner. At the output port of PSA  120 , the amplified two-carrier signal may be separated out from the optical pump(s), e.g., using an appropriate optical filter or dispersive spectral element (not explicitly shown in  FIG. 1 ). The separated amplified two-carrier signal may then be applied to the downstream fiber section  106  for further transmission through link  104 . In an alternative configuration, the optical pump(s) may be applied to the downstream fiber section  106  together with the amplified two-carrier signal. 
         [0024]    In various embodiments, PSA  120  can be a distributed fiber-based amplifier or a lumped optical amplifier. A representative PSA that can be used as PSA  120  in system  100  is disclosed, e.g., in U.S. Pat. No. 7,483,203, which is incorporated herein by reference in its entirety. 
         [0025]    In one embodiment, receiver  140  uses a conventional homodyne or intradyne signal-detection scheme to recover the data of data stream  102  based on the two-carrier signal received from link  104 . More specifically, receiver  140  is configured to select one of the modulated carriers of the two-carrier signal and discard (e.g., block or drop) the other. The selected modulated carrier is then demodulated and decoded, e.g., by (i) optically splitting it into two attenuated copies, for example, in a balanced (50/50) optical beam splitter; (ii) mixing each of the copies with an appropriately phase-shifted local-oscillator signal to measure the in-phase (I) and quadrature-phase (Q) components of the modulated carrier; (iii) mapping the resulting (I,Q) pair onto the appropriate constellation to determine the symbol carried by the modulated carrier in the corresponding time slot; and (iv) decoding the symbol to recover the corresponding bit word (fragment) of data stream  102 . Either the “signal” or the “idler” mode can be selected for demodulation and decoding in this embodiment of receiver  140 . The recovered data fragments are concatenated to generate an output data stream  102 ′, which is directed to external circuitry. Representative optical receivers that can be used to implement this embodiment of receiver  140  are disclosed, e.g., in U.S. Patent Application Publication Nos. 2010/0158521 and 2011/0038631, and U.S. Pat. Nos. 7,688,918 and 7,711,273, all of which are incorporated herein by reference in their entirety. 
         [0026]    Note that the use of an optical splitter and concomitant detection of attenuated signal copies in the above-described signal-detection scheme imposes an automatic signal-to-noise ratio (SNR) penalty of up to 3 dB. However, in an alternative signal-detection scheme that can be implemented in another embodiment of receiver  140 , this SNR penalty can be obviated through the use of both modulated carriers (i.e., both the “signal” and the “idler” modes) of the received two-carrier signal for data recovery. More specifically, in this particular embodiment, receiver  140  is configured to mix the modulated carriers of the received two-carrier signal in a nonlinear optical medium using a Bragg-scattering (BS) process, a non-degenerate FWM process, in which one photon from one of the two pumps and one signal photon are destroyed, and one idler photon and one photon for the other pump are created, e.g., π s +π q →π p +π i , where π x  represents a corresponding photon (x=q, p, s, i). Receiver  140  uses the BS process to mix the modulated carriers so that (i) the mixed signal having the first carrier frequency (e.g., that of the “signal” mode) primarily carries the I component of the original modulation signal and (ii) the mixed signal having the second carrier frequency (e.g., that of the “idler” mode) primarily carries the Q component of the original modulation signal. Each of these mixed optical signals is detected in receiver  140  to recover the corresponding (I,Q) pair. The recovered (I,Q) pair is then constellation-mapped and decoded in a conventional manner to recover the corresponding fragment of data stream  102 . 
         [0027]    Below, a brief theoretical analysis of the latter signal-detection scheme is presented first. A practical implementation of this scheme is then described in more detail in reference to FIGS.  3  and  4 A- 4 B. 
