All-optical storage of a picosecond-pulse packet using parametric amplification
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1 All-optical storage of a picosecond-pulse packet using parametric amplification Glenn D. Bartolini, Darwin K. Serkland, and Prem Kumar Department of Electrical and Computer Engineering, Northwestern University, 2145 N. Sheridan Road, Evanston, Illinois Abstract We demonstrate all-optical storage of a picosecondpulse packet of ones and zeros in a fiber buffer in which loss is compensated by parametric amplification. An all-fiber phase-sensitive parametric amplifier, which exploits a nonlinear Sagnac loop made of standard polarization-maintaining fiber to provide gain, regenerates the stored pulses on each round-trip. The parametric amplifier and the storage fiber combine to form a non-self-starting degenerate optical parametric oscillator. In such a device, the zeros do not build up from noise, and the phase-sensitive nature of the amplifier provides stability to the ones. In our experiment, 32-bit packets with different bit patterns are loaded and stored in the buffer. Storage for periods of time up to 1 ms has been observed and single-shot loading of the data packet is demonstrated. Data packets of 1 s of kilobits could be stored in this device with use of a higher repetition-rate pump source. Key Words Nonlinear optical devices, Nonlinear optics fibers, Optical data storage, Optical amplifiers, Parametric oscillators and amplifiers, Pulse propagation and solitons, Optical communications, Fiber-optic networks. Introduction Optical storage buffers are expected to be an important component in high-speed TDM optical networks. They can be used for queuing packets while transmitters await access to the network, for enabling receivers to handle data at rates faster than can be processed, and for rate-conversion in conjunction with optical switches. Such devices will be required to store packets with lengths on the order of 1 kbits and storage times approaching hundreds of microseconds. 1 Previous experiments using fiber logic gates 2 6 have demonstrated long-term storage at rates up to 1 GHz for packets that are several hundreds of bits long. Storage loops capable of up to 8-GHz bit rates have been demonstrated; however, these require either direct amplitude modulation 7 9 or indirect optical modulation via crossgain saturation 1 to maintain the bit timing. Such devices have made use of Er-doped fiber amplifiers (ED- FAs) to compensate for the linear loss and require filtering to suppress the amplified spontaneous-emission noise. We have proposed the use of phase-sensitive optical parametric amplification as a means for overcoming the fiber loss in soliton storage loops. 11 The use of a phase-sensitive parametric amplifier (PSA) in place of an EDFA considerably simplifies the storage loop design. Using standard fibers, we recently demonstrated all-optical storage of a picosecond-pulse packet in a fiber buffer that made use of a fiber-optic PSA to overcome the loss. 12 In addition to simplifying the storage loop design, the use of a PSA provides stability to the stored bitstream while regenerating the bit pattern. Such a system has been shown to be self-stabilizing and robust against noise. 13 PSAs in Sagnac-interferometer configurations have been demonstrated that achieve gains as high as 23 db 14,15 with use of a single 1.5 µm source for both the pump and signal pulses. Their use as in-line amplifiers has been proposed for stable soliton propagation, 16 dispersion compensation, 17 and noise control in fiberoptic networks. 18,19 Recently, the use of PSAs for amplitude-noise suppression 15 and, with independent phase-locked sources, 2,21 as in-line amplifiers has been demonstrated. In this paper we present further results pertaining to our demonstration 12 of the use of a PSA in a fiber buffer that can store picosecond-pulse packets of ones and zeros. In particular, we present data showing storage for up to 1 ms and, in addition, demonstrate single-shot loading of the injected packet. The latter
