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Abstract
Polarization attraction of a 10-Gb/s non-return-to-zero binary phase-shift keyed (NRZ-BPSK) signal has been successfully demonstrated for the first time in a counter-propagating beam configuration using a continuous-wave pump, in a highly nonlinear fiber, by utilizing the Kerr nonlinear cross-polarization process inherent to that fiber. The efficacy of mitigating polarization-dependent loss across polarization-sensitive devices was emulated with a linear polarizer located before the receiver. The receiver sensitivity penalty at 10−9 bit-error-rate relative to the baseline NRZ-BPSK signal was < 0.5 dB, when polarization attraction was employed for a polarization-scrambled signal (after achieving a degree of polarization > 90%). The results confirm that polarization attraction is independent of modulation format.
© 2017 Optical Society of America
1. Introduction
Within a short propagation distance of several kilometers in standard fibers, the optical field experiences random polarization fluctuations induced by polarization mode dispersion (PMD) [1–3]. The fiber Kerr nonlinearity has also been found to contribute to depolarization [4–6]. Polarization-sensitive nonlinear optical signal processing (NOSP)-based techniques however are adversely affected by polarization fluctuations [7]. In this context, development of techniques with the capability to control and stabilize randomly polarized optical signals can facilitate the development of NOSP-based functions. The simplest solution to polarize a signal would be the use of an inline standard linear polarizer to allow 100% transmission for a single state of polarization (SOP) at the expense of other SOPs [8]. However, a signal with a scrambled polarization would experience significant amplitude fluctuations after passing through the polarizer. The resultant polarization-dependent loss (PDL) would create serious penalties when implementing NOSP-based techniques sensitive to amplitude fluctuations [9,10]. For these reasons, there has been a strong interest in developing lossless polarizers.
Historically, the first lossless polarizer used two-beam coupling within a photorefractive material [11], but the application of this device in telecommunications was limited by the slow response time (on the order of multiple seconds) of photorefractive crystals. Nonlinear lossless polarizers (NLPs) that utilized the ultra-fast Kerr nonlinearity within optical fibers showed a response time more applicable to telecommunications [12]. The phenomenon, termed “polarization attraction”, is characterized by the re-polarization of an unpolarized signal when it interacts with a fully-polarized continuous-wave (CW) beam through a Kerr, nonlinear cross-polarization process, as discussed in section 2. The first fiber-based NLP experimentally demonstrated polarization attraction in a 2-m-long, isotopic, highly nonlinear fiber (HNLF) with a counter-propagating CW pump beam [12,13]. One of the limitations of this demonstration was the need for very high-power signal/pump beams (≈45W) to obtain a sufficient nonlinear interaction. Using a longer length of fiber (≈20-km), a similar NLP with a reduced power requirement (<1 W) was later demonstrated in a Non-Zero Dispersion-Shifted Fiber [14]. Following this experiment, two more demonstrations were reported for a relatively shorter fiber span of 6.2 km and a similarly reduced power requirement (<1.1 W) [15,16]. Simulations and studies of polarization attraction corroborated that the phenomenon could potentially occur in isotropic fibers [17], highly birefringent spun fibers [18], and randomly birefringent fibers [19,20] as well. The theory presented in [21] derived a general model for fiber-based NLPs, covering all three of the fiber types reported. Several more realizations of polarization attraction have been demonstrated on pulse train [22] and on-off keyed (OOK) signals [23–27]. All of the referenced practical demonstrations were conducted with fibers characterized by low PMD values (<0.05 ps/km1/2) [14]. A low-PMD fiber was reported to support a more effective polarization attraction [15,17,21,28]. The demonstration within this report will follow suite with past successful experiments and utilize a HNLF with a low-PMD value (≈0.02 ps/km1/2).
While OOK is the simplest and the most cost-efficient modulation scheme, there are transmission advantages to using alternative modulation schemes that rely on the phase of the signal instead of its amplitude. The simplest such signal is binary phase-shift keying (BPSK). Theoretically, BPSK requires a minimum of 3 dB less OSNR than OOK to reach a given BER, for amplified spontaneous emission (ASE)-limited transmission [29]. Furthermore, it has been speculated that the effectiveness of polarization attraction might improve when employed for PSK modulation formats, since the nonlinear interaction would occur between the CW pump and a signal characterized by constant intensity [25]. However, a constant intensity BPSK signal is generated using a waveguide phase modulator, whereas a Mach-Zehnder modulator (MZM) was used for this report. Although an MZM can be superior in performance when properly biased and driven, it also introduces undesirable amplitude modulation - consequently, the BPSK signal was periodic, but not constant in intensity. In this report, polarization attraction in a HNLF is experimentally demonstrated to all-optically control and stabilize the SOP of a 10-Gb/s non-return-to-zero (NRZ)-BPSK signal. In section 2, the principle of operation of polarization attraction is summarized and the sensitivity to the CW pump SOP and power are emphasized. Section 3 is broken down into three subsections which collectively cover all the experimental results. In 3.1, the details of the experimental setup are discussed, then in 3.2 the mitigation of stimulated Brillouin scattering (SBS) is demonstrated. Finally in 3.3, qualitative polarization attraction observations are presented along with the receiver sensitivity measurements, and the report concludes with Section 4.
