A newly proposed concept, which is called hybrid optical phase squeezer (HOPS), achieves multi-level optical phase quantization through coherent addition of two (dual-wave scheme) or three (triple-wave scheme) optical waves exploiting optical parametric processes and electro-optic modulation. The triple-wave scheme enables signal phase regeneration free from phase-to-amplitude noise transfer, which is inevitable in the dual-wave scheme. By using HOPS in the dual-wave scheme, 3-fold phase-noise reduction was achieved for 24-Gb/s QPSK signals with a slight increase of amplitude noise. On the other hand, HOPS in the triple-wave scheme allowed phase regeneration of 12-Gb/s BPSK signal with a suppression of phase-to-amplitude noise transfer.
© 2015 Optical Society of America
Advanced modulation formats, which exploit both phase and amplitude of a light wave, have become an important technology of today’s optical fiber communications. Consequently, all-optical processing of these phase encoded signals has generated considerable research interest. In this context, phase sensitive amplification (PSA) is one of the well-studied methods to realize various optical signal processing applications, such as phase regeneration of binary phase shift keying (BPSK) and differential phase shift keying signals [1–4], phase regeneration of a quadrature phase shift keying (QPSK) signal [5, 6], phase de-multiplexing of a QPSK signal [7, 8], format conversion of QPSK signal  and phase comparison .
In the aforementioned demonstrations, the signal phase is quantized into two or four levels exploiting phase sensitive optical parametric gain. The basic principle of M-level phase quantization is based on coherent addition of two waves, which are the signal and the (M-1)th order phase harmonic conjugate, which we refer to as a dual-wave scheme . In this scheme, the associated cosine phase-to-amplitude transfer function leads to phase noise inevitably be transferred to amplitude noise . Such a phase-to-amplitude (PM-AM) noise transfer can be suppressed if the transfer function is properly tailored. Adding another high order phase harmonics to the signal, that is, as in a triple-wave scheme, achieves this effectively by flattening the amplitude transfer function .
On the other hand, PSA implementation has two important issues. First, as PSA is based on optical parametric gain, it requires a highly nonlinear and durable optical material able to handle the compulsory high optical pump power. This feature limits its prospects for future application. Second, the ability of long-term reliable operation remains unclear. Although a recently developed carrier recovery technique allows preparing a pair of pumps with phase coherent relation to an incoming signal , the final phase locking between signal and pumps is maintained by a servo system that can compensate for only a limited amount of phase drift. We note that a recent method called polarization-assisted PSA (PA-PSA) is basically free from the first discussed issue since optical parametric gain is irrelevant to the phase quantization process . However, PA-PSA also suffers from the issues concerning material selection and long-term operation.
As can be seen, to progress in the PSA implementation, the selection of the optical material needs to be broadened and the implementation needs to be reliable, offering long-term operation. In light of this, we have proposed a novel approach called hybrid optical phase squeezer (HOPS). The concept behind HOPS is to separately perform processes necessary for phase quantization so that performance is maximized and a number of applications can be enabled. In particular, in our approach, the coherent addition of the involved optical waves is realized by an electro-optic modulator without relying on the optical parametric gain . Consequently, HOPS enables signal phase regeneration using any type of nonlinear optical material as long as it exhibits an optical nonlinearity sufficient for performing four-wave mixing (FWM). In addition, HOPS guarantees long-term stable operation because phase-locking is maintained by a phase-lock loop (PLL), which constitutes the core of this concept.
Using HOPS in the 2-level quantization scheme (2-level HOPS),we have demonstrated simultaneous phase regeneration of coherent-WDM BPSK signals  and phase-regenerative multicasting of BPSK signals . We have also presented a concept for 4-level quantization (4-level HOPS) with two different pump configurations; single-pump HOPS for a wavelength-shift-free operation and dual-pump HOPS for a wavelength-converted operation . We have shown that 4-level HOPS in the single-pump configuration could effectively reduce the phase noise of QPSK signals . Interestingly, single-pump 4-level HOPS can be transformed to 2-level HOPS based on triple-wave coherent addition by changing a few parameter settings. As recalled, the triple-wave coherent addition leads to suppression of the PM-AM noise transfer, which was exploited in the phase regeneration of BPSK signals .
