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We measure impairment of on-off-keyed and differential-phase-shift-keyed signals imposed by gain saturation in a fiber parametric amplifier. Phase modulation is observed to be more robust, particularly for deep (15 dB) saturation.
©2007 Optical Society of America
1. Introduction
Parametric processes in high-confinement fibers have been used to demonstrate record amplification [1,2] and signal conversion performance [3]. In contrast to conventional parametric gain in crystals [4], fiber parametric amplifiers (FPA's) offer considerably longer interaction lengths and are capable of high gain and conversion efficiency, even with continuous-wave (CW) inputs [1,2]. While a well-engineered periodically-poled lithium-niobate (PPLN) device provides centimeters of interaction length [4], FPA's can be constructed using hundreds of meters of highly nonlinear fiber (HNLF). However, this long interaction length presents a dubious advantage since it requires precise phase matching over hundreds of meters [5]. More importantly, the long interaction length poses design challenges in highly depleted parametric devices [6]. Efficient FPA operation dictates maximal transfer of pump power to the signal and idler bands, which is feasible even with moderate signal input powers [6,7]. (We adopt here the usual nomenclature in which the pump or pumps are of higher power and relinquish two photons that are converted to a signal photon and an idler photon, the idler and signal frequencies being spaced symmetrically about the mean pump frequency.) However, the depleted pump can cause serious impairment for intensity-modulated input. Signal-pump-signal power transfer is a well recognized problem in transmission links amplified by co-directional Raman pumps [8] and can be mitigated by the introduction of high dispersion segments in order to achieve rapid signal-pump walk-off. Unfortunately, the introduction of a high dispersion section to an FPA would destroy the phase matching provided by low-dispersion HNLF. As an illustration, a co-directionally pumped Raman link is operated approximately 100 nm away from the fiber zero-dispersion wavelength (λ 0) while an FPA typically operates zero to tens of nm from the HNLF λ 0. In addition, typical transmission fiber used in Raman gain (such as non-zero dispersion-shifted fiber) has dispersion slopes of 0.05 to 0.08 ps/(km-nm2), while the dispersion slopes in HNLF can be lower than 0.003 ps/(km-nm2).
Pattern-dependent pump depletion in FPAs can be avoided by amplifying constant-amplitude signals. This is the case for phase-coded signals that have not experienced significant net dispersion, allowing, in principle, the FPA to operate in the highly depleted pump regime. Performance of phase modulated signals has been recently studied in [9,10]. However previous investigations did not focus on the depletion aspects of FPA operation. Furthermore, the modulation formats used in [9, 10] relied on intensity shaping by means of return-to-zero/non-return-to-zero differential phase shift keying (RZ/NRZ-DPSK) modulation [11].
This paper describes an experimental study of a two-pump depleted FPA operation and compares phase-shift-keyed (PSK) performance to amplitude-shift-keyed (ASK) performance. In the investigation, the depletion is achieved by loading the FPA by a single modulated channel. Although, from a wavelength division multiplexing (WDM) system point of view, a case of interest would correspond to a multiple channel loading, as demonstrated by our results, significant FPA depletion is achievable even in a single channel scenario. The adopted approach in this work (single channel investigation) has an added benefit of decoupling the depletion effects on the system performance from the inter-channel four wave mixing, which is unavoidable and has been demonstrated to lead to penalties even in the undepleted FPA operation [9,10].
2. Experiment
Figure 1 shows the two-pump amplifier apparatus used in the FPA depletion study. External-cavity lasers (ECL P1 and ECL P2) tuned to 1563 nm and 1600 nm, and amplified to 0.34 W and 0.23 W, respectively, served as pump seeds that were coupled to the HNLF. Sinusoidal phase modulation at three radio-frequencies (RF) broadened the seed spectra to increase the threshold for stimulated Brillouin scattering (SBS) in the HNLF to beyond 0.45 W. While the phase of the amplified signal does not depend on the phase of the broadened pump spectra, the converted signal phase is highly influenced by the pumps’ and signal’s phases [1,2], presenting, thus, a serious obstacle to attaining an undistorted idler. This impediments can be overcome by employing the single-modulator counter-phased-pump technique [13,14]. The sum of the instantaneous pump frequencies is maintained constant by ensuring that the two pumps are phase-modulated in an exact opposition at the input of the HNLF. In a departure from the digital phase modulation previously used for pump counter-phasing [13,14], summation of three harmonics is an analog fashion, with properly adjusted phase delays, was used for the first time in this configuration. A multiplexer (WDMC) combined the seed pump signals prior to modulation. Three radio frequency (RF)
Fig. 1. Apparatus used to study pump depletion containing external-cavity lasers (ECL), wavelength multiplexers and demultiplexers (WDMC), a phase modulator (PM), an optical delay (τ), optical amplifiers (A), optical filters (F), an isolator (I), an amplitude or phase modulator (AM/PM), variable optical attenuators (VOA), an optical noise source (ASE), a bit-error-rate test set (BERT), and optical spectrum analyzers (OSA). The frequencies, f1, f2, and f3, were used in the suppression of stimulated Brillouin scattering.