2 is a considerable improvement over our initial demonstration 12 in which the data packet had to be multiply presented to the storage buffer before loading would occur. Experimental Setup Figure 1. Experimental configuration of the storage buffer; MLFL, mode-locked fiber laser; FPC, fiber polarization controller; AM, amplitude modulator; PSA, phase-sensitive amplifier. The layout of our storage experiment is shown in Fig. 1. A saturable-absorber mode-locked Er:Yb-fiber laser (PriTel, Model PFL-155) was used to generate 3.2 ps FWHM pulses at 1543 nm with a repetition rate of 29 MHz. The average output power was 4 mw; 1% of which was used to drive the synchronization electronics. The remaining 9% power was split using an 8/2 coupler. The 8% output was amplified using a home-built Er:Yb-fiber amplifier to increase the average power to 5 mw, which was used to pump a fiber PSA that is in the configuration of a nonlinear Sagnac interferometer. 14 The 2% output was amplified with a second home-built Er:Yb-fiber amplifier and used to create the injected packets. As shown in Fig. 1, the PSA consisted of a variable 5/5 fiber coupler (Canadian Instrumentation and Research, Model 95-P) with its two outputs spliced to the ends of a 5 m piece of standard polarization-maintaining (PM) fiber (3M, Model FS-PM-7621). One input of the 5/5 coupler was connected to a 32-bit storage line that was made of standard fiber (Corning, Model SMF-28). The other input was used to inject pump pulses into the PSA. The storage line and the PSA combination formed the fiber buffer, which had a total round-trip length of 227 m. The variable 5/5 coupler was balanced to minimize pump leakage into the storage line to less than.4% of the incident pump power. The storage line also contained a fiber-stretching phase controller, a fiber polarization controller (FPC), a collimating lens, and a movable mirror M1 (18.2% transmission) to tune the length of the storage line to an exact multiple of the laser repetition period. The length adjustment was required to ensure that the stored pulses after each roundtrip overlapped with the incoming pump pulses in the PSA. A line configuration for storage was chosen because it had less total round-trip loss ( 7 db) than the loop configuration; the fiber circulator required to complete a storage loop was found to have too much loss (3 db per pass). The signal arm was used to inject bit patterns, which were created using an amplitude modulator (AM) in conjunction with timing circuitry that was synchronized to the laser pulses. Phase-Sensitive Fiber Parametric Amplifier We first tested the PSA by disconnecting the storage line (at C in Fig. 1) from the rest of the setup. Extra fiber was inserted into the signal arm to delay the signal pulses by exactly one pulse period as compared to pulses in the pump arm. By heating this extra length of fiber to vary its optical path, we made sure that the pump and signal pulses overlapped each other within the PSA. The FPC s in the pump and signal arms were used to align the polarizations of the respective pulses with one axis of the PM fiber (the fast axis was chosen) to ensure self-phase modulation (SPM) of the interferometricallycombined pump and signal pulses within the PSA. In this way, pulse-energy gains as high as 2 could be obtained with 5 mw of average input pump power. Autocorrelation Power (a.u.) Input Pump & Signal Reflected Pump Amplified Signal Time (ps) Figure 2. Autocorrelation traces of the input pump and signal pulses (thick), the reflected pump pulses (dashed), and the amplified signal pulses (thin) from the fiber PSA. 2
3 Figure 2 shows autocorrelation traces of the input pump and signal pulses to the PSA (thick curve), the reflected pump pulses from the PSA (dashed curve), and the amplified signal pulses with 13 db energy gain (thin curve). The input pump and signal pulses to the PSA had FWHM pulsewidths of 3.2 ps, the returning pump pulses from the PSA had a FWHM pulsewidth of 1.5 ps, and the amplified signal pulses for the case of 13 db gain had a FWHM pulsewidth of 1. ps. The pump pulses underwent SPM that resulted in their narrowing from 3.2 to 1.5 ps upon propagation in the anomalousdispersion PM fiber of the PSA. Furthermore, since the PSA gain is proportional to the peak power of the pump pulse, the central part of the signal pulse was amplified more than the wings, resulting in narrowing of the amplified signal pulse from 3.2 to 1.5 ps. In