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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 13, Iss. 26 — Dec. 26, 2005
  • pp: 10483–10493
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Gain characteristics of a frequency nondegenerate phase-sensitive fiber-optic parametric amplifier with phase self-stabilized input

Renyong Tang, Jacob Lasri, Preetpaul S. Devgan, Vladimir Grigoryan, Prem Kumar, and Michael Vasilyev  »View Author Affiliations


Optics Express, Vol. 13, Issue 26, pp. 10483-10493 (2005)
http://dx.doi.org/10.1364/OPEX.13.010483


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Abstract

We experimentally demonstrate, for the first time to our knowledge, a phase-sensitive amplifier based on frequency nondegenerate parametric amplification in optical fiber, where the input signal-idler pair is prepared all-optically. Using two fiber-optic parametric amplifier sections separated by a fiber-based wavelength-dependent phase shifter, we observe and investigate phase-sensitive gain profile in the 1550 nm region both experimentally and theoretically. The realized scheme automatically generates gain-defining phase that is environmentally stable, making it advantageous for building phase-sensitive transmission links.

© 2005 Optical Society of America

1. Introduction

Optical amplifiers are used to boost the signal power which decays due to distributed propagation loss as well as lumped losses in lightwave systems. Commonly used amplifiers, such as erbium-doped-fiber amplifiers (EDFAs), semiconductor optical amplifiers, or Raman amplifiers, belong to the category of phase-insensitive amplifiers (PIAs), i.e., their gain does not depend on the optical phase of the input signal. On the other hand, fiber-optic parametric amplifiers (FOPAs) utilizing the χ (3) nonlinear Kerr effect, can be used as either phase-insensitive or phase-sensitive amplifiers, depending on the configuration of the FOPA. The phase-sensitive amplifier (PSA) only amplifies the in-phase component of the signal, while attenuating the quadrature component [1

1 . C. M. Caves , “ Quantum limits on noise in linear amplifiers ,” Phys. Rev. D 26 , 1817 – 1839 ( 1982 ). [CrossRef]

, 2

2 . H. P. Yuen , “ Design of transparent optical networks using novel quantum amplifiers and sources ,” Opt. Lett. 12 , 789 – 791 ( 1987 ). [CrossRef] [PubMed]

, 3

3 . H. P. Yuen , “ Reduction of quantum fluctuation and suppression of the Gordon-Haus effect with phase-sensitive linear amplifiers ,” Opt. Lett. 17 , 73 – 75 ( 1992 ). [CrossRef] [PubMed]

]. The most well-studied implementation of fiber PSA is a frequency-degenerate FOPA based on nonlinear fiber Sagnac interferometer, first realized in the visible region [4

4 . M. E. Marhic , C. H. Hsia , and J. M. Jeong , “ Optical amplification in a nonlinear fiber interferometer ,” Electron. Lett. 27 , 210 – 211 ( 1991 ). [CrossRef]

]. Based on this configuration, the first fiber-based telecom-band PSA was demonstrated with phase-sensitive gain of 10 dB [5

5 . G. Bartolini , R. D. Li , P. Kumar , W. Riha , and K. V. Reddy , “ 1.5- μ m phase-sensitive amplifier for ultrahigh-speed communications ,” in Proc. Opt. Fiber Commun. Conf . ( Optical Society of America, Washington, D.C. , 1994 ), pp. 202 – 203 .

]. This configuration was also used to achieve nearly-noiseless amplification [6

6 . D. Levandovsky , M. Vasilyev , and P. Kumar , “ Amplitude squeezing of light by means of a phase-sensitive fiber parametric amplifier ,” Opt. Lett. 24 , 984 – 986 ( 1999 ). [CrossRef]

, 7

7 . D. Levandovsky , M. Vasilyev , and P. Kumar , “ Near-noiseless amplification of light by a phase-sensitive fibre amplifier ,” Pramana J. Phys. 56 , 281 – 285 ( 2001 ). [CrossRef]

, 8

8 . W. Imajuku , A. Takada , and Y. Yamabayashi , “ Low-noise amplification under the 3 dB noise figure in high-gain phase-sensitive fibre amplifier ,” Electron. Lett. 35 , 1954 – 1955 ( 1999 ). [CrossRef]

, 9

9 . W. Imajuku , A. Takada , and Y. Yamabayashi , “ Inline coherent optical amplifier with noise figure lower than 3 dB quantum limit ,” Electron. Lett. 36 , 63 – 64 ( 2000 ). [CrossRef]

]. In addition to improving the noise figure, the PSAs also perform phase regeneration, which enabled the demonstrations of long-term soliton storage [10

10 . G. D. Bartolini , D. K. Serkland , P. Kumar , and W. L. Kath , “ All-optical storage of a picosecond-pulse packet using parametric amplification ,” IEEE Photonics Technol. Lett. 9 , 1020 – 1022 ( 1997 ). [CrossRef]

] and, more recently, regeneration of differential phase-shift-keying signals [11

11 . K. Croussore , I. Kim , Y. Han , C. Kim , G. F. Li , and S. Radic , “ Demonstration of phase-regeneration of DPSK signals based on phase-sensitive amplification ,” Opt. Express 13 , 3945 – 3950 ( 2005 ). [CrossRef] [PubMed]

