The possibility of all-optical phase-preserving amplitude regeneration for star-8QAM is demonstrated using a modified nonlinear optical loop mirror. Experiments show a reduction in amplitude noise on both amplitude levels simultaneously, considering two different types of signal distortions: deterministic low-frequency amplitude modulation and broadband amplitude noise. Furthermore, using this amplitude regeneration, the robustness against nonlinear phase noise from fiber nonlinearity in a transmission line is increased. The scheme suppresses the conversion of amplitude noise to nonlinear phase noise. This is shown for simultaneous amplitude regeneration of the two amplitude states as well as for amplitude regeneration of the high-power states only. If the transmission is limited by nonlinear phase noise, single-level operation at the more critical higher-power state will benefit because of the wider plateau region. Numerical simulations confirm the experimental results.
© 2014 Optical Society of America
Quadrature amplitude modulation (QAM) as a combination of amplitude- and phase-shift keying increases the spectral efficiency in optical communication systems and thus enhances the transmission capacity . At the same time, QAM formats show a higher sensitivity to amplitude and phase noise . Amplitude noise, in particular, does not only diminish the separation of different amplitude states but it can also be converted into nonlinear phase noise in the transmission fiber due to the Gordon-Mollenauer effect which is one of the major limiting factors for phase-encoded, dispersion-managed transmission systems  and due to cross-phase modulation in multichannel transmission . Of course, distortions in the signal phase can be directly regenerated but it is quite complex. An alternative way is phase-preserving amplitude regeneration to reduce amplitude fluctuations and, therefore, the origin of nonlinear phase noise .
All-optical signal regeneration offers potential ways of noise reduction and benefits from the ultrafast response of nonlinear effects and hence its bit-rate transparency. For simple modulation formats, like binary and quadrature phase-shift keying consisting of a single none-zero amplitude level, all-optical phase-preserving amplitude regeneration has been already demonstrated using different approaches [6–9]. For multilevel phase-preserving amplitude regeneration, modified nonlinear optical loop mirrors, e.g. the nonlinear amplifying loop mirror (NALM), are promising candidates due to the periodic behavior of their power transfer characteristic [10, 11].
In this paper, we demonstrate experimentally the possibility of multilevel phase-preserving amplitude regenerator for a QAM format consisting of two amplitude levels and four phase states, so-called star-8QAM, using an attenuation-imbalanced nonlinear optical loop mirror (aNOLM) for two different types of amplitude noise: deterministic amplitude modulation at alow frequency and broadband ASE-like amplitude noise. Furthermore, we demonstrate that multilevel amplitude regeneration directly increases the transmission robustness against the generation of nonlinear phase noise from amplitude noise by fiber nonlinearity. We also show that for highly nonlinear transmission lines as well as for modulation formats with a high state power ratio, single plateau operation is already sufficient to counteract signal distortions by nonlinear phase noise.
2. Operation principle and transfer function of the regenerator
The operation principle of modified Sagnac-interferometers for phase-preserving amplitude regeneration is as follows: Incoming signals are split up and counter-propagate in a fiber loop. Due to an asymmetric arrangement of components inside the interferometer loop, only the weaker partial signal gets the power-dependent phase shift, proportional to the signal power, while the stronger one remains linear. These two partial signals interfere at the device output. Therefore, the output phase is hardly power dependent while the amplitude transfer characteristic is strongly nonlinear. It has already been shown that such asymmetry can be induced in a number of schemes: By the use of amplifiers and attenuators, an asymmetry in average power can be realized [9, 12, 13] while dispersion management will result in asymmetries of the peak power . Nevertheless, the principle and the performance remains the same. Because of a reduced complexity, it is suitable to use a simple attenuator as an unbalancing component although a bidirectional amplifier should be used for practical applications to completely replace in-line amplifiers with such regenerators.