oscillators, tuned to 49, 197 and 670 MHz, (f1,2,3), were combined and amplified to drive a phase modulator (PM) which simultaneously modulated both pump seed signals. A demultiplexer (WDMC) then separated the pump seed signals to allow separate amplification. The separate paths traversed by the two pump signals, after the second WDMC, allowed precise insertion of a differential delay, τ, between the pumps, facilitating the counter phasing in the HNLF. Each RF frequency was tuned to minimize phase modulation of the idler signal at the FPA output. The installed delay between the C and the L-band pumps extended over multiple harmonics’ periods, corresponding to the length difference between the C and L-band erbium-doped fiber amplifiers (EDFAs) in the corresponding experimental setup arms (>2m). The two pump seeds were amplified (A), filtered and combined once again in a wavelength multiplexer (WDMC). The polarizations of the pumps were independently controlled using polarization controllers. The counter-phased pumps were combined with the signal path and launched into a 1000-m-long HNLF. The HNLF had a zero-dispersion wavelength of 1583 nm, a dispersion slope of 0.03 ps/km-nm2, and nonlinear parameter, γ, of 16 W-1km-1. Light from an external-cavity laser tuned to a wavelength of 1575.7 nm (ECL S) was modulated to create the signal. Two modulation formats were tested: (i) non-return-to-zero intensity modulation (IM) with 12.5 dB extinction ratio, and (ii) phase modulation (PM) by means of a differential-phase-shift-keyed (DPSK) format, both at 10 Gb/s data-rate. The short-term spectral linewidths of the ECL's used in the experiment were less than 100 kHz, well below the requirements for DPSK modulation at 10 Gb/s [15]. The converted signal performance was measured using the 1586.7-nm idler positioned in the second (2-) inner parametric band of the two-pump system [7]. The transfer of pump modulation to the idler could be observed by using an unmodulated signal.
Figure 2 shows the spectral properties of the idler wave observed with a heterodyne optical spectrum analyzer having a spectral resolution of 10 MHz. The minimum carrier-to-sideband suppression obtained was 18 dB. The worst carrier to sideband corresponded to an artifact tone 200 MHz away from the fundamental harmonic of the second (197 MHz) oscillator. The strong artifact tone was present throughout the measurements (see Fig. 2), and could not be suppressed by frequency tuning. However, the sidebands from the three oscillators were over 30 dB lower than the carrier and, were contained in a ±1GHz bandwidth around the carrier, enabling an error-free parametric wavelength conversion of PSK signals in the experiment, as opposed to the digital pumps’ phase high-speed modulation by a PRBS data pattern, which had been attempted originally and resulted in massive (intolerable) performance penalties. Note that the last fact points that pumps’ counter-phasing achieved was not perfect, and leaves room for further improvements.
Fig. 2. Heterodyne spectrum of 1586.7-nm idler showing influence of counter-phased pump modulation. The signal was unmodulated for this measurement.
A bit-error-rate testing (BERT) section was built for both modulation formats. The desired output wavelength of the FPA (amplified signal or idler) was filtered, amplified and combined with optical noise from a free-running amplifier (ASE). Variable optical attenuator 1 (VOA1) was used to maintain constant average input power to the preamplifier at -5 dBm and hence the constant inversion level. VOA2 adjusted the input power to the receiver to approximately 0 dBm, while VOA3 was used to vary the optical signal-to-noise ratio (OSNR). The configuration allowed measurement of the bit- error-rate (BER) as a function of OSNR for a large range of output signals. In the BER measurement process in the case of DPSK, the analyzer part of the bit-error-rate tester was pre-programmed for the transmitted sequence, instead of relying on electronic decoding of the differentially encoded information. The analyzer memory depth restricted the PRBS length to 223, which was used for both modulation formats.