In this paper, we complement our previous results [17, 18] by describing in detail the concept and implementation of the single-pump 4-level HOPS and its transformation into 2-level HOPS. The remainder of this paper is organized as follows. In Section 2, we explain the concept of HOPS based on the basic theory of phase quantization. In Section 3, we present two proof-of-concept experiments including phase regeneration of a 24-Gb/s QPSK signal and phase regeneration of a 12-Gb/s BPSK signal with suppressed PM-AM noise transfer. Finally, we discuss implementation aspects of HOPS in Section 4.
As it is well known, M-level phase quantization can be achieved by coherently adding two waves, which are the signal and the (M-1)th order phase harmonic conjugate . This dual-wave scheme exhibits a sinusoidal function of the phase with a 2π/M periodicity, and a large power variation. To reduce this power variation as a function of phase, a third wave can be coherently added as follows: In HOPS, optical phase quantization is achieved based on the transformation expressed as,12]. The coefficients (p, q and r) represent the mixing ratio of the three waves, which are original signal, phase conjugate (PC) and 3rd order phase harmonic (PH). When p = 0 and r/q ≈1/3, signal phase is quantized into four levels. When r = 0 and q/p = 1, signal phase is quantized into two levels with a step-like phase response and a large output power variation reaching 100% in magnitude. When q/p ≈ 1/2 and r/p ≈-1/6, signal phase is quantized into two levels with a reduced phase dependent output power variation. Figures 1(a) and 1(b) show the amplitude and phase transfer functions, respectively, calculated for the three particular cases; 2-level (r = 0, q/p = 0.99) and 4-level (p = 0 and r/q = 0.34) phase quantization based on dual-wave coherent addition and 2-level phase quantization based on triple-wave coherent addition (q/p = 0.65, r/p = −0.2). It is observed that the plateau of the amplitude transfer function is considerably broadened in the triple-wave scheme compared to the dual-wave scheme. Whereas, the flat region of the phase transfer function is reduced to approximately one half. Therefore, 2-level phase quantization scheme based on the triple-wave coherent addition is expected to be most effective for the BPSK signals with a phase noise of ∼ π/2 rad pk-pk.
HOPS performs separately processes in the phase quantization ; phase conjugation, multiplication and coherent addition. This approach gives a flexibility to optimize each process alone allowing practically full control of the involved parameters. Hence, either two-wave or three-wave coherent addition with a desired mixing ratio is possible. In Fig. 2(a), we illustrate the conceptual diagram to perform phase regeneration of QPSK signal using 4-level HOPS based on dual-wave coherent addition. The signal at νs is mixed with a pump at νp and launched into a nonlinear optical medium, where cascaded FWM occurs. Then, PC generated at νs – 2Ω and 3rd PH generated at νs + 2Ω are filtered out, where Ω (≡νs – νp) is the frequency difference between the signal and the pump. After adjustment of the power ratio, the two waves are amplified using a standard optical amplifier such as an EDFA and guided to an amplitude modulator (AM). Here, we assume the case when AM is over driven so that second order sidebands are generated for the input waves. If the modulation frequency, f, is equal to the frequency difference between the signal and the pump, i.e. f = Ω, up-shifted component of the PC by 2f and down-shifted component of the 3rd PH by 2f are located in the same frequency ( = νs) and interfere. If the two signals interfere constructively, phase regenerated signal is obtained. In HOPS, the modulation frequency of AM is controlled using a phase-lock loop (PLL) so that the assumption made here holds. When f ≠ Ω, the power of the interference signal oscillates at four times the difference frequency, i.e. 4(f -Ω). This suggest that if this power is stabilized to a constant value through feedback control of the modulation frequency, f = Ω is fulfilled. Once this phase locking is established, the two waves can be coherently added with a desired relative phase.
Conveniently, as shown in Fig. 2(b), the 4-level HOPS, QPSK phase regeneration arrangement, can be easily converted into 2-level HOPS based on three-wave coherent addition. This configuration can be exploited for BPSK regeneration with suppressed PM-AM noise transfer. In this case, the three waves, which are PC, original signal and 3rd PH, should be filtered out from the nonlinear optical medium and guided to AM. When the condition of f = Ω is fulfilled, up-shifted component of the PC by 2f and down-shifted component of the 3rd PH by 2f interfere with un-shifted component of the original signal in a fixed phase relationship. Thus, triple-wave coherent addition as expressed in Eq. (1) occurs provided that the phases of the three waves are properly adjusted.