]. The frequency-degenerate, i.e., interferometer-based, PSAs, however, have several significant drawbacks. First of all, they are inherently single-channel devices not compatible with wavelength-division multiplexing (WDM) operation. Second, they are highly susceptible to guided acoustic-wave Brillouin scattering (GAWBS) noise [12

12 . R. M. Shelby , M. D. Levenson , and P. W. Bayer , “ Guided acoustic-wave Brillouin scattering ,” Phys. Rev. B 31 , 5244 – 5252 ( 1985 ). [CrossRef]

] producing phase fluctuations that are converted by the interferometer into amplitude noise. Without complicated GAWBS cancellation schemes [6

6 . D. Levandovsky , M. Vasilyev , and P. Kumar , “ Amplitude squeezing of light by means of a phase-sensitive fiber parametric amplifier ,” Opt. Lett. 24 , 984 – 986 ( 1999 ). [CrossRef]

, 13

13 . K. Bergman , C. R. Doerr , H. A. Haus , and M. Shirasaki , “ Sub-shot-noise measurement with fiber-squeezed optical pulses ,” Opt. Lett. 18 , 643 – 645 ( 1993 ). [CrossRef] [PubMed]

], the signal’s spectral content up to 2 GHz is severely degraded. Finally, to provide phase-sensitive amplification, the pump should have exactly the same frequency as the signal, and the relative phase between the pump and the signal must be carefully controlled using either pump injection-locking [14

14 . A. Takada and W. Imajuku , “ In-line optical phase-sensitive amplifier employing pump laser injection-locked to input signal light ,” Electron. Lett. 34 , 274 – 275 ( 1998 ). [CrossRef]

] or optical phase-locking loop [15

15 . W. Imajuku and A. Takada , “ In-line phase-sensitive amplifier with optical-PLL-controlled internal pump light source ,” Electron. Lett. 33 , 2155 – 2156 ( 1997 ). [CrossRef]

].

An alternative implementation of fiber PSA is based on frequency nondegenerate FOPA, where two pump photons with frequency ωp produce one signal photon at frequency ωs and one idler photon at frequency ωi, so that ωs +ωi = 2ωp. If only the pump and the signal are present at the input of the nonlinear fiber, the nondegenerate FOPA operates as a PIA. In order for this FOPA to be used as a PSA, the idler must be excited at the input of the fiber together with the pump and the signal (a two-pump FOPA can also be used in a similar manner [16

16 . C. J. McKinstrie and S. Radic , “ Phase-sensitive amplification in a fiber ,” Opt. Express 12 , 4973 – 4979 ( 2004 ). [CrossRef] [PubMed]

]). Such a process has been previously used in the visible region to demonstrate squeezing of classical noise [17

17 . M. D. Levenson , R. M. Shelby , and S. H. Perlmutter , “ Squeezing of classical noise by nondegenerate four-wave mixing in an optical fiber ,” Opt. Lett. 10 , 514 – 516 ( 1985 ). [CrossRef] [PubMed]

] and amplification of signal-idler sidebands produced by acousto-optic modulation of the pump [18

18 . I. Bar-Joseph , A. A. Friesem , R. G. Waarts , and H. H. Yaffe , “ Parametric interaction of a modulated wave in a single-mode fiber ,” Opt. Lett. 11 , 534 – 536 ( 1986 ). [CrossRef] [PubMed]

]. In a recent experiment, a telecom band fiber PSA was demonstrated by use of the double-sideband modulation format [19

19 . R. Tang , P. Devgan , P. L. Voss , V. S. Grigoryan , and P. Kumar , “ In-Line Frequency-Nondegenerate Phase-Sensitive Fiber-Optical Parametric Amplifier ,” IEEE Photonics Technol. Lett. 17 , 1845 – 1847 ( 2005 ). [CrossRef]

]. Data at 2.5 Gb/s was transmitted over 60 km of dispersion-compensated fiber with bit-error rate performance better than that obtainable with a FOPA of the same gain in a PIA configuration [20

20 . R. Tang , P. Devgan , V. S. Grigoryan , and P. Kumar , “ Inline frequency-non-degenerate phase-sensitive fibre parametric amplifier for fibre-optic communication ,” Electron. Lett. 41 , 1072 – 1073 ( 2005 ). [CrossRef]

]. In both these experiments the phase-coherent sidebands were created by high-speed electro-optic modulation of a continuous-wave (CW) light, which was carried along with the sidebands in the transmission line. This CW carrier was then extracted and used as pump in the PSA after boosting its power with a conventional EDFA. The creation of phase-coherent sidebands with modulation of the pump, however, is limited by electronics and does not permit full utilization of the wide parametric-amplification bandwidth capable of supporting many WDM channels.

In this paper, we report on the first PSA based on frequency nondegenerate optical parametric amplification wherein the input phase-coherent signal-idler pair is prepared by all-optical means, which is potentially compatible with wideband WDM operation. Preliminary results from the scheme described in this paper were presented in an invited talk at LEOS 2003 [21

21 . P. Kumar , J. Lasri , P. Devgan , and R. Tang , “ Fiber Nonlinearity Based Devices for Advanced Fiber-Optic Communication and Signal Processing ,” in Proceedings of the 16th Annual Meeting of the IEEE Lasers and Electro-Optics Society, Tucson, Arizona, October 26-30, 2003 ; Vol. 1 , pp. 103 – 104 .