         [0028]    Let a 1  and a 2  denote the first and second modulated carriers, respectively, of the two-carrier signal received by PSA  120   2  from fiber section  106   c,  and let b 1  and b 2  denote the amplified modulated carriers directed by the PSA to receiver  140  (see  FIG. 1 ). Then, assuming no loss in fiber section  106   d,  one can write: 
         [0000]        b   1   =μa   1   +νa*   2    (1a)
 
         [0000]        b   2   =νa*   1   +μa   2    (1b)
 
         [0000]    where μ and ν are the transfer coefficients of the PSA, and |μ| 2 −|ν| 2 =1. Let c 1  and c 2  denote the mixed signals produced by the optical Bragg-scattering (BS) mixer (also often referred to as “frequency converter”) in receiver  140 . Then: 
         [0000]        c   1   =τb   1   +ρb   2    (2a)
 
         [0000]        c   2   =−ρ*b   1   +τ*b   2    (2b)
 
         [0000]    where τ and ρ are the transfer coefficients of the frequency converter, and |τ| 2 +|ρ| 2 =1. By combining Eqs. (1) and (2), one finds that: 
         [0000]        c   1 =(τμ) a   1 +(ρν) a*   1 +(ρμ) a   2 +(τν) a*   2    (3a)
 
         [0000]        c   2 =−(ρ*μ) a   1 +(τ*ν) a*   1 +(τ*μ) a   2 −(ρ*ν) a*   2    (3b)
 
         [0029]    To demonstrate the proof of principle, we will now analyze Eqs. (3a)-(3b) by assuming that the transfer coefficients are all real and positive. If one treats the operators in Eqs. (3a)-(3b) like complex numbers and lets a j =a jr +ia ji , where the subscripts r and i denote the real and imaginary parts, respectively, and j=1, 2, then, for real positive transfer coefficients, Eqs. (3a) and (3b) can be rewritten as: 
         [0000]        c   1r =(τμ+ρν) a   1r +(ρμ+τν) a   2r    (4a)
 
         [0000]        c   1i =(τμ−ρν) a   1i +(ρμ−τν) a   2i    (4b)
 
         [0000]        c   2r =(τν−ρμ) a   1r +(τμ−ρν) a   2r tm ( 4c)
 
         [0000]        c   2i =−(τν+ρμ) a   1i +(τμ+ρν) a   2i    (4d)
 
         [0030]    It is evident from Eqs. (4a)-(4d) that, for the first mixed signal (c 1 ) in receiver  140 , the real quadrature is stretched and the imaginary quadrature is squeezed, whereas for the second mixed signal (c 2 ), the real quadrature is squeezed and the imaginary quadrature is stretched. One of ordinary skill in the art will understand that, for a high-gain PSA (e.g., μ+ν&gt;&gt;1 and μ−ν&lt;&lt;1) and a balanced frequency converter (τ 2 =ρ 2 =½), the squeezed quadratures are negligible because the detector noise swamps the diminished input noise and also likely swamps the diminished communication signal. In contrast, the stretched quadratures are readily detectable because the amplified input noise (which is presumably relatively low compared to the amplified communication signal) swamps the detector noise. 
         [0031]    These results imply that the I component of the original modulated signal can be recovered by applying homodyne or intradyne detection to the first mixed signal. The Q component of the original modulated signal can similarly be recovered by applying homodyne or intradyne detection to the second mixed signal. Note that the first and second mixed signals have the first carrier frequency and the second carrier frequency, respectively, and, as such, can be spatially separated from one another in receiver  140  in a relatively straightforward manner, e.g., using a dispersive spectral element, such as a prism or a grating. Each of the separated mixed signals can then be directed to a respective homodyne or intradyne detector for optical-to-electrical conversion and post-conversion processing in the electrical domain. 
         [0032]    Note that the amplitude of the real quadrature of the first mixed signal (c 1r , Eq. (4a)) is maximal if a 2r =a 1r . The amplitude of the imaginary quadrature of the second mixed signal (c 2i , Eq. (4d)) is maximal if a 2i =−a 1i . These two results suggest a modulation scheme that can be implemented in transmitter  110  to generate the corresponding original two-carrier signal in an optimal manner. A representative example of such a modulation scheme is described below in reference to  FIG. 5 . 
