Phase-preserving principle of all-optical regenerators with applications to MZI-nested NOLM structure

Biao Guo; Baojian Wu; Feng Wen; Kun Qiu

doi:10.1364/OE.456384

1. Introduction

With the rapid development of modern communication networks, large capacity and high rate transmission has become their main requirement. High-order modulated signals can increase spectral efficiency, but be easily interfered by various crosstalk and ASE noise [1]. All-optical regeneration technology is very useful for suppressing the degraded factors and improving optical signal-to-noise ratio (OSNR) [2]. All-optical regeneration means that optical signals are directly processed in the optical domain, from OOK formats for incoherent communication systems, to higher-order modulation formats such as QPSK and QAM widely used for coherent communication systems.

All-optical amplitude or phase regeneration can be implemented by the optical nonlinear effects such as Kerr nonlinearities in highly nonlinear fibers (HNLFs), resulting in some representative structures of nonlinear optical loop mirror (NOLM), Mach-Zehnder interferometer (MZI), phase sensitive amplifier (PSA), semiconductor optical amplifier(SOA) and so on [3–8]. Most of these structures are aimed at amplitude regeneration. For quadrature amplitude modulation (QAM) signals, the multi-level amplitude regeneration should be implemented by approximately preserving origin phases or reducing phase noise. The former is called phase-preserving amplitude regeneration (PPAR) [9]. Several PPAR configurations based on nonlinear amplifying loop mirror (NALM), optical fiber parametric amplification (FOPA), or its cascaded structure [9–12] were presented. Our research group also put forward some modified PPAR schemes, including cascaded MZI, conj-NOLM, att-NALM, on-chip MZI [13–16]. The simple and practical PPAR schemes with lower phase disturbation will be more desirable in the future.

To explain the phase-preserving principle in the process of amplitude regeneration, we will build up a theoretical model composed of a self-phase modulation (SPM) nonlinear unit and the optical coupler, which are also necessary components for the above-mentioned PPAR schemes. Based on this principle, we propose a MZI-nested NOLM structure for the QPSK or 16QAM PPAR function and the phase perturbation can be as small as 2.45 degrees by optimizing the optical couplers used in this structure. The feasibility of the proposed PPAR scheme is also verified by experiment.

The rest of the paper is organized as follows. Section 2 analyzes the basic principle why phase information can be preserved in the process of amplitude regeneration. Then, we put forward and experimentally verify the MZI-nested NOLM PPAR scheme in Section 3 and 4, respectively. Section 5 discusses the influence of the coupler parameters on the PPAR performance. In Section 6, we simulate the PPAR performance of the 16QAM signals by optimizing the power transfer function of the MZI-nested NOLM regenerator, and make a comparison with other NOLM schemes. Section 7 gives the final conclusion.

2. Phase preserving principle of regenerators

At present, all-optical PPAR schemes are mostly based on MZI and NOLM structures with self-phase modulation (SPM). However, the power dependence of SPM-induced phase shift will give rise to an additional phase disturbation for the regenerated signals. The concept of PPAR means actually that the phase disturbation is sufficiently small as possible in the process of amplitude regeneration. Both the SPM nonlinear unit and the optical coupler are indispensable in the PPAR schemes with MZI or NOLM structure.

To explain the principle of phase preserving, we may build up the theoretical model as shown in Fig. 1(a). An input optical beam with the complex amplitude of ${A_{in}} = |{{A_{in}}} |{e^{j{\varphi _{in}}}}$ is divided into two parts and one of them will go through a nonlinear process, equivalent to a gain G and a nonlinear phase shift (NPS). Then, the two beams are coupled by a coupler with the coupling ratio $\rho $, and the output complex amplitude can be deduced as follows:

(1)$${A_{out}} = \sqrt \rho |{{A_{in}}} |{e^{j({\varphi _{in}} + \frac{\pi }{2})}}\left[ {1 + \frac{1}{{\sqrt R }}{e^{j({\varphi_{NL}} - {\varphi_{in}} - \frac{\pi }{2})}}} \right]\; $$

where, $R = \rho /[{({1 - \rho } )G} ]$ is the power ratio of two output components, related to the linear phase shift (LPS) and nonlinear phase shift (NPS), respectively; and the SPM-induced NPS is ${\varphi _{NL}} = \gamma G{|{{A_{in}}} |^2}{L_{eff}}$ with the fiber nonlinear coefficient $\gamma $ and effective length ${L_{eff}}$. The LPS component can be easily compensated in coherent communication systems.