3. Experimental results and discussion
To demonstrate the two types of operation principles discussed above, we carried out two proof-of-concept experiments; namely phase regeneration of QPSK signal and phase regeneration of BPSK signal with suppressed PM-AM noise transfer. Furthermore, to prove the potential of low power operation, we used two standard highly nonlinear fibers (HNLFs) as the nonlinear optical medium. The pump power in the two HNLFs (L = 100 m) was at most 19 dBm to avoid the onset of stimulated Brillouin scattering (SBS). Yet, the two HNLFs could be used to generate 3rd PH efficiently through two separate stages of FWM, as it will be shown. In the following, the experimental demonstrations are explained in detail.
3.1 Phase regeneration of QPSK signal
Figure 3 shows the experimental setup used in the phase regeneration of QPSK signals. The signal and pump were obtained from an optical comb generator, whose center frequency and mode separation are ν0 = 193.54 THz (wavelength: 1550.0 nm) and Ω0 = 43 GHz, respectively. From the comb, the mode at ν0 was used to generate 24-Gb/s QPSK signals (PRBS: 215-1) and the mode at ν0 - Ω was used as the pump. To emulate the effect of nonlinear phase noise, 1-GHz sinusoidal phase modulation was applied to the QPSK signals using a phase modulator (PM). The QPSK signal with the power of 1 dBm was mixed with the pump (power: 1dBm) and launched into HNLF-1 (λ0 = 1534 nm, dispersion slope = 0.0035 ps nm−2 km−1, γ = 23 km−1W−1), after amplification by an EDFA. To increase the generation efficiency of 3rd PH in the second FWM stage, the output spectra of HNLF-1 was tailored using a programmable optical filter (PF1). PF1 selected three waves (pump, signal and 2nd PH) from the output of HNLF-1 applying 9 dB of attenuation to the signal and the pump. The output of PF1 was amplified to 22 dBm by an EDFA and launched into HNLF-2 (λ0 = 1590 nm, dispersion slope = 0.0118 ps nm−2 km−1, γ = 23 km−1W−1). The inset of Fig. 2 shows the input/output spectra of HNLF-1 and HNLF-2. In the two FWM stages, the pump power in the HNLF was ∼19 dBm, which was below the SBS threshold.
At the HNLF-2 output, three unnecessary waves around the signal frequency (pump, signal and 2nd PH) were attenuated using a tunable notch filter (NF1: attenuation > 40 dB). The output of NF1 was amplified and divided into two branches; main branch (upper) for the phase regeneration and sub branch (lower) for the PLL. In the two branches, PC and 3rd PH were coherently added using a Mach-Zehnder amplitude modulator (MZM) and the interference signal generated at ν0 was filtered out using an optical bandpass filter. The two MZMs were driven by the same RF signal from a voltage controlled oscillator (VCO) at 43 GHz with a modulation index of approximately 1.6. The bias level of MZM was adjusted to maximize the power of the 2nd order sideband. The efficiency of 2nd order sideband and loss of the input signal was −12 dB and −6 dB, respectively.
The role of the sub branch is to generate a phase discrimination signal necessary for controlling the VCO frequency by dual-wave coherent addition with 1:1 mixing ratio. For this purpose, unnecessary waves around the signal frequency were thoroughly rejected using a second NF (NF2: attenuation > 40dB) and the center frequency and the bandwidth of NF2 were carefully adjusted so that two waves, PC and 3rd PH, passed the MZM with equal powers. This arrangement resulted in an interference signal with ∼100% contrast. The power of the interference signal was monitored by a photo detector and stabilized through feedback control of the VCO frequency. The feedback loop (bandwidth: ∼1 MHz) ensured that the modulation frequency of the MZM was equal to the frequency separation between the signal and the pump.
In the main branch, two waves, PC and 3rd PH, were filtered out using a second PF (PF2), which also allowed adjusting the power and the phase of the two waves independently. The mixing ratio chosen in this experiment was approximately r/q = 0.4. Figure 4(a) shows the input and output spectra of the MZM used in the main branch. For comparison, the input/output spectra of MZM in the sub branch are also shown in Fig. 4(b).