         [0033]    For complex transfer coefficients μ, ν, τ, and ρ, the analysis of Eqs. (3a)-(3b) is significantly more complex and, for the sake of brevity, is not provided here. However, the major conclusions derived from the above-presented analysis of the special case of all-real transfer coefficients remain valid. More specifically, provided that a particular relationship exists between the phases of the first and second modulated carriers (a 1  and a 2 ) of the two-carrier signal, the optical BS mixer of receiver  140  will convert (i) the I components of the two carriers that are in phase with one another (e.g., have the same sign) to the first carrier frequency and (ii) the Q components of the two carriers that are out of phase with one another (e.g., have opposite signs) to the second carrier frequency. The resulting mixed signals can then be separated from one another and individually detected as already indicated above. 
         [0034]      FIG. 3  shows a block diagram of an optical receiver  300  that can be used as receiver  140  according to one embodiment of the invention. Receiver  300  is configured to receive a two-carrier input signal  302 , e.g., from PSA  120   2  (see  FIG. 1 ). Receiver  300  is further configured to process signal  302 , e.g., as described below, to generate an output data stream  392  that can serve as output data stream  102 ′ in system  100  ( FIG. 1 ). 
         [0035]    Receiver  300  has an optical frequency converter (BS signal mixer)  330  that receives as inputs (i) two-carrier signal  302  and (ii) optical-pump signals  312   1  and  312   2  generated by optical-pump sources (e.g., lasers)  310   1  and  310   2 , respectively. The wavelengths (frequencies) of optical-pump signals  312   1  and  312   2  are selected to enable the two carriers of signal  302  and the two optical-pump signals to optically mix, via a Bragg-scattering (BS) process, in the corresponding nonlinear optical medium of optical frequency converter  330 . 
         [0036]      FIGS. 4A-4B  show frequency diagrams corresponding to two different flavors of the BS process that can be used in optical frequency converter  330 . Note that  FIGS. 4A-4B  adhere to the same nomenclature as  FIGS. 2A-2D . 
         [0037]    As already indicated above, Bragg scattering is a non-degenerate FWM process, in which one photon from one of the two pumps and one signal photon are destroyed, and one idler photon and one photon for the other pump are created, e.g., π s +π q →π p +π i , where π x  represents a corresponding photon (x=q, p, s, i). In the frequency diagrams of  FIGS. 4A-4B , downward arrows denote the optical modes that lose photons in the corresponding BS process, whereas upward arrows denote the optical modes that gain photons in that process. The BS-process flavor shown in  FIG. 4A  is sometimes referred to as distant Bragg scattering because the signal and idler can have a relatively large spectral separation due to the presence of one of the optical pumps in the spectral range between them. The BS-process flavor shown in  FIG. 4B  is sometimes referred to as nearby Bragg scattering because the signal and idler are located next to each other on the same side of the optical-pump pair. 
         [0038]    Referring back to  FIG. 3 , a multiplex  332  of mixed optical signals produced by optical frequency converter  330  is applied to an input port of a spectral separator  340 . Spectral separator  340  is configured to (i) block or dump the mixed signals having the optical-pump frequencies, (ii) direct a mixed signal  342   1  having the first carrier frequency to a first output port, and (ii) direct a mixed signal  342   2  having the second carrier frequency to a second output port. In various embodiments, separator  340  can be based on a prism, a grating, an optical de-multiplexer, a dichroic filter, or any other suitable optical device designed to spatially separate light of different colors. 
