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Abstract
We experimentally demonstrate an ultra-low-noise pre-amplification using a non-degenerate phase-sensitive amplifier (ND-PSA) with an optically dispersion-unmanaged link. Chromatic dispersion (CD) compensation is required for phase-sensitive amplification after fiber transmission. In the conventional transmitter configuration for ND-PSAs in which phase-conjugated light (idler light) is optically generated, it is necessary to optically compensate for the CD, for example, by using dispersion-compensating fibers. In this work, we propose an ND-PSA scheme using a digitally generated idler and CD pre-equalization by means of digital signal processing. We conduct an unrepeated transmission over a 200-km single-mode fiber with a 10-Gbaud 64QAM signal using the periodically poled LiNbO3-based PSA. The experimental results demonstrate that the proposed ND-PSA scheme provides a low-noise pre-amplification that outperforms the EDFA without optical CD compensation.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The growth in communication traffic has surged upward in recent years, and the demand for high-speed optical communication has increased. Higher-order quadrature amplitude modulation (QAM) is one of the approaches to achieve high-speed optical channels, and a 1-Tbps/carrier transmission with 64QAM has been demonstrated [1]. The multi-level capability of the modulation is restricted by the optical signal-to-noise ratio (OSNR), which deteriorates due to amplified spontaneous emission (ASE) noise from the optical amplifiers. Typical optical amplifiers, such as the erbium-doped fiber amplifier (EDFA), are classified as phase-insensitive amplifiers (PIAs) and have a 3-dB noise figure (NF) limit [2].
In order to break this noise limit of PIAs, phase-sensitive amplifiers (PSAs) have attracted much attention [3]. Theoretically, PSAs can achieve a 0-dB NF by amplifying only one of the quadrature phase components of the input light. In addition, nonlinear phase noise stemming from the Kerr-effect in optical fibers, such as self- and cross-phase modulation, can be compensated by the phase regeneration in PSAs [4,5]. Recently, an application of PSAs to free-space optical communication as well as to fiber communication has also been demonstrated [6]. Phase-sensitive amplification is performed by means of an optical parametric amplification (OPA) process in nonlinear media such as the periodically poled LiNbO3 (PPLN) waveguide [7] and highly nonlinear fiber [8,9]. Although PSAs can typically amplify only single-polarized (SP) signals, polarization-diversity configurations have been developed for application to polarization-division multiplexing signals [10,11]. A frequency non-degenerate PSA (ND-PSA) utilizes a configuration in which pairs of signals and phase-conjugated lights (idler lights) at different frequencies, called phase-conjugated twin waves (PCTWs), are used as input lights [12–14]. Unlike a frequency-degenerate PSA, an ND-PSA can amplify arbitrary modulation formats such as higher-order modulation formats [15,16]. Note that the signals and idlers in the PCTWs must have uncorrelated noise components for phase-sensitive amplification. Therefore, it is necessary to generate the PCTWs on the transmitter side for decorrelation of the noise components via transmission loss [17].
For the ideal signal amplification by PSAs, a phase matching among signal, idler, and pump lights is essential. Therefore, a chromatic dispersion (CD), which make a phase variation between signal and idler lights, is one of the most pressing issues in PSAs. Under the residual CD condition, PSAs generate a gain ripple [18,19]. Conventional studies on PSA were performed in optically dispersion-managed links using dispersion-compensation modules (DCMs) such as reverse-dispersion fibers [15] and fiber-Bragg gratings [13,16]. The use of such optical DCMs results in degradation of the NF of the PSA link due to excessive optical loss and complicates the design of the transmission link. Moreover, the optical CD compensation in each span might enhance nonlinear phase noise because of small walk off. On the other hand, the CD can be compensated by pre-equalization using the impulse response of the transmission link in the digital signal processer (DSP) on the transmitter side [20]. However, in the conventional transmission systems for ND-PSAs, idler lights are optically generated as phase-conjugated copies of signal lights after optical modulation. The digital pre-equalization can be applied to only signal components. It is difficult to compensate for the CD of idler components by performing digital pre-equalization on only the signal components because both signals and applied impulse response are simultaneously conjugated in the optical domain.