The phase regenerated signals were assessed using an optical modulation analyzer (OMA). When the PLL was closed and the relative phase between the two waves was properly adjusted through PF2, stable phase regenerated QPSK signals were obtained. As an example, we show in Fig. 5 how the constellation of the output signal changed when the relative phase was varied. Figure 5(a) shows the constellation of the input QPSK signal with a phase distortion of 54 deg pk-pk. Figures 5(b)-5(d) show the constellation of the output signal when the phase was at the top (b), slope (c) and bottom (d) of the amplitude transfer function. In the optimum condition, i.e. in the case of Fig. 5(b), the phase error was reduced from 19.1 deg RMS to 6.0 deg RMS, which is more than 3-fold phase noise decrease. The effectiveness of the phase regeneration comes, however, at the expense of amplitude error increase owing to the cosine PM-AM noise transformation and extremely high level of phase distortion. In this case, the amplitude error was increased from 4.0% to 16.6%. Yet, the initial error vector magnitude (EVM) of 33.2% was reduced to 19.5% after phase regeneration.
Figure 6 plots EVM measured for QPSK signals with two different levels of phase distortion before and after phase regeneration when signal OSNR was degraded by amplified spontaneous emission (ASE) noise. The phase distortion applied to the signal was 34 deg pk-pk (high level) and 28 deg pk-pk (low level). It is confirmed that phase regeneration alone could effectively reduce EVM. Furthermore, the regenerated curves practically overlap regardless of the amount of phase distortion. Hence, the regeneration scheme offered greater benefit to the high level phase distorted signal, for which the EVM was reduced approximately to one half.
To prove the long-term stable operation, we plot in Fig. 7 the bit-error-rate (BER) performance measured for highly phase distorted QPSK signals before (diamond) and after (square) phase regeneration. For reference, the BER of the input QPSK signal without phase distortion (circle) is also shown. In the figure, also shown are sample constellation diagrams of the signal before and after phase regeneration. It is confirmed that 1dB improvement of OSNR penalty was achieved in spite of the presence of PM-AM noise transfer. This result suggests the effectiveness of 4-level HOPS in the mitigation of nonlinear impairment associated with QPSK transmissions. Further enhancement is expected if the amplitude noise is reduced using a phase-preserving amplitude limiter .
3.2 Phase regeneration of BPSK signal without PM-AM noise transformation
Using the same setup as shown in Fig. 3, we demonstrated phase regeneration of BPSK signals with suppressed PM-AM noise transfer, where the coherent addition of three waves plays the key role. Here, 12-Gb/s BPSK signals (PRBS: 215-1) were generated using a comb mode at ν0 and two notch filters (NF1 and NF2) were used to reject only the pump from the HNLF-2 output. In the sub branch, the conventional (dual-wave coherent addition) 2-level quantization scheme was employed to generate a phase discrimination signal. For this purpose, the center frequency and the bandwidth of NF2 were adjusted so that PC and original signal were transmitted with equal powers to allow 1:1 coherent addition at the MZM output. The resultant high contrast interference signal generated at ν0 - Ω was filtered out and monitored to control the VCO frequency. In the main branch, the three waves to be mixed (PC, original and 3rd PH) were filtered out using PF2. The power and the phase of PC and 3rd PH were optimized through PF2, monitoring the constellation of the regenerated signal. Figures 8(a) and 8(b) show the input and output spectra of MZM in the main branch and sub branch, respectively. To compare the performance between the “dual-wave” and “triple-wave” phase regeneration approaches, the main branch was also configured in the conventional scheme as was done in the sub branch.
Figure 9 shows the constellation of an input BPSK signal with a phase distortion of 27 deg RMS (a) and the phase regenerated signals obtained by dual-wave scheme (b) and triple-wave scheme (c). Due to equipment availability, the amount of phase distortion applied to the BPSK signal was unfortunately limited to less than ± π/4 rad. Yet, this was sufficient to demonstrate the suppressed PM-AM noise transfer nature of the triple-wave scheme. In the dual-wave scheme, the regenerated signal exhibited a phase error of 3.8 deg RMS and an amplitude error of 10.9%. However, in the triple-wave scheme, the amplitude error was reduced to 7.0% with a slight increase of the phase error from 3.8 deg RMS to 5.3 deg RMS. All in all, a performance improvement of the three-wave approach over the two-wave approach was observed through the reduction of the EVM from 12.8% (dual-wave) to 11.8% (triple-wave).
According to Fig. 1(a), note that the PM-AM noise suppression given by the triple-wave scheme is most effective when the phase noise is limited to ± π/4 rad. Although the amount of phase noise might not be limited to ± π/4 rad in the real system, the increase of amplitude noise is expected to be small with respect to the dual-wave scheme. An evaluation with more heavily, single-tone or broadband, noise loaded signals would reveal the effectiveness of the triple-wave phase regeneration scheme more clearly.
