Patent Publication Number: US-2004042060-A1

Title: Parametric amplification using two pump waves

Description:
BACKGROUND OF THE INVENTION  
       [0001] 1. Field of the Invention  
       [0002] The present invention relates to optical communication equipment.  
       [0003] 2. Description of the Related Art  
       [0004] 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 optical communication system is an optical parametric amplifier (OPA). As known in the art, an OPA is a device that produces a tunable coherent optical output via nonlinear optical processes, in which, typically, one or two pump-wave photons are converted into two new photons with conservation of photon energy and momentum. The waves corresponding to the two new photons are usually referred to as a signal and an idler. In an OPA, noise levels at the input and the output are substantially equivalent and the idler is a phase conjugate of the signal.  
       [0005]FIG. 1 shows a representative OPA  100  of the prior art 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 a long-haul optical fiber. OPA  100  has a coupler  104  configured to combine an optical communication signal from section  102  with a pump wave generated by a pump-wave source  106  (e.g., a laser). Depending on the implementation of OPA  100 , the pump wave may be a continuous-wave (CW) or pulsed optical signal. The combined signal is directed into a highly nonlinear fiber (HNLF)  108 , where the optical communication signal is amplified by way of parametric amplification. A filter  110  placed at the end of HNLF  108  separates the amplified optical communication signal (e.g., from the pump wave and an idler signal generated in HNLF  108 ) for further transmission in the communication system via section  102 .  
       [0006] One attractive feature of OPA  100  is that it can be designed to provide signal amplification at arbitrary wavelengths. In addition, OPA  100  can be configured to conjugate signals and/or change their wavelengths. However, one problem with OPA  100  is that the spectral width of its gain band may be relatively narrow. Also, the spectral shape of that band is typically not flat. One additional problem is that the intensity of the pump wave and therefore the gain in OPA  100  are limited by Brillouin scattering. These problems impede the use of OPAs in optical communication systems.  
       SUMMARY OF THE INVENTION  
       [0007] Certain embodiments of the present invention provide an optical parametric amplifier (OPA) driven with at least two pump waves. The pump waves may be configured such that the OPA produces uniform exponential gain over a range of wavelengths that extends, for example, at least  30  nm on either side of the average pump-wave wavelength. In addition, since the Brillouin scattering limit applies to each pump wave independently, substantially twice the amount of energy may be pumped into an OPA of the present invention compared to that in the corresponding single pump wave OPA of the prior art. An OPA of the present invention may be used in a WDM communication system and configured for simultaneous signal amplification and wavelength conversion.  
       [0008] According to one embodiment, the present invention is a device comprising a nonlinear optical medium and configured to apply an input optical signal and at least two pump waves comprising a first pump wave and a second pump wave, to the nonlinear optical medium; and to generate an amplified optical signal corresponding to the input optical signal by way of optical parametric amplification.  
       [0009] According to another embodiment, the present invention is a method of amplifying an input optical signal, comprising the steps of: (a) applying the input optical signal and at least two pump waves comprising a first pump wave and a second pump wave, to a nonlinear optical medium; and (b) generating an amplified optical signal corresponding to the input optical signal by way of optical parametric amplification.  
       [0010] According to yet another embodiment, the present invention is an optical amplifier for converting an input signal into an amplified output signal, comprising: (a) at least two optical pumps, each configured to generate a pump wave; and (b) one or more combiners configured to apply the two or more pump waves and the input signal to a nonlinear optical medium, wherein the input signal is parametrically amplified in the nonlinear optical medium. 
     
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
     [0011] 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:  
     [0012]FIG. 1 shows a representative optical parametric amplifier (OPA) of the prior art as part of a long-haul transmission line in an optical communication system;  
     [0013]FIG. 2 illustrates the process of parametric amplification in the OPA of FIG. 1;  
     [0014]FIG. 3 illustrates the gain bands in the OPA of FIG. 1 as a function of the pump wave wavelength;  
     [0015]FIG. 4 shows an OPA according to one embodiment of the present invention;  
     [0016]FIG. 5 illustrates a representative frequency structure in the OPA of FIG. 4;  
     [0017]FIG. 6 illustrates generation of secondary pump waves in one configuration of the OPA of FIG. 4 via the pump-to-pump interaction;  
     [0018] FIGS.  7 A-B illustrate the behavior of the OPA of FIG. 4 driven by relatively widely-spaced pump waves;  
     [0019] FIGS.  8 A-D illustrate the effect of fiber properties and pump waves configuration on the operation of the OPA of FIG. 4;  
     [0020]FIG. 9 illustrates how the spectral characteristics of the OPA of FIG. 4 may be changed by tuning the frequencies of pump waves;  
     [0021]FIG. 10 illustrates how the gain level of the OPA of FIG. 4 is affected by the intensities of pump waves; and  
     [0022] FIGS.  11 A-B illustrate simultaneous amplification and wavelength conversion of a wavelength-division-multiplexed (WDM) optical communication signal using the OPA of FIG. 4. 