In an earlier work, we proposed a simple transmitter configuration without optical idler creation for single-channel transmission systems using ND-PSAs [21]. In the configuration, idler light is digitally calculated and simultaneously generated with the signal light by means of double-sideband (DSB) optical modulation. By using this transmitter configuration, the DSP can handle the whole bandwidth of the PCTW. In the present work, we extend our earlier scheme to an unrepeated transmission with digital CD pre-equalization. Our proposed scheme enables phase-sensitive pre-amplification without the need for optical dispersion management.
In section 2 of this paper, we explain the proposed scheme and show the experimental validation using an SP-16QAM signal with a PPLN-based OPA module. In section 3, we perform the unrepeated transmission of a SP-64QAM signal through a dispersion-unmanaged 200-km single-mode fiber (SMF) link using an ND-PSA as a pre-amplifier. The transmission results are then compared with those for the transmission link using only EDFAs.
2. Proposed ND-PSA scheme with digital idler creation and CD pre-equalization
Our proposed ND-PSA scheme is based on digital idler creation using DSB modulation, which we previously proposed in [21]. By generating the idler light in the digital domain, the CD pre-equalization using DSP can be performed in the whole bandwidth between the signal and idler. The CD pre-equalization allows phase-sensitive amplification to be performed without optical DCMs. This section describes the effects of the CD on the amplification characteristics and compares the proposed scheme with the conventional scheme using the optical DCM. We also experimentally validate our proposed scheme using an SP-16QAM signal transmitted over an 80-km SMF.
2.1 Method
The phase difference Δϕ between the input and pump lights affects the gain of PSAs G as follows [22]:
Considering only the 2nd-order dispersion term, Δϕ (f) is expressed as
where D is the amount of CD, c is the speed of light, and fc is the center frequency in the phase-matching of the amplification medium. When the ripple overlaps the signal, the signal suffers from passband narrowing and is significantly degraded [19].Figure 1 shows an unrepeated transmission system using an ND-PSA as a pre-amplifier with the (a) conventional [13,15,16] and (b) proposed schemes. A PIA is used as a post-amplifier before a transmission line. In the conventional configuration, called the copier-PSA scheme, the idler light is generated by an optical phase conjugator (OPC) operated by means of phase-insensitive OPA after optical signal modulation [Fig. 1(a)]. This configuration can simultaneously generate the idlers of wavelength-division multiplexing (WDM) signals. However, since the CD pre-equalization using DSP can be applied to only signal components, optical DCMs are required for PSA operation. In contrast, our proposed transmitter configuration generates the idler in the digital domain [21]. The PCTW is calculated in the DSP and generated by means of optical signal modulation without the OPC, so the DSP can handle both the signal and idler components. As such, the CD pre-equalization over the whole bandwidth of the PCTW can be implemented. Figure 1(b) shows the system with the proposed scheme. The multiplexed signal x´(t) of two subcarriers, which consists of the original signal x(t) = A(t)exp[jϕ(t)] and its conjugate, is calculated as
Fig. 1. Unrepeated transmission system using ND-PSA as pre-amplifier. DSP: digital signal processer, DAC: digital-analog converter, LD: laser diode, IQM: I/Q modulator, OPC: optical phase conjugator, DCM: dispersion-compensation module. (a) Conventional scheme using OPC (copier-PSA) and optical DCM. (b) Proposed scheme using digital idler creation and CD pre-equalization.
The CD with an opposite sign to that generated over a transmission link is pre-loaded to the PCTW by this calculation. The optical PCTW is generated by means of I/Q modulation using s(t). The pre-loaded CD is canceled out by the propagation via the transmission link. Thus, phase-sensitive pre-amplification can be performed without optical DCMs, since the phase variation in the PCTW is compensated at the PSA input. The proposed transmitter configuration can be applied for only single-channel transmission, unlike the copier-PSA, and the bandwidth of the ND-PSA is restricted by the bandwidths of the transmitter components, such as the I/Q modulator and digital-analog converters. In order to apply this digital pre-equalization to wideband WDM transmission, it is required to use a PSA array for each channel or to modulate the signals and idlers independently with different optical carriers and modulators. Note that, each carrier of WDM-PCTW requires a synchronization for phase-sensitive operation. WDM-PCTWs created by the conventional copier-PSA scheme are synchronized by simultaneous optical phase conjugation using a shared pump light.