]. We use three sections of fibers in a straight-line configuration. The first is a dispersion-shifted fiber (DSF) that acts as a FOPA-based PIA. In our configuration, the signal, pump, and idler have different frequencies. Through the parametric process in the PIA section, the generated idler automatically acquires a certain phase relationship with the pump and signal. Then, the pump, signal, and the generated idler from the PIA section enter a single-mode fiber (SMF) whose dispersion produces wavelength-dependent phase shifts changing the relative phase between the three waves. Even though the phase is modified by the SMF, the new relative phase is stable and no phase-locking control is needed. After the SMF, the pump, signal, and idler enter a third fiber section, which is a second DSF that acts as a FOPA-based PSA. Depending on the signal wavelength, the SMF-induced phase shift leads to either amplification or de-amplification, demonstrating the phase-sensitive behavior of the frequency nondegenerate FOPA.

It may appear at first that a nondegenerate PSA would be wasteful of bandwidth, as it requires twice the optical bandwidth compared to a corresponding degenerate PSA. This is, however, not true since a nondegenerate PSA amplifies simultaneously both the sum of the amplitude quadratures of the signal and idler fields and the difference of their phase quadratures [22

22 . M. Vasilyev , “ Distributed phase-sensitive amplification ,” Opt. Express 13 , 7563 – 7571 ( 2005 ). [CrossRef] [PubMed]

]. Thus, a nondegenerate PSA transmits twice as much information as a degenerate PSA, while occupying twice as much bandwidth. The amplitude information can be easily recovered by directly detecting either the signal or the idler fields only. However, if both quadratures are encoded (i.e., the signal spectrum is not symmetric), then a more elaborate detection scheme would be required, e.g., homodyne detection of the signal field alone.

The structure of this paper is as follows. In section 2 we apply a general theoretical model of a frequency nondegenerate FOPA to the special case of a FOPA-based PSA to predict the PSA gain characteristics. The details of the parametric-gain derivation are provided in the appendix. In section 3, we present a series of experiments confirming the theoretical predictions, and summarize the paper in section 4.

2. Theory

In a FOPA, gain is a consequence of the four-wave mixing (FWM) process in which two photons from the pump are converted into a pair of signal and idler photons. The basic equations describing this process, in terms of optical powers and phases, are [23

23 . G. Cappellini and S. Trillo , “ Third-order three-wave mixing in single-mode fibers: exact solutions and spatial instability effects ,” J. Opt. Soc. Am. B 8 , 824 – 831 ( 1991 ). [CrossRef]

]:

dPpdz=αPp4γ(Pp2PsPi)12sinθ,
(1)
dPsdz=αPs2γ(Pp2PsPi)12sinθ,
(2)
dPidz=αPi2γ(Pp2PsPi)12sinθ,
(3)
dz=Δβ+γ{2PpPsPi
+[(Pp2PsPi)12+(Pp2PiPs)124(PsPi)12]cosθ},
(4)

where Pp, Ps and Pi are the optical powers for pump, signal and idler, respectively. α is the linear loss coefficient of the gain medium fiber. γ=2 π n 2/λ Aeff is the nonlinear coefficient with n 2 and Aeff as the fiber’s nonlinear index and effective mode area, respectively. Δβ = βs + βi - 2βp is the linear phase mismatch per unit length between the signal, idler and pump with propagation constants βs, βi, and βp. The relative phase difference is

θ(z)=Δβz+ϕs(z)+ϕi(z)2ϕp(z),
(5)

where ϕs, ϕi, and ϕp are the phases of the signal, idler and pump, respectively.

When the pump, signal, and idler waves are present at the input of the fiber, Eqs. (1)–(4) show that the power flow depends on the relative phase between the three waves, i.e., it can be transferred either from the pump to the signal and idler (when θ = π/2, parametric amplification) or from the signal and idler to the pump (when θ = -π/2, parametric de-amplification). This gives us the possibility to create an optical amplifier whose gain depends on the phase of the input signal, i.e., a PSA.

Figure 1 schematically describes our PSA model, which is comprised of three segments of fibers. In the first segment, DSF1 is configured as a PIA, in which signal is amplified and the idler is generated. The relative phase relationship between the three waves at the output of the PIA, θ Out_PIA depends on the gain and the phase-matching characteristics of DSF1. The second segment consists of a piece of SMF which acts as a wavelength-dependent phase shifter, where the phase relationship between the pump, signal and idler is changed. For pump, signal and idler angular frequencies (ωp, ωs, and ωi = 2ωp - ωs, respectively) satisfying ∣ ωs - ωp∣ = ∣ωi - ωp∣ <<ωp, one can expand Δββ 2(ωs - ωp)2, where β 2 is the group-velocity-dispersion coefficient of the SMF. After propagating through the SMF, the relative phase at the input of the PSA-DSF2 segment becomes:

θIn_PSA(ω)=θOut_SMF(ω)=θOut_PIA(ω)+ΔβLSMF
θOut_PIA(ω)+β2(ωωp)2LSMF,
(6)
Fig. 1. Schematic of the phase-sensitive fiber parametric amplification model; p: pump, s: signal, i: idler.

where L SMF is the length of the SMF section and the various superscripts distinguish θ(ω) at various locations along the three-segment fiber line. Note that in the derivation of Eq. (6), the nonlinear phase shift inside the SMF is neglected since it is much smaller than the linear phase shift. Because of its large dispersion, even a few meters of SMF can cause tremendous changes in θ(ω), varying as a function of wavelength. After conversion from frequency to wavelength, Eq. (6) becomes:

θIn_PSA(λ)θOut_PIA(λ)2πc(λpλλ)2DLSMF,
(7)

where D is the dispersion coefficient of the SMF at the pump wavelength and c is the vacuum speed of light.