    
    
     DETAILED DESCRIPTION  
     [0023] 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 mutually exclusive of other embodiments.  
     [0024] Before embodiments of the present invention are described in detail, different factors affecting the performance of prior art OPA  100  of FIG. 1 are briefly characterized.  
     [0025]FIG. 2 illustrates the process of parametric amplification in OPA  100 . Signal amplification in OPA  100  is governed by a degenerate four-wave mixing (FWM) process, in which two pump photons (labeled P in FIG. 2) combine to generate one signal photon and one idler photon (labeled s and i, respectively, in FIG. 2) according to the following equation:  
     2ω P =ω s +ω i    (1)  
     [0026] where ω P , ω s , and ω i , are the frequencies of the pump, signal, and idler photons, respectively. The nonlinear medium, in which the FWM process occurs (e.g., HNLF  108 ), is characterized by a nonlinearity coefficient (γ) and a set of dispersion coefficients. Of significance for this analysis are the second-, third-, and fourth-order dispersion coefficients (β 2 , β 3 , and β 4 , respectively), each of which is frequency dependent. The frequency or wavelength at which β 2 =0 is referred to as the zero-dispersion frequency (ω 0 ) or wavelength (λ 0 ). The regions in which β 2  is positive and negative are referred to as the normal dispersion region and the anomalous dispersion region, respectively.  
     [0027]FIG. 3 illustrates representative gain bands in OPA  100  as a function of the pump wave wavelength. For the degenerate FWM process to occur, the wavelength of the pump wave must be in the anomalous dispersion region of HNLF  108 . For example, when the wavelength of the pump wave is just inside the normal dispersion region, as for the pump wave labeled P n  in FIG. 3, there is substantially no parametric gain, as can be seen from the corresponding gain curve labeled  302 . On the other hand, when the wavelength of the pump wave is in the anomalous dispersion region, as for the pump waves labeled P a1  and P a2  in FIG. 3, the corresponding parametric gain bands develop, as can be seen from gain curves  304  and  306 , respectively. However, the farther the pump wave wavelength is from the zero-dispersion wavelength, the narrower the corresponding gain bands become, as can be seen from the comparison of curves  304  and  306  in FIG. 3.  
     [0028] It is known in the art that the gain of OPA  100  depends on the intensity of the pump wave (I p ) and the length of HNLF  108 . Depending on the relationship between the wave-vector mismatch coefficient (κ) in HNLF  108 , γ, and I p , OPA  100  can produce either exponential or quadratic gain (each determined by the functional dependence of gain on the length of HNLF  108 ). For example, if the intensity of the pump wave is chosen such that κ=−γI p , then the gain is relatively high and exponential. In contrast, if OPA  100  is designed such that κ=0, then the gain is quadratic. Other values of κ will correspond to a relatively low exponential gain.  
     [0029]FIG. 4 shows an OPA  400  according to one embodiment of the present invention. OPA  400  is similar to OPA  100  of FIG. 1. In particular, in FIG. 4, the components in OPA  400  analogous to those in OPA  100  are illustrated using labels having the same last two digits. However, one difference between OPA  400  and OPA  100  is that two different pump waves generated by two pump-wave sources  406  and  406  are used in OPA  400  to amplify an optical communication signal instead of one pump wave in OPA  100 . The two pump waves are combined together using coupler  404  and further combined with the optical communication signal using coupler  404 . Alternatively, a three way coupler may be used to combine the optical communication signal with the pump waves. Filter  410  extracts the amplified optical communication signal for transmission in the communication system.  
