We demonstrate phase-sensitive amplification of multiple wavelength-division-multiplexed continuous-wave (CW) signals by frequency nondegenerate four-wave-mixing process in optical fiber. By fine-tuning the optical wavelengths of the CW signals, simultaneous phase-sensitive in-line amplification of three signal channels is realized. This indicates the possibility of amplifying multiple data channels by an in-line phase-sensitive fiber parametric amplifier. We also discuss a potential system architecture employing such amplifiers.
©2008 Optical Society of America
Fiber-optic parametric amplifiers (FOPAs) can be used to boost the signal power which decays due to distributed propagation loss as well as lumped loss in fiber-optic systems. FOPAs can operate either as phase-insensitive amplifiers (PIAs), similar to erbium-doped-fiber amplifiers (EDFAs) and Raman amplifiers, or as phase-sensitive amplifiers (PSAs) depending on the configuration of the FOPA. Phase-sensitive amplifiers amplify the in-phase component of the signal, while attenuating the quadrature component [1–3]. Fiber PSAs have been well studied in the frequency-degenerate condition, where a nonlinear fiber Sagnac interferometer configuration is generally applied. The first fiber PSA was realized in the visible region . The first 1550-nm-band fiber PSA was demonstrated with gain of 10 dB in Ref. 5. This configuration was also used to achieve nearly-noiseless amplification of the frequency degenerate signal [6–9]. Other applications, such as long-term soliton storage  and regeneration of differential phase-shift-keying signals , have also been implemented using frequency-degenerate PSAs. Among the drawbacks of using frequency-degenerate PSAs, three are significant. First, frequency-degenerate PSAs are inherently single-channel devices not compatible with wavelength-division multiplexing (WDM) operation. Second, such PSAs are highly susceptible to guided acoustic-wave Brillouin scattering noise  producing phase fluctuations that are converted by the interferometer into amplitude noise. Finally, the pump and the signal should have exactly the same frequency, and the relative phase between the pump and signal must be well controlled using either pump injection-locking  or optical phase-locking loop .
FOPAs can also be implemented as frequency nondegenerate PSAs, where two pump photons at frequency ωp produce one signal photon at frequency ωs and one idler photon at frequency ωi satisfying ωs+ωi=2ωp. Such a FOPA acts as a PIA when only the pump and signal are present at the input of the nonlinear fiber. For this FOPA to be used as a PSA, the idler must be excited at the input of the nonlinear fiber together with the pump and signal (a two-pump FOPA can also be used in a similar manner ). Single-pump frequency nondegenerate PSAs have been previously used in the visible region to demonstrate squeezing of classical noise  and amplification of signal-idler sidebands produced by acousto-optic modulation of the pump . Recently, a 1550-nm-band frequency nondegenerate PSA was demonstrated by use of the double-sideband modulation format . Using this PSA, data at 2.5 Gb/s was transmitted over 60 km of dispersion-compensated fiber with bit-error rate performance better than a FOPA of the same gain in a PIA configuration . The phase-coherent sidebands, taken as signal and the idler, were created by high-speed electro-optic modulation of a continuous-wave (CW) light. The CW light was propagating along with the sidebands in the transmission line. This CW carrier was then extracted and used as pump in the fiber PSA after being boosted with a conventional EDFA. Such double-sideband modulation scheme for generating signal and idler sidebands, however, is limited by the speed of the electro-optic modulator and does not permit full utilization of the wide parametric-amplification bandwidth capable of supporting many WDM channels.
In this paper, we report simultaneous in-line phase-sensitive amplification of three channels of CW light and discuss the aspects of its potential application in a transmission system. This in-line PSA is based on frequency nondegenerate four-wave-mixing process wherein the input phase-coherent signal-idler pair is prepared by all-optical means [20, 21]. First, three channels of CW light are amplified by a FOPA-based PIA in order to generate the three idlers, each having a certain phase relationship with the pump and its corresponding signal channel. This phase relationship is adjusted by subsequent propagation in the dispersive single-mode fiber (SMF). At the receiver/repeater end, a PSA unit similar to that described in  is used, with pump at the same frequency as the PIA pump. It performs simultaneous phase-sensitive amplification of all three pairs of signal-idler when the three CW signals are tuned to proper optical frequencies. Preliminary data from this project was shown in our conference presentation .