this way the pump acted as an intensity filter for the signal, reshaping the signal pulse and recentering it in the time slot dictated by the pump-pulse repetition rate and pulsewidth. Analysis and numerical simulations of pulse propagation in the Sagnac loop of the PSA 22 show pulse narrowing for the reflected pump and the amplified signal pulses comparable to those presented in Fig. 2. The simulations show that the pulse narrowing can be reduced by using low-dispersion PM fiber in the PSA. Gain Average Signal Power (µw) Average Pump Power (mw) Figure 3. Measured PSA gain (symbols) versus pump average power for four values of the input-signal average power. Note that for the parameters of our laser, P peak (W) = 1 P avg(mw). Dashed and solid curves are fits using Eqs. (1) and (2); see text for details. Phase-sensitive gain for different pump and signal powers was measured by injecting the pump and signal pulses into the PSA and observing the average power of the amplified output-signal pulses at port C (cf. Fig. 1). The data was corrected for the pump leakage, which was less than.4%, by subtracting the leakage average power from the amplified-signal average power. The results are plotted by the symbols in Fig. 3, where we show the PSA gain as a function of the average pump power for various average input signal powers. For CW excitation, the PSA gain is given by 23 G = cos 2 ( Φ nl ) + P p sin 2 ( Φ nl ) P s Pp P s sin (2 Φ nl ) sin (φ p φ s ), (1) where the differential nonlinear phase shift is Φ nl = 2πn 2L λa eff Ps P p cos (φ p φ s ). (2) In these formulas, P s (P p ) is the power of the signal (pump) wave, n 2 is the fiber nonlinearity, L is the length of the fiber (5 m in our experiment), λ = µm is the wavelength of the laser, A eff is the effective area of the fiber mode, and φ s (φ p ) is the phase of the signal (pump) wave. When (2πn 2 L/λA eff ) P s P p 1, a condition that is satisfied in our experiment, maximum gain occurs for φ s = φ p, which then defines the signal gain quadrature. Strictly speaking, since Eqs. (1) and (2) assume a CW interaction, they cannot be used to describe the data in Fig. 3. In addition, there is significant pulse evolution in our PSA as shown by the autocorrelation traces in Fig. 2. Nevertheless, to gauge the extent of the validity of Eqs. (1) and (2), we have plotted them (dashed and solid curves) in Fig. 3 for the choice φ s = φ p and by taking P s (P p ) to be the peak signal (pump) power. Other parameters used are: n 2 = m 2 /W and A eff = m 2. However, to obtain a reasonable fit over the whole range of the average pump powers, we had to assume a reduced pulsewidth for the pump pulses (2.9 ps instead of 3.5 ps) for average powers above 2 mw. Although such a procedure is ad hoc, it is supported by the pump-pulse narrowing shown in Fig. 2. We have extensively modeled the behavior of a Sagnac-loop PSA under pulsed excitation, 22 taking into account the time-varying SPM interaction and the dispersion properties of the fiber. Numerical simulations with pulse energies and widths equal to those used in the experiment give gain curves that are qualitatively similar to those plotted in Fig. 3. In the storage experiments described below, the PSA gain was chosen to be large enough to overcome the round-trip loss of the circulating pulses in the storage line. Fiber-optic Degenerate Parametric Oscillator After characterizing the PSA as described in the previous section, we re-connected the storage line at port C (cf. Fig. 1). We then disconnected the signal path and unbalanced the variable 5/5 coupler to allow more of the pump power to leak into the storage line. In this case the system acted as a degenerate optical parametric oscillator (DOPO). 24,25 When the total roundtrip accumulated phase, both linear and nonlinear, of a 3