The copier-PSA scheme with dispersion-management lines can provide inline phase-sensitive amplifiers in a multi-span transmission because the CD can be compensated in each repeater stage. On the other hand, because the digital pre-equalization is only effective for the first PSA stage, the proposed scheme is particularly effective for transmission systems using an ND-PSA as a pre-amplifier. In a multi-span transmission with a PSA as a pre-amplifier and PIAs as inline amplifiers, a low-noise performance of the PSA contributes little to the SNR, and the frequency-diversity effect between the signal and idler provides only a 3-dB SNR improvement. In this case, a phase-sensitive pre-amplification is equivalent to digital diversity reception of a PCTW [23] and is not effective. In the unrepeated transmission (a single span), a phase-sensitive pre-amplification can improve the SNR by up to 6 dB thanks to the 0-dB NF of a PSA and the frequency-diversity effect. From the above, we conclude that an unrepeated transmission is the most suitable for the proposed scheme. In the following sections, we utilize a multi-stage pre-amplifier consisting of a PSA and an EDFA to compensate for large transmission loss.
2.2 Experimental validation
To validate the proposed ND-PSA scheme, we performed an amplification experiment with an SP-16QAM signal using a PPLN-based OPA module [24]. Figure 2 shows the experimental setup. The length of each PPLN waveguide for OPA was 45 mm, and its 3-dB gain bandwidth was 10.5 THz. We used a laser driven at 193.0 THz which is the center frequency of phase-matching in our PPLNs with a 2-kHz linewidth. An arbitrary waveform generator (AWG) provided an electrical modulator-driving signal input to an I/Q modulator. The electrical signal was calculated according to the flow as shown in Fig. 1(b). After the optical modulation, a PCTW consisting of 10-Gbaud Nyquist-pulse-shaped SP-16QAM signals was generated. The roll-off factor of the Nyquist-pulse shaping was 0.1. The Δf was set to 5.5 GHz. The bias of the modulator was manually set to the null point. The transmission line was an 80-km SMF. The CD and transmission loss of the 80-km SMF were measured using a dispersion analyzer at +1359 ps/nm and 15.9 dB, respectively. The signal light was attenuated using a variable optical attenuator (VOA) to −15 dBm at the 80-km SMF input. The input power was in the linear transfer region. The PSA stage consisted of a cascade of two PPLNs for OPA and second-harmonic generation (SHG) [25]. A second-harmonic (SH) pump light was generated by a local oscillator (LO) with a 5-kHz linewidth and SHG in PPLN2. The frequency of the LO was stabilized to the carrier component of the PCTW by an optical phase-locked loop (OPLL). The carrier recovery in the OPLL was carried out by sum-frequency generation using a PPLN [26]. We used a piezoelectric-transducer-based PLL (PZT-PLL) to compensate for the relative phase drifts between the PCTW and SH pump. The PZT-PLL monitored the power of the output PCTW extracted with an optical band-pass filter (BPF) and maximized the monitored power by controlling optical delay. A phase modulator was used to modulate the SH pump by a 1-MHz dither signal for PZT-PLL. The OPLL and PZT-PLL utilized the signal light tapped using 10% couplers. The PCTW was tuned to TM polarization using a polarization controller (PC) and a polarizer. No PC is required in the polarization-diversity configuration achieved by replacing a polarizer with a polarization beam splitter [10]. The gain of the PSA stage was 20 dB. After the PSA stage, the PCTW was received using a coherent receiver and demodulated by offline DSP. The optical BPFs with 100-GHz bandwidth were used for suppressing the ASE light at unnecessary band output from amplifiers. The signal and idler components were digitally separated during offline DSP, which was operated using only the signal component. The unique frame length of the transmitted signal was 40,000 symbols derived from pseudo-random binary sequence (PRBS) with a length of 223−1. The received signal was demodulated with pre-convergence using training symbols and tracking using the decision-directed least mean square (DD-LMS) algorithm. The signal qualities were evaluated by calculating their SNR based on the variance of the signal after the symbol decision from desired symbols. We conducted the pre-equalization of some CD values to the electrical signal and measured the equalization tolerance for the 10-Gbaud 16QAM PCTW.