The experimental setup of the aNOLM is depicted in Fig. 1. Incoming signals are amplified by a high-power erbium-doped fiber amplifier. Afterwards, they are split up asymmetrically by a fiber coupler with a power ratio of 85:15 in our case and propagate in both directions along the aNOLM fiber loop. The stronger partial signal – in Fig. 1 propagating in the clockwise direction – is attenuated first by about 20 dB. As its power in the nonlinear fiber is about one order of magnitude below the other partial signal, it is hardly afflicted by nonlinear phase shifts. The counter-propagating weaker partial signal is passing the nonlinear fiber without attenuation. As it is not yet attenuated, its high power leads to a nonlinear phase shift. Afterwards, it is also attenuated by 20 dB to restore the initial splitting ratio. Interference at the fiber coupler is depending on the power-depending phase shift of the weaker partial signal.
The 25-GBd 33%-RZ star-8QAM signal at 1558.1 nm was generated in our experiments by 33% pulse carving and QPSK modulation followed by two-level amplitude-shift keying (2-ASK) modulation of a continuous-wave (CW) signal from an external-cavity diode laser. The booster amplifier in front of the aNOLM was operated in constant gain mode. The nonlinear fiber in the aNOLM has a length of 750 m, a total nonlinearity of about 6 rad W−1 and a total dispersion of −0.2 ps/nm.
A typical power transfer characteristic can be seen on the left side of Fig. 1 normalized with respect to the low-power state to illustrate the state power ratio. It was measured with pure QPSK modulation while the amplitude modulator was used to generate a sine-wave amplitude modulation at a frequency of about 15 MHz. Therefore, the amplitude variation between subsequent pulses was small while a high range of input powers was swept. The dotted lines correspond to a measurement of more than 100 modulation periods with the average value, shown as a solid line.
To optimize the power transfer function for phase-preserving amplitude regeneration of a two-amplitude level modulation format, the birefringence of the nonlinear fiber in the aNOLM was used to provide a constant phase bias between the two counter-propagating partial signals. This offset of the interference conditions gives the possibility to control the input power required for the plateau areas keeping unchanged the power increase between thefirst and the second plateau area, which corresponds to an additional nonlinear phase shift of 2π, because it is given only by the fiber length and nonlinearity . In principle, more than two plateaus are possible by increasing the input power to the aNOLM. In contrast to numerical simulations, no optical bandpass filter was used in the setup . Optical filtering in a range of about 400 GHz would have no effect because the filter bandwidth is still much larger than the 50 GHz electrical bandwidth of the photodiodes.
3. Experimental setup and results
In the experiments on noise processing, a star-8QAM signal was used. For driving the QPSK and AM modulators three decorrelated 215-1 pseudo-random bit sequences were used. As already mentioned, for a two-amplitude level modulation format, the second plateau of the regenerator’s transfer function has to be optimized most carefully because the high-power states are much more critical to nonlinear phase noise. For a given coupler splitting ratio, this could be realized only by adjusting the phase bias, while the modulation format, namely the state power ratio, was adjusted to fit the plateau power ratio given by the optimization.
As an aNOLM provides only amplitude regeneration, pure amplitude noise was modulated on the signal to investigate the regeneration quality. This noise was generated in a so-called noise stage which consists of an additional intensity modulator. The electrical signal which drives the noise stage was operated in two modes: single-frequency operation with a sinusoidal voltage of a frequency of up to 1 GHz, i.e. more than one order of magnitude below the symbol rate, and operation with broadband Gaussian-distributed noise with a bandwidth of about 10 GHz. Since single frequency modulation results in a square-like amplitude noise distribution with two peaks at the edges, this type of deterministic fluctuation provides the possibility to show the regeneration limits. On the other hand, broadband amplitude noise is the most realistic scenario to simulate the effect of amplified spontaneous emission (ASE) in fiber amplifiers. To generate such type of pure amplitude noise, the intensity modulator was driven with an electrical signal obtained from a photodiode detecting the ASE noise from an erbium-doped fiber amplifier operated without input signal. A similar setup was used in , but for the generation of pure phase noise.