4 leakage pulse through the storage line was optimum for amplification by the PSA, the leakage pulse got amplified over successive round-trips until the PSA saturated. This also required that the storage line polarization be aligned with the fast axis of the PM fiber, thus ensuring maximum amplification by the PSA. Autocorrelation Power (a.u.) Reflected Pump Depleted Pump DOPO Pulse Time (ps) Figure 4. Autocorrelation traces of the DOPO output pulses (thin) and the reflected pump pulses from the PSA, with (dashed) and without (thick) the DOPO action. Figure 4 shows autocorrelation traces of the reflected pump pulses for the cases where the DOPO was inactive (thick solid line) and active (dashed line), as well as for the output DOPO pulses (thin solid line). As before, the pump pulses underwent SPM that resulted in their narrowing from 3.2 to 1.5 ps FWHM upon propagation in the anomalous-dispersion PM fiber of the PSA. When the DOPO was active, the reflected pump pulses narrowed further from 1.5 to 1.2 ps FWHM due to pump depletion caused by build up of the DOPO pulses. Moreover, as shown by the thin solid line in Fig. 4, the profile of the DOPO pulses followed closely that of the depleted pump pulses in the central region. In the wings the difference is possibly due to phase chirp introduced onto the DOPO pulses upon roundtrip propagation through the storage line. The total average power of the pulses in the storage line reached nearly 2. mw for an average pump power of 5 mw. We were able to stabilize the DOPO output using feedback to the fiber phase controller for periods of up to 1 hour. The DOPO described above is bistable; it is a nonself-starting oscillator, requiring a minimum injected signal power (pump leakage in the above experiment) to initiate oscillation. Injected signal pulses with sufficient power (ones) experience SPM, which counteracts dispersion and produces the required nonlinear phase shift for optimum amplification by the PSA. Low-power signal pulses (zeros), however, are not optimally amplified since they experience only a linear phase shift. In addition, they see an effective loss due to dispersion, which shifts energy out of the gain window set by the pump pulses. In this way both the ones and the zeros in the DOPO remain stable, making the device suitable for optical storage. Storage Experiments To demonstrate storage of a bit pattern in the fiber buffer, we re-balanced the variable 5/5 coupler (cf. Fig. 1) to reduce the pump leakage to below.4%, which was insufficient to turn on the DOPO, and injected pulses from the signal arm into the storage line. The AM was used to create 32-bit packets that consisted of 8 successive ones followed by 24 zeros, with a one (zero) represented by the presence (absence) of a pulse. We note here that the choice of 8 successive ones followed by 24 zeros was completely arbitrary and was motivated by our technique of observing the stored packet for long periods of time with the use of a slow-response photodetector (see below). We have also achieved storage with bit patterns of 6 successive ones followed by 26 zeros (used in the 1 ms storage experiment described below), 4 successive zeros followed by 28 successive ones, as well as with all ones (the DOPO experiment described above). In our initial experiment, packets with 2 µw of average signal power were injected into the PSA through the storage line using a 1/9 coupler, again taking care to align the polarization of the input signal pulses with the fast axis of the PM fiber. With such a low average signal power, however, it was necessary to repeatedly load the packet upon several successive round-trips until the power in the storage line was sufficient to maintain storage. The bistability of the DOPO ensured that the ones did not build up where there were zeros in the signal packet. In subsequent experiments (see below), we increased the average signal power to a value such that only a single injection of the packet was sufficient to load the storage line. With the above scheme of using an AM to load the storage line, loading occurs only when the input signal phase is optimum for amplification by the PSA. Rather than actively stabilizing both the input-signal and the storage-line phases, we simply allowed the two to drift. Occasional storage of pulse packets occurred when the two phases drifted to their optimum values, lasting for about a millisecond, which is the characteristic time scale of the phase drift. We note here that loading of the storage line can be accomplished in a manner which does not depend on the phase of the signal pulses. For example, if the signal pulse arriving from a remote location is used to cross-phase modulate the pump pulse in the Sagnac loop of the PSA, then a portion of the pump pulse will be switched into the storage line, representing an in-phase copy of the signal pulse. When a zero arrives, no cross-phase modulation occurs, and no pulse will be injected into the storage line. We are in 4