Fig. 2. (a): Plot of the sine values of the relative phase at the input of DSF2; (b): Plot of the calculated gain of the PSA (DSF2).

Figure 2 clearly shows that the gain spectrum follows θ In_PSA(λ) with a quasi-periodically-varying profile that contains peaks corresponding to maximum amplification and valleys corresponding to maximum attenuation (de-amplification). For example, once θ In_PSA(λ) changes from - π/2 (module 2π) at wavelength λ min,k to +π/2 at wavelength λ max,k and back to - π/2 at λ min,k+1, the signal gain will change from a minimum point (at λ min,k+1) to a maximum point (at λ max,k) and to another minimum point (at λ min,k+1), respectively. Thus, a 2π change in θ In_PSA(λ) from one wavelength to another will generate either one peak and two valleys when starting from a valley location or one valley and two peaks when starting from a peak location.

To study the gain characteristics of a FOPA with and without an idler at its input, an analytical solution for the gain of a FOPA-based PSA can be obtained. By using the procedure described in appendix A, we obtain:

GPSA(θ)=1+{1+4γ2Pp2η2+κ2+4γκPpηcos(θ)4g2}sinh2(gL)
+γPpηsin(θ)gsinh(2gL),
(8)

where, due to the fact that only the PSA section (DSF2) is considered, θ = ϕs + ϕi - 2ϕp, κ = Δβ + 2γPp is the net phase mismatch, g = [(γPp)2 - (κ/2)2]1/2 is the parametric-gain coefficient, and η2=Pi(0)Ps(0) is the power ratio between the idler and the signal at the input of the PSA.

The following two cases should be considered in the solution for the gain in Eq. (8):

  1. When the phase-matching condition is perfect (κ = 0) and the power of the idler at the input is the same as that of the signal (η = 1), the maximum gain is obtained for θ = π/2, which has the following form:

    Gmaxwithidler=1+2sinh2(gL)+sinh(2gL)
    =[exp(gL)]2.
    (9)

    Fig. 3. Experimental setup of the PSA based on a nondegenerate FOPA; PM: phase modulator; OBF: optical bandpass filter; ONF: optical notch filter; FPC: fiber polarization controller; TLS: tunable laser source; DFB: distributed feedback laser.

    Fig. 3.Experimental setup of the PSA based on a nondegenerate FOPA; PM: phase modulator; OBF: optical bandpass filter; ONF: optical notch filter; FPC: fiber polarization controller; TLS: tunable laser source; DFB: distributed feedback laser.
  2. When there is no idler at the FOPA input, i.e., η = 0, the FOPA acts as a PIA and for perfect phase-matching condition the maximum gain becomes

    Gmaxwithoutidler=1+sinh2(gL)
    [exp(gL)2]2,forgL1.
    (10)

Equations (9) and (10) show that when the idler is present at the input together with the signal and the pump, the maximum gain of the signal is larger by 6 dB compared with the case when the idler is not present at the input. Physically, this is because when the idler is present, the effective input to the amplifier is a coherent sum of the signal and idler (giving a factor of 2 in the fields, or factor of 4 in the powers). For the same pump power as in the PIA case (no input idler), this effective input is transformed into a 4-times higher output signal, leading to 6-dB gain increase when we consider the power gain of the signal mode alone. Of course, this holds only at large gains [limiting case in Eq. (10)], and only for the signal and idler fields that align perfectly in phase. When the PSA gain is not large, the 6-dB advantage is reduced somewhat, as is the case in the experiment below [see discussion after Fig. 6(b)].

3. Experiment

The experimental setup of the nondegenerate PSA is shown in Fig. 3. Two spools of DSFs were used to create the PIA and PSA sections. The parameters of the DSFs are the same as given in the theoretical model. The CW pump light at 1559.8 nm was phase-modulated to suppress the stimulated Brillouin scattering in the DSFs, strongly amplified by an EDFA, filtered by a 1-nm optical bandpass filter to remove the out-of-band amplified spontaneous emission (ASE) coming from the EDFA, and then coupled into the PIA stage via a 90/10 coupler. A wavelength-tunable laser (TLS) was used as the signal source. Between the PIA and PSA stages, a piece of SMF was used to create the wavelength-dependent phase shift, followed by a 95/5 splitter whose 95% output was connected to the PSA and the 5% output was used to monitor the PSA input. A 0.2 nm optical notch filter (an isolator followed by a fiber Bragg grating) centered at the pump wavelength (1559.8 nm) was connected after the PSA to remove the high-power pump before the signal was detected with an optical spectrum analyzer.