         [0039]    Mixed signals  342   1  and  342   2  are applied to optical mixers  350   1  and  350   2 , respectively, as indicated in  FIG. 3 . Optical mixer  350   1  also receives an appropriately phase-shifted local-oscillator (LO) signal  328   1  produced by a local-oscillator source (LO 1 )  320   1  and a phase shifter (PS 1 )  324   1 . Optical mixer  350   2  similarly receives an appropriately phase-shifted LO signal  328   2  produced by a local-oscillator source (LO 2 )  320   2  and a phase shifter (PS 2 )  324   2 . LO signals  328   1  and  328   2  have frequencies corresponding to the first and second carrier frequencies, respectively, of two-carrier signal  302 . As used here, the word “corresponding” means that the frequencies in each pair are sufficiently close to each other to enable homodyne or intradyne signal detection. A controller  360  controls the phase shifts imparted by phase shifters  324   1  and  324   2 , e.g., to align (i) LO signal  328   1  with the I quadrature of mixed signal  342   1  and (ii) LO signal  328   2  with the Q quadrature of mixed signal  342   2 . 
         [0040]    Each of optical mixers  350   1  and  350   2  operates to combine its input signals to produce two corresponding interference signals, each having an intensity that is: (i) proportional to the intensities of the input signals and (ii) related to an instant phase offset between those input signals. More specifically, the interference signals produced by optical mixer  350  are such that the intensity difference between these interference signals is proportional to cos(Δφ), where Δφ is the instant phase offset. A pair of balanced photo-detectors (e.g., photodiodes)  354  coupled to a respective one of differential amplifiers  370   1  and  370   2  continuously measures the intensity difference for the interference signals produced by the respective one of optical mixers  350   1  and  350   2  and applies the measurement results to a respective one of synchronized analog-to-digital converters (ADCs)  380   1  and  380   2 . Using these measurement results, each of ADCs  380   1  and  380   2  produces a respective one of digital signals  382   1  and  382   2 , both of which are applied to a digital signal processor (DSP)  390 . 
         [0041]    One of ordinary skill in the art will understand that digital signal  382   1  provides a measure of the I component of the original modulation signal, and that digital signal  382   2  similarly provides a measure of the Q component of the original modulation signal. DSP  390  processes digital signals  382   1  and  382   2  to obtain, for each time slot, a respective (I,Q) pair. DSP  390  then maps each (I,Q) pair onto the operative constellation to determine the constellation symbol carried by input signal  302  in the corresponding time slot. Finally, DSP  390  decodes each of the determined constellation symbols to produce a corresponding bit word and then concatenates the bit words to generate output data stream  392 . 
         [0042]    In one embodiment, DSP  390  is also configured to generate a feedback signal  394  for controller  360 . Feedback signal  394  can be generated, e.g., based on the average energy of each of digital signals  382   1  and  382   2 , with the averages being repeatedly taken over a fixed-width time window that covers a relatively large number of signal time slots. Controller  360  can then use the average energy of digital signal  382   1  to adjust the phase shift imparted by phase shifter  324   1  to keep the average energy near a maximum level, thereby maintaining a proper phase alignment between signals  328   1  and  342   1 . Controller  360  can similarly use the average energy of digital signal  382   2  to adjust the phase shift imparted by phase shifter  324   2  to maintain a proper phase alignment between signals  328   2  and  342   2 . 
         [0043]      FIG. 5  shows a block diagram of an optical transmitter  500  that can be used as transmitter  110  ( FIG. 1 ) according to one embodiment of the invention. Transmitter  500  is configured to receive an input data stream  502  that can be, e.g., input data stream  102  ( FIG. 1 ). Transmitter  500  is further configured to generate, e.g., as described below, a two-carrier optical output signal  592  that carries the data of input data stream  502 . Signal  592  can be applied, e.g., to fiber section  106   a  for transmission through link  104  in system  100  ( FIG. 1 ). 
