Abstract:
Two-pump optical parametric devices (OPDs), and methods of operating the same, generate desired output signals and idlers having reduced stimulated Raman scattering (SRS) noise levels. When the two-pump OPD is used as a two-pump optical parametric amplifier (OPA), the pumps are polarized perpendicular to each other, and the lower-frequency sideband (signal or idler) is polarized parallel to the lower-frequency pump (perpendicular to the higher-frequency pump). The desired output may be an amplified signal or a generated idler. When the two-pump OPD is used as a two-pump optical frequency converter (OFC), the pumps can be polarized parallel to one another, in which case the signal and idler are both perpendicular to the pumps, or perpendicular to one another, in which case the lower-frequency sideband (signal or idler) is polarized parallel to the lower-frequency pump (perpendicular to the higher-frequency pump).

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is related to a continuation-in-part (CIP) U.S. patent application Ser. No. 11/068,555, filed Feb. 28, 2005, the teachings of which are incorporated herein by reference. 
     FIELD OF THE INVENTION 
     The present invention relates to optical parametric devices (OPDs), such as optical parametric amplifiers (OPAs) and optical frequency converters (OFCs), and more particularly to two-pump OPDs having reduced stimulated Raman scattering (SRS) noise levels in their output signals or idlers. 
     BACKGROUND OF THE INVENTION 
     Optical communication systems employ optical amplifiers, e.g., to compensate for signal attenuation in optical fibers. One type of amplifier that may be used in a fiber-based communication system is an OPA. As known in the art, an OPA is a device that produces a tunable coherent optical output via a nonlinear optical processes called four-wave mixing (FWM), in which two photons from one pump wave, or two pump waves, are destroyed and two new photons are created, with conservation of the total photon energy and momentum. The waves corresponding to the two new photons are usually referred to as the signal wave and the idler wave. This process amplifies a weak input signal and generates an idler, which is a frequency converted (FC) and phase-conjugated (PC) image of the signal. As known in the art, there is another type of FWM process, in which one signal photon and one pump photon are destroyed, and one idler photon and one different pump photon are produced, with conservation of the total photon energy and momentum. This process transfers power from the signal to the idler, which is a FC image of the signal. Optical frequency converters, OFCs, can be used to perform switching and routing in communication systems. The fundamentals of FWM are discussed in a book by G. P. Agrawal [“Nonlinear Fiber Optics, 3rd Edition,” Academic Press, 2001, hereafter referred to as GPA]. 
     However, a problem with two-pump OPDs is the SRS noise that appears in the output signals and idlers. Because of SRS noise, the output signals or idlers produced by OPDs have lower signal-to-noise ratios (SNRs) than the input signals, which reduces the effectiveness of OPDs in communication systems. 
     SUMMARY OF THE INVENTION 
     In accordance with the present invention, two-pump OPDs, and methods of operating the same are described, which generate desired output signals and idlers having reduced SRS noise levels. In the case of a two-pump OPA, the pumps are polarized perpendicular to each other, and the lower-frequency sideband (signal or idler) is polarized parallel to the lower-frequency pump (perpendicular to the higher-frequency pump). The desired output may be an amplified signal or a generated idler (frequency-shifted copy of the signal). In the case of a two-pump OFC, the pumps can be polarized parallel to one another, in which case the signal and idler are both perpendicular to the pumps, or perpendicular to one another, in which case the lower-frequency sideband (signal or idler) is polarized parallel to the lower-frequency pump (perpendicular to the higher-frequency pump). The desired output may be an amplified signal or a generated idler. 
     More particularly, I describe a method of operating a two-pump optical parametric device, OPD, as an amplifier, OPA, that generates a desired output signal having a reduced stimulated Raman scattering, SRS, noise level. The method comprising the steps of
         (1) applying first and second polarized pumps to the OPA, the frequency of the first pump, P 1 , being lower than the frequency of the second pump, P 2 , and the polarization of P 1  being perpendicular to the polarization of P 2 ;   (2) applying a polarized input signal S as an inner sideband adjacent to P 1  or P 2 ;   (3) outputting the desired output signal from an inner sideband adjacent to P 1  or P 2 ;   (4) wherein the inner sideband adjacent to P 1  is polarized parallel to P 1  and wherein
           (a) when the desired output is an amplified signal S, the input signal S is applied as an inner sideband adjacent to P 1  and the SRS noise level in the desired output signal is reduced by establishing the polarization of S to be perpendicular to the polarization P 2  and   (b) when the desired signal is a generated PC idler, 2−, the input signal S is applied as an inner sideband adjacent to P 2  and the SRS noise level in idler 2− is reduced by establishing the polarization of S to be parallel to the polarization of P 2 .   
               