Figure 4(a) shows the optical spectra of the parametrically amplified spontaneous emission, known as parametric fluorescence (PF), at the input (black curve) and output (blue curve) of the PSA segment (500-m-long DSF) when only the pump was present at the input of the PIA and the length of the SMF was chosen to be 10 m. The pump powers into the PIA and PSA stages were 265 mW and 180 mW, respectively. This figure shows that, unlike the well-known smooth PF curve generated by a PIA (black curve in the figure), the PF at the output of the PSA changes quasi-periodically, with peaks and valleys unevenly distributed in the wavelength domain. The phase-sensitive gain performance of the PSA can be evaluated on a logarithmic scale (without introducing an input signal) by subtracting the input PF from the output PF, as shown by the black curve in Fig. 4(b). The quasi-periodic dependence of the PF gain on wavelength demonstrates the phase-sensitive performance of the amplifier, which is matched pretty well by the theoretical calculation of the PSA gain shown by the blue curve in Fig. 4(b). However, there is a noticeable mismatch at the edges of the optical spectra shown. The cause of this can be attributed to the following: (1) the actual dispersion slope of the SMF around 1550 nm varies, whereas in the simulation it is kept constant; (2) the signal experiences a nonlinear polarization rotation due to the strong pump, which is not taken into account in the simulation; (3) the Raman effect accompanying the parametric process is not included in the simulation, and (4) fluctuations in the zero-dispersion wavelength of the fiber can cause some gain to appear in wavelength regions where the theory for uniform zero-dispersion wavelength does not predict any gain [24

24 . M. Farahmand and M. de Sterke , “ Parametric amplification in presence of dispersion fluctuations ,” Opt. Express 12 , 136 – 142 ( 2004 ). [CrossRef] [PubMed]

, 25

25 . J. M. C. Boggio , A. Guimaraes , F. A. Callegari , J. D. Marconi , and H. L. Fragnito , “ Q penalties due to pump phase modulation and pump RIN in fiber optic parametric amplifiers with non-uniform dispersion ,” Opt. Commun. 249 , 451 – 472 ( 2005 ). [CrossRef]

].

Fig. 4. (a) Measured input (black) and output (blue) PF spectra of DSF2 with 10-m-long SMF. (b) Measured (black) and calculated (blue) PF gain with 10-m-long SMF. (c) and (d) show the measurements and calculations [similar to (a) and (b), respectively] for a 15-m-long SMF.

To further verify the phase dependence of the gain, we also measured the PF and the gain spectra with 15-m-long SMF, as plotted in Figs. 4(c) and (d), respectively. These figures show that the PF and gain profiles change due to the change of the relative phase spectrum at the input of the DSF2, which is a function of the SMF’s length. When the input phase relationship changes, the gain property of the DSF2 changes [as predicted by Eqs. (1)–(7)], resulting in shifts in the positions of the peaks and valleys in the spectra.

Fig. 5. Calculated (black curve) and measured gain (diamonds) and attenuation (squares) of the PSA segment for (a) 1000-m-long PIA and 500-m-long PSA and (b) 500-m-long PIA and 1000-m-long PSA.

Next, we investigated the parametric amplification/deamplification performance of the non-degenerate PSA with an incoming signal, whose wavelength was tuned to the peaks and valleys of the PF-gain spectra. The SMF between the PIA and PSA stages was 10 m long. Figure 5(a) shows the calculated gain spectra of the PSA together with the measured signal gain at the wavelengths of the peaks and valleys. One can note that the measured PSA gain (attenuation) is larger (smaller) on the Stokes side (signal whose wavelength is longer than that of the pump) and smaller (larger) on the anti-Stokes side of the pump (signal whose wavelength is shorter than that of the pump). We believe that the main reason for this is the Raman-assisted gain (loss) seen by a signal on the Stokes (anti-Stokes) side. This effect is not included in our theoretical model. Otherwise, the experimental results match reasonably well with the theoretical predictions.

The parametric gain/attenuation characteristics of the nondegenerate PSA with an incoming signal were also measured when the shorter DSF (DSF2) was used as the PIA segment and the longer DSF (DSF1) as the PSA segment, as shown in Fig. 5(b). Similar differences between the experimental data and the theoretical simulation are seen in Fig. 5(b), as in Fig. 5(a), owing to the Raman effect. Additionally, because a longer DSF is used in the PSA stage, the gain of the PSA is larger for the same amount of pump power, as is expected for any kind of FOPA in general.

Fig. 6. Measured gain with input idler (squares), without input idler (triangles), and the difference of gains with and without input idler (circles). (a) and (b) are for measurement results with 500-m-long and 1000-m-long DSFs, respectively.

4. Conclusion

We have demonstrated, for the first time, a phase-sensitive amplifier based on the frequency-nondegenerate parametric amplification process in optical fibers wherein the input is prepared by all-optical means. This is achieved by using a phase-insensitive parametric amplifier to create an input signal-idler pair which is then sent into a second, phase-sensitive, parametric amplifier. We have presented a model describing the two fiber-optic parametric amplifier sections separated by a wavelength-dependent phase shifter. The wavelength-dependent gain profile of the phase-sensitive amplifier is calculated and confirmed in a series of experiments. In agreement with the theory, we have observed that, when the idler is present at the input together with the pump and the signal, not only is the amplification sensitive to the phase of the incoming signal, but also the maximum gain of the signal is approximately four-fold greater than that in the case when the idler is not present at the input. Even though the separation between the phase-insensitive and phase-sensitive amplifiers in our experiments is only 10–15 m, the demonstrated technique can be used to generate an automatically phase-matched signal-idler pair at the transmitter for launching into a phase-sensitively amplified long-distance communication line, thereby facilitating the practical realization of the phase-sensitive amplification technology. One must note that the total dispersion in the long-fiber line would need to be compensated to less than the equivalent dispersion of 10–15 m of SMF. This requirement, however, is not significantly more stringent than the dispersion map accuracy requirement of 100 m of SMF in 40Gb/s systems wherein it is easily handled by tunable dispersion compensators.