2. Principle of operation
The scheme for polarization attraction is shown in Fig. 1. It involves a data-bearing signal with a scrambled SOP injected into a HNLF, along with a counter-propagating, fully-polarized CW pump. The SOP of the signal at the output of the HNLF converges onto a tightly localized statistical distribution of SOPs. In this paper, the signal SOP is analyzed using Stokes parameters, displayed onto a Poincaré sphere via a commercially available polarization analyzer (PA).
Fig. 1 Scheme for polarization attraction to a polarized SOP, of a signal with a scrambled SOP. PA visualizations of the signal are shown at the input and output planes of the HNLF.
The generic model for polarization attraction derived in [21] is based on four-wave mixing equations for two counter-propagating beams, and makes two assumptions regarding fiber length L. First, the birefringence orientation varies randomly over distance with a characteristic correlation length Lc, such that L >> Lc. Second, a statistical parameter unique to the fiber, the differential beat length is much greater than L, in order to obtain significant re-polarization. Starting from the equations of motion for the pump and signal derived under the unidirectional and slowly-varying envelope approximations [30], coupled differential equations governed by the signal and pump Stokes vectors may be formulated [17,21,31]. These coupled equations imply that the signal and pump interact through a Kerr cross-polarization process, where the evolution of the SOP of the signal relies on the SOP of the pump, and vice versa. An important feature demonstrated in [21,25] shows that not all pump SOPs result in successful polarization. It was theoretically shown [21] that the signal is attracted to only one of two SOPs, either to that of the CW pump, or to an SOP orthogonal to that of the pump. Moreover, it was also found that the success of signal repolarization is a sensitive function of the average pump power and average signal power. Both average powers must be sufficiently high to maximize the nonlinear cross-polarization process, but the average signal power will be fixed to 0.32 W during this experiment to limit SPM-induced spectral broadening.
The effectiveness of the polarization attraction is determined by the signal SOP distribution on the Poincaré sphere, measured by the degree of polarization (DOP) after averaging the Stokes vector [24],
where the average of each of the Stokes parameters may be treated either as a time average or an ensemble average [16]. A DOP of unity represents perfectly polarized light and a single SOP on the Poincaré sphere, while a DOP of zero represents polarization-scrambled light, and a full spherical coverage, within the context of this experiment. While past reports show that polarization attraction can be effective on CW beams and NRZ/RZ-OOK signals, the goal of this demonstration was to achieve polarization attraction for a NRZ-BPSK signal with a scrambled SOP, and to establish whether additional impairments (beyond those for OOK) may affect the performance of a phase-shift-keyed signal.3. Experimental results and discussion
3.1 Experimental setup
The experimental setup for polarization attraction of a NRZ-BPSK signal is shown in Fig. 2. The NRZ-BPSK signal is a 10-Gb/s 231-1 pseudo-random bit sequence (PRBS) centered around 1545.3 nm and may be polarized (scrambled) by turning off (on) the polarization scrambler (PS). The signal is generated by biasing a MZM at its transmission null and driving it at twice its Vπ-voltage. The selection of the signal wavelength was motivated by the use of a 100-GHz channel-spaced arrayed waveguide grating (AWG) in the receiver chain. The scrambling speed of the PS was ≈12 kHz. The CW pump laser is centered at 1547.5 nm and phase modulated (PM) at ≈335 MHz in order to suppress SBS, as discussed in section 3.2. As will be seen later, the wavelength of the CW pump is not critical for the fiber used. Mechanical polarization controllers were used between the lasers and the modulators due to the dearth of polarization-maintaining components. The launch powers for the signal and pump are approximately 0.32 W and 1.4 W, respectively, and their selection is discussed in the following section. The 1-km standard HNLF manufactured by OFS with part number “HNLF-ST-1000-1-1-z0”, exhibits a nonlinear coefficient of γ ≈11W−1·km−1, a dispersion coefficient of D ≈-0.16 ps·nm−1·km−1, and a PMD parameter of ≈0.02 ps/km1/2. The circulator allows nearly 100% coupling of the CW pump into the HNLF, simultaneously with nearly 100% coupling of the HNLF output to the receiver. The PA monitors the signal SOP and DOP beyond an optical bandpass filter tuned to the signal