Fig. 1. The principle of phase preserving: (a) Theoretical model; (b) Phase disturbation

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Equation (1) can also be illustrated in the complex plane as given in Fig. 1 (b). By considering that the phase disturbation is very small for PPAR function, the maximum phase disturbation relative to the input light field is as follows:

(2)$$\Delta {\varphi _{\textrm{max}}} = arcsin\frac{1}{{\sqrt R }} \approx \frac{1}{{\sqrt R }}$$

According to Eq. (1), the variations of output phase and amplitude with the increase of input power for $R = 10,20,30,40$ are plotted in Fig. 2, where $\rho = 0.99$, $\gamma = 10.8/W/km$ and ${L_{eff}} = 1km$. From Fig. 2, the phase variations of the output light fields with the input power are periodic due to the self-phase modulation, and the maximum phase changes relative to the zero-phase input signal are 18.43°, 12.92°, 10.51° and 9.09° for the different R values, respectively. Clearly, the larger the power ratio R, the smaller the phase disturbation. Thus, we can obtain the phase preserving condition for all-optical regenerators that the LPS component of output light field must be greatly dominant over the NPS component in optical power.

Fig. 2. Output light fields in terms of complex amplitude for different R values

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3. MZI-nested NOLM regenerator

In what follows, we propose a new PPAR scheme based on the MZI-nested NOLM structure and deduce the power and phase transfer functions for QPSK or 16QAM regeneration. The corresponding parameters are determined by the phase preserving condition mentioned above. The proposed MZI-nested NOLM regenerator is shown in Fig. 3. The optical coupler (OC₀) is used to form the NOLM loop. A section of highly nonlinear fiber (HNLF) as the MZI’s lower arm is connected to the NOLM loop through the optical couplers, OC₁ and OC₂. The optical couplers have the coupling efficiencies of ${\rho _0}$, ${\rho _1}$ and ${\rho _2}$, respectively.

Fig. 3. MZI-nested NOLM regenerator

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For the whole NOLM structure, the complex amplitudes of the regenerated signal and the reflected light, ${E_{out}}$ and ${E_r}$, can be given as follows [17–19]:

(3)$$\left( {\begin{array}{{c}} {{E_{out}}}\\ {{E_r}} \end{array}} \right) = \left( {\begin{array}{{c}} {i\sqrt {{\rho_0}} }\\ {\sqrt {1 - {\rho_0}} } \end{array}\begin{array}{{c}} {\sqrt {1 - {\rho_0}} }\\ {i\sqrt {{\rho_0}} } \end{array}} \right)\left( {\begin{array}{{c}} {{E_{f2}}}\\ {{E_{b2}}} \end{array}} \right)$$

where ${E_{f2}}$ and ${E_{b2}}$ designate the complex amplitudes output from the MZI unit along the clockwise and counterclockwise propagating directions, respectively.

We can deduce ${E_{f2}}$ and ${E_{b2}}$ from the complex amplitudes input to the MZI unit along the clockwise and counterclockwise propagating directions, ${E_{f2}}$ and ${E_{b2}}$, namely [16]:

{}{\left( {\begin{array}{{c}} {{E_{f2}}}\\ / \end{array}} \right) = \left( {\begin{array}{{c}} {i\sqrt {{\rho_2}} }\\ {\sqrt {1 - {\rho_2}} } \end{array}\begin{array}{{c}} {\sqrt {1 - {\rho_2}} }\\ {i\sqrt {{\rho_2}} } \end{array}} \right)\left( {\begin{array}{{c}} 1\\ 0 \end{array}\begin{array}{{c}} 0\\ {{t_f}} \end{array}} \right)\left( {\begin{array}{{c}} {i\sqrt {{\rho_1}} }\\ {\sqrt {1 - {\rho_1}} } \end{array}\begin{array}{{c}} {\sqrt {1 - {\rho_1}} }\\ {i\sqrt {{\rho_1}} } \end{array}} \right)\left( {\begin{array}{{c}} {{E_{f1}}}\\ 0 \end{array}} \right)}\\ {\left( {\begin{array}{{c}} {{E_{b2}}}\\ / \end{array}} \right) = \left( {\begin{array}{{c}} {i\sqrt {{\rho_1}} }\\ {\sqrt {1 - {\rho_1}} } \end{array}\begin{array}{{c}} {\sqrt {1 - {\rho_1}} }\\ {i\sqrt {{\rho_1}} } \end{array}} \right)\left( {\begin{array}{{c}} 1\\ 0 \end{array}\begin{array}{{c}} 0\\ {{t_b}} \end{array}} \right)\left( {\begin{array}{{c}} {i\sqrt {{\rho_2}} }\\ {\sqrt {1 - {\rho_2}} } \end{array}\begin{array}{{c}} {\sqrt {1 - {\rho_2}} }\\ {i\sqrt {{\rho_2}} } \end{array}} \right)\left( {\begin{array}{{c}} {{E_{b1}}}\\ 0 \end{array}} \right)}

where ${t_f}$ and ${t_b}$ are the transmission coefficients for the HNLF arm of the MZI unit, corresponding to the clockwise and counterclockwise propagating directions, respectively. ${E_{f1}}$ and ${E_{b1}}$ can be expressed by the input field of the whole NOLM structure, that is, ${E_{f1}} = \sqrt {1 - {\rho _0}} {E_{in}}$ and ${E_{f1}} = i\sqrt {{\rho _0}} {E_{in}}$.

Thus, the output field can be deduced from Eqs. (3)-(5) as follows:

(6)$$\begin{aligned}{E_{out}} &= {E_{in}}{e^{ - \alpha L}}\sqrt {({1 - {\rho_1}} )({1 - {\rho_2}} )} [{({1 - {\rho_0}} ){e^{i{\varphi_f}}} - {\rho_0}{e^{i{\varphi_b}}}} ]- {E_{in}}({1 - 2{\rho_0}} )\sqrt {{\rho _1}{\rho _2}} \\ &= {E_{in}}{\rho _0}\sqrt {{\rho _1}{\rho _2}} \left[ {1 - {e^{ - \alpha L}}\sqrt {\frac{{({1 - {\rho_1}} )({1 - {\rho_2}} )}}{{{\rho_1}{\rho_2}}}} {e^{i{\varphi_b}}}} \right] - {E_{in}}({1 - {\rho_0}} )\sqrt {{\rho _1}{\rho _2}}\\ &\left[ {1 - {e^{ - \alpha L}}\sqrt {\frac{{({1 - {\rho_1}} )({1 - {\rho_2}} )}}{{{\rho_1}{\rho_2}}}} {e^{i{\varphi_f}}}} \right] \end{aligned}$$

where, ${\varphi _f} = \gamma {P_{in}}({1 - {\rho_0}} )({1 - {\rho_1}} ){L_{eff}}$ and ${\varphi _b} = \gamma {P_{in}}{\rho _0}(1 - {\rho _2}){L_{eff}}$ are respectively the nonlinear phase shifts in the clockwise and counterclockwise directions [20], and $\textrm{ }{L_{eff}} = [{1 - \exp ({ - \alpha L} )} ]/\alpha $ with the loss coefficient $\alpha $. The power transfer function (PTF) and phase disturbation curves from the input to output field can be obtained from Eq. (6).