The following simplified equations describe the four-wave-mixing process used to amplify input signals in a FOPA 
where Pp, Psj, and Pij are the optical powers for the pump, the signal of channel j, and the idler of channel j, respectively; α is the linear-loss coefficient of the gain-medium fiber; γ=2πn 2/λA eff is the nonlinear coefficient with n 2 and A eff being the fiber’s nonlinear refractive index and effective area, respectively; Δβj=βsj+βij-2βp is the linear phase mismatch per unit length between the pump and signal-idler pair of channel j, with propagation constants βp, βsj, and βij, respectively. The relative phase difference is
where ϕsj, ϕij, and ϕp are the phases of signal of channel j, idler of channel j, and the pump, respectively. Four-wave-mixing process between the different channels is neglected since optical power of each channel is small.
Equations (1)–(5) demonstrate that when an idler is excited at the input of an in-line PSA, the optical power flow between the pump and the signal-idler pair is determined by their relative phase relationship. The phase relationships between the pump and different signal-idler pairs [θj(z=0)] may vary with j, causing signals at different channels not to experience simultaneous phase-sensitive amplification. One possible way to achieve simultaneous phase-sensitive amplification for multiple channels is to set one channel as a reference and fine-tune the optical wavelength/frequency of the other signal channels. When their wavelengths are tuned, θj(z=0) is tuned in a fine manner owing to the dispersion of SMF between the PIA and PSA, helping channels to achieve amplification simultaneously with the reference channel.
The experimental setup for in-line phase-sensitive amplification of multiple CW-signal channels is shown in Fig. 1. Three signal channels (λs1, λs2, and λs3) are combined by an arrayed waveguide grating (AWG) and then injected into 850-meter-long highly nonlinear fiber (HNLF) together with a pump wave through a 10:90 coupler. The 850-meter-long HNLF is the gain medium for a phase-insensitive FOPA, in which three idlers (λi1, λi2, and λi3) are generated corresponding to the three signal channels. This HNLF consists of two fiber spools: one spool is 500 meters long with zero-dispersion wavelength of 1556 nm, and the other spool is 350 meters long with zero-dispersion wavelength of 1561 nm. Both of them have dispersion slope of 0.018 ps/nm2/km and nonlinear coefficient of 9 W-1km-1. After the HNLF, a pump attenuator, consisting of an isolator followed by a pump-reflecting fiber Bragg grating (FBG) filter, acts as a notch filter on the pump wavelength and rejects most of the pump power.
The three signal-idler pairs, along with the residual attenuated pump enter the in-line PSA, shown inside a yellow block in Fig. 1. Operation of the in-line PSA, including phase modulation of the pump for suppression of the stimulated Brillouin scattering, is described in detail in . First, the remaining pump (“pilot tone”) is separated from the signal by a combination of an FBG and a circulator. The pump is amplified, recombined with the signal, and then sent into the PSA gain medium consisting of 1000 meters of HNLF with zero-dispersion wavelength of 1558 nm, dispersion slope of 0.018 ps/nm2/km, and nonlinear coefficient of 9 W-1km-1. A dithering technique is implemented for phase-locking inside the PSA in order to track the phase fluctuations arising from the pump propagating through the separate EDFA path before being recombined with the signals. Pump rejection optics (an isolator and an FBG centered at the pump wavelength) following the HNLF removes the pump at the output of the in-line PSA. After phase-sensitive amplification, the output from the in-line PSA is wavelength de-multiplexed by a second AWG (AWG2), and each channel is sent to an individual photodiode PD for measurement. A digital oscilloscope having multiple-channel input collects and shows the output of the in-line PSA.
As a first step, we achieved phase-locking with a single signal-idler pair (sweeping signal from 1547 nm to 1572 nm) and measured the corresponding phase-sensitive gain. The PSA pump wavelength is 1559.8 nm with 140 mW average power. The measured PSA gain is shown as diamonds in Fig. 2. With the same pump power and the same nonlinear fiber (1000 meters of HNLF) as the gain medium, the corresponding phase-insensitive gain was also measured and is shown as squares in Fig. 2. Circles show the difference between the measured PSA and PIA gains; theory predicts this difference to approach 6 dB at high gains.