3. Results
The experimental results will be discussed from two perspectives: (i) parametric gain evolution, discussed in the parts A and B of this section, and (ii) transmission performance dependence on the power input to an FPA (or, equivalently, the FPA gain evolution), covered in the subsection C.
Fig. 3. Evolution of optical spectrum at output of highly-nonlinear fiber with changing signal power for average input powers of a)-27.8 dBm, b) -8.5 dBm, c) +3.3 dBm and d) +12.2 dBm. The NRZ-modulated signal shown here had a wavelength of 1575.7 nm.
A.Optical spectrum evolution
A two-pump FPA operating in the undepleted regime amplifies and simultaneously copies a single signal to three idler bands, as shown in Fig. 3(a). As an intuitive approach to investigating the effect of saturation, Fig. 3 displays the evolution of the parametric spectra. The output spectrum started from a traditional Four-side-band parametric process that involves 4 idlers. With the increase of signal input power, a progressively increasing number of the higher order tones is generated, as the parametric interaction among the lower order tones intensifies. At the maximum signal input power in the experiment (approximately 12dBm), about 30 tones of considerable strength are generated (see Fig. 3), even though the FPA was loaded by a single channel. The described behavior bears significant implications on the performance on WDM systems with FPAs under depletion, and was the major reason for focusing on the single channel investigation in this work. The spectral evolution shown in Fig. 3 was measured using an NRZ modulated signal. However, nearly identical spectral behavior was observed for the DPSK modulation format.
B. Gain saturation and pump depletion
The most important effects of saturation are related to signal gain, idler conversion efficiency and the pump depletion. The measurement results are shown in Figs. 4 and 5.
The FPA saturation was characterized by measuring the on/off conversion efficiency, and the pump depletion, as shown in Fig. 4. The on/off conversion efficiency is defined as the ratio of the power in the generated idler, to the unamplified signal power (pumps not coupled into the HNLF).
The most important finding of our investigation is the existence of multiple saturation points. The results in Fig. 4 indicate that the gain reaches the first saturation point for the input powers higher than -10dBm. After the first local minimum point, the gain grows back again with further increase in input power, followed by a yet another descent (for the input powers surpassing 10 dBm). Thus, owing to the four-wave mixing interactions (which are governing the FPA dynamics), it is possible to drive an FPA out of saturation by a further increase of the input powers. This behavior clearly distinguishes the parametric amplifiers from other types of optical amplifiers, and implies that the term ‘saturation’ may be used only loosely in the context the FPAs. Small input resulted in a nearly linear FPA response (input power variation from -30 to -10 dBm), which in the case of DPSK produced less than 3-dB variation in conversion efficiency (see Fig. 4). The NRZ modulation exhibited a slightly faster saturation trend, as expected from the higher instantaneous powers associated with the format.
Both modulation schemes reached a local minimum in the gain compression point near 0-dBm input power level. As demonstrated in Fig. 4, the depletion of the C-band (1563 nm) and L-band (1600 nm) pumps differed, as a consequence of the Raman power transfer [12], in addition to the different level of the pump launch powers. The maximum depletion of the short- and long-wavelength pumps were 9 dB and 5.5 dB, respectively. The maximum depletion condition occurred at the input signal power of 9 dBm, exhibiting a 3-dB difference with signal modulation format. The C- and L-band pumps’ ratio (influenced by depletion as well as the Raman power transfer [12]) is closely mimicked by the signal and idler growths, as demonstrated in Fig. 5. For low input power cases, the two bands’ output powers are almost identical (see Fig. 5). However, for high input powers, the idler powers are always higher than those of the signal, again attributed to the Stimulated Raman Scattering effect [12].
We note that a simple four-sideband parametric model [7,16], could not account for the observations in the measured results. Indeed, as indicated by the spectral evolution in Fig. 3, in the saturated operating regime, a non-negligible pump power is transferred to higher-order tones [7], in direct contradiction to the contained four-sideband energy conservation, assumed by that model.
C. Impact of saturation on transmission performance
Unlike other optical amplifiers, one of the most unique features of a parametric amplifier is its ultra-fast nonlinear response, resulting in a diverse impact of saturation on different modulation formats.
