Optical Phase Conjugation Research Articles

Optical Phase Conjugation With Complex-Valued Deep Neural Network for WDM 64-QAM Coherent Optical Systems

We experimentally demonstrated a photoelectric nonlinear compensation scheme of optical phase conjugation (OPC) with complex-valued deep neural network (CVDNN) to mitigate fiber nonlinearity in wavelength division multiplexing (WDM) 64-QAM coherent optical transmission system. The factors to affect the performance of OPC and CVDNN are comprehensively considered. OPC in WDM system is experimentally optimized to alleviate the deployment requirements of strict symmetrical distributed power and chromatic dispersion. The performance penalty caused by the simplification of the OPC is further compensated by the CVDNN. The selections of the input neurons’ number and the optimization algorithm are also considered to design a simple two-hidden-layer-structure CVDNN. The proposed method is experimentally verified and evaluated in a 12.5-GBd 4-channel WDM 64-QAM 160-km standard single-mode fiber (SSMF) transmission system with channel spacing of 50-GHz. The experimental results show that the proposed nonlinear equalizer based on the OPC with CDVNN has a strong robustness to the input signal power and wavelength, which can not only improve the Q factor of the signal by 1.5-dB, but also greatly increase the total launched signal power.

Fiber nonlinearity compensation using optical phase conjugation in dispersion-managed coherent transmission systems

Abstract In the discretely amplified transmission systems with erbium-doped fiber amplifiers, the system performance of nonlinearity-compensated optical transmission based on pre-dispersed spectral inversion (PSI) is investigated numerically. We find that PSI offers more significant performance improvement in dispersion-managed (DM) links than that in non-dispersion-managed (noDM) links. On the other hand, the DM link is more sensitive to the span offset from the center of the transmission link than noDM link. The performance difference between DM and noDM links is 1 dB if the span offset equals four spans in 20 × 90 km nonlinear transmission. Furthermore, we show that for the dispersion-managed transmission, in order to obtain the best system performance, the amount of pre-dispersion of the PSI, should be optimized over different dispersion maps.

Nonlinear/dispersion compensation in dual polarization 128-QAM system incorporating optical backpropagation

Abstract In order to cater long distance optical network units (subscribers), optical networks with prolonged reach are needed. In this study, an optical back propagation (OBP) dual polarization (DP)-128 QAM-based system is proposed to cope with nonlinear impairments in wavelength division multiplexing (WDM) systems. In pre, post and symmetrical configurations, the OBP module consisting of the optical phase conjugator (OPC), Raman fiber amplifier (RFA) and erbium doped fiber amplifier (EDFAs) is examined. Using dispersion compensation fiber (DCF) as RFA with dual directional pumping, ideal OBP conditions are simulated. DP-128 quadrature amplitude modulation (QAM) system is proposed with symmetrical OBP and compared with single channel digital back propagation (DBP), wideband DBP, pre OBP-forward pumping, pre OBP with backward pumping, pre OBP with dual directional pumping, post OBP with dual directional pumping. It is observed that symmetrical OBP configuration with dual direction pumping provide enhanced results and successfully cover 6500 km at bit error rate (BER) 10−3.

Digital compensation of imperfect pump counter-phasing induced phase distortion in optical phase conjugation of high-order QAM.

We propose a new two-stage digital signal processing scheme to suppress the phase distortion that arises from imperfect pump counter-phasing in a dual-pump fibre-based optical phase conjugation system. We demonstrate experimentally and numerically a signal-to-noise ratio improvement of more than 4 dB relative to conventional phase noise compensation, when the proposed scheme is used with 16/64/256 quadrature-amplitude modulation signals at pump-phase mismatch values as large as 8°.

Information rates in Kerr nonlinearity limited optical fiber communication systems.

Achievable information rates of optical communication systems are inherently limited by nonlinear distortions due to the Kerr effect occurred in optical fibres. These nonlinear impairments become more significant for communication systems with larger transmission bandwidths, closer channel spacing and higher-order modulation formats. In this paper, the efficacy of nonlinearity compensation techniques, including both digital back-propagation and optical phase conjugation, for enhancing achievable information rates in lumped EDFA- and distributed Raman-amplified fully-loaded C -band systems is investigated considering practical transceiver limitations. The performance of multiple modulation formats, such as dual-polarisation quadrature phase shift keying (DP-QPSK), dual-polarisation 16 -ary quadrature amplitude modulation (DP-16QAM), DP-64QAM and DP-256QAM, has been studied in C -band systems with different transmission distances. It is found that the capabilities of both nonlinearity compensation techniques for enhancing achievable information rates strongly depend on signal modulation formats as well as target transmission distances.