Appendix A

For a single-pump FOPA, when applying Bj(z) = Aj(z)exp[-i2γPpz], j = s,i, where As(z) and Aj(z) stand for the amplitudes of the signal and idler, respectively, and z is the distance along the fiber, one can follow the procedure in [26

26 . G. P. Agrawal , Nonlinear Fiber Optics ( Academic Press , 1995 ).

] to obtain:

dBsdz=Ppexp(i2ϕp)exp(iκz)Bi*,
(11)
dBi*dz=Ppexp(i2ϕp)exp(iκz)Bs.
(12)

Here Pp and ϕp are the power and phase of the pump, respectively, and κ = Δβ + 2γPp is the net phase mismatch. The general solution for Bs and Bi is

Bs(z)=(a3egz+b3egz)exp(iκz2),
(13)
Bi*(z)=(a4egz+b4egz)exp(iκz2),
(14)

where g = [(γPp)2 - (κ 2)2]1/2 is the parametric gain coefficient. The coefficients a 3, a 4, a 3, and a 4 can be obtained by applying the initial conditions. They are,

a3=(g+2)Bs(0)+Ppe2iϕpBi*(0)2g,
(15)
b3=(g2)Bs(0)Ppe2iϕpBi*(0)2g,
(16)
a4=(g2)Bi*(0)Ppe2iϕpBs(0)2g,
(17)
b4=(g+2)Bi*(0)+Ppe2iϕpBs(0)2g.
(18)

By substituting the coefficients above in Eqs. (13) and (14), we obtain the solutions as

Bs(z)={(g+2)Bs(0)+Ppei2ϕpBi*(0)2gegz
+(g2)Bs(0)Ppei2ϕpBi*(0)2gegz}eiκz2,
(19)
Bi*(z)={(g2)Bi*(0)Ppei2ϕpBs(0)2gegz
+(g+2)Bi*(0)+Ppei2ϕpBs(0)2gegz}eiκz2.
(20)

The relationship between the signal and idler at z = 0 is then given by

Bi*(0)=ηBs(0)exp(iθd),
(21)

where η 2Pi(0)/Ps(0) is the power ratio between the input idler and signal, and ϕd ≡ - (ϕs + ϕi). By substituting Eq. (21) in Eq. (19), we find the gain of the FOPA to be described as

GPSA=1+{1+4γ2Pp2η2+κ2+4γκPpηcos(θ)4g2}sinh2(gL)
+γPpηsin(θ)gsinh(2gL),
(22)

where θ = ϕs + ϕi - 2ϕp.

Acknowledgments

This research was supported in part by the U.S. National Science Foundation under Grant No. ECS-0401251.

References and links

1 .

C. M. Caves , “ Quantum limits on noise in linear amplifiers ,” Phys. Rev. D 26 , 1817 – 1839 ( 1982 ). [CrossRef]

2 .

H. P. Yuen , “ Design of transparent optical networks using novel quantum amplifiers and sources ,” Opt. Lett. 12 , 789 – 791 ( 1987 ). [CrossRef] [PubMed]

3 .

H. P. Yuen , “ Reduction of quantum fluctuation and suppression of the Gordon-Haus effect with phase-sensitive linear amplifiers ,” Opt. Lett. 17 , 73 – 75 ( 1992 ). [CrossRef] [PubMed]

4 .

M. E. Marhic , C. H. Hsia , and J. M. Jeong , “ Optical amplification in a nonlinear fiber interferometer ,” Electron. Lett. 27 , 210 – 211 ( 1991 ). [CrossRef]

5 .

G. Bartolini , R. D. Li , P. Kumar , W. Riha , and K. V. Reddy , “ 1.5- μ m phase-sensitive amplifier for ultrahigh-speed communications ,” in Proc. Opt. Fiber Commun. Conf . ( Optical Society of America, Washington, D.C. , 1994 ), pp. 202 – 203 .

6 .

D. Levandovsky , M. Vasilyev , and P. Kumar , “ Amplitude squeezing of light by means of a phase-sensitive fiber parametric amplifier ,” Opt. Lett. 24 , 984 – 986 ( 1999 ). [CrossRef]

7 .

D. Levandovsky , M. Vasilyev , and P. Kumar , “ Near-noiseless amplification of light by a phase-sensitive fibre amplifier ,” Pramana J. Phys. 56 , 281 – 285 ( 2001 ). [CrossRef]

8 .

W. Imajuku , A. Takada , and Y. Yamabayashi , “ Low-noise amplification under the 3 dB noise figure in high-gain phase-sensitive fibre amplifier ,” Electron. Lett. 35 , 1954 – 1955 ( 1999 ). [CrossRef]

9 .

W. Imajuku , A. Takada , and Y. Yamabayashi , “ Inline coherent optical amplifier with noise figure lower than 3 dB quantum limit ,” Electron. Lett. 36 , 63 – 64 ( 2000 ). [CrossRef]

10 .

G. D. Bartolini , D. K. Serkland , P. Kumar , and W. L. Kath , “ All-optical storage of a picosecond-pulse packet using parametric amplification ,” IEEE Photonics Technol. Lett. 9 , 1020 – 1022 ( 1997 ). [CrossRef]

11 .