wavelength. The null modulator is an un-driven conventional x-cut LiNbO3 modulator (PDL ≈25.4 dB) and behaves as a polarizer due to the presence of a polarizing element at its input plane, and therefore emulates the behavior of a polarization-sensitive device. The received signal is monitored at the output of the null modulator to test the quality of the polarization attraction. The initial pump SOP has a significant impact on the output signal’s DOP [21,25], where some pump SOPs produce a DOP > 90% whereas others may produce a DOP comparable to that of partially polarized light (< 20%). Therefore, the pump SOP is adjusted using a mechanical polarization controller (MPC3) after its HP-EDFA to optimize the polarization attraction effect. After the signal SOP had undergone polarization attraction, the new signal SOP must be adjusted via MPC5 directly before the null modulator to ensure maximum transmission. The NRZ-BPSK signal is evaluated as a NRZ-DPSK signal using a differential, direct-detection receiver. The DPSK receiver consists of a dual-stage, high-gain, low-noise-figure (LNF) EDFA utilizing a 100 GHz AWG with a Gaussian passband −3-dB-bandwidth of 0.45 nm. The AWG is used in the receiver chain so that this same receiver could be used with a DWDM system in a future experiment. The chosen inter-stage filter for the elimination of out-of-band ASE is a Gaussian filter with a −3dB-bandwidth of 1 nm. The rest of this receiver consists of a 1-bit-delay AMZI, a balanced photo-detector (BPD), a limiting amplifier (LA), a clock/data recovery module (CDR), and an error detector (ED). During receiver sensitivity measurements, the OSNR is varied by varying the attenuation before the LNF-EDFA, and the detected power is kept constant at approximately 0 dBm by adjusting the attenuation after the LNF-EDFA.
Fig. 2 Experimental setup for polarization attraction of a NRZ-BPSK signal. Each split in the optical path followed by a percentage indicates the presence of an optical coupler. (PPG: pulse pattern generator, PRBS: pseudo-random bit-sequence, PM: phase modulator, MPC: mechanical polarization controller, SBS: Stimulated Brillouin Scattering, Circ: circulator, : variable optical attenuator, PS: polarization scrambler, HP-EDFA: high power erbium-doped fiber amplifier, LNF-EDFA: low-noise-figure EDFA, HNLF: highly nonlinear fiber, AWG: arrayed waveguide grating, AMZI: asymmetric Mach–Zehnder interferometer, PD: photo-detector, BPD: balanced PD, LA: limiting amplifier, VTH: threshold voltage, CDR: clock/data recovery module, CR: clock recovery module, ED: error-detector, OSNR: optical signal-to-noise ratio measurement, Trig.: Trigger for sampling oscilloscope, PRX: received power, PDET: detected power).
3.2 Stimulated Brillouin scattering suppression
Stimulated Brillouin scattering (SBS) is a nonlinear inelastic scattering process that originates from a physical phenomenon called electrostriction [32,33]. The efficacy of the scattering process is dependent on the signal's power. The undesirable effects of SBS are easily observed from the input-output characteristic of the CW pump wave propagating through the HNLF [34]. The result in Fig. 3 (red diamonds) shows that the output power begins to saturate at a threshold input power level of approximately 16 dBm (0.04 W), and the output power is never able to exceed 19 dBm. The SBS threshold may be generally explained as the threshold of input power where the Stokes wave power begins to increase rapidly and to approach the input signal power [32], [35].
Fig. 3 Input-output characteristic of the CW pump wave propagating in the HNLF with SBS suppression off (red diamonds), and SBS suppression on (green circles). A linear least-squares fit (black line) may be plotted for the latter, with a coefficient of determination R2 = 0.9999.
As discussed in section 2, a high CW pump power is necessary to induce strong polarization attraction. In this context, it is desirable to increase the SBS threshold of the CW pump in the fiber, which can be achieved by using external phase modulation [36]. This leads to pump linewidth broadening and a significant rise in SBS threshold [37]. The optimal phase modulation frequency was found by keeping the pump input power constant while varying the frequency from DC to 500 MHz to find a maximum pump output power. When the CW pump is phase modulated at a frequency of ≈335 MHz, SBS is sufficiently suppressed in the HNLF so that the output power for the pump is maximized, as shown in Fig. 3 (green circles). With SBS suppression (SBSS) turned on, the CW pump may reach an output power > 31.76 dBm (1.5 W), which is high enough to meet the 1.4 W CW pump requirement in the polarization attraction experiment demonstrated.