     According to one embodiment, I describe a two-pump optical parametric amplifier, OPA, to generate a desired output signal having a reduced stimulated Raman scattering, SRS, noise level. The OPA comprises
         a first polarized coupler for coupling a first pump, P 1 , to the two-pump OPA;   a second polarized coupler for coupling a second pump, P 2 , to the two-pump OPA, wherein the frequency of P 1  is lower than the frequency of P 2  and the polarization of the first polarized coupler is perpendicular to the polarization of the second polarized coupler;   a third polarized coupler for coupling an input signal S in an inner sideband adjacent P 1  or P 2 ;   means for outputting the desired output signal (or idler) from an inner sideband adjacent to P 1  or P 2 , and   wherein the inner sideband adjacent to P 1  is polarized parallel to P 1  and wherein
           (a) when the desired output is an amplified signal S, the input signal S is applied as an inner sideband adjacent to P 1  and the SRS noise level in the desired output signal is reduced by establishing the polarization of S to be perpendicular to the polarization P 2  and   (b) when the desired signal is a generated PC idler, 2−, the input signal S is applied as an inner sideband adjacent to P 2  and the SRS noise level in the idler 2− is reduced by establishing the polarization of S to be parallel to the polarization of P 2 .   
               

     According to another aspect of the invention, I describe a method of operating a two-pump optical parametric device, OPD, as an optical frequency converter, OFC, to convert an input signal at a first frequency to a desired output idler I at a second frequency having a reduced stimulated Raman scattering, SRS, noise level. The method comprising the steps of:
         (1) applying a first polarized pump, P 1 , and a second polarized pump, P 2 , to the OFC, the frequency of P 1  being lower than the frequency of P 2 ;   (2) applying a polarized input signal S as an inner sideband 1+ adjacent to P 1  or an outer sideband 2+ adjacent to P 2 ; and   (3) outputting the desired output idler I from an outer sideband 2+ adjacent to P 2  or an inner sideband 1+ adjacent to P 1 .       

     In another embodiment, I describe a two-pump optical frequency converter, OFC, for converting an input signal at a first frequency to a desired output idler at a second frequency having a reduced stimulated Raman scattering, SRS, noise level. The OFC comprises
         a first polarized coupler for coupling a first pump, P 1 , to the two-pump OFC;   a second polarized coupler for coupling a second pump, P 2 , to the two-pump OFC, wherein the frequency of P 1  is lower than the frequency of P 2 ;   a third polarized coupler for coupling an input signal S in an inner sideband 1+ adjacent to P 1  or an outer sideband 2+ adjacent to P 2 ; and   means for outputting the desired output idler, I, from an outer sideband 2+ adjacent to P 2  or an inner sideband 1+ adjacent to P 1 .       

