1. Introduction

Optical signal regeneration that does not require electrical conversion is a highly desired functionality for future optical transmission systems [1]. A candidate for optical regeneration is the fiber optic parametric amplifier (FOPA) [2]. It is known that when operating in saturated regime, the FOPA can be utilized for equalizing an optical input signal [3–7]. However, when considering traditional on-off keying (OOK) systems, the regenerative properties of the amplified signal will only be experienced by the ‘on’ state symbols. Due to a higher gain for the ‘off’ state symbols, the extinction ratio is impaired and the ‘off’ state symbols become more noisy after regeneration [8, 9]. By utilizing a saturable absorber [10] or a higher order idler [4] equalization of both the ‘on’ and ‘off’ state can be accomplished to some extent. However, this results in higher complexity and/or is associated with a simultaneous wavelength conversion of the signal. For these reasons, we believe the saturated FOPA is not so suitable as a regenerator in OOK systems, but more promising in a phase modulated system with all symbols containing equal average optical power. On the other hand, the information in such systems is encoded in the optical phase, which is not regenerated by the FOPA. Still amplitude regenerative FOPAs can be used to improve long distance differential phase shift keying (DPSK) communication systems by suppressing amplitude noise from in-line amplifiers and consequently counteract the origin of nonlinear phase noise [11, 12]. The improved performance by intensity regenerating FOPA have been experimentally verified in 10 Gbit/s DPSK systems by investigations of the DPSK demodulated signal [13, 14]. An experimental study of the regeneration influence on amplitude and phase separately was conducted in [15] on a 1 Gbit/s DPSK signal by using coherent detection.

In this paper, we consider the regenerative properties of a saturated FOPA on a 10 Gbit/s DPSK signal. The regenerative properties in both amplitude and phase are investigated, by means of a coherent detection scheme and analysis of the signal space constellation diagrams. Signal quality improvement after differential detection is also verified.

2. Saturated FOPA as regenerator

The single-pumped FOPA relies on a strong pump signal at the wavelength, λ_p, which is operated near the zero-dispersion wavelength, λ ₀, of the highly non-linear fiber (HNLF) for broadband amplification around the pump wavelength. It is combined with a weaker signal at λ_s, which experiences gain while an idler wave is generated at λ_i≈2λ_p-λ_s when the pump power is transferred to the signal and idler wavelengths through the four-wave mixing process. Since the required pump power to obtain large small-signal gain is rather high compared to an erbium-doped fiber amplifier (EDFA), a very high output signal power can also be obtained if a large fraction of pump power is converted to the signal and idler waves. A record 99.9% pump depletion and a record high pump power efficiency above 50% were recently demonstrated experimentally [17]. Since the parametric gain process is very fast, an amplitude-varying signal will instantly saturate the pump differently dependent on the input signal power. This gives rise to a nonlinear gain transfer function that can be utilized for ultra-fast signal equalization [4, 6, 9]. The optimum equalization is achieved for a specific average input power and therefore such regenerative FOPA can be suitable in systems using modulation formats with equal power symbols, such as phase modulated systems. To investigate this we implemented a regenerative FOPA and used it to regenerate a DPSK signal.

3. Experimental setup

Figure 1 shows a detailed illustration of the experimental setup of the FOPA regenerator together with the DPSK transmitter and receivers. An external cavity laser at 1589 nm and with specified linewidth <3 MHz was used as light source. The optical signal was split by a 50/50 fiber coupler in order to use half of the signal as local oscillator (LO) for the coherent detection to avoid the use of a second laser as an LO. The signal carrier was frequency shifted 27 MHz by an acousto-optic modulator (AOM) to generate an intermediate frequency (IF) at the receiver. For signal and LO path length differences longer than the coherence length of the laser source (approximately 200 m for a laser linewidth of 1 MHz), this resembles a practical system using a second free-running laser as LO. The benefit is that the approach eliminates long term wavelength drifts and thus eliminates the need for wavelength tracking. The 10 Gbit/s BPSK modulation was applied by a dual-drive Mach-Zehnder modulator (DDMZM) operated in push-pull mode, which gives the characteristic intensity dips (see waveforms in Fig. 1) as the trajectories between different phase symbols pass through the signal space origin [18]. The phase modulated signal then passed through a variable attenuator before amplification in two cascaded EDFAs with 2 nm optical bandpass filters after each EDFA. This is the input signal to the FOPA regenerator. By adjusting the attenuators (Att1, Att2) the OSNR and signal power level into the FOPA could be varied over a wide range. The FOPA pump at 1583 nm was phase modulated with four RF tones (100 MHz, 300 MHz, 900 MHz, and 2.7 GHz) to avoid stimulated Brillouin scattering (SBS), which otherwise would limit the input pump power into the 500 m HNLF to about 16 dBm. By applying four tones the SBS threshold increased by approximately 19 dB [19]. The phase modulated pump was amplified in two EDFAs and the pump was coupled together with the input signal into the HNLF via a 10 dB coupler. The HNLF had a nonlinear coefficient of approximately 10 W^-1km^-1 and an average zero-dispersion wavelength of 1569 nm. When the pump power was set to 1 W, the small-signal fiber gain in the HNLF was approximately 35 dB. The signal spectrum before and after the FOPA and the amplified spontaneous emission (ASE) spectrum is shown in Fig. 2