5 the process of setting up an experiment to demonstrate such loading of the storage line. limitations of our oscilloscope. The packet was stored for 132 µs before the next loading session began. Figure 5. Output of the storage buffer. (a) Top trace shows the injected packets with the bottom trace showing storage of the loaded packet for 12 round-trips. (b) Close-up view of the stored packet. For comparison, three simulated packets have been overlain onto the photodiode response. Figure 5(a) shows the injected signal used to load the storage line as well as the output of the storage line. The contents of the storage line were monitored by detecting the light transmitted through mirror M1 with an InGaAs photodiode having a 1 ns response time and a digital oscilloscope. Each large spike contains the 8 one bits whereas the valleys correspond to the 24 zero bits, their combination creating the 32-bit packet. As shown in the top trace of Fig. 5(a), we loaded the same packet for 8 round-trips (starting at 5 µs) and then switched it off for the next 12 round-trips. The bottom trace in Fig. 5(a) shows the circulating packet in the storage buffer. From 5 to 13 µs the signal packet was being loaded into the storage buffer, and from 13 to 145 µs the loaded packet was maintained in the storage buffer by the PSA until the next set of 8 injected packets arrived. Figure 5(b) shows a closer view of the stored packet from 81 to 84 µs, which displays the photodiode response more clearly. The 8 ones charged the photodiode, with a slight discharge between the successive ones. During the 24 zeros the photodiode discharged slowly, until the packet arrived again on the next round-trip in the storage buffer. Use of a slow photodiode thus allowed us to record long data streams within the memory Loading Packets.8 Stored Packets Time (ms) Normalized Power Normalized Power Normalized Power Normalized Power Stored Packets Time (ms) Loading Packets Stored Packets Time (ms) Stored Packets Time (ms) Figure 6. Output of the storage buffer showing the loaded packet being refreshed and maintained for up to 1 ms. Top trace shows the injected packets with the bottom trace showing the output of the storage buffer. By delaying the subsequent loading sessions, we have observed a packet being stored for up to 1 ms, or about 9 round-trips in the storage buffer. Figure 6 shows the injected signal used to load the storage line as well as the output of the storage line for this case. In this experiment, we presented the same packet, which consisted of 6 successive ones followed by 26 zeros, to the storage line for 8 consecutive round-trips (from.1 to.18 ms, top trace) and then observed the contents of the storage line (bottom trace) for 54 round-trips until the next set of 8 injected packets arrived at.563 ms. As shown, the phase of the injected signal pulses in the second loading session (from.563 to.57 ms, top trace) was still matched to the circulating pulses in the storage line (bottom trace), since the two sets of pulses added coherently. The stored packet was thus refreshed and the data maintained in the storage line, even after the second loading session, until beyond our observation window of 1 ms. Figure 7 shows a closer view of the stored packet for three regions of interest: (a) from 2 to 4 µs, i.e., just after the initial loading session; (b) from 46 to 48 µs, i.e., after 4 round-trips; and 5