    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Other aspects, features, and advantages of the present invention will become more fully apparent from the following detailed description, the appended claims, and the accompanying drawings in which: 
         FIG. 1  shows a two-pump OPD in accordance with one embodiment of the present invention; 
         FIG. 2  illustrates a representative frequency structure in the OPD of  FIG. 1 ; 
         FIG. 3  shows the spectral (frequency) characteristics of an input signal (S) that is simultaneously amplified and replicated within four output spectral bands. If the signal is in band 1+, the 1−, 2− and 2+ bands are referred to as idler (I) bands; 
         FIG. 4  shows an illustration of the SRS noise signals (SRS 1  and SRS 2 ) for a two pump OPA, where the two pumps P 1  and P 2 , the input signal S in band 1+, and idler I in band 2− are all parallel polarized; 
         FIG. 5  shows the input signal S in band 2− and the idler I in band 1+, reversed from the positions shown in  FIG. 4 ; 
         FIG. 6  shows the SRS 2  noise when the polarization of the input signal S in band 1+ is parallel to pump P 2 ; 
         FIG. 7  shows the SRS 2  noise when the polarization of the input signal S in band 1+ is perpendicular to pump P 2 ; 
         FIG. 8  shows the SRS 2  noise when the polarization of the input signal S in band 2− is parallel to pump P 2 ; 
         FIG. 9  shows the SRS 2  noise when the polarization of the input signal S in band 2− is perpendicular to pump P 2 ; 
         FIG. 10  shows the general frequency characteristics of the invented OPA, in which the desired output signal is in band 1+ (or 2−) and an idler is in band 2− (1+); 
         FIGS. 11A through 11C  show the decrease in n 1+  as the idler 1+ increases in frequency from the frequency of pump P 1  to the frequency of pump P 2 ; 
         FIG. 12  shows that when the pumps P 1  and P 2  are parallel and idler 1+ is perpendicular to P 1 , then n 1+  is zero and idler 2+ is perpendicular to P 1 ; 
         FIG. 13  shows that when the pump P 1  is perpendicular to pump P 2  and idler 1+ is parallel to P 1 , then n 1+  and R 2+  are zero and idler 2+ is perpendicular to P 1 ; and 
         FIG. 14  shows that when the pump P 1  is perpendicular to pump P 2  and idler 1+ is perpendicular to P 1 , then no idler 2+ is generated. 
     
    
    
     DETAILED DESCRIPTION 
       FIG. 1  shows, in accordance with one embodiment of the present invention, a two-pump OPD  100  that is configured for use in a long-haul transmission line of an optical communication system. OPA  100  is coupled between two sections  102  and  102 ′ of long-haul optical fiber. The input optical signal S from section  102  is received or coupled via polarization coupler  103  to a coupler  104  of the OPA  100 . The coupler  104  is configured to combine an input signal S from section  102  with two different pump waves generated by two pump-wave sources (e.g., lasers)  111  and  112 . The output of pump sources  111  and  112  are received or coupled via polarization couplers  113  and  114 , respectively, and are combined in coupler  115 . The combined two-pump signal P 1 +P 2  from coupler  115  is then further combined with input signal S in coupler  104 . Depending on the implementation of OPD  100 , each of the pump wave sources  111  and  112  may be a continuous-wave (CW) or pulsed optical field. The combined optical output from coupler  104  is coupled into a highly nonlinear fiber (HNF)  108 , in which the signal is amplified by FWM. Frequency shifted copies of the signal are also produced. While the present invention describes the use of HNF  108  for OPA and OFC, it should be understood that other χ (3)  media that exhibit FWM, such as Kerr media, could be used. Additionally, a three-way coupler may be used to replace couplers  104  and  115  to combine the input signal S with the two pumps P 1  and P 2 . A filter  109  is placed at the end of HNF  108  to pass the desired output optical sideband  110  (amplified signal or generated idler) and block the undesired sidebands. For example, if the desired output sideband  110  is an amplified version of input signal S from fiber  102 , then filter  109  passes that amplified signal S and filters out the pump signals P 1  and P 2 , and the one or more idlers generated in the HNF  108 . Conversely, if the desired output sideband  110  is one of the idlers, then filter  109  filters out the pump signals P 1  and P 2 , the amplified signal S from fiber  102 , and the undesired idlers generated in the HNF  108 . The desired output signal  110  is then transmitted over section  102 ′. One attractive feature of a two-pump OPD  100  is that the desired output sideband  110  can be selected to be an amplified or non-amplified, and conjugated or non-conjugated, version of input signal S at an arbitrary frequency (wavelength). In accordance with the present invention, as will be discussed in more detail in later paragraphs, the polarization of each of the couplers  103 ,  113 , and  114 , is selected to control the polarization of the input signal S, pump  111 , and pump  112 , respectively, so as to minimize SRS noise in the desired output signal  110  of OPD  100 . 
       FIG. 2  shows a simplified diagram of the output frequency structure developed in HNLF  108  of OPD  100 . In addition to two pumps labeled P 1  and P 2  and located at frequencies ω 1  and ω 2 , respectively, and a signal S (illustratively a sideband at frequency ω 1+ ), various FWM processes in HNLF  408  produce three complementary sidebands at frequencies ω 1− , ω 2− , and ω 2+ . In general, the frequency of the signal S may be at any one of the four sidebands, with the remaining three sidebands being generated by FWM processes in OPD  100 . 
     The following paragraphs describe the FWM processes in OPD  100  leading to the frequency structure of  FIG. 2 . Suppose that the optical signal S is at frequency ω 1+  and the remaining three sidebands ω 1− , ω 2− , and ω 2+  are idler sidebands. Then a modulation interaction (MI) produces the first idler sideband at frequency ω 1+ , according to the frequency-matching condition
 