3.1 Deterministic amplitude fluctuations in a back-to-back configuration
To show the regeneration ability as well as the regeneration performance of an aNOLM, a configuration without transmission line was evaluated first. A photodiode with 50-GHz bandwidth was used as a direct-detection receiver to observe the power eye diagrams of the star-8QAM signal. The results are shown in Fig. 2. The average power into the aNOLM coupler is 34 dBm. The undistorted signal (left), detected directly after the transmitter, has a state power ratio of 1:3. This ratio was chosen in order to fit the plateau power ratio given by the aNOLM’s power transfer characteristics after optimization. The particular value of thestate power ratio plays a minor role for these experiments, because it was already shown that modified Sagnac-Interferometers can process, in general, a two-level signal with any statepower ratio . The corresponding eye diagram of a noisy signal is shown in the middle of Fig. 2. The broadening of both amplitude levels as well as a smaller power eye opening can be clearly seen. After the regeneration by the aNOLM, a significant reduction in amplitude noise and also an increased power eye opening was observed (right side in Fig. 2).
These results are confirmed by the power histograms detected in the center of each symbol window which are shown in Fig. 3 for the distorted signal, as well as for the regenerated one. The characteristic features of the sinusoidal noise modulation are present in the histograms of the distorted signal. With this square-like amplitude noise distribution only the overall slope of the power transfer characteristics will be dominant while the local slope will play a minor role. After the regeneration, the probability distributions of both power states are clearly compressed. The so-called regeneration ability was used as a quality factor which is defined as the ratio of the standard deviation of the amplitude distribution before and after the regenerator, both normalized to its corresponding mean power. For the high-power states, a regeneration ability of 2.2 dB was achieved while a regeneration ability of almost 1 dB was measured on the low-power states simultaneously . This is in good agreement with the transfer function which was optimized for flatness on the second plateau region so that a residual slope remains on the first plateau.
Another observed effect is a shift in the centers of mass of both state power distributions. This results from the nonlinear behavior of the power transfer function with its two plateau regions. An increase in state power ratio from 1:3 to about 1:3.6 was observed, which is also visible in the power transfer function in Fig. 1. It can be seen as an increase of the eye opening in the eye diagrams (Fig. 2) and, therefore, an increased separation of the two states (Fig. 3). In addition to suppression of amplitude noise, also this state separation will increase the tolerance against amplitude-based bit errors in a subsequent transmission. However such an increased separation will result in a slightly stronger nonlinear phase shift for the high-power states the transmission fiber. Furthermore, the impact of ASE noise on the low-power states will become stronger compared to the high-power states.
3.2 ASE-like amplitude noise in a nonlinear transmission line
Phase-preserving amplitude regeneration not only reduces amplitude noise in particular but also increasing the tolerance against the generation of nonlinear phase noise (NPN) along transmission lines. A higher tolerance against NPN can be used to increase the fiber launch power in order to improve either the signal-to-noise ratio on the receiver side of a transmission line – in case of being limited by the ASE noise resulting from in-line amplification - or directly increase the transmission distance. In order to evaluate the regenerator performance in reducing NPN, an additional nonlinear fiber was placed after the regenerator. This nonlinear fiber was used to emulate a transmission line being limited by nonlinear effects. The experimental scheme is shown in Fig. 4. The signal is degraded first by the amplitude noise stage. Then this noisy signal is either regenerated by the aNOLM or bypasses the regenerator for comparison. The detour includes a variable optical attenuator in order to provide the same input power in the subsequent booster amplifier in front of the nonlinear transmission line. An additional variable optical attenuator is used to control the average power launched into the nonlinear fiber in a range of to up to 15 dBm. The total nonlinearity of the fiber was 30 W−1, and the total losses less than 3 dB. An average power into the aNOLM coupler of 34 dBm was used. A homodyne coherent receiver is now employed for the evaluation. It is based on a continuous wave local oscillator (tapped from the transmitter before modulation), a 90°-hybrid, balanced photodiodes, two analog-to-digital converters (80 GS/s, 30-GHz bandwidth) and a desktop computer for offline-processing. The DSP is kept at a minimum level using only resampling, clock-recovery and Viterbi-Viterbi based carrier-phase estimation with a fixed block size of 61 samples.