It is seen from Eq. (6) that, the output of the MZI-nested NOLM regenerator can be regarded as the combination of the clockwise and counterclockwise beams in the form similar to Eq. (1). According to the theoretical model given in Section 2 and the symmetry of the regenerator’s structure, we might take into account the case with ${\rho _0} > \textrm{ }0.5$. In the case, a simplest process is that only the counterclockwise beam is retained. That is, ${\rho _0}$ should be close to 1 as possible. At the same time, according to the optimization method presented in [15], ${\rho _2}$ may take the values close to 0.5 for a lower working point power of amplitude regeneration. Further, it is known from Eq. (1) that, the parameter $R = \frac{{{\rho _1}{\rho _2}}}{{({1 - {\rho_1}} )({1 - {\rho_2}} )}}$ should be as large as possible in order to realize the phase preserving function.

Based on the above analysis, we here take the optimized parameters available in our laboratory as follows: ${\rho _0} = 0.99$, ${\rho _1} = 0.995$, ${\rho _2} = 0.5$, $\alpha = 0.7dB/km$, $L = 1.5km$, and $\gamma = 10.8/W/km$. Figure 4 plots the PTF and phase disturbation curves calculated from Eq. (6). From Fig. 4, the PTF curve has two flatter steps capable of amplitude compression, whose centers are usually regarded as the working points (WPs), matching with the input level powers of 0.6W and 1.4W, respectively. At the WPs, an excellent phase preserving performance can be achieved, with the phase disturbation of about 3.8 degree.

Fig. 4. The PTF and phase disturbation curves for the MZI-nested NOLM regenerator

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4. Experiment and transmission simulation of QPSK regeneration

In order to verify the PPAR scheme proposed in the paper, we built up an experimental setup as shown in Fig. 5, and the experimental parameters are the same as used in Fig. 4. The whole experimental system is composed of three parts, those of degraded QPSK signal generator, the regenerator under test, and IQ demodulator with an oscilloscope (OSC). The IQ modulator and arbitrary waveform generator (AWG) are used to generate QPSK signals of 10Gbit/s. Then, the optical signal is degraded by ASE noise resulting from an erbium-doped fiber amplifier (EDFA1) and an optical attenuator is used to adjust the WP power input to the regenerator. The regenerated QPSK signal is coherently demodulated by an IQ demodulator, with the help of the local laser followed by the second erbium-doped fiber amplifier (EDFA2). The demodulated data are gathered by the OSC to calculate the error rate. At the receiver end, the data are recovered at the sampling rate of 100GS/s. All of the polarization controllers (PCs) as shown in Fig. 5 are indispensable for our experimental test.

Fig. 5. Experimental system of QPSK regeneration

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Firstly, the PTF curve is measured to obtain the working points for amplitude regeneration. In the case, the IQ modulator and demodulator should be removed from the setup as shown in Fig. 5, that is, The continuous wave emitted from the CW laser is directly amplified by EDFA1 and the optical power output from the regenerator is tested by an optical power meter. The optical power input to the regenerator is adjusted by the optical attenuator after EDFA1. Figure 6 gives the PTF data measured experimentally and the theoretical curve given in Fig. 4. It is seen from Fig. 6 that, the experimental data are basically consistent with the theoretical results, especially at the input working points of 600mW and 1400mW, which means the correctness of our theoretical analysis done in Section 3.

Fig. 6. PTF curves obtained by experiment and simulation

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Then, the PPAR experiment on QPSK signals is implemented at the first WP with the input power of 600mW. The QPSK signals can be degraded by adjusting the gain of EDFA2 for different signal-to-noise ratio (SNR) in electrical domain. Figure 7 (a) plots the constellation diagrams for the degraded and regenerated QPSK signals when the input SNR is SNR_in= 17dB, and there is a 3dB improvement in noise reduction ratio (NRR), defined as $NRR = 20\textrm{lg}(EV{M_{in}}/EV{M_{out}})$[16], where the parameter EVM represents error vector of magnitude. We also measured the NRR data and phase disturbation at different input SNRs, as shown in Fig. 8(b), including the linear fitting curve of the measured NRRs. From Fig. 8(b), the NRR gradually increases with the input SNR and its fitting curve has the slope of 0.78, i.e. NRR = 0.78* SNR_in -9.97. Accordingly, the phase disturbation ranges from 2.8 to 6 degrees, and the average phase disturbation is 4.37 degree, very close to the theoretical value of 3.8 degree.