To investigate in-line phase-sensitive amplification of multiple channels of CW light, we chose three signals with wavelengths at 1550.23 nm, 1551.88 nm, and 1553.97 nm and labeled them as channel 1, channel 2, and channel 3, respectively. The idlers corresponding to these signal channels are generated in the phase-insensitive FOPA (i.e. in 850-m-long HNLF). At the input to the 1000-m-long HNLF constituting the in-line PSA, there exists an initial phase relationship θj(z=0) between the signal, idler, and pump waves for each channel. For each signal channel j, θj(z=0) depends on the individual phase-matching condition in the PIA and the amount of dispersion introduced by the single-mode fiber between the PIA and the PSA. Thus, the in-line PSA does not necessarily amplify (i.e. provide maximum gain to) all three signal channels simultaneously. We apply a 25 Hz triangular voltage wave to drive the piezoelectric transducer (PZT) shown in Fig. 1 in order to produce a periodic change of θj(z=0) for all channels (j=1, 2, 3). With this periodic change, the PSA output at each channel varies accordingly and is recorded by a digital oscilloscope. Movie 1 (left) shows the condition in which the in-line PSA provides asynchronous amplification to the three channels of CW light. From bottom to top the purple, blue, and red traces represent the outputs of channel 1 to channel 3, respectively. The triangular trace shown at the bottom of Movie 1 (left) represents the voltage wave driving the PZT and provides a time reference for the other traces. Due to the different initial phase relationships θj(z=0) for different j’s, the three signal channels do not obtain their maximum gains at the same time. When one channel output reaches its maximum level, the other two channel outputs are not at their maximum levels.
To achieve simultaneous amplification for all three signal channels, we need to adjust θj(z=0) for each channel at the input of the HNLF inside the in-line PSA. These adjustments can be made, for example, by using the dispersion accumulated in SMF between the PIA and PSA. Then, θj(z=0) can be tuned as follows. We set one signal channel (channel 2, at the wavelength of 1551.88 nm) as a reference channel. Then we fine-tune the wavelengths of the CW signals at channel 1 and channel 3 at the transmitter, while monitoring the output of the in-line PSA by a digital oscilloscope. When the wavelengths of channel 1 (1550.23 nm) and channel 3 (1553.97 nm) are tuned to 1550.08 nm and 1554.18 nm, respectively, we observed synchronous phase-sensitive amplification for all three signal channels as shown in Movie 1 (right).
Movie 2(right) shows that the three signal channel outputs reach their maximum level at the same time. Once the wavelength of each signal channel, corresponding to synchronous amplification, is selected, we turn on the phase-locking unit of the in-line PSA to achieve phase-locking between the pump and the signal-idler pair for each channel. We observe that all three channels are locked to their maximum power levels simultaneously.
Figure 3 shows the optical spectrum at the PSA output when synchronous phase-sensitive amplification has been achieved. The phase-sensitive gains are 12 dB, 12.9 dB, and 12.7 dB for the channels at wavelengths of 1554.18 nm, 1551.88 nm, and 1550.08 nm, respectively. Note that, even though we operate the FOPAs in the small-signal amplification regime, several small spurious peaks, each arising from the interaction of two signals and the pump (“wavelength conversion” process rather than the “parametric amplification” process) are observed on both sides of the pump wavelength. The presence of such peaks can be mitigated by using guard bands around the pump or by further reducing the input signal powers.
4. System considerations
Let us note that the combination of a PIA and a PSA, as described in our experiments, by itself does not offer the advantage of having a noise figure (NF) below the PIA quantum limit of 3 dB. Indeed, the NF of a PIA-PSA combination is determined by the PIA NF, which is subject to the 3-dB limit. Therefore, the PIA-PSA combination can not be used as a lumped noiseless amplifier (For this purpose, however, one can use the frequency degenerate PSAs [6, 7, 9, 11] or frequency nondegenerate PSAs with signal-idler prepared through the wavelength conversion process , although these approaches are not WDM compatible.) On the other hand, using a PIA at the transmitter to prepare the signal-idler pairs for subsequent propagation through a chain of PSA-amplified links is the most attractive application of our multi-channel PSA scheme. In such a scenario, the net noise is determined by the multiple PSA-amplified spans with a negligible contribution from the first PIA, resulting in a 3-dB NF advantage compared to an all-PIA chain.