Optical information transmission through complex scattering media with optical-channel-based intensity streaming

For the past decade, optical wavefront shaping has been the standard technique to control light through scattering media. Implicit in this dominance is the assumption that manipulating optical interference is a necessity for optical control through scattering media. In this paper, we challenge this assumption by reporting on an alternate approach for light control through a disordered scattering medium – optical-channel-based intensity streaming (OCIS). Instead of actively tuning the interference between the optical paths via wavefront shaping, OCIS controls light and transmits information through scattering media through linear intensity operations. We demonstrate a set of OCIS experiments that connect to some wavefront shaping implementations, i.e. iterative wavefront optimization, digital optical phase conjugation, image transmission through transmission matrix, and direct imaging through scattering media. We experimentally created focus patterns through scattering media on a sub-millisecond timescale. We also demonstrate that OCIS enables a scattering medium mediated secure optical communication application.

Fully autocompensating high-dimensional quantum cryptography by quantum degenerate four-wave mixing

We present a bidirectional quantum communication system based on optical phase conjugation for achieving fully autocompensating high-dimensional quantum cryptography. We prove that random phase shifts and couplings among 2N spatial and polarization optical modes described by SU(2N) transformations due to perturbations are autocompensated after a single round trip between Alice and Bob. Bob can use a source of single photons or, alternatively, coherent states and then Alice attenuates them up to a single photon level, and thus non-perturbated 1-qudit states are generated for high-dimensional QKD protocols, as the BB84 one, of a higher security.

Compensation of SOA-induced nonlinear phase distortions by optical phase conjugation

To answer the question: "Is optical phase conjugation (OPC) capable of compensating nonlinear distortions caused by not only Kerr effect of optical fibre, but also the carrier dynamics of semiconductor optical amplifiers (SOAs)?", we investigate the effectiveness of OPC-based nonlinear compensation for SOAs amplifying a few-channel WDM signal modulated with m-QAM. We use a pair of SOAs with an OPC stage sandwiched between the two so that the combination works as a low-distortion amplifier. Symbol-period longer than the gain recovery time is chosen in our experiments to avoid bit-pattern effects introduced by the SOA. We amplify a 12Gbaud, 16QAM modulated three-channel WDM signal with this technique in the back-to-back configuration which remarkably outperforms a single SOA in the nonlinear regime of operation with an average Q2 improvement better than 4 dB for an output power of 4 dBm. We further demonstrate the practical advantage of the low distortion higher output power capability of the SOA shown in the back-to-back result by carrying out a transmission of the amplified signal through a 160-km fibre, where relatively high launch power is desirable. We also study the case of 64QAM signals and show that approximately a 3 dB Q2 factor improvement can be obtained over single SOA, while without nonlinear phase distortion compensation, the demodulation is nearly impracticable.

PERFORMANCE IMPROVEMENT OF NONLINEARITY COMPENSATION USING OPTICAL PHASE CONJUGATION FOR METRO DWDM SYSTEMS WITH OPTICAL ADD DROP MULTIPLEXERS

Wavelength Division Multiplexing (WDM) has been widely applied in optical adddrop multiplexing (OADM) fiber metro systems with an increasing number of wavelength channels and sufficiently narrow channel spacing. The problem that appears here is the signal distortion produced by dispersion and nonlinearity effects. To cope with these effects, many compensation solutions have been introduced, such as digital compensation (DC) solutions on technology of digital signal processing (DSP) or optical phase conjugation (OPC) on alloptical domain. In fact, research on using OPC to compensate for dispersion and nonlinearity in metro transmission systems are incomplete, especially with large number multiplexing systems. In this paper, we propose to use OPC for dispersion and nonlinear compensation in DWDM metro systems. Specifically, we focus on two common types of modulation signals: QPSK and 16-QAM; operations in 16- and 32-channel dense WDM system. The simulation results show that the system quality increases significantly when using OPC to compensate for dispersion and nonlinearity, e.g. when transmitting 16-QAM signals in a 32-channel system passing through 20 add/drop nodes, the gain of Q factor is greater than 2 dB.