Fig. 7. PPAR experiment on QPSK signals: (a) Constellation diagrams for the degraded and regenerated QPSK signals; (b) NRR data at different input SNR

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Fig. 8. Simulation system of cascading EDFAs with the regenerator: (a) Cascaded EDFA simulation system with the regenerator; (b) BER performance of regenerator in transmission link

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The all-optical regenerator is very useful for improving the quality of degraded signals in data transmission without bit errors. In other words, the EVM reduction, as shown in the regeneration experiment, can help to increase the transmission distance. At the same time, the regeneration performance can also be illustrated by a bit error rate curve [21]. For this purpose, we build up a simulation system of cascading EDFAs with the regenerator [5,14]. As shown in Fig. 8 (a), the 50Gbps QPSK signal is amplified by a series of amplifiers (red triangle) periodically, and an all-optical regenerator is inserted in the middle of the link. In the simulation system, the total ASE noise introduced by the EDFAs before and after the regenerator is always identical, in terms of the signal-to-noise ratio input to the regenerator. Under two cases with / without regeneration, the bit error rates (BERs) at the ideal receiver end are simulated for the different SNRin in electric domain. The corresponding BER curves are plotted in Fig. 8 (b). For any given SNRin, the BER with the regenerator is lower than that without the regenerator. The capacity limit of noise can be improved by about 1dB at the FEC threshold of BER= 10-3.

5. Analysis and discussion

5.1. Influence of the optical couplers on regeneration performance

The buildup of our experiment takes advantage of the optical couplers available in the laboratory and the coupling ratio of these couplers may further be optimized for a better regeneration performance. According to Eq. (6), we calculate the variations of the first WP power with ${\rho _0}$ and ${\rho _1}$ when ${\rho _2} = 0.5$, as shown in Fig. 9(a). From Fig. 9(a), the increase of ${\rho _0}$ helps to reduce the working point power and is basically not affected by ${\rho _1}$ for large ${\rho _0}$. Figure 9(b) plots the dependence of the first WP power on ${\rho _2}$ when the other couplers keep fixed. It is known from Fig. 9(b) and the expression of $R = \frac{{{\rho _1}{\rho _2}}}{{({1 - {\rho_1}} )({1 - {\rho_2}} )}}$ that, ${\rho _2}$ should be selected by compromise between the WP power and phase disturbation. Fortunately, the phase disturbation can be further cut down by taking a large ${\rho _1}$ as possible.

Fig. 9. The influence of the optical couplers on the first WP powers

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When ${\rho _1}$ increases to $0.998$ from 0.995 and the other parameters are same as those used in Fig. 4, we can re-plot the phase disturbation curves and NRR data dependent on the input SNR, as shown in Fig. 10. By comparison of two cases, it is clear that, (1) the maximum phase disturbation reduce to 2.45 degrees from 3.8 degrees; (2) the NRR performance for QPSK regeneration is improved by 3∼6 dB dependent on the input SNR; and (3) from Fig. 10(b), the simulated curve of NRR is consistent with the experimental fitting one for the case with ${\rho _1} = 0.995$. It can be seen that ${\rho _1}$ has a great influence on phase preserving performance, instead of the power of working point. According to the analysis in Section 3 for better PPAR performance,

Fig. 10. Comparison of regeneration performance between ${\rho _1} = 0.995$ and ${\rho _1} = 0.998$: (a) The phase disturbation curves; (b) NRR data dependent on the input SNR

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${\rho _0}$ should be close to 1 as possible. In the case, Eq. (6) can be approximately reduced to