6 (c) from 8 to 82 µs, i.e., well after the second loading session. The righthand column in Fig. 7 shows an expanded view of the photodiode response, with simulated packets overlain onto the curves to emphasize the packet structure of 6 consecutive ones and 26 zeros. (a) (b) (c) Figure 7. Expanded views of the storage-buffer output for the data shown in Fig. 6 (bottom trace). The lefthand plots show the data packet at various times as it circulates in the storage line. The righthand plots show the photodiode response in more detail; simulated packets have been overlain to highlight the 6 consecutive ones followed by the 26 zeros. For the close-up views, three times were arbitrarily chosen: (a) immediately following the initial loading session, (b) after 4 round-trips, and (c) well after the second loading session. As mentioned before, active phase stabilization of the storage line was not implemented for the above set of experiments. Although for the data shown in Fig. 6, the stored packet was maintained for a period of time that is longer than our recording window of 1 ms, we expect a millisecond to be the typical holding time without active stabilization. This is because the characteristic time scale of the phase drift between the stored-signal pulses and the pump pulses is on that order. However, we anticipate that active stabilization of the phase drift in the storage buffer will significantly increase the holding time. Single-Shot Loading In the storage experiments described above, data packets had to be multiply presented to the storage buffer before loading would occur. This was due to insufficient power in the signal arm (cf. Fig. 1). To demonstrate single-shot loading of the storage buffer, we added a home-built Er:Yb-fiber amplifier in the signal arm to increase the average signal power by 1 db. With this amplifier in place, packets with 2 µw of average signal power were injected into the PSA through the 1/9 coupler. An injected packet experienced a single-pass gain of 4.5 upon propagation through the PSA, thereby producing 1 mw of average power in the storage line, which was sufficient to initiate storage. Figure 8(a) shows the injected signal packet used to load the storage line as well as the output of the storage line. Beginning at 29 µs, the top trace in Fig. 8(a) shows the single loading packet that consisted of 8 successive ones followed by 24 zeros. The bottom trace displays the photodiode response caused by the circulating packet in the storage line for 64 round-trips. Figure 8(b) shows an expanded view of the stored packet from 8 to 84.5 µs, displaying a much clearer view of the packet structure within the photodiode response. Figure 8. Output of the storage buffer for the case with single-shot loading. (a) Top trace shows the injected packet with the bottom trace showing storage of the loaded packet for 64 round-trips. (b) An expanded view of the stored packet. For comparison, simulated packets have been overlain onto the photodiode response. 6
7 Conclusion In summary, we have demonstrated all-optical storage of a picosecond-pulse packet of ones and zeros in a fiber buffer in which loss is compensated using phasesensitive parametric amplification. Storage for periods of time up to 1 ms was observed and single-shot loading of the data packet was demonstrated. Long-term phase stabilization of the storage line was achieved for the case where pump leakage was used to load the buffer with all ones. With enhanced phase stabilization and, for example, a 29-GHz-repetition-rate source, 26,27 long-term storage of 32-kbit packets should be possible, making this device a potential buffer for use in high-speed optical networks. At such high data rates though, a PSA made with either a longer-length or higher-nonlinearity fiber will be needed to lower the required average power. Acknowledgments This work was supported in part by the DARPA under the MURI program. The authors acknowledge useful discussions with Antonio Mecozzi. References 1. R. A. Barry, V. W. S. Chan, K. L. Hall, E. S. Kintzer, J. D. Moores, K. A. Rauschenbach, L. E. Adams, E. A. Swanson, C. R. Doerr, S. G. Finn, H. A. Haus, E. P. Ippen, W. S. Wong, and M. Haner, All-Optical Network Consortium Ultrafast TDM Networks, IEEE J. Select. Areas Commun. 14, (1996). 2. V. I. Belotitskii, E. A. Kuzin, M. P. Petrov, and V. V. Spirin, Demonstration of over 1 million round-trips in recirculating fibre loop with all-optical regeneration, Electron. Lett. 29, 49 5 (1993). 3. H. Avramopoulos and N. A. Whitaker, Jr., Addressable fiber-loop memory, Opt. Lett. 18, (1993). 4. A. J. Poustie, R. J. Manning, and K. J. Blow, Alloptical circulating shift register using a semiconductor optical amplifier in a fiber loop mirror, Electron. Lett. 32, (1996). 