2ω 1 =ω 1− +ω 1+ ,  (1)
 
a phase-conjugated (PC) process produces a second idler sideband at frequency ω 2−  according to the frequency-matching condition
 
ω 1 +ω 2 =ω 1+ +ω 2− ,  (2)
 
and a Bragg scattering (BS), or frequency converter (FC), process produces a third idler sideband at frequency ω 2+  according to the frequency-matching condition
 
ω 1+ +ω 2 =ω 1 +ω 2+ .  (3)
 
In addition, each of the three idler sidebands is coupled to the other two idler sidebands by an appropriate FWM process, i.e., MI, BS, or PC, which obeys an equation analogous to Eq. (1), (2) or (3).
 
     In addition to the sidebands illustrated in  FIG. 2 , OPD  100  may also generate several additional sidebands (not shown). For example, MI with P 2  generates additional sidebands with frequencies 2ω 2 −ω 1−  and 2ω 2 −ω 1+  and MI with P 1  generates additional sidebands with frequencies 2ω 1 −ω 2−  and 2ω 1 −ω 2+ . However, unlike the four original sidebands shown in  FIG. 2 , each of which is coupled to all of the other three, none of the additional sidebands is coupled to all of the original four or all of the other three additional sidebands. Furthermore, for most values of ω 1+ , the additional sidebands are driven non-resonantly. Consequently, the effects of the additional sidebands on the operation of OPD  100  are not considered further. 
     Since OPD  100  relies on FWM enabled by the Kerr effect to amplify and generate sidebands, the first and second pumps (P 1  and P 2 ) are not required to be applied to HNF  108  in a prescribed order; ω 1  and ω 2  are not required to be derived based on or have a specific relationship with the specific energy-level transitions of the material of the HNF  108 ; and neither pump power is required to exceed the level that produces electromagnetically induced transparency (EIT) in HNF  108 . 
     With reference to  FIG. 3 , there are shown illustrative frequency characteristics of a modulated input signal S, in band 1+, that is simultaneously amplified and replicated within four spectral bands 1−, 1+, 2− and 2+. The generated idlers are either spectrally-mirrored images of the modulated input signal S (idler bands 1− and 2−) or a translated (frequency-shifted) replica (idler band 2+). The spectrally-mirrored idlers are PCs, which offer the potential for mitigating impairments. The four signal bands produced by two-pump OPD  100  allow for considerable flexibility in selecting the properties of the desired output signal or idler. An inner band placement of input signal S (i.e., in bands 1+ and 2− located between the pumps P 1  and P 2 ) generates both an outer band nonPC (replica) and PCs located in the inner and outer bands. Thus, as shown in  FIG. 3 , an input signal S in band 1+ produces a nonPC in band 2+ and PCs in both inner band 2− and outer band 1−. An outer band placement of input signal S (i.e., in bands 1− and 2+) generates both an inner band nonPC (replica) and PCs located in the inner and outer bands. The existence of multiple bands depends on the presence of both pumps P 1  and P 2 . The frequency of pumps P 1  and P 2  can be tuned in ways such that the signals and idlers in all four bands are strongly coupled, the signal and idler in bands 1+ and 2− are strongly coupled (OPA enabled by PC), or the signal and idler in bands 1+ and 2+ are strongly coupled (OFC enabled by BS). 
     Consider OPA enabled by phase-conjugated (PC) process. In this process γ 1 +γ 2 →γ 1+ +γ 2− : Two pump photons (γ) are destroyed (one from each pump), and one signal and one idler photon are created. OPA is characterized by the input-output relations
 
 A   1+ ( z )=μ( z ) A   1+ (0)+ν( z ) A   2− (0)*,  (4)
 