The BER is the most important figure of merit for communication systems. The traditional BER measurements with respect to the signal-to-noise ratio (SNR) in an FPA are impeded by the inherent coupling between the signal and noise levels, in addition to the effect of the pumps’ phase modulation transfer to the generated idlers. For this reason, and as explained in the experimental setup description, the FPA output was noise loaded with an ASE source, allowing BER measurements for each fixed FPA operation point, independently of its gain, or the input power condition. Furthermore, the adopted arrangement allowed for the performance measurements decoupled from the clock-recovery circuits whose non-negligible input power requirements are known to affect BER measurements made with respect to the received power level. Consequently, the performance in all instances was measured for the generated narrow idler in reference to the optical signal to noise ratio (OSNR) i.e. with respect to the ASE noise, in a 0.1 nm reference bandwidth resolution. The BER varied widely with pump depletion, as illustrated in Figs. 6 and 7. The 7.5 dB discrepancy in performance at back to back between the two modulation formats is attributed to the difference between the (RF) spectral characteristics of the photo-detectors with integrated trans-impedance amplifiers used in the two cases, as illustrated by the eye-diagrams at back-to-back in Fig. 9. A different receiver for the NRZ would, undoubtedly, have been beneficial in obtaining a 3dB (rather than a 7.5dB) performance gain for the DPSK modulation format.
Figures 6 and 7 show the BER measurements for different signal input powers in both NRZ and DPSK cases. Fig.8 and 9 demonstrate the OSNR penalty and the eye diagram evolution for the increase in the signal input power, respectively. The OSNR penalty is defined as the necessary improvement in the optical signal to noise ratio, with respect to the back-to-back performance, needed to achieve the 10-9 BER level for each of the modulation formats. As observable from Figs 8–9, the penalty reaches negligible values for both modulation formats at several input power intervals, distinct from the saturation points.
For both modulation formats (NRZ and DPSK), four distinctive stages of the transmission performance evolution with respect to the input power can be discerned. We refer to the very low input power up to the point of minimum performance penalty as the stage I. Initially, in the stage I, an error floor above the 10-9 BER level can be observed in Fig. 6, for the NRZ format. The origin of the relatively poor performance of the NRZ is the non-ideal pump counter-phasing achieved. The high gain in this stage of operation transfers the pump phase modulation to intensity fluctuations of the idler. In other words, although the phase fluctuations imposed on the pumps are deterministic, they are experienced as noise in the case of NRZ detection [17,18]. In a sharp contrast, the differential demodulation process associated with the DPSK signals is able to partially equalize the low-rate phase (and intensity) fluctuations of the pumps, resulting in a significantly lower (but finite) penalty and the ability of errorless performance for high enough OSNRs. In the stage I, the performance penalty is decreasing with the increase of the input power, as a consequence of the intensity noise being clamped by the parametric regeneration. In addition, the improved performance with the signal input power increase in this stage is, in part, attributed to the gain decrease, resulting in a lower fluctuations transfer from the pumps to the signal [17,18]. After a certain power level, the evolution develops into the saturation stage, denoted as stage II, which extends between the first local penalty minimum and the point corresponding to the maximum performance penalty in Fig. 8. In this stage, the NRZ “0” level can attain higher power than the level “1”, after amplification, owing to a finite extinction ratio (12.5 dB) achieved in the modulation process. This anomalous behavior can be explained by a closer examination of the input-output (I/O) characteristic in Fig. 5, according to which, the negative slope of the I/O dependence in the [-8.5dBm, 0dBm] average input power interval causes the level inversion for the ASK signals. The described level inversion leads to a complete loss of information and a massive penalty, accompanied by the apparition of the error floors in BER curves (see Fig. 6). It should be pointed out that the data-polarity inversion on the BERT analyzer (with unchanged pattern generator polarity) in this interval of input powers enabled finite BER measurements, clearly demonstrating the inversion of the logical information for the intensity modulated waveforms.