         [0044]    Transmitter  500  has an encoder  510  configured to transform input data stream  502  into a corresponding sequence of constellation symbols and provide the (I,Q) pair representing each constellation symbol to a digital-to-analog converter (DAC)  520  via signals  512   I  and  512   Q , wherein, in each time slot, signal  512   I  has the I value of the corresponding (I,Q) pair, and signal  512   Q  has the Q value of that pair. DAC  520  transforms signals  512   I  and  512   Q  into the corresponding electrical analog signals  522   I  and  522   Q  and applies those signals to a drive circuit  530 . Based on signals  522   I  and  522   Q , drive circuit  530  generates, as known in the art, one or more appropriate drive signals  532  and applies those drive signals to an optical modulator  560 . 
         [0045]    Drive signal(s)  532  drive(s) modulator  560  thereby causing it to modulate an optical input signal  552  and convert the latter into a modulated optical signal  562 . Optical signal  552  is a pulse train that is generated by a pulse carver  550 , e.g., by gating, at a specified clock rate, a CW optical beam  542  generated by a laser  540 . Laser  540  is configured to generate beam  542  so that the beam has a first carrier frequency intended for two-carrier output signal  592 . One of ordinary skill in the art will understand that modulated optical signal  562  has the same carrier frequency as beam  542 . 
         [0046]    Modulated optical signal  562  is applied to an optical fiber amplifier (OFA)  570 , where it is converted into two-carrier output signal  592  as further described below. In various configurations, OFA  570  can be operated with one or two optical-pump signals  576   1  and  576   2 . In a one-pump configuration, one of optical-pump sources  572   1  and  572   2  can be turned off. In a two-pump configuration, both optical-pump sources  572   1  and  572   2  are turned on. 
         [0047]    OFA  570  has two optical couplers  578  and  582  that are configured to combine signals  562 ,  576   1 , and  576   2  and couple the resulting multiplexed signal into a highly nonlinear fiber (HNLF)  586 . An appropriate nonlinear optical process in HNLF  586  then produces a “copy” of modulated optical signal  562 , with said copy having a second carrier frequency intended for two-carrier signal  592 . An optical filter  590  placed at the distal end of HNLF  586  separates signal  562  and its “copy” generated in the HNLF from optical-pump signals  576   1  and  576   2 , thereby producing two-carrier signal  592 . A representative OFA that can be configured to operate as OFA  570  in transmitter  500  is described in more detail, e.g., in the above-cited U.S. Pat. No. 7,164,526. 
         [0048]    In one embodiment, HNLF  586  is a fiber that is designed and configured to enable therein a modulation-interaction (MI) process that is analogous to the MI process depicted in  FIG. 2A . Since the MI process can be implemented with a single optical-pump signal (the “p” mode in  FIG. 2A ), one of optical-pump sources  572   1  and  572   2  can be turned off or removed from transmitter  500 . The other optical-pump source is configured to generate the corresponding optical-pump signal  576  at an optical frequency (wavelength) that causes the MI process in HNLF  586  to generate photons at the second carrier frequency of two-carrier signal  592 . In the frequency diagram of  FIG. 2A , the first and second carrier frequencies of signal  592  are represented by the “s” and “i” modes. In different configurations, modulated optical signal  562  can correspond to either the “s” mode or the “i” mode. For example, if modulated optical signal  562  corresponds to the “s” mode of  FIG. 2A , then the MI process in HNLF  586  generates the “i” mode. Alternatively, if modulated optical signal  562  corresponds to the “i” mode of  FIG. 2A , then the MI process in HNLF  586  generates the “s” mode. Note that the MI process implemented in HNLF  586  differs from the MI process implemented in the corresponding embodiment of PSA  120  ( FIG. 1 ) in that the PSA is configured to receive, as input signals, both the “s” and “i” modes of  FIG. 2A , whereas the HNLF is configured to receive only one of those modes. Additional details on copying optical signals via an MI process can be found, e.g., in Renyong Tang, Jacob Lasri, Preetpaul S. Devgan, et al., “Gain Characteristics of a Frequency Nondegenerate Phase-Sensitive Fiber-Optic Parametric Amplifier with Phase Self-Stabilized Input,” OPTICS EXPRESS, 2005, vol. 13, No. 26, pp. 10483-10493, which is incorporated herein by reference in its entirety. 