 

Fig. 1. Experimental setup of the 10 Gbit/s DPSK system and the FOPA. The inset waveforms shows the measured signal intensity before and after the FOPA when input signal OSNR=26 dB. ECL: External Cavity Laser, AOM: Acousto-Optic Modulator, PM: Phase Modualtor, MZM: Dual-Drive Mach-Zehnder Modulator, PC: Polarization Controller, Att.: Variable attenuator, EDFA: Erbium-Doped Fiber Amplifier, HNLF: Highly Non-Linear Fiber, PBS: Polarization Beam Splitter, ADC: Analog-to-Digital Converter, DSP: Digital Signal Processing.

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After the FOPA, the regenerated signal was coherently detected by an intradyne phase-diversity detection scheme [20]. The incoming optical signal was combined using a 50/50 fiber coupler with the signal from a local oscillator, in this case the unmodulated part of the light. The combined signals then passed through a polarization beam splitter (PBS), which govern the phase-diversity when the signal is linearly polarized and aligned 45° relative the transmission axes of the PBS, whereas the local oscillator should be circularly polarized. The two outputs from the PBS were detected by two AC-coupled matched receivers with 11 GHz bandwidth and digitized with 50 GSample/s, which subsequently were interpolated to 200 GSample/s to smooth the acquired waveforms and facilitate the sample selection for the SNR measurements. The acquired in-phase and quadrature-phase components of the data signal depend on the beating between the signal and LO according to [21]

where ℜ is the detector responsivity, R_L is the detector load resistance, P_s/P_LO is the signal/LO power, ϕ_mod(t) is the phase due to the data modulation, ϕ_LO is the LO phase relative phase the signal, and ω_IF=ω_s-ω_LO is the angular frequency due to the 27 MHz frequency difference of the signal and LO. With the AC-coupled receivers the Eqs. 1 and 2 reduced to their last term, given that P_s≫P_LO. To obtain the data phase modulation the IF phase, ω_IFt, has to be estimated and removed. Similar to [22, 23], the IF calculation was done by squaring the composed signal E=V ₁+iV ₂, which eliminates the binary phase modulation (ϕ_mod(t)=0,π), and the IF phase can be determined by ϕ_IF(t)=arg(E(t)²)/2. The continuous ϕ_IF(t) was bandpass filtered and subsequently subtracted from the detected signal phase and the remaining signal is the phase modulated data signal. The derived signal can conveniently be analyzed in the complex plane. Since the distributions of the received symbols are not uniform after the regenerating FOPA, we choose to separate the noise variances into the radial and angular directions, thus determining the SNR in amplitude and phase separately. For comparison, the signal SNR was also measured before and after regeneration with DPSK demodulation in a Mach-Zehnder delay interferometer (DI) using (single-ended) direct detection (40 GHz detector) and an equivalent time oscilloscope with 26 GHz bandwidth.

 

Fig. 2. Signal spectrum before and after the FOPA and the FOPA ASE spectrum.

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4. Results

The performance of the regenerator was investigated by measurements of the signal-to-noise ratio (SNR) in both amplitude and phase, before and after regeneration. The power transfer function of the black-box FOPA is shown in Fig. 3. The output power was constant within 0.5 dB for input power between -9 and 1 dBm. The input optical signal-to-noise ratio (OSNR) was varied, whereas the average input power was kept at -4 dBm to ensure optimum intensity regeneration. In contradiction to what is indicated by Fig. 3, the regeneration performance becomes limited by the pump OSNR, since pump fluctuations are transferred to the signal during the four-wave mixing process. Furthermore, the pump wavelength change due to the phase modulation gives rise to a gain fluctuation in the regenerator [10], which further degrades the regeneration. The limit manifests as a maximum signal OSNR after the FOPA as the input OSNR increases. We found experimentally that a 2 dB degradation of the pump OSNR resulted in a 2 dB lower maximum signal OSNR on the output. Thus, the pump noise is of utmost importance to accomplish good regeneration. The input pump OSNR used in this paper was 50 dB (0.1 nm reference bandwidth) and then the SNR saturation starts at a signal input OSNR of approximately 32 dB.

 

Fig. 3. Measured average power transfer characteristics of the parametric amplifier (black-box). Dotted lines serve as guides to the eye.

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Fig. 4. Constellation diagrams of 10 Gbit/s DPSK before (left) and after (right) regeneration. Dashed lines indicate the measured ±3σ spread of each distribution.

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Fig. 5. Measured SNR in amplitude (circles) and phase (squares) before (dashed lines) and after (solid lines) regeneration in the FOPA.