Fig. 2. Experimental setup for validation of proposed ND-PSA scheme. LD: laser diode, AWG: arbitrary waveform generator, IQM: I/Q modulator, VOA: variable optical attenuator, PC: polarization controller, POL: polarizer, PZT: piezoelectric transducer, BPF: band-pass filter, PD: photodiode, LO: local oscillator, PM: phase modulator, PLL: phase-locked loop, OPLL: optical PLL.
Figure 3 shows the input and output spectra of the PSA stage measured with 0.02-nm resolution. Without CD pre-equalization, the PCTW suffered from a gain ripple caused by the phase variation due to the CD of the 80-km SMF. With CD pre-equalization, the output spectrum without a ripple was obtained. This result demonstrates that phase-sensitive amplification can be performed without optical DCMs. Figure 4 shows the tolerance of the amount of pre-loaded CD for the 10-Gbaud 16QAM PCTW. The tolerance range for a 0.5-dB SNR penalty was about 700 ps/nm, which demonstrates that it is robust to fluctuations in the CD; for example, those due to temperature variation. If the amount of compensation was significantly excessive or insufficient, it means the signal was deteriorated by inter-symbol interference due to the passband narrowing. On the other hand, the phase variation with respect to the amount of CD is proportional to the square of the frequency, according to Eq. (3). For example, assuming the OPA bandwidth is wide enough, the 3-dB bandwidth of PSA B as a function of residual CD is expressed as
Therefore, the wideband signal has a low tolerance for the CD, and a more accurate equalization is required. Wideband ripple characteristics due to slight CD, for example, have been reported in other studies [19,27].
Fig. 3. Spectra of PCTW consisting of 10-Gbaud 16QAM signal and its idler amplified by ND-PSA with and without CD compensation.
3. Unrepeated transmission over a 200-km dispersion-unmanaged SMF link
We applied the proposed ND-PSA scheme to a 200-km unrepeated transmission in order to compare the amplification characteristics of an EDFA. Two types of pre-amplification were applied by multi-stage amplifiers consisting of PSA/EDFA or EDFA/EDFA. Figure 5 shows the experimental setup. The configuration of the PSA stage was the same as in the previous experiment (section 2). The modulation format of the PCTW was 10-Gbaud Nyquist-pulse-shaped SP-64QAM. The NF of the EDFA used for comparison was 4.1 dB, and its gain was adjusted to 20 dB which is the same as that of the PSA stage. The PSA and EDFA were cascaded with another EDFA to compensate for the transmission loss. The CD and transmission loss of the 200-km SMF were measured at +3376 ps/nm and 42.4 dB, respectively. Pre-equalization according to −3376-ps/nm CD was conducted for both ND-PSA and EDFA. To measure the fiber-nonlinearity tolerance, fiber-input power Pin was varied from 0 to 9 dBm in the PCTW. We demodulated the received signals with pre-convergence and tracking by DD-LMS algorithm using only the signal component in the PCTW. We also demodulated the signals with frequency-diversity reception using both the signal and idler components in the offline DSP. In this demodulation, the signal and idler components separated with digital BPF were coherently combined using a time-domain adaptive filter controlled by the DD-LMS algorithm. The adaptive filter played the role of a 2 × 1 multiple-input single-output equalizer. As in the first experiment, the unique frame length of the transmitted signal was 40,000 symbols derived from PRBS with a length of 223−1. The signal qualities were evaluated by their SNR calculated from recovered symbols and the achievable information rate (AIR).
Fig. 5. Experimental setup for comparison between PSA and EDFA as pre-amplifier in 200-km unrepeated transmission.
Figure 6 shows the spectra of the PCTW amplified by PSA and EDFA at Pin = 5 dBm. The spectra were measured after the first pre-amplifier had been applied. The PZT-PLL was so unstable that the phase-sensitive amplified spectrum without CD compensation could not be measured. An OSNR difference of 8.3 dB was observed in the ASE floors between the PSA and EDFA cases. Because the OPA process in the PPLN had a polarization sensitivity, the ASE light output from the PSA stage consisted of only TM polarization. In the EDFA case, there was a 3-dB penalty, which did not affect the signal quality on the measured spectrum, because the ASE light of the TE polarization was also output. Considering the 3-dB penalty due to the polarization state of the ASE light, the OSNR improvement contributed by the PSA was estimated to be 5.3 dB.