The same input-output characteristic measurements may also be applied to the NRZ-BPSK signal, to look for an indication of an SBS threshold. The plot in Fig. 4 shows that no significant SBS exists for the NRZ-BPSK signal propagating in the HNLF for input power ≤ 26.53 dBm (0.45 W) and for 231-1 PRBS, and therefore no SBSS was required for the signal.
Fig. 4 Input-output characteristic of the NRZ-BPSK signal propagating in the HNLF, where no SBS suppression was required. A linear least-squares fit (black line) may be plotted with a coefficient of determination R2 = 0.9999.
3.3 Demonstration of polarization attraction of a NRZ-BPSK signal
To maximize the effect of polarization attraction as described in section 2, the CW pump average power and SOP are optimized to achieve the highest signal DOP at the HNLF output. The signal DOP increases almost linearly with respect to the pump average power until a saturation pump power is reached, as demonstrated in [24]. The optimal pump average power in this demonstration is approximately 1.4 W (for a signal average power of 0.32 W) since no significant improvement to the output signal DOP occurs for pump power >1.4 W - this is confirmed by Fig. 5. It was also confirmed that no detectable signal power depletion occurred at the output, when the pump power was increased to its optimal level. The pump SOP is also adjusted via a MPC3 to maximize the signal DOP at the HNLF output, since some pump polarizations perform attraction better than others [21]. Under these conditions, a signal DOP ≈91% was achieved, as shown in Fig. 6. An additional MPC5 is required after the HNLF to adjust the attracted signal SOP for maximum transmission through the null modulator. Receiver sensitivity measurements were taken at the output of the null modulator. The signal launch power of 0.32 W was selected since this power results in the lowest BER for a given OSNR.
Fig. 5 Output signal DOP as a function of CW pump power, demonstrating that DOP saturation is achieved at ≈1.3 W.
Fig. 6 Polarization analyzer visualizations of the scrambled NRZ-BPSK signal’s state of polarization are captured with an average over 100 measurements. Figures are taken at the output of the HNLF with (a) CW pump off, DOP ≈9.4%, and (b) with CW pump on, DOP ≈91.2%.
It was confirmed that polarization attraction was fairly independent of the pump wavelength in the HNLF, over the ITU-T C-band (Fig. 7). The result was achieved by keeping the signal wavelength fixed, while varying the pump wavelength, and subsequently re-assessing signal DOP. This indicates that the differential inverse beat length, a statistical parameter for the HNLF, is apparently weakly dependent on wavelength. The DOP roll-off in Fig. 7 occurs for wavelengths < 1532 nm and > 1564 nm as a consequence of the spectral limitations of the EDFA gain used for the pump in the setup.
Fig. 7 Polarization attracted signal DOP as a function of CW pump wavelength. The signal wavelength was held fixed at 1545.3nm.
Spectra captured at different locations in the experimental setup at a resolution bandwidth (RB) = 0.01 nm are shown in Fig. 8. The top row shows the baseline spectra of the signal centered at 1545.3 nm (red) and pump centered at 1547.5 nm (blue) before they are launched into the HNLF. The spectra in the second row of Fig. 8 are the spectra of the signal and pump after simultaneous propagation in the HNLF. The signal experiences spectral broadening due to SPM, but the broadening is confined to spectral components > 20 dB below the spectral peak, as would be the case for super-Gaussian pulses. The AWG filter profile (black) is plotted in the third row, and the detected signal (green) is plotted on the bottom row. The −3-dB-bandwidth of the detected signal is unchanged from the unfiltered HNLF output, since the AWG filter −3-dB-bandwidth is 0.45 nm and broad enough to prevent any excessive filtering penalty. Any differences between the baseline and detected signal spectra occur > 20 dB below the spectral peak.
Fig. 8 Power Spectra captured at a resolution bandwidth of 0.01 nm for the signal (red) and pump (blue) before injection into the HNLF (top row), the signal and pump after propagating the HNLF (second row), the AWG filter profile (black, third row), and the detected signal (green, bottom row).