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Figure 4 shows constellation diagrams before and after the FOPA for different input OSNR values. The DPSK signal SNR in amplitude and phase, defined as |E|²/σ² _|E| and 1/σ² _arg(E) respectively, were measured from the constellation diagram and the result is plotted in Fig. 5. At the input of the FOPA the noise distribution is uniform and the phase and amplitude SNR are equal as expected. After regeneration the symbols are compressed in amplitude due to the regeneration, whereas the phase fluctuations are essentially unchanged, giving oval shaped symbol distributions. Furthermore, when the input OSNR is high (>25 dB) the phase fluctuations are increased after the FOPA. Here it should be emphasized that the upper limits of the amplitude SNR and the phase SNR visible in Fig. 5 have different origins. The constellation diagrams can be regarded as two-dimensional eye diagrams and consequently the SNR measurements are affected by the intersymbol interference (ISI). The coherent receiver is bandwidth-limited by the 11 GHz receivers and this together with non-ideal driving signals to the DDMZM limits the measurable amplitude SNR to approximately 28 dB. However, the bandwidth limitation is primarily a problem in amplitude and the phase at the decision point is only marginally affected by the ISI, as illustrated by the averaged amplitude and phase eye diagrams in Fig. 6. The overshoots in the phase eye diagram is a mathematical artifact due to phase wrapping. It should be mentioned that the ISI limitation could be reduced by modulating the DPSK with a phase modulator which leaves the intensity constant at all times. The drawback with this modulation scheme is that the modulated phases become more sensitive to non-ideal modulator driving signals due to the linear transfer function between electrical field and optical phase of the phase modulator. Since the measured maximum phase SNR is not limited due to ISI and the fact that the phase noise limit depends on the pump OSNR [15], the conclusion can be drawn that FOPA-induced phase noise limits the maximum phase SNR. This phase noise arises from the pump amplitude noise via cross-phase modulation just as the conventional nonlinear phase noise arises from a signal’s own amplitude noise via self-phase modulation (SPM). An important difference though is that the pump induced phase noise results in the circle-segment shaped constellations, as we also can see in Fig. 4, whereas conventional SPM induced nonlinear phase noise causes spiraling constellations [16]. Constellation diagrams give the correct information of how the symbols are effected by the FOPA. However, it is the performance after differential phase demodulation, i.e. when the phase modulation is converted into an amplitude modulation, that really matters in a differentially encoded phase modulated system. Figure 7 shows the measured intensity SNR of the demodulated DPSK signal after the DI with and without regeneration in the FOPA. These SNRs were measured on waveforms trigged on the pattern, thus the measurements are not affected by ISI. The FOPA significantly reduces the demodulated symbol intensity fluctuations and the measured intensity SNR increases up to 10 dB. The improvement limitation due to the pump OSNR that was seen for the phase SNR is visible after demodulation as well. Note that the noise distribution after the DI and after the regenerator is not Gaussian. Thus, it is not straightforward to transform the SNR improvement into a corresponding bit error rate improvement. It may seem unexpected that the SNR after DPSK demodulation can be improved by the intensity regeneration despite the fact that the phase noise has increased. This is explained by the fact that the amplitude variations transfer linearly through the demodulator whereas the phase differences transfer into amplitude (single-ended detection) as P_demod.=(1+cos(Δϕ))/2, where Δϕ is the phase difference between two adjacent symbols. Consequently, the demodulated SNR is more sensitive to amplitude fluctuations than to phase fluctuations. Thus the regeneration amplitude improvement overcomes the degradation due to the induced phase noise after demodulation. However, it should be emphasized that this is only the case in the binary situation. In differential quaternary phase shift keyed (DQPSK) systems the phase fluctuation tolerance is generally smaller due to the closer symbol separation. In addition, the ±π/4 biasing of the two DIs in a conventional DQPSK demodulator alters the phase-to-amplitude transformation to P_demod.=(1+cos(Δϕ±π/4))/2, which in itself converts phase fluctuations into amplitude fluctuations to a larger extent compared to the binary case. As a result, a DQPSK system may have more limited improvement after regeneration in a FOPA, although the intensity fluctuations in front of the demodulator may be small.

 

Fig. 6. Amplitude (left) and phase (right) separated eye diagrams after regeneration illustrating the different influence of ISI in amplitude and phase. Average of 7 patterns and input OSNR=33 dB. Dashed lines indicate the decision time.

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Fig. 7. Measured SNR after DPSK demodulation before (diamonds) and after (squares) regeneration in the FOPA. Insets show typical waveforms before and after regeneration measured on the destructive interference port of the delay interferometer.

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5. Conclusions

We have investigated regeneration of 10 Gbit/s DPSK signals when amplitude regenerated in a saturated FOPA. Amplitude and phase regeneration properties were separated by the use of coherent receiver and constellation diagram analysis. The amplitude regeneration effectively reduced amplitude fluctuations. After DPSK demodulation in a delay interferometer the regeneration significantly improves the measured SNR. We also found that the regenerator introduce phase noise. The amount of this phase noise depends on the OSNR of the FOPA pump. Such induced phase noise could be an important limitation in higher-level phase modulated systems, which are less tolerant to phase noise than binary phase modulated systems.