 A   2− ( z )*=ν( z )* A   1+ (0)+μ( z )* A   2− (0)*,  (5)
 
where A 1+  and A 2−  are the amplitudes of the 1+ and 2− sidebands, respectively, and the transfer functions satisfy the auxiliary equation |μ| 2 −|ν| 2 =1 [C. J. McKinstrie, S. Radic and M. G. Raymer, “Quantum noise properties of parametric amplifiers driven by two pump waves,” Opt. Express 12, 5037-5066 (2004), hereafter referred to as MRR]. One can model the effects of SRS noise (approximately) by adding random (and independent) amplitude fluctuations δa to each of the input amplitudes. Because ω 1+  and ω 2−  are both less than ω 2 , δa 1+  and δa 2−  are both nonzero (unless 1+ or 2− is perpendicular to P 2 ). If the input consists solely of noise, the outputs
 
 R   1+ ( z )=| A   1+ ( z )| 2 =|μ( z )| 2   |δa   1+ | 2 +|ν( z )| 2   |δa   2− | 2 =|μ( z )| 2   n   1+ +|ν( z )| 2   n   2− ,  (6)
 
 R   2− ( z )=| A   2− ( z )| 2 =|ν( z )| 2   |δa   1+ | 2 +|μ( z )| 2   |δa   2− | 2 =|ν( z )| 2   n   1+ +|μ( z )| 2   n   2− ,  (7)
 
where n 1+  and n 2−  are the input noise powers, and R 1+  and R 2−  are the output noise powers, respectively. The SRS noise photons at ω +  are amplified by FWM, which also couples the noise photons at ω 2−  to the output at ω 1+ . A similar statement can be made about the output at ω 2− . These equations imply that R 1+ −R 2− =n 1+ −n 2−&gt; 0 (unless 1+ is perpendicular to P 2 ). The gain G=|μ| 2 . The auxiliary equation implies that |ν| 2 =G−1. In the high-gain regime (G&gt;&gt;1), |ν| 2 ≈|μ| 2 , and R 1+ ≈R 2− ≈G(n 1+ +n 2− ). Thus, as a general rule, one can minimize the noise in both outputs by setting 1+ perpendicular to P 2 , in which case n 1+ =0 [R. H. Stolen, “Polarization effects in fiber Raman and Brillouin lasers,” IEEE J. Quantum. Electron. 15, 1157-1160 (1979), hereafter referred to as RHS].
 