     [0030]FIG. 5 shows a simplified diagram of the frequency structure developed in HNLF  408  of OPA  400 . In addition to two pump waves labeled P 1  and P 2  and located at frequencies ω 1  and ω 2 , respectively, and an optical communication signal (illustratively a sideband at frequency ω 1− ), there are three complementary sidebands at frequencies ω 1+ , ω 2− , and ω 2+  generated by OPA  400 . In general, the optical communication signal may correspond to any one of the four sidebands, with the remaining three sidebands being generated by OPA  400 .  
     [0031] The following describes nonlinear optical processes in OPA  400  leading to the frequency structure of FIG. 5. Assuming that the optical communication signal is at frequency ω 1−  and the remaining three sidebands are idler sidebands, the modulational interaction (MI) produces a first idler sideband at frequency ω 1+  according to Equation (2) as follows:  
     2ω 1 =ω 1− +ω 1 +   (2)  
     [0032] a Bragg scattering (BS) process produces a second idler sideband at frequency ω 2−  according to Equation (3) as follows:  
     ω 1− +ω 2 =ω 2− +ω 1    (3)  
     [0033] and a phase-conjugation (PC) process produces a third idler sideband at frequency ω 2+  according to Equation (4) as follows:  
     ω 1 +ω 2 =ω 2+ +ω 1−   (4)  
     [0034] 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, that can be expressed by an equation analogous to Equations (2), (3), or (4).  
     [0035] In addition to the sidebands illustrated in FIG. 5, OPA  400  may also generate several additional sidebands (not shown). For example, MI with P 2  generates an additional sideband at frequency 2ω 2 −ω 1 +δω, where δω=ω 1 −ω 1− . Also, a BS process with respect to P 1  generates another sideband at frequency 2ω 1 −ω 2 −δω. Similarly, the sidebands at frequencies ω 1+  and ω 2−  are each coupled to additional sidebands at frequencies 2ω 2 −ω 1 −δω and 2ω 1 −ω 2 +δω, and the sideband at frequency ω 2+  is coupled to the aforementioned additional sidebands with frequencies 2ω 2 −ω 1 +δω and 2ω 1 −ω 2 −δω. However, unlike the four original sidebands shown in FIG. 5, each of which is coupled to each 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 δω, the additional sidebands are driven non-resonantly. Consequently, effects of the additional sidebands on the operation of OPA  400  are not considered here. Numerical simulations validate this omission.  
     [0036]FIG. 6 illustrates a process of secondary pump wave generation in OPA  400  via pump-to-pump FWM interaction. More specifically, FIG. 6 shows a representative frequency structure developed in HNLF  408  of OPA  400  when two pump waves are co-polarized and relatively closely spaced (e.g., have a separation of |ω 2 −ω 1 |δ8 THz or |λ 2 −λ 1 |δ 10 nm). In particular, for the case shown in FIG. 6, ω 2 =−2.3 THz and ω 2 =1.5 THz, where the frequencies are given relative to the zero-dispersion frequency in HNLF  408 . As demonstrated by FIG. 6, the pump-to-pump FWM process leads to a progression of secondary pump waves separated from each other by 3.8 THz (=ω 2 −ω 1 ). In addition, the intensities (I i ) of the two original pump waves (P 1  and P 2  in FIG. 6) are altered from the initial input levels such that I 1  and I 2  are decreased by different amounts.  
     [0037] The background curve labeled  602  in FIG. 6 corresponds to the interaction of pump waves in OPA  400  with broad-bandwidth noise. In the presence of an optical communication signal in OPA  400 , background curve  602  would also correspond to the gain curve in OPA  400  for that particular OPA configuration. As can be seen in FIG. 6, on average, the gain level would be about 10-15 dB. However, generation of secondary pump waves is detrimental to the gain level produced by OPA  400  because the energy used for that process reduces the energy available for the intended signal amplification process. Also, various additional sidebands generated due to the complex secondary pump-wave frequency structure may interfere with the optical communication signal and/or its idlers. One possible way of overcoming these impediments is to use differently (e.g., orthogonally) polarized pump waves. A model that ignores the generation of secondary pump waves in the OPA configuration illustrated by FIG. 6 indicates that the gain level may be substantially increased.  