In contrast to the previous results, a more realistic scenario with broadband amplitude noise generation is used. The corresponding constellation diagram of the distorted signal can be seen in Fig. 5a. The shape of the broadband amplitude distributions is now close to Gaussian and therefore more realistic, being similar to real ASE noise. The generated nonlinear phase noise resulting from the amplitude noise along the nonlinear transmission line can be seen clearly in Fig. 5b for the signal bypassing the regenerator. The corresponding average power launched into the nonlinear (transmission) fiber was set here to 13 dBm. In the case of amplitude regeneration by the aNOLM depicted in Fig. 5c, the signal shows a reduction in amplitude noise together with a typical phase shift of the high-power states resulting from the imperfect phase transfer function of the regenerator, which can be easily corrected by applying a phase-recovery algorithm to each amplitude state ring separately at the receiver side. A clear suppression in NPN can be seen in Fig. 5d when the regenerated signal is transmitted through the nonlinear fiber. In contrast to the bypass signal, the phase noise on the high-power states is reduced by 1 dB by the regenerator when comparing the standarddeviation without and with regeneration. This is a direct effect from the suppression of the amplitude noise. Nevertheless, this effect can be hardly observed for the low-power states for two reasons: First of all, nonlinear effects scale with power and, therefore, are much stronger for high-power states than for low-power ones. Second, the amount of amplitude noise added to both signal amplitudes in the noise stage is also scaling proportional to the signal state power. This is the fact because amplitude modulation was used in the noise stage instead of optical ASE noise. In other words, in our scenario the state OSNR is the same for each amplitude state. While dealing with complex modulation formats and ASE noise, the state OSNR is usually different for each amplitude state.
3.3 First-plateau-only operation for minimization of nonlinear phase noise
As the NPN at the low-power states is less, we considered also the use of the first plateau for processing of the high-power states by reduction of the aNOLM input power. In this case, the operation point on the power transfer characteristic of the regenerator corresponding to the low-power states is not located at a plateau so that minor degradations might occur for these states. However, the condition results in a larger relative plateau width and enables better amplitude regeneration though optimization is limited to the first plateau. The setup remained the same with the signal either regenerated or bypassing the aNOLM and afterwards transmitted through the nonlinear fiber for transmission emulation. The average power to the aNOLM coupler was reduced to 30 dBm in order to match the high-power state to the first plateau. The constellation diagrams are shown in Fig. 6 in the common order: first the reference signal without regeneration before and after the nonlinear transmission line and then the regenerated signal for comparison. The difference between both signals is also illustrated in the histograms of the signal phase, obtained with the coherent receiver for different fiber launch power. It is shown in Fig. 7. The histograms of the signal phase are shown separately for the two amplitude states and normalized to their respective phase state value. Nonlinear phase noise is suppressed by up to 1.7 dB, measured in terms of the standard deviation, for the high-power states depending on the fiber launched power. An asymmetry in the phase distribution for the high-power states is originating from asymmetries in the amplitude distribution caused by the aNOLM regeneration process. A negative third moment of the phase distribution of −0.3 was found for the regenerated signal but not for the reference signal. Due to the regeneration process the amplitude distribution is compressed and converted to nonlinear phase noise by the Gordon-Mollenauer effect in the subsequent nonlinear transmission line. As expected, the low-power states are degraded by about 0.4 dB due to the first-plateau-only operation.