         [0049]    In another embodiment, HNLF  586  is a fiber that is designed and configured to enable therein a phase-conjugation (PC) process that is analogous to one of the PC processes depicted in  FIGS. 2B-2C . Since the PC process employs two optical-pump signals (the “p” and “q” modes in  FIGS. 2B-2C ), both optical-pump sources  572   1  and  572   2  are turned on and configured to generate optical-pump signals  576   1  and  576   2  at respective optical frequencies (wavelengths) that cause the corresponding PC process in HNLF  586  to generate photons at the second carrier frequency of two-carrier signal  592 . For example, if modulated optical signal  562  corresponds to the “s” mode of one of  FIGS. 2B-2C , then the PC process in HNLF  586  generates the “i” mode. Alternatively, if modulated optical signal  562  corresponds to the “i” mode of one of  FIGS. 2B-2C , then the PC process in HNLF  586  generates the “s” mode. Again, the PC process implemented in HNLF  586  differs from the PC process implemented in the corresponding embodiment of PSA  120  ( FIG. 1 ) in that the PSA is configured to receive, as input signals, both the “s” and “i” modes of  FIG. 2B  or  2 C, whereas the HNLF is configured to receive only one of those modes. 
         [0050]    Note that, for both of the above-described embodiments of OFA  570 , transmitter  500  may need to incorporate, at its output port, an optical phase controller or optical processor (e.g. a Finisar Waveshaper, not explicitly shown in  FIG. 5 ) so that two-carrier signal  592  generated by transmitter  500  has appropriate characteristics to: (i) lend itself to phase-sensitive amplification in link  104  ( FIG. 1 ), and (ii) enable proper operation of receiver  300  ( FIG. 3 ) at the remote end of that link. Either the MI process or the PC process implemented in OFA  570  in the above-described manner can cause the “copy” of modulated optical signal  562  generated in HNLF  586  to have an optimal relationship with that modulated optical signal for these purposes. For example, recall that the above-presented analysis of Eqs. (4a)-(4d) suggested the following possible optimal relationship for the quadratures of the two-carrier signal: a 2r =a 1r  and a 2i =−a 1i . One of ordinary skill in the art will appreciate that either the MI process or the PC process in HNLF  586  is capable of producing signals that can be processed to have this particular relationship for two-carrier signal  592 . One or more additional instances of a similar optical phase controller or optical processor may need to be incorporated into link  104  before and/or after each amplifier  120 . 
         [0051]    One of ordinary skill in the art will further appreciate that system  100  can employ various alternative embodiments of transmitter  110  ( FIG. 1 ), e.g., an optical transmitter that is different from transmitter  500  but is still able to generate the first and second modulated carriers so that a 2 =a 1 *, where a 1  and a 2  denote the first and second modulated carriers, respectively. 
         [0052]    For example, a first alternative embodiment of transmitter  110  can be constructed by modifying transmitter  500  of  FIG. 5  as follows. 
         [0053]    First, all elements shown in  FIG. 5  downstream from modulator  560  are removed. The removed elements include optical-pump sources  572   1  and  572   2  and OFA  570 . 
         [0054]    Second, a second optical branch is added in parallel to the optical branch having laser  540 , pulse carver  550 , optical modulator  560 , and drive circuit  530 . This second optical branch is analogous to the existing optical branch and includes its own laser, pulse carver, optical modulator, and drive circuit. 
         [0055]    Third, a phase-lock circuit is added and configured to lock the phases of the optical output beams generated by laser  540  and the laser of the second (added) optical branch. One circuit that can operate as such phase-lock circuit is disclosed, e.g., in L. H. Enloe and J. L. Rodda, “Laser Phase-Locked Loop,” Proc. IEEE, vol. 53, pp. 165-166 (1965), which is incorporated herein by reference in its entirety. 