5. A. J. Poustie, K. J. Blow, R. J. Manning, All-optical regenerative memory, in Nonlinear Guided Waves and Their Applications, Vol. 15, 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), postdeadline paper SUB4. 6. N. A. Whitaker, Jr., M. C. Gabriel, H. Avramopoulos, and A. Huang, All-optical, all-fiber circulating shift register with an inverter, Opt. Lett. 16, (1991). 7. J. D. Moores, K. L. Hall, S. M. LePage, K. A. Rauschenbach, W. S. Wong, H. A. Haus, and E. P. Ippen, 2-GHz Optical Storage Loop/Laser Using Amplitude Modulation, Filtering, and Artificial Fast Saturable Absorption, IEEE Photon. Technol. Lett. 7, (1995). 8. J. D. Moores, 8-Gb/s 9-kbit optical pulse storage loop, in Optical Fiber Communication Conference, Vol. 6 of 1997 OSA Technical Digest Series, (Optical Society of America, Washington, D.C., 1997), pp J. D. Moores, W.S. Wong, and K. L. Hall, 5-Gb/s optical pulse storage ring using novel rational-harmonic modulation, Opt. Lett. 2, (1995). 1. K. L. Hall, J. D. Moores, K. A. Rauschenbach, W. S. Wong, E. P. Ippen, and H. A. Haus, All-Optical Storage of a 1.25 kb Packet at 1 Gb/s, IEEE Photon. Technol. Lett. 7, (1995). 11. A. Mecozzi, W. L. Kath, P. Kumar, and C. G. Goedde, Long-term storage of a soliton bit stream by use of phase-sensitive amplification, Opt. Lett. 19, (1994). 12. G. D. Bartolini, D. K. Serkland, P. Kumar, and W. L. Kath. All-optical storage of a picosecond-pulse packet using parametric amplification, IEEE Photon. Technol. Lett. 9, (1997). 13. W. L. Kath, A. Mecozzi, P. Kumar, and C. G. Goedde, Long-term storage of a soliton bit stream using phasesensitive amplification: Effects of soliton-soliton interactions and quantum noise, to be published. 14. G. Bartolini, R.-D. Li, P. Kumar, W. Riha, and K. V. Reddy, 1.5 µm phase-sensitive amplifier for ultrahighspeed communication, in Optical Fiber Communication Conference, Vol. 4 of 1994 OSA Technical Digest Series, (Optical Society of America, Washington, D.C., 1994), pp A. Takada and W. Imajuku, Amplitude noise suppression using a high-gain phase-sensitive amplifier as a limiting amplifier, Electron. Lett. 32, (1996). 16. J. N. Kutz, C. V. Hile, W. L. Kath, R.-D. Li, and P. Kumar, Pulse propagation in nonlinear optical fiber-lines that employ phase-sensitive parametric amplifiers, J. Opt. Soc. Am. B 11, (1994). 17. R.-D. Li, P. Kumar, and W. L. Kath, Dispersion compensation with phase-sensitive amplifiers, J. of Lightwave Technol. 12, (1994). 18. H. P. Yuen, Reduction of quantum fluctuation and suppression of the Gordon-Haus effect with phasesensitive linear amplifiers, Opt. Lett. 17, (1992). 19. W. Imajuku and A. Takada, Reduction of fibernonlinearity-enhanced amplifier noise by means of phase-sensitive amplifiers, Opt. Lett. 22, (1997). 2. W. Imajuku and A. Takada. In-line phase-sensitive amplifier with optical-pll-controlled internal pump light source, in Optical Amplifiers and Their Applications Topical Meeting, (Optical Society of America, Washington, D.C., 1997), postdeadline paper PDP W. Imajuku and A. Takada, Optical phase-sensitive amplification using two phase-locked light sources, in 7
8 Optical Amplifiers and Their Applications Technical Digest, (Optical Society of America, Washington, D.C., 1997), pp G. Kanter, P. Kumar, and W. L. Kath, Pulsed response of a fiber-optic phase-sensitive parametric amplifier, to be presented at the 1997 Optical Society of America Annual Meeting, Long Beach, CA, October See Supplement to Optics and Photonics News, Vol. 8, No. 8, August 1997, pp. 112, Paper TuCCC M. E. Marhic and C.-H. Hsia, Optical amplification in a nonlinear interferometer, Electron. Lett. 27, (1991). 24. S. Longhi, Ultrashort-pulse generation in degenerate optical parametric oscillators, Opt. Lett. 2, (1995). 25. S. Longhi, Effects of dispersion and mode locking in optical parametric oscillators, Opt. Lett. 2, (1995). 26. E. A. Swanson and S. R. Chinn, 23-GHz and 123-GHz Soliton Pulse Generation Using Two CW Lasers and Standard Single-Mode Fiber, IEEE Photon. Technol. Lett. 6, (1994). 27. D. K. Serkland, G. D. Bartolini, P. Kumar, W. L. Kath, and A. V. Sahakian, Rate doubling of a highly-stable soliton source, in Optical Fiber Communication Conference, Vol. 6 of 1997 OSA Technical Digest Series, (Optical Society of America, Washington, D.C., 1997), pp
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