K. Croussore , I. Kim , Y. Han , C. Kim , G. F. Li , and S. Radic , “ Demonstration of phase-regeneration of DPSK signals based on phase-sensitive amplification ,” Opt. Express 13 , 3945 – 3950 ( 2005 ). [CrossRef] [PubMed]

12 .

R. M. Shelby , M. D. Levenson , and P. W. Bayer , “ Guided acoustic-wave Brillouin scattering ,” Phys. Rev. B 31 , 5244 – 5252 ( 1985 ). [CrossRef]

13 .

K. Bergman , C. R. Doerr , H. A. Haus , and M. Shirasaki , “ Sub-shot-noise measurement with fiber-squeezed optical pulses ,” Opt. Lett. 18 , 643 – 645 ( 1993 ). [CrossRef] [PubMed]

14 .

A. Takada and W. Imajuku , “ In-line optical phase-sensitive amplifier employing pump laser injection-locked to input signal light ,” Electron. Lett. 34 , 274 – 275 ( 1998 ). [CrossRef]

15 .

W. Imajuku and A. Takada , “ In-line phase-sensitive amplifier with optical-PLL-controlled internal pump light source ,” Electron. Lett. 33 , 2155 – 2156 ( 1997 ). [CrossRef]

16 .

C. J. McKinstrie and S. Radic , “ Phase-sensitive amplification in a fiber ,” Opt. Express 12 , 4973 – 4979 ( 2004 ). [CrossRef] [PubMed]

17 .

M. D. Levenson , R. M. Shelby , and S. H. Perlmutter , “ Squeezing of classical noise by nondegenerate four-wave mixing in an optical fiber ,” Opt. Lett. 10 , 514 – 516 ( 1985 ). [CrossRef] [PubMed]

18 .

I. Bar-Joseph , A. A. Friesem , R. G. Waarts , and H. H. Yaffe , “ Parametric interaction of a modulated wave in a single-mode fiber ,” Opt. Lett. 11 , 534 – 536 ( 1986 ). [CrossRef] [PubMed]

19 .

R. Tang , P. Devgan , P. L. Voss , V. S. Grigoryan , and P. Kumar , “ In-Line Frequency-Nondegenerate Phase-Sensitive Fiber-Optical Parametric Amplifier ,” IEEE Photonics Technol. Lett. 17 , 1845 – 1847 ( 2005 ). [CrossRef]

20 .

R. Tang , P. Devgan , V. S. Grigoryan , and P. Kumar , “ Inline frequency-non-degenerate phase-sensitive fibre parametric amplifier for fibre-optic communication ,” Electron. Lett. 41 , 1072 – 1073 ( 2005 ). [CrossRef]

21 .

P. Kumar , J. Lasri , P. Devgan , and R. Tang , “ Fiber Nonlinearity Based Devices for Advanced Fiber-Optic Communication and Signal Processing ,” in Proceedings of the 16th Annual Meeting of the IEEE Lasers and Electro-Optics Society, Tucson, Arizona, October 26-30, 2003 ; Vol. 1 , pp. 103 – 104 .

22 .

M. Vasilyev , “ Distributed phase-sensitive amplification ,” Opt. Express 13 , 7563 – 7571 ( 2005 ). [CrossRef] [PubMed]

23 .

G. Cappellini and S. Trillo , “ Third-order three-wave mixing in single-mode fibers: exact solutions and spatial instability effects ,” J. Opt. Soc. Am. B 8 , 824 – 831 ( 1991 ). [CrossRef]

24 .

M. Farahmand and M. de Sterke , “ Parametric amplification in presence of dispersion fluctuations ,” Opt. Express 12 , 136 – 142 ( 2004 ). [CrossRef] [PubMed]

25 .

J. M. C. Boggio , A. Guimaraes , F. A. Callegari , J. D. Marconi , and H. L. Fragnito , “ Q penalties due to pump phase modulation and pump RIN in fiber optic parametric amplifiers with non-uniform dispersion ,” Opt. Commun. 249 , 451 – 472 ( 2005 ). [CrossRef]

26 .

G. P. Agrawal , Nonlinear Fiber Optics ( Academic Press , 1995 ).

OCIS Codes
(060.2320) Fiber optics and optical communications : Fiber optics amplifiers and oscillators
(060.2330) Fiber optics and optical communications : Fiber optics communications
(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers
(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing
(190.4970) Nonlinear optics : Parametric oscillators and amplifiers

ToC Category:
Research Papers

Citation
Renyong Tang, Jacob Lasri, Preetpaul S. Devgan, Vladimir Grigoryan, Prem Kumar, and Michael Vasilyev, "Gain characteristics of a frequency nondegenerate phase-sensitive fiber-optic parametric amplifier with phase self-stabilized input," Opt. Express 13, 10483-10493 (2005)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-26-10483