         [0056]    Fourth, the drive circuit of the second (added) optical branch is connected to receive, as input signals, a copy of electrical analog signal  522   I  and an inverted copy of electrical analog signal  522   Q . The inversion of signal  522   Q  can be implemented using a conventional signal inverter, e.g., a differential amplifier configured to (i) receive signal  522   Q  at its inverting input port and (ii) operate with a gain of one. 
         [0057]    Finally, an optical combiner that is similar to combiner  582  is added to combine the optical signals generated by the two optical branches. The optical output signal generated by the optical combiner has the requisite characteristics and can be used in the same way as output signal  592 . 
         [0058]    A second alternative embodiment of transmitter  110  can be constructing by further modifying the just-described first alternative embodiment, e.g., by replacing the laser of the second optical branch with an optical fiber amplifier that is similar to OFA  570 , but is configured to operate using a Bragg-scattering (BS) process. When a (diverted) portion of CW optical beam  542  is applied, as an input signal, to that optical fiber amplifier, the BS process therein produces an idler that is a direct (non-conjugated) copy of the input signal. Then, the two modulators of the above-described two optical branches can be used to impart conjugate information (I and Q, and I and −Q), on the non-diverted portion of beam  542  and on the idler generated by the optical fiber amplifier, respectively. After being combined in an optical combiner, the two modulated signals form a requisite two-carrier signal that can be used in the same way as output signal  592 . 
         [0059]    Referring back to  FIG. 1 , in one embodiment, MI- or PC-based optical-signal copying in transmitter  110 , phase-sensitive amplification in PSAs  120 , and BS-based frequency conversion in receiver  140  are all implemented in polarization-independent manners. More specifically, there are three main types of nonlinear media that are currently available for the implementation of MI, PC, and BS processes: (i) randomly birefringent fiber (RBF), (ii) rapidly spun fiber (RSF), and (iii) strongly birefringent fiber (SBF). MI is generally polarization sensitive in RBF and RSF. However, one can make it polarization insensitive by using a polarization-diversity scheme similar to that disclosed in an article by T. Hasegawa, K. Inoue, and K. Oda, entitled “Polarization Independent Frequency Conversion by Fiber Four-Wave Mixing with a Polarization Diversity Technique,” published in IEEE Photon. Technol. Letters, 1993, v. 5, pp. 947-949, which article is incorporated herein by reference in its entirety. This scheme can also be adapted, in a relatively straightforward manner, to make PC and BS processes polarization insensitive. 
         [0060]    PC and BS driven in RBF or RSF by optical pumps with parallel polarizations are polarization sensitive. However, PC driven by orthogonal pumps in RBF is intrinsically polarization independent (see, e.g., R. M. Jopson and R. E. Tench, “Polarization-Independent Phase Conjugation of Lightwave Signals,” Electron. Letters, 1993, v. 29, pp. 2216-2217, and C. J. McKinstrie, H. Kogelnik, R. M. Jopson, S. Radic, and A. V. Kanaev, “Four-Wave Mixing in Fibers with Random Birefringence,” Opt. Express, 2004, v. 12, pp. 2033-2055, which are incorporated herein by reference in their entirety). This property of RBF is advantageous for a two-pump design. PC driven by perpendicular linearly polarized pumps or counter-rotating circularly polarized pumps in RSF is also polarization independent (see, e.g., C. J. McKinstrie, H. Kogelnik, and L. Schenato, “Four-Wave Mixing in a Rapidly-Spun Fiber,” Opt. Express 2006, v. 14, pp. 8516-8534, which is incorporated herein by reference in its entirety). BS driven by co-rotating circularly polarized pumps in RSF is polarization independent (see the above-cited Opt. Express 2006, v. 14, pp. 8516-8534). 