Fig. 6. Spectra of PCTW consisting of 10-Gbaud 64QAM signal and its idler amplified by ND-PSA and EDFA.
Figure 7 shows the transmission characteristics for Pin. In the linear region at Pin = 0 dBm, the SNR difference of 4.4 dB was observed between the PSA and EDFA cases. The improvement in SNR after the demodulation was smaller than the difference in OSNR because of the noise transfer from the pump light and fluctuation of the PLLs. With the diversity reception, the SNR improvement of 2.8 dB was observed in the EDFA case at 0 dBm. The diversity gain increased toward the non-linear region, and the maximum gain was 3.8 dB at 8 dBm. This is thanks to the nonlinear phase noise mitigation effect of the diversity reception using a PCTW [23]. On the other hand, in the PSA cases, the diversity gain was around 0.5 dB regardless of Pin. The signal and idler lights already had correlated noise components due to the coherent superposition in the PSA. Therefore, additional diversity gain could not be obtained in principle. The reason for the slight diversity gain of 0.5 dB is that additional uncorrelated noise was generated in the EDFA and the coherent receiver after the PSA stage. Comparing the PSA and EDFA with the diversity reception at 0 dBm in the linear region, we can see that an SNR improvement of 2.2 dB was obtained. The same improvement was confirmed by comparing the optimal input powers. Consequently, the effective NF of the PSA stage in this setup was estimated to be 1.9 dB, which is lower than the 3-dB noise limit of PIAs. This NF contained a loss of the 10% coupler for OPLL (0.47 dB). The maximum SNR in the case of EDFA with the diversity reception was 16.9 dB at 6-dBm input. The same SNR was achieved at approximately 2.8-dBm input in the case of PSA because of the receiver-sensitivity improvement. The AIR results demonstrate an improvement of 8.3% corresponding to the maximum throughput enhancement from 51.9 Gbit/s to 56.2 Gbit/s compared to the case of EDFA with the diversity reception at optimal input powers.
Fig. 7. Comparison of transmission characteristics with PSA, PSA with diversity reception, EDFA, and EDFA with diversity reception. (a) SNR calculated from recovered symbols and (b) AIR as function of fiber-input power. (c) Constellation in each case at 7-dBm input power.
Figure 8 shows the ΔSNR indicating the amount of SNR improvement by PSA or diversity reception compared to the EDFA-only case. The difference between the two lines shows a contribution of PSA for SNR improvements. ΔSNR between the cases of PSA and only EDFAs increased toward the nonlinear region from 4.4 to 5.5 dB (red line). This is due to the nonlinear phase noise mitigation thanks to the phase regeneration of the PSA. The improvement of fiber-nonlinearity tolerance similar to that thanks to diversity reception using the PCTW was confirmed (blue line). This result is reasonable because both the nonlinearity compensation by the diversity reception and that by the superposition between signal and idler in ND-PSA are similar principles.
Fig. 8. ΔSNR indicating the amount of SNR improvement by PSA or diversity reception compared to EDFA-only case.
4. Conclusion
With the objective of applying ND-PSA to optically dispersion-unmanaged transmission links, we proposed an ND-PSA scheme using the digital idler creation and CD pre-equalization. We performed an amplification experiment using a PPLN-based OPA module with the SP-16QAM signal and found that the phase-sensitive amplification can be performed without optical DCMs by the proposed scheme. We also demonstrated unrepeated transmission through an optically dispersion-unmanaged 200-km SMF link using the 10-Gbaud SP-64QAM PCTW. In the transmission using the ND-PSA as a pre-amplifier, the SNR improvement of 2.2 dB was obtained compared with the case of using only EDFAs. The NF of our PSA stage was estimated to be 1.9 dB, which is lower than the NF limit of PIAs. The receiver sensitivity for the maximum SNR obtained with the EDFA-only pre-amplification was improved by 3 dB with the PSA pre-amplification. We also confirmed that the PSA improved the fiber-nonlinearity tolerance. These results demonstrate that the proposed scheme can provide a phase-sensitive pre-amplification without the need for optical dispersion management.
Disclosures
The authors declare no conflicts of interest.
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