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References

  1. C. M. Caves, "Quantum limits on noise in linear amplifiers," Phys. Rev. D 26, 1817-1839 (1982). [CrossRef]
  2. H. P. Yuen, "Design of transparent optical networks using novel quantum amplifiers and sources," Opt. Lett. 12 789-791 (1987). [CrossRef] [PubMed]
  3. H. P. Yuen, "Reduction of quantum fluctuation and suppression of the Gordon-Haus effect with phase-sensitive linear amplifiers," Opt. Lett. 17, 73-75 (1992). [CrossRef] [PubMed]
  4. M. E. Marhic, C. H. Hsia, and J. M. Jeong, "Optical amplification in a nonlinear fiber interferometer," Electron. Lett. 27, 210-211 (1991). [CrossRef]
  5. G. Bartolini, R. D. Li, P. Kumar,W. Riha, and K. V. Reddy, "1.5- µm phase-sensitive amplifier for ultrahigh-speed communications," in Proc. Opt. Fiber Commun. Conf. (Optical Society of America, Washington, D.C., 1994), pp. 202-203.
  6. D. Levandovsky, M. Vasilyev, and P. Kumar, "Amplitude squeezing of light by means of a phase-sensitive fiber parametric amplifier," Opt. Lett. 24, 984-986 (1999). [CrossRef]
  7. D. Levandovsky, M. Vasilyev, and P. Kumar, "Near-noiseless amplification of light by a phase-sensitive fibre amplifier," Pramana J. Phys. 56, 281-285 (2001). [CrossRef]
  8. W. Imajuku, A. Takada, Y. Yamabayashi, "Low-noise amplification under the 3 dB noise figure in high-gain phase-sensitive fibre amplifier," Electron. Lett. 35, 1954-1955 (1999). [CrossRef]
  9. W. Imajuku, A. Takada and Y. Yamabayashi, "Inline coherent optical amplifier with noise figure lower than 3 dB quantum limit," Electron. Lett. 36, 63-64 (2000). [CrossRef]
  10. G. D. Bartolini, D. K. Serkland, P. Kumar, W. L. Kath, "All-optical storage of a picosecond-pulse packet using parametric amplification," IEEE Photonics Technol. Lett. 9, 1020-1022 (1997). [CrossRef]
  11. K. Croussore, I. Kim, Y. Han, C. Kim, G. F. Li and S. Radic, "Demonstration of phase-regeneration of DPSK signals based on phase-sensitive amplification," Opt. Express 13, 3945-3950 (2005). [CrossRef] [PubMed]
  12. R. M. Shelby, M. D. Levenson, and P. W. Bayer, "Guided acoustic-wave Brillouin scattering," Phys. Rev. B 31, 5244-5252 (1985). [CrossRef]
  13. K. Bergman, C. R. Doerr, H. A. Haus, and M. Shirasaki, "Sub-shot-noise measurement with fiber-squeezed optical pulses," Opt. Lett. 18, 643-645 (1993). [CrossRef] [PubMed]
  14. A. Takada,W. Imajuku, "In-line optical phase-sensitive amplifier employing pump laser injection-locked to input signal light," Electron. Lett. 34, 274-275 (1998). [CrossRef]
  15. W. Imajuku, A. Takada, "In-line phase-sensitive amplifier with optical-PLL-controlled internal pump light source," Electron. Lett. 33, 2155-2156 (1997). [CrossRef]
  16. C. J. McKinstrie and S. Radic, "Phase-sensitive amplification in a fiber," Opt. Express 12, 4973-4979 (2004). [CrossRef] [PubMed]
  17. M. D. Levenson, R. M. Shelby, and S. H. Perlmutter, "Squeezing of classical noise by nondegenerate four-wave mixing in an optical fiber," Opt. Lett. 10, 514-516 (1985). [CrossRef] [PubMed]
  18. I. Bar-Joseph, A. A. Friesem, R. G. Waarts, and H. H. Yaffe, "Parametric interaction of a modulated wave in a single-mode fiber," Opt. Lett. 11, 534-536 (1986). [CrossRef] [PubMed]
  19. R. Tang, P. Devgan, P. L. Voss, V. S. Grigoryan, and P. Kumar, "In-Line Frequency-Nondegenerate Phase- Sensitive Fiber-Optical Parametric Amplifier," IEEE Photonics Technol. Lett. 17, 1845-1847 (2005). [CrossRef]
  20. R. Tang, P. Devgan, V. S. Grigoryan, and P. Kumar, "Inline frequency-non-degenerate phase-sensitive fibre parametric amplifier for fibre-optic communication," Electron. Lett. 41, 1072-1073 (2005). [CrossRef]
  21. P. Kumar, J. Lasri, P. Devgan, and R. Tang, "Fiber Nonlinearity Based Devices for Advanced Fiber-Optic Communication and Signal Processing," in Proceedings of the 16th Annual Meeting of the IEEE Lasers and Electro- Optics Society, Tucson, Arizona, October 26-30, 2003; Vol. 1, pp. 103-104.
  22. M. Vasilyev, "Distributed phase-sensitive amplification," Opt. Express 13, 7563-7571 (2005). [CrossRef] [PubMed]
  23. G. Cappellini and S. Trillo, "Third-order three-wave mixing in single-mode fibers: exact solutions and spatial instability effects," J. Opt. Soc. Am. B 8, 824-831 (1991). [CrossRef]
  24. M. Farahmand and M. de Sterke, "Parametric amplification in presence of dispersion fluctuations," Opt. Express 12, 136-142 (2004). [CrossRef] [PubMed]
  25. J. M. C. Boggio, A. Guimaraes, F. A. Callegari, J. D. Marconi, H. L. Fragnito, "Q penalties due to pump phase modulation and pump RIN in fiber optic parametric amplifiers with non-uniform dispersion," Opt. Commun. 249, 451-472 (2005). [CrossRef]
  26. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 1995).

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