Qualitative comparisons of the NRZ-BPSK signal eye-diagrams captured under various conditions are shown in Fig. 9. The signal in all four eye-diagrams has been polarization scrambled at the transmitter. The CW pump is only turned on in the last figure, and all eye-diagrams are viewed after the AMZI, which translates phase information into amplitude. Figure 9(a) shows the baseline scrambled NRZ-BPSK signal with an oscilloscope Q value ≈23.7 dB. The signal appears to experience some slight compression after propagating through the HNLF in Fig. 9(b) due to SPM-induced phase shifts during symbol transitions. For a constant-amplitude BPSK signal, SPM phase shifts would theoretically be cancelled out in differential detection. The signal in this report has periodic amplitude dips during symbol transitions due to MZM signal generation and finite-bandwidth baseband components. The eye-diagram (Fig. 9(c)) opening is filled after passing through the null modulator, which contains a polarizer, resulting in error detector synchronization loss. These fluctuations are mitigated when polarization attraction is employed (Fig. 9(d)), when the CW pump is turned on and each MPC adjusted for optimal performance. The final Q value ≈21 dB for the attracted signal.
Fig. 9 Polarization scrambled NRZ-BPSK signal eye-diagrams captured in color-grade infinite persistence mode using a sampling oscilloscope module with a 50 GHz bandwidth and a 50 GHz balanced photo-detector at an OSNR > 40 dB/0.1nm. Figure 9(a) displays the signal captured for the baseline (HNLF bypassed), Fig. 9(b) displays the signal after propagating through the HNLF, Fig. 9(c) displays the signal at the output of the null modulator where polarization fluctuations are translated into PDL, and Fig. 9(d) displays the polarization-attracted signal at the output of the null modulator, when the eye-diagram opening is cleared of errors, using polarization attraction.
For the baseline eye-diagram shown in Fig. 9(a), essentially error free detection is possible for an OSNR > 11 dB/0.1 nm (Fig. 10). The polarization attraction case shown in Fig. 9(d) demonstrates a 10−9-BER penalty < 0.5 dB relative to the baseline case, shown in Fig. 10. The theoretical receiver sensitivity for DPSK direct-detection in ASE-limited transmission systems, with a matched optical filter and no electrical post-filtering is also plotted in Fig. 10, and defined as [38]:
where represents the ratio of OSNR resolution bandwidth to bit-rate.Fig. 10 Receiver sensitivity measurements for NRZ-BPSK when the signal was scrambled, polarization attraction was employed, and the signal was observed at the output of the null modulator (red circles), compared against the baseline (black circles). When the CW pump was off, synchronization loss resulted at the error detector. An exponential least-squares fit may be applied to the polarization attraction data points with R2 = 0.999 (dotted red line), and another exponential least-squares fit may be applied to the baseline data points with R2 = 0.9995 (dotted black line). The theoretical receiver sensitivity for DPSK direct-detection in ASE-limited transmission systems, with a matched optical filter and no electrical post-filtering is also plotted (solid black line).
4. Conclusions
For the first time, a 10-Gb/s NRZ-BPSK signal polarization attraction experiment was successfully demonstrated via a counter-propagating configuration, in a 1-km-long HNLF. This was achieved by adjusting the CW pump's average power and its SOP in order to maximize the interactions within the Kerr cross-polarization process. SBS induced by the CW pump was suppressed via phase modulation at ≈335 MHz in order to attain the optimal pump average power. Compared to the back-to-back baseline, the 10−9–BER receiver sensitivity penalty was < 0.5 dB, with the penalty most likely due to the signal's incomplete polarization attraction (≈91% DOP instead of 100% DOP), and therefore undesired amplitude modulation due to passage through the null modulator (polarizer). The experiment confirms that polarization attraction with counter-propagating beams is practically insensitive to modulation format. The choice of nonlinear fiber required for efficacious polarization attraction without incurring undesirable (possibly nonlinear) impairments has been analyzed by Barozzi and Vannucci [39].
Polarization attraction should be amenable to QPSK (which is comprised of two BPSK signals in quadrature), although the penalty due to incomplete polarization attraction will be higher due to the reduced intersymbol distance for QPSK, relative to BPSK. For 100 Gb/s applications and irrespective of format, polarization attraction would not be possible without some sort of polarization diversity, since standard 100 Gb/s employs polarization multiplexing. The difficulty arises due to cross-polarization modulation, which plagues both deterministic and randomly-varying birefringent nonlinear fibers. Furthermore, this experiment may be extended to an alternate omnipolarization configuration in polarization mode [40], where a signal self-organizes its own SOP, without the need for additional controlling beams, resulting in a simpler implementation. However, the response time could be slower by a factor of 10 compared to that attainable with the counter-propagating configuration.
Funding
United States Department of Defense (DoD) (100000005).
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