     [0038] FIGS.  7 A-B illustrate another way of reducing secondary pump wave generation and, also, a way of removing the generated secondary-pump frequencies from the ranges of signal and idler frequencies. More specifically, FIGS.  7 A-B show the behavior of OPA  400  when two pump waves have a relatively wide separation (e.g., corresponding to |ω 2 −ω 1 |&gt;8 THz or |λ 2 −λ 1 |&gt;10 nm). In particular, for the case shown in FIGS.  7 A-B, λ 1 =1568.7 nm and λ 2 =1600.0 nm, and the zero-dispersion wavelength in HNLF  408  is 1585.0 nm. FIG. 7A shows the OPA behavior in the spectral region between 1500 and 1670 nm and FIG. 7B is an expanded view of the data shown in FIG. 7A in the spectral region between 1560 and 1610 nm.  
     [0039]FIG. 7A shows that, in the case of widely spaced pump waves (P 1  and P 2  in FIG. 7A), the secondary pump waves (P 4− , P 3− , P 3+ , and P 4+  in FIG. 7A) have relatively low intensities. More specifically, with respect to P 1  and P 2 , the intensities of P 4− , P 3− , P 3+ , and P 4+  are approximately −52 dB, −27 dB, −22 dB, and −47 dB, respectively. Consequently, the problems indicated above for the OPA configuration corresponding to FIG. 6 do not significantly affect the operation of OPA  400  configured according to FIG. 7.  
     [0040] Referring now to FIG. 7B, curve  702  is the gain curve of OPA  400  when P 2  is blocked and only P 1  is present. In agreement with the results of FIG. 3 (curve  302 ), curve  702  indicates no gain (because λ 1  is in the normal dispersion region of HNLF  408 ). Similarly, curve  704 , which is the gain curve of OPA  400  when P 1  is blocked and only P 2  is present, indicates the presence of a relatively narrow gain band that is analogous to, e.g., curve  306  in FIG. 3. Finally, curve  706  is the gain curve of OPA  400  when both pump waves, P 1  and P 2 , are present. The comparison of curves  704  and  706  indicates that an OPA driven with two pump waves produces a higher gain level than the corresponding OPA driven by a single pump wave. In addition, the available spectral bandwidth is significantly wider than that achieved in the single pump-wave OPA. Also, the spectral gain profile is relatively flat.  
     [0041] Similar to OPA  100 , the gain in OPA  400  depends on the intensity of the pump waves and the length of HNLF  408 . However, in OPA  400 , the gain remains exponential even when κ=0. Furthermore, since the Brillouin scattering limit applies to each pump wave independently, substantially twice the amount of energy may be pumped into OPA  400  compared to that in OPA  100  possibly resulting in further gain increase.  
     [0042] FIGS.  8 A-D illustrate the effects of fiber (i.e., HNLF  408 ) properties and configuration of pump waves on the operation of OPA  400 . In particular, FIG. 8A shows the gain curve for an OPA configuration in which: β 3 =0.12 ps 3 /km; β 4 =0; ω 1 =−30 THz; and ω 2 =30 THz, where the pump-wave frequencies are measured with respect to the zero-dispersion frequency in HNLF  408  and the values of dispersion coefficients are given at the average pump-wave frequency (defined as ω a =(ω 1 +ω 2 )/2). As can be seen in FIG. 8A, this configuration produces a gain level of about 30 dB for optical communication signals with frequencies, e.g., between −25 and 0 THz. Similarly, FIG. 8B shows that a comparable gain level is obtained using the configuration of FIG. 8A for optical communication signals whose frequencies are, e.g., below −35 THz.  
     [0043]FIG. 8C illustrates possible behavior of OPA  400  when β 4 ≠0. In particular, FIG. 8C shows the gain curve for the OPA configuration in which all the parameters are the same as for FIG. 8B, except that β 4 =2.5×10 −4  ps 4 /km. The results of FIG. 8C indicate that the parametric gain (e.g., characterized by the available gain level and bandwidth) may be adversely affected by the effects of fourth-order dispersion.  
     [0044]FIG. 8D illustrates that the effects of fourth-order dispersion may be partially offset, e.g., by detuning one of the pump waves from the symmetrical configuration of FIGS.  8 A-C. In particular, FIG. 8D shows the gain curve for the configuration in which all the parameters are the same as for FIG. 8C, except that ω 1 =−31.4 THz instead of −30 THz. As seen in FIG. 8D, this particular configuration produces a gain level of about 35 dB for optical communication signals with frequencies, e.g., between −55 and −35 THz.  