In the realization of optical phase quantization, there are two subjects that have to be accomplished. One is to generate a phase discrimination signal which is necessary for stable phase locking. The other is to generate a high order phase harmonic signal which has sufficiently high quality. In the following, we discuss the aspect of these subjects.
Ideal phase quantization scheme is considered to have a stair-like phase transfer function and an amplitude transfer function that is independent on signal phase. However, such an ideal scheme prohibits obtaining a phase discrimination signal from the output signal. Similarly, in the phase quantization based on triple-wave coherent addition, obtaining a phase discrimination signal becomes a hard task because of the flat-top amplitude transfer function. In HOPS, this difficulty was overcome by splitting the stream of optical waves into two branches: phase quantization is performed by coherent addition of multiple optical waves with an optimum power ratio, while phase discrimination signal is generated in another branch by dual-wave coherent addition with 1:1 mixing ratio. The effectiveness of this concept successfully led to the two experimental demonstrations.
In general, 3rd PH generated by cascaded FWM processes suffers from ASE noise accompanying the pump and phase noise originating from self-phase modulation (SPM) and cross-phase modulation (XPM). However, we could generate 3rd PH with an OSNR of > 35 dB by introducing two separate stages of FWM, where the power ratio of the optical waves was optimized in each stage. The total (signal and pump) optical power in the HNLF was 22 dBm, which resulted in a nonlinear phase shift (NPS) of ∼0.4 rad. This value was approximately half of that in the typical HNLF-based PSA . Thus, when several nonlinear optical materials are available, it is advantageous to use them in multi stage rather than in a single stage. As an example, Fig. 10 shows two optical spectra obtained using two HNLFs with CW signal. One was obtained with dual-stage FWM and the other was obtained with single-stage FWM, where HNLF-1 and HNLF-2 were concatenated. In the dual-stage FWM, 3rd PH was generated with 12 dB larger power and 8 dB higher OSNR than in the single-stage FWM. We note that a different scheme of spectral shaping after HNLF-1may be found to further improve the efficiency. Also, as phase control is not needed, PF1 can be replaced by a pair of band-pass filter and a notch filter. Recently, Bottrill et al. verified the concept of dual-pump 4-level HOPS demonstrating wavelength-converted phase regeneration of QPSK signal using a HNLF with a total optical power of 24 dBm . We point out that dual-stage FWM is also applicable to the dual-pump 4-level HOPS to allow much lower power operation.
In the experiment, AMs have been preferably used because of the high extinction ratio (ER). In the case when a high ER is not required, e.g. in the 3-wave coherent addition or in the PLL branch, the AMs can be replaced by PMs, which are simpler and less energy demanding. In either case, the amount of frequency shift should be large enough compared to the signal bandwidth. In this context, HOPS can support Nyquist filtered signals whose bandwidth is as wide as the modulation bandwidth of the AM/PM.
Furthermore, different from legacy PSA approaches, which used bulky materials such as SBS-suppressed HNLF  and PPLN , HOPS is more flexible in the choice of optical materials. Especially, for the purpose of system integration, HOPS can exploit integratable optical materials such as Si- , SiGe waveguide  or SOA as a nonlinearity medium, and Si  or InP  as a high speed optical modulator for the coherent addition. Therefore, HOPS is expected to enable photonic integration of the signal regenerator with lower energy consumption and cost for practical applications.
We have exploited the flexibility offered by HOPS to enable tailored phase-regenerative transfer functions based on two-wave or three-wave coherent addition. Using a dual-wave 4-level HOPS, the phase error of a heavily phase distorted 24-Gb/s QPSK signal was reduced by a factor of more than three with a slight increase of amplitude error. Also, 1 dB improvement of OSNR penalty in the BER performance was achieved by phase regeneration alone. The dual-wave 4-level HOPS could be operated as a triple-wave 2-level HOPS with a small adjustment of parameter settings. Using the triple-wave 2-level HOPS, we also demonstrated phase regeneration of 12-Gb/s BPSK signal with suppressed PM-AM noise transfer and observed improved performance over the conventional dual-wave method through the EVM reduction. We remark that these results were obtained using two standard HNLFs and pump power of at most 19 dBm. Thus, HOPS relaxes the selection of the nonlinear optical material used in phase regeneration.
This work was supported by Project for Developing Innovation Systems of the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan.
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