         [0061]    One can make MI in SBF polarization independent by using a linearly polarized pump that is inclined at 45 degrees to the birefringence axes (see, e.g., Z. Wang, N. Deng, C. Lin, and C. K. Chan, “Polarization-Insensitive Widely Tunable Wavelength Conversion Based on Four-Wave Mixing Using Dispersion-Flattened High-Nonlinearity Photonic Crystal Fiber with Residual Birefringence,” Proc. of the 2006 European Conference on Optical Communications, paper We3.P.18, which is incorporated herein by reference in its entirety). One can also make PC and BS in SBF polarization independent by using two linearly polarized pumps that are inclined at 45 degrees to the birefringence axes (see, e.g., C. J. McKinstrie and C. Xie, “Polarization-Independent Amplification and Frequency Conversion in Strongly-Birefringent Fibers,” Opt. Express, 2008, v. 16, pp. 16774-16797, and U.S. Pat. No. 7,764,423, which are incorporated herein by reference in their entirety). 
         [0062]    While this invention has been described with reference to illustrative embodiments, this description is not intended to be construed in a limiting sense. Various modifications of the described embodiments, as well as other embodiments of the invention, which are apparent to persons skilled in the art to which the invention pertains are deemed to lie within the principle and scope of the invention as expressed in the following claims. 
         [0063]    Unless explicitly stated otherwise, each numerical value and range should be interpreted as being approximate as if the word “about” or “approximately” preceded the value of the value or range. 
         [0064]    The use of figure numbers and/or figure reference labels in the claims is intended to identify one or more possible embodiments of the claimed subject matter in order to facilitate the interpretation of the claims. Such use is not to be construed as necessarily limiting the scope of those claims to the embodiments shown in the corresponding figures. 
         [0065]    Although the elements in the following method claims, if any, are recited in a particular sequence with corresponding labeling, unless the claim recitations otherwise imply a particular sequence for implementing some or all of those elements, those elements are not necessarily intended to be limited to being implemented in that particular sequence. 
         [0066]    Reference herein to “one embodiment” or “an embodiment” means that a particular feature, structure, or characteristic described in connection with the embodiment can be included in at least one embodiment of the invention. The appearances of the phrase “in one embodiment” in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments necessarily mutually exclusive of other embodiments. The same applies to the term “implementation.” 
         [0067]    Also for purposes of this description, the terms “couple,” “coupling,” “coupled,” “connect,” “connecting,” or “connected” refer to any manner known in the art or later developed in which energy is allowed to be transferred between two or more elements, and the interposition of one or more additional elements is contemplated, although not required. Conversely, the terms “directly coupled,” “directly connected,” etc., imply the absence of such additional elements. 
         [0068]    The description and drawings merely illustrate the principles of the invention. It will thus be appreciated that those of ordinary skill in the art will be able to devise various arrangements that, although not explicitly described or shown herein, embody the principles of the invention and are included within its spirit and scope. Furthermore, all examples recited herein are principally intended expressly to be only for pedagogical purposes to aid the reader in understanding the principles of the invention and the concepts contributed by the inventor(s) to furthering the art, and are to be construed as being without limitation to such specifically recited examples and conditions. Moreover, all statements herein reciting principles, aspects, and embodiments of the invention, as well as specific examples thereof, are intended to encompass equivalents thereof. 
         [0069]    The functions of the various elements shown in the figures, including any functional blocks labeled as “processors” and “controllers,” may be provided through the use of dedicated hardware as well as hardware capable of executing software in association with appropriate software. When provided by a processor, the functions may be provided by a single dedicated processor, by a single shared processor, or by a plurality of individual processors, some of which may be shared. Moreover, explicit use of the term “processor” or “controller” should not be construed to refer exclusively to hardware capable of executing software, and may implicitly include, without limitation, digital signal processor (DSP) hardware, network processor, application specific integrated circuit (ASIC), field programmable gate array (FPGA), read only memory (ROM) for storing software, random access memory (RAM), and non volatile storage. Other hardware, conventional and/or custom, may also be included.