A potential implementation of such multi-channel-PSA-based transmission-link architecture is shown in Fig. 4, extending the approach of . Each PSA node (dashed-line shaded box), possibly featuring add/drop capability, sits on a bus carrying the multiple signal-idler pairs, as well as a remainder (pilot tone) of the pump. Thus, the transmission link preserves the phase relationship between the signals, idlers and the pump, except for possible small drifts from the optimum phase and polarization owing to chromatic and polarization-mode dispersions, respectively. These small and slow drifts (if any) can be compensated for by dispersion and polarization trimming of the signal channels before they enter each PSA. At the input of each PSA node, the pump pilot tone (or tones, in case of 2-pump PSAs) is separated from the bus and used for phase locking of a local pump. Thus, each PSA can use a local pump with very small relative intensity noise (RIN) to avoid the signal degradation by pump RIN [24, 25]. (In our experiment, for a proof of concept only, we simply amplified the pilot tone to produce the pump; this may lead to excessive RIN and should be avoided in a real system.) Using the relatively strong pump pilot tone rather than a weak signal after the transmission span can greatly improve the phase recovery in both injection-locking [13, 26] and optical phase-locked-loop  schemes. Local transmitter (add port of the node) consists of a conventional transmitter (or multiple transmitters for multiple added channels) followed by a PIA to produce a two-sideband spectrum (signals+idlers). The pump of the PIA is also locked to the same pilot tone as the PSA pump, thereby producing the signal-idler pairs automatically matched for the best PSA gain. The local channels are added to the bus channels and are amplified by the PSA before being sent to the next transmission span. The co-transmission of the remainder of the pump as a pilot tone distributes the relative signal-idler-pump phase information over the transmission link and hence makes the bus phase-synchronous. Since the phase locking is only needed for one or two pumps, its complexity does not increase with the number of WDM channels, which makes this scheme economically feasible.
In addition to low-noise amplification of the amplitude, the PSA also performs regeneration of the binary phase information, such as that in differential or binary phase-shift keying (e.g., ). Since phase regeneration undoes the frequency chirp and jitter due to intra-and inter-channel nonlinearities, it can result in suppression of the timing jitter, thereby leading to multi-channel re-timing. At the same time, the WDM channels can be totally independent, with no need for clock synchronization among them. This makes a good case for the PSA as an enabler of multichannel all-optical 3R regeneration, particularly, in combination with multichannel amplitude regenerators [27, 28].
Let us, however, point out the difference between the phase regeneration obtained using the frequency degenerate versus the frequency nondegenerate PSAs. The degenerate PSA performs regeneration by directly stabilizing the signal phase with respect to the pump. The nondegenerate PSA, on the other hand, stabilizes the sum of the signal and idler phases, i.e., it makes the phase noises anticorrelated in the two beams. Thus, if both the signal and idler are modulated by the same DPSK pattern, one can take advantage of this anticorrelation to cancel the noise at the receiver by detecting both the signal and the idler beams with DPSK-type receivers and subsequently adding their photocurrents. One can also employ a wavelength converter  at the receiver, which would recombine the signal and idler into a single beam with suppressed phase noise. Perhaps, in the future, even simpler coding/detection schemes can be developed with this signal-idler phase anticorrelation in mind.
We have demonstrated, for the first time, a phase-sensitive fiber parametric amplifier for simultaneous amplification of multiple channels of CW light. This is achieved by using a phase-insensitive parametric amplifier to create three signal-idler pairs that are then sent into an in-line phase-sensitive amplifier based on the frequency nondegenerate four-wave-mixing process. After fine-tuning of the wavelength of each individual channel, the in-line PSA is able to simultaneously amplify all three signal channels. This indicates that the in-line PSA can potentially amplify multiple wavelength-division multiplexed data signals. We have also introduced a potential system architecture that can take full advantage of our approach to the generation and frequency nondegenerate phase-sensitive amplification of multiple signals.
This research was supported in part by the U. S. National Science Foundation under Grant No. ECS-0401251.
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