     [0045]FIG. 9 illustrates how the spectral gain profile of OPA  400  may be varied by tuning the frequencies of pump waves. For example, curve  902  is the gain curve of OPA  400  in which λ 1 =1553.9 nm and λ 2 =1598.8 nm. As seen in FIG. 9, this configuration exhibits a region of low gain between about 1563 and 1588 nm. However, when the pump waves are tuned to λ 2 ′=1560.9 nm and λ 2 ′=1592.8 nm, respectively, a relatively high gain level is obtained in that region as shown by curve  904 .  
     [0046]FIG. 10 illustrates how the gain of OPA  400  is affected by the intensities of pump waves. More specifically, curves  1002 ,  1004 , and  1006  in FIG. 10 are the gain curves corresponding to different pump-wave intensities in OPA  400  in which λ 1 =1568.9 nm and λ 2 =1598.8 nm. Curve  1002  corresponds to I 1 =189 mW and I 2 =85 mW; curve  1004  corresponds to I 1 =220 mW and I 2 =107 mW; and curve  1006  corresponds to I 1 =380 mW and I 2 =178 mW. The results of FIG. 10 indicate that the performance of OPA  400  is characterized by gain equalization over a wide wavelength range even when the OPA is driven by pump waves whose intensities are substantially different. As a result, OPA  400  may be configured for applications previously considered impractical with prior art OPAs as further described below.  
     [0047] FIGS.  11 A-B illustrate simultaneous amplification and wavelength conversion (mirroring) of a wavelength-division-multiplexed (WDM) optical communication signal using OPA  400 . More specifically, FIGS. 11A and 11B illustrate wavelength up- and down-conversion, respectively. In particular, a representative WDM signal  1102  shown in FIG. 11A comprises six WDM components (channels) labeled  1  through  6 . An amplified signal  1104 , also shown in FIG. 11A, includes the corresponding amplified components  1  through  6 . However, in addition to those components, signal  1104  also includes the amplified red-shifted components labeled  1  through  6  . The primed components are idlers of the corresponding unprimed components and therefore carry the same information. Consequently, one or more of the primed components may be used to generate a new WDM signal corresponding to signal  1102  and employing a different set of wavelengths. For example, the new WDM signal carrying the same information as signal  1102  may have the following components:  1 ,  2 ,  3 ,  4 ,  5 , and  6 . Similarly, FIG. 11B illustrates the generation of the blue-shifted primed components labeled  7  through  12  in an amplified signal  1108 , which correspond to components  7  through  12 , respectively, of a WDM signal  1106 . Consequently, one or more of those primed components may also be used to generate a new WDM signal corresponding to signal  1106  and having a different set of wavelengths.  
     [0048] While this invention has been described with reference to illustrative embodiments, this description is not intended to be construed in a limiting sense. For example, in different OPA implementations, optical fibers having different properties (e.g., β 2 , β 3 , and β 4 ) may be used. Also, an OPA may be configured such that the average pump-wave frequency (ω 1 ) is either in the anomalous dispersion region or the normal dispersion region, or corresponds to the zero-dispersion frequency (ω 0 ) In addition, both pump waves may be in the anomalous dispersion region. Although, the representative OPA configurations described in this specification have a pump-wave separation of up to about 75 nm (or 60 THz), configurations with separations of up to about 150 nm were successfully implemented, and even higher pump-wave separations may be used. The pump waves may be CW or pulsed. Two or more pump waves may be used. The frequencies of the pump waves may be chosen such that (i) one frequency falls within the normal dispersion region and one frequency falls within the anomalous dispersion region; or (ii) two frequencies fall within the anomalous dispersion region. Idler components may be filtered out or used in the communication system, e.g., as a protection signal in a 1+1 protection scheme. Pump-wave frequencies may be dithered, as known in the art, to reduce the effects of Brillouin scattering. Furthermore, the two pump waves may be dithered such that the average frequency remains constant, e.g., as disclosed in U.S. Pat. No. 5,386,314, the teachings of which are incorporated herein by reference. As a result, idler frequencies will not be time-dependent and the corresponding idler bands will not be broadened. This is advantageously different from an OPA driven by a single pump wave, in which the pump-wave dithering causes the idler frequencies to be time-dependent and the corresponding idler bands to be broadened. 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.  
     [0049] 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.