At the same time, although subject to deterioration, the DPSK in this stage exhibits significantly lower penalties than the NRZ format, owing to the constant power envelope, as well as to the differential-decoding detection process (the details of this phenomenon will be revisited in more detail in the next Section). The eye diagrams in Fig. 9 for the input powers of -2.58 dBm, as well as the waveform traces in Fig. 10, clearly demonstrate the exacerbation amplitude variations of the non-ideally phase only modulated signal. With further increase of the input power, the penalties experience yet another drop, and the evolution enters into the stage III, bounded by the second minimum in the performance penalty from the upper side
Finally, in the subsequent evolution, the penalties ascend one more time in the stage IV, albeit to a lower degree than in the stage II. . It is important to note that, similarly to the depletion (and saturation) results in Figs. 4 and 5, this second descent in performance penalties has not been theoretically emphasized previously, although the observed behavior (back-and-forth power exchange between the pumps and the signal and idler) is predicted by both the Nonlinear Schrodinger Equation (NLSE), as well as the coupled mode equations [7]. It is equally important to note that both modulation formats exhibited the same consistent behavior. Our results clearly imply, as initially pointed out in [7], that a full scale nonlinear Schrodinger equation is required in order to capture the complete dynamics’ description (of the numerous four-wave mixing tones generated) in stages III and IV, instead of a three-(four-) wave coupled equations often used to simplify the analytics.
We note that, in general, the average signal input powers of the penalty turning points for DPSK are 3dB higher than those for NRZ, implying that it is the peak, rather than the average power that determines the fiber-based parametric amplifier mode of operation. This last observation is also reflected in Fig. 4.
Although the four stages of the transmission performance, defined above, bear similarity to the I/O evolution in Fig. 5, the two characteristics should be distinguished. The primary goal of this manuscript is the investigation of digital communication systems performance under parametric amplification and/or the gain saturation and pumps’ depletion in FPAs, in contrast to the numerous studies of the parametric gain published previously.
4. Discussion
As described in the previous section, both DPSK and NRZ signals experience penalties when FPA gain saturates. For the NRZ format, the different sections of the information-bearing waveforms experience different amounts of gain due to the ultra-fast FPA response. This type of nonlinear reshaping degrades the quality of the NRZ signals making it more difficult (or even impossible, in the worst case scenario) to discern logical ones from the zeros. Correspondingly, the DPSK format is also subject to saturation penalties, however to a substantially lesser amount. In the latter instance of phase modulated signals, the penalties are attributed to the phase-modulation to amplitude-modulation (PM/AM) conversion. In a realistic case, some level of amplitude modulation will always be present on the phase modulated signal envelope, as illustrated in Fig. 10 that shows generated DPSK idler waveforms, which are expected to be uniform in the ideal case. The solid line with the Y1 marker corresponds to 0mW power level for the DPSK waveforms. These undesirable amplitude fluctuations are induced in the (phase) modulation process, subsequently subject to a PM/AM transfer imposed by the dispersive components in the system. In the saturation regime, this PM/AM conversion is further exacerbated by the afore-mentioned saturated FPA nonlinear reshaping, giving rise to a finite amount of the performance deterioration.
5. Conclusion
A narrow idler, with hundreds MHz linewidth, was generated in a dual-pump parametric amplifier, taking advantage of the RF counter phased pump dithering scheme, and was used to study different effects of saturation. The experimental results corroborate theoretically predicted resilience of uniform power envelope signals, such as DPSK, to saturation effects in parametric amplifiers. The cause of the saturation penalty for intensity modulated signals case is inherent, and is a consequence of gain clamping around the saturation point. In the case of DPSK modulation format, it was found that, unlike the ideal case, a limited amount of penalty can materialize. The penalty for the phase-modulated signals is induced by the PM/AM conversion induced by the dispersive elements in the experimental setup acting on the phase-modulated signal and resulting in the non-ideal phase-only modulation process. The experimental results presented confirm that the intensity modulated signals are significantly more vulnerable to saturation in FPA, admitting even infinite penalties in the worst case scenario. On the other hand, the performance penalties for the DPSK modulation format in the saturation regime are confined to the 0 to 6 dB interval. The most important finding is the existence of multiple saturation points, which is a consequence of the quasi-periodic energy exchange between the pumps and the signal and idlers through the underlying four-wave mixing processes. Furthermore, it was demonstrated that it is possible to force an FPA out of an undesirable saturation condition by an additional increase of the input signal power, in contrast to the conventional (e.g. EDFA) amplifiers.
Finally, the benefits of differential detection in FP-amplified systems, with relatively slow pumps phase modulation, have been established. It was found that differential detection can partially equalize the unwanted PM/AM transfer induced fluctuations from the pumps to the idler, thus significantly improving the performance of FP-amplified systems with phase-modulated pumps.
Acknowledgments
The authors would like to thank the anonymous reviewers for their constructive comments and suggestions, which have significantly improved the presentation of the material.
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