     With reference to  FIG. 4 , there is shown an illustration of the resulting SRS noise fields SRS 1  and SRS 2  for a two-pump OPA  100 , where the two pumps P 1  and P 2 , input signal S (sideband 1+) and idler II (sideband 2−) are all parallel polarized. As shown, the SRS 1  noise field lies in the same plane as the pump P 1  and the SRS 2  noise field lies in the same plane as the pump P 2 . Since pumps P 1  and P 2  are parallel (i.e., both are shown vertically polarized) SRS 1  and SRS 2  are in the same plane. Note that the amplitudes of the SRS 1  and SRS 2  noise fields increase to a well-defined peak values with increasing frequency separation from pumps P 1  and P 2 , respectively. (For example, if the wavelength of pump P 2  is 1440 nm, then SRS 2  peaks at about 110 nm from the pump wavelength, at about 1550 nm.) Notice that in the example of  FIG. 4 , since the frequencies of the input signal S and idler I lie between the frequencies of pumps P 1  and P 2 , the SRS 1  noise field has no direct effect on these signals. Thus, since it is only the SRS 2  noise field that affects directly the desired output signal or idler  110  of OPA  100 , the effects of the SRS 1  noise field will not be considered further. It follows from Eqs. (6) and (7) that R 1+ =Gn 1+ +(G−1)n 2−  and R 2− =(G−1)n 1+ +Gn 2− . Because noise photons at both input frequencies are coupled to both outputs, the output noise powers of the sidebands are comparable. However, R 2 − is slightly lower than R 1 +, as stated above. In this configuration, the idler is the desired output. 
     With reference to  FIG. 5 , there is shown the input signal S (in band 2−) and idler I (in band 1+) reversed from the positions shown in  FIG. 4 . Once again, it follows from Eqs. (6) and (7) that R 1+ =Gn 1+ +(G−1)n 2  and R 2− =(G−1)n 1+ +Gn 2− . Because noise photons at both input frequencies are coupled to both outputs, the output noise powers of the sidebands are comparable. However, R 2 − is slightly lower than R 1 +, as stated above. In this configuration, the signal is the desired output. 
     In accordance with the present invention, I have recognized that the SRS growth rate g R , and the amplified noise field that results, is polarization dependent. As stated in [RHS], the SRS growth rate of a signal that is perpendicular to the pump is an order-of-magnitude lower that the growth rate of a signal that is parallel to the pump. Since the output amplitude A(z)=A(0)exp(g R z), an order-of-magnitude difference in the gain exponent g R z causes a many-orders-of magnitude difference in the gain exp(g R z) and, hence, in the output amplitude A(z): For practical purposes, the SRS noise field that is perpendicular to pump  2  can be neglected. Hence, in  FIGS. 6-9  the noise field SRS 2  is drawn parallel to pump  2 . 
     In  FIGS. 6-9  and the discussion that follows, two signals are said to be parallel if both signals are vertical or both signals are horizontal. Similarly, two signals are said to be perpendicular (orthogonal) if one signal is vertical and the other is horizontal, or vice-versa. The concept of orthogonality is not limited to the linearly-polarized states illustrated in the figures. For example, right-circularly-polarized and left-circularly-polarized states are also orthogonal, even though neither state is linearly polarized [C. J. McKinstrie, H. Kogelnik, R. M. Jopson, S. Radic and A. V. Kanaev, “Four-wave mixing in fibers with random birefringence,” Opt. Express 12, 2033-2055 (2004), hereafter referred to as MKJRK]. Although these figures were drawn for linearly-polarized states (horizontal and vertical), they also represent more-general polarization states that are parallel or orthogonal.  FIG. 6  shows the input signal S in band 1+ polarized in direction X and the idler I in band 2− polarized in direction Y.  FIG. 7  shows the input signal S in band 1+ polarized in direction Y and the idler I in band 2− polarized in direction X.  FIG. 8  shows the input signal S in band 2− polarized in direction X and the idler I in band 1+ polarized in direction Y.  FIG. 9  shows the input signal S in band 2− polarized in direction Y and the idler I in band 1+ polarized in direction X. In  FIGS. 6-9  the polarization of the generated idler I is perpendicular to the polarization of the input signal S [see reference MKJRK], regardless of whether the idler frequency is higher or lower than the signal frequency. In addition, the pumps P 1  and P 2  are perpendicular. (If pumps P 1  and P 2  were parallel, a perpendicular input signal S would not generate an idler [MKJRK]. This configuration is not useful.) The parametric gain produced by FWM is polarization-independent [MKJRK]: It is the same regardless of whether the input signal S is parallel or perpendicular to pump P 1  (or P 2 ). For the configuration shown in  FIG. 6 , R 1+ =Gn 1+  and R 2− =(G−1)n 1+ . The output idler (2−) has slightly less noise than the output signal (1+), but both are noisy. For the configuration shown in  FIG. 7 , R 1+ =(G−1)n 2−  and R 2− =Gn 2− . The output signal (1+) has slightly less noise than the output idler (2−), but neither is noisy. If the desired output is the 1+ signal, the second configuration is better (because G−1&lt;G and n 2− &lt;&lt;n 1+ ). If the desired output is the 2− idler, the second configuration is better (because G−1≈G and n 2− &lt;&lt;n 1+ ). 
     For the configuration shown in  FIG. 8 , R 1+ =(G−1)n 2−  and R 2− =Gn 2− . The output idler (1+) has slightly less noise than the output signal (2−), but neither is noisy. For the configuration shown in  FIG. 9 , R 1+ =Gn 1+  and R 2− =(G−1)n 1+ . The output signal (2−) has slightly less noise than the output idler (1+), but both are noisy. If the desired output is the 2− signal, the first configuration is better (because G−1≈G and n 2− &lt;&lt;n 1+ ). If the desired output is the 1+ idler, the first configuration is better (because G−1&lt;G and n 2− &lt;&lt;n 1+ ). 
     It follows from the analyses of  FIGS. 6-9  that, if OPA  100  is to be operated as a low-noise device, the higher-frequency sideband should be parallel to pump  2  (so the noise source is n2−). In this case the lower-frequency sideband has slightly less noise, but neither sideband is noisy. This optimal configuration is illustrated in  FIG. 10 . 
     Now consider OFC enabled by BS. In this process γ 1+ +γ 2 →γ 1 +γ 2+ : One pump and one signal photon are destroyed and one pump and one idler photon are created. OFC is characterized by the input-output relations
 