(7)$${E_{out}} \approx {E_{in}}{\rho _0}\sqrt {{\rho _1}{\rho _2}} \left[ {1 - {e^{ - \alpha L}}\sqrt {\frac{{({1 - {\rho_1}} )({1 - {\rho_2}} )}}{{{\rho_1}{\rho_2}}}} {e^{i{\varphi_b}}}} \right]$$

where ${\varphi _b} = \gamma {P_{in}}{\rho _0}(1 - {\rho _2}){L_{eff}}$. According to the method of [17], the power at the first working point is independent of ${\rho _1}$ and can be expressed by ${P_{wp}} \approx \frac{{1.5\pi }}{{\gamma {\rho _0}(1 - {\rho _2}){L_{eff}}}}$, corresponding to the theoretical result of 608 mW, which is almost consistent with the experimental data given in Fig. 6. Similarly, the phase disturbation of the output light field may also be analyzed form Eq. (7) according to the explanation presented in Section 2. As shown in Fig. 10 (a), the phase disturbation is sensitive to ${\rho _1}$ and then acts on the regeneration performance [22].

The above analysis on the MZI-nested NOLM regenerator shows that, the NOLM structure composed of a larger ${\rho _0}$ coupler is helpful for the reduction of the working point powers and the function of phase preserving is realized by the MZI unit with a sufficiently large ${\rho _1}$.

5.2. Comparison of NOLM-based regeneration structures

So far, some variations of NOLM-based regeneration structures have been put forward, including those of simple NOLM [5], cascaded NOLM [17], NOLM-nested MZI [23], attenuation-imbalanced NOLM (aNOLM) [9], conj-NOLM [14], Att-NOLM [15], et.al. By contrast, the MZI-nested NOLM proposed in the paper has some advantages of low phase disturbation (4.4°) and simple structure (without optical amplifier or attenuators), easy to realize experimentally. Table 1 lists the comparison of these NOLM regeneration structures. From Table 1, our scheme based on MZI-nested NOLM experiment for QPSK signals has a smaller first-level power and better phase preserving performance compared with the aNOLM-based regenerator for 8-QAM signals [9]. Other schemes are limited to theoretical research or no phase-preserving function. In a word, the MZI-nested NOLM structure is a promising PPAR platform for higher-order modulation signals.

Table 1. Comparison of these NOLM regeneration structures

View Table

6. Conclusion

An MZI-nested NOLM PPAR scheme is put forward and theoretically analyzed by means of the basic principle of phase preserving regeneration presented in this paper. The PPAR performance for QPSK signals is measured by the experiment, with the regenerative input power of 27.8dBm and average phase disturbation of 4.37 degree. The influence of the optical couplers on the PPAR performance is also discussed in detail.

Funding

National Natural Science Foundation of China (61975027, 62001086).

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Type	Regenerated signals	Minimum level power	Phase disturbation
Simple NOLM [5]	PAM-4	22.5dBm	No phase-preserving (Experimental)
NOLM-nested MZI [23]	256QAM	/	No phase-preserving (Theoretical)
Cascaded NOLM [17]	PAM-8	27dBm	No phase-preserving (Theoretical)
aNOLM [9]	8-QAM	34dBm	/ (Experimental) 17.18°(Theoretical)
Conj- NOLM [14]	16-QAM	27dBm	8.8°(Theoretical)
Att-NALM [15]	16-QAM	24.7dBm	6.3°(Theoretical)
Our scheme	QPSK	27.8dBm	4.37°(Experimental) 3.8°(Theoretical)

Phase-preserving principle of all-optical regenerators with applications to MZI-nested NOLM structure

Abstract

1. Introduction

2. Phase preserving principle of regenerators

3. MZI-nested NOLM regenerator

4. Experiment and transmission simulation of QPSK regeneration

5. Analysis and discussion

5.1. Influence of the optical couplers on regeneration performance

5.2. Comparison of NOLM-based regeneration structures

6. Conclusion

Funding

Disclosures

Data availability

References

Data availability

Cited By

Figures (10)

Tables (1)

Equations (20)

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