This operation condition is representative for scenarios where the high-power state is most critical, e.g., in highly nonlinear transmission lines or for the use of state power ratios of more than 1:3. In these cases, it is possible to simplify the regeneration process with hardly any performance penalty because transmission is mainly limited by the high-power states which will be regenerated.
4. Numerical simulations
Performance optimization of NOLM-based amplitude regenerators for multilevel operation has been discussed in  using numerical simulations. Our experiments confirm the results for the optimization of the transfer function as well as for the regeneration performance. Similar to numerical simulations, a simultaneous optimization of both plateau regions was not possible by either adjusting the directional phase bias or the coupler splitting ratio. Efficient phase-preserving amplitude regeneration was demonstrated in experiments for both amplitude states, although a performance compromise between the two states has to be made. This is in a good agreement with the numerical simulations. In contrast to numerical simulations in , the regeneration performance obtained from the experiments is lower than expected. The reason for this is the difference in noise parameters in the two cases. In the experiments, a deterministic, single-frequency amplitude modulation was used for the signal distortions while in  Gaussian noise distribution was considered. Although in the experiments broadband noise was used, the standard deviations in both cases were different.For the comparison to numerical simulations, we have chosen the scenario with the deterministic single-frequency amplitude modulation. Such a degraded input signal allows covering a wide range of amplitudes on the aNOLM transfer function. In order to compare the experimental results to a numeric analysis, the simulations described in  were applied assuming the input noise distributions obtained in the experiments. By controlling the directional phase bias in the simulations, the transfer function for the average power, shown in Fig. 7, was adjusted in good agreement to the measured transfer function shown in Fig. 1. The transfer function is shown in terms of peak-power as well as average power. Experimentally measurable is only the average power transfer curve whilst the peak-power is important for assessment of the regeneration. The plateau spacing as well as the slopes on both plateaus is in a good agreement to the experimentally observed transfer function for the average power. In addition to the transfer function, the noise distribution from the experiment which is used in the simulation is also shown in the appropriate scale. The maximum achievable regeneration ability for the power states with such a distribution was 3.8 dB for the low-power states and 3.6 dB on the high-power states (see Fig. 8). The performance on the high-power state in simulations is in good agreement with the experiments. For the low-power states, these simulations give only an upper limit in the regeneration performance due to the difference between the experimental achieved plateau power ratio and the state power ratio of the modulation format. The transfer function in the simulations was optimized to exactly fit to the state power ratio; therefore, both states are exactly centered in the plateau region. In the experiments, a simultaneously optimized regeneration on the low-power states was of minor priority. In favor of a better performance on the high-power states, the plateau power ratio might be a bit different so that the high-power state was still on the second plateau, but the low-power states were slightly offset from their ideal position relative to the transfer function.
5. Summary and conclusions
We have demonstrated all-optical phase-preserving amplitude regeneration for star-8QAM. Experiments show that it is possible to reduce amplitude noise simultaneously on both amplitude levels. This could be shown for two different noise types: deterministic, low-frequency amplitude modulation and broadband amplitude noise. Furthermore, we demonstrated that this amplitude regeneration allows reduction of nonlinear phase noise accumulation when used before a transmission segment which is limited by fiber nonlinearity. The performance has been demonstrated for simultaneous amplitude regeneration on both amplitude states as well as for amplitude regeneration on the high-power states only. In case of being limited by nonlinear phase noise, single-level operation will benefit because of a wider plateau region for the more critical high-power states for the sake of minor degradations in the low-power states. In addition, it has been shown that the experiments are in good agreement with numerical simulations. Intermediate phase conjugations in a nonlinear transmission channel with cascaded regenerators can in principle mitigate the nonlinear relative phase rotation between power states from the previous regeneration stage. This can also be done by modifying the DSP-algorithms in order to compensate for the constant phase difference between both amplitude states.
The authors gratefully acknowledge funding of the Erlangen Graduate School in Advanced Optical Technologies (SAOT) by the German Research Foundation (DFG) in the framework of the German excellence initiative.
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