 A   1+ ( z )=μ( z ) A   1+ (0)+ν( z ) A   2+ (0),  (8)
 
 A   2+ ( z )=−ν*( z ) A   1+ (0)+μ( z )* A   2+ (0),  (9)
 
where the transfer functions satisfy the auxiliary equation |μ| 2 +|ν| 2 =1 [MRR]. As before, consider the effects of SRS noise, which are modeled (approximately) as random amplitude fluctuations δa added to the input amplitudes. Because ω 2+ &gt;ω 2 , δa 2+ =0. It follows from this fact that, if the input consists solely of noise,
 
 R   1+ ( z )=| A   1+ ( z )| 2 =|μ( z )| 2   |δa   1+ | 2 =|μ( z )| 2   n   1+ ,  (10)
 
 R   2+ ( z )=| A   2+ ( z )| 2 =|ν( z )| 2   |δa   1+ | 2 =|ν( z )| 2   n   1+ ,  (11)
 
where R 2+  is the output SRS noise power at frequency ω 2+ .
 
     First, suppose that 1+ is the signal and 2+ is the idler. Then the output noise R 2+ =|ν| 2 n 1+ . Because the 2+ idler is desired (A 2+ =−ν*A 1+ ), in a typical experiment |ν| 2 ≈1 and, hence, |μ| 2 ≈0. If the pumps are parallel and 1+ is parallel to P 1 , then R 2+  is always nonzero. As ω 1+  increases from ω 1  to ω 2 , n 1+  decreases, as illustrated in  FIG. 11 . If the pumps are parallel and 1+ is perpendicular to P 1 , as illustrated in  FIG. 12 , then n 1+ =0, 2+ is generated perpendicular to P 1  [see MKJRK] and R 2+ =0: SRS noise is eliminated completely. If P 1  and P 2  are perpendicular and 1+ is parallel to P 1  (perpendicular to P 2 ), as illustrated in  FIG. 13 , then n 1+ =0, 2+ is generated perpendicular to P 1  (parallel to P 2 ) [MKJRK] and R 2+ =0: SRS noise is eliminated completely. If P 1  and P 2  are perpendicular and 1+ is perpendicular to P 1  (parallel to P 2 ), as illustrated in  FIG. 14 , no 2+ idler is generated [MKJRK]. 
     Second, suppose that 2+ is the signal and 1+ is the idler. Then the output noise R 1+ =|μ| 2 n 1+ . Because the 1+ idler is desired (A 1+ =νA 2+ ), in a typical experiment |ν| 2 ≈1 and, hence, |μ| 2 ≈0: Most SRS noise photons at ω 1+  are frequency shifted to ω 2+ . Few remain at ω 1+  to pollute the idler. SRS noise is eliminated completely if the pumps are parallel and 2+ is perpendicular to P 2 , in which case 1+ is generated perpendicular to P 2  [MKJRK], or if the pumps are perpendicular and 2+ is parallel to P 2  (perpendicular to P 1 ), in which case 1+ is parallel to P 1  (perpendicular to P 2 ) [MKJRK]. If the pumps are perpendicular and 2+ is perpendicular to P 2  (parallel to P 1 ), no 1+ idler is generated [MKJRK]. 
     It follows from the analyses of  FIGS. 11-14  that, if OFC  100  is to be operated as a low-noise device, the lower-frequency sideband should be perpendicular to pump  2  (so the noise source is zero). In this case neither sideband has noise. These optimal configurations were illustrated in  FIGS. 12 and 13 . 
     Various modifications of the described embodiments, as well as other embodiments of the inventions (OPAs and OFCs), which are apparent to persons skilled in the art to which the inventions pertain, are deemed to lie within the principle and scope of the inventions as expressed in the following claims. 
     Although the steps 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 steps, those steps are not necessarily intended to be limited to being implemented in that particular sequence.