Effect of shift in refractive index of dispersive elements in waveband-shift-free optical-phase conjugator based on DFG

In this study, the effect of the shift in the refractive index between two dispersive elements on the output phase-conjugated (PC) wave power of waveband-shift-free optical-phase conjugators based on difference-frequency generation (DFG-OPCs) is analyzed. First, a numerical model of the DFG-OPC is built by considering the shift ∆n in the refractive index. The derived formula shows that the output PC wave power of DFG-OPCs depends on the shift in the refractive index. Subsequently, the dependence of the output PC wave power on the shift is confirmed analytically. Calculations indicate that the output PC wave power varies according to the shift. For a relatively fractional shift ∆n = 1.0e-6, the output PC power is degraded by 3 dB. Finally, acceptable values of the shift and temperature difference are calculated as functions of the length of the dispersive element. It is illustrated in this study that the acceptable value of shift in the refractive index increases as the length of the dispersive element is reduced and that the output PC wave power can be stabilized against changes in temperature.

Symmetry Enhancement Through Advanced Dispersion Mapping in OPC-Aided Transmission

In this work, we present a novel strategy to satisfy the nonlinearity compensation criteria by optical-phase-conjugation (OPC). Contrary to the most common approach, which relies on tailoring power profiles using distributed Raman-amplification, we achieve the required OPC propagation symmetry through optimized dispersion management across the link. The method is applied to transmission systems with periodic lumped amplification, and the symmetry enhancement is directly translated into a substantial increase in the OPC compensation gains. This study is based on a numerical analysis combined with experimental validation of the findings. The numerical part provides a comprehensive overview of different dispersion management techniques, and compares them against the symmetric schemes we propose. It is consistently shown that the symmetry-optimized systems provide the best performance when OPC is included, with the signal-to-noise ratio (SNR) gains reaching up to 6.6 and 5.2 dB for transmission of a single and seven wavelength channels, respectively. These results are verified in an experimental investigation, where we implemented and compared a standard dispersion mapping scheme to the optimized design. For all distances considered, the optimized link is demonstrated superior once OPC is included, leading up to 1.9 dB improvement in SNR for seven-channel transmission.

Performance Evaluation of Highly Nonlinear Fiber (HNLF) Based Optical Phase Conjugation (OPC) in Long Haul Transmission of 640 Gbps 16-QAM CO-OFDM

This paper presents the quantitative measurement through an experimental test of 640 Gbps 16-QAM coherent-optical orthogonal frequency-division multiplexing (CO-OFDM) over 800 km optical fiber with mid-link optical phase conjugation (OPC) using highly nonlinear fiber (HNLF). The first focus is the OPC parameter optimization, including the optimization of HNLF length and signal/pump power that inputs into OPC. Four different HNLFs, as the illustrative examples, are investigated. The second focus is to investigate the effects of fiber dispersion, nonlinearity, and amplified spontaneous emission (ASE) noise on the long-haul transmission of 16-QAM CO-OFDM signal, and the OPC compensation efficiency. The performance evaluation focuses on the conversion efficiency (CE), received signal constellation, Q-factor improvement, and bit error rate (BER) at the receiver end. Such end-to-end performance evaluation is important because the 16-QAM CO-OFDM signal status is heterogeneous and the mitigation of transmission impairments to the signal is still unclear. The OPC parametric optimization is achieved experimentally using commercially available HNLFs with different scenarios and the numerical results are interpreted in conjunction with simulations.

Optical phase conjugation with dual frame OFDM for dispersion and nonlinearity mitigation over multimode fiber

This paper presents a modification in conventional asymmetrically clipped optical OFDM (ACO-OFDM) frame for direct detection intensity modulation (DD-IM) system. The conventional ACO-OFDM for DD-IM utilizes only one-fourth of available subcarriers for information symbols and therefore the bandwidth efficiency is very low. Authors propose to retain the othwerwise discarded negative polarity symbols to increase the bandwidth efficiency and transmission power for given number of subcarriers in ACO-OFDM. Proposed dual frame OFDM consists of two similar subframes and one of them is transmitted with optical phase conjugation for dispersion and non-linearity mitigation in multimode optical fiber. Proposed system is compared with another scheme-phase conjugated sub-carrier coding (PCSC) in OFDM. At − 15 dBm received optical power, proposed dual frame shows bit error rate (BER) $$1.974*10^{-3}$$ when compared to PCSC that shows BER value of $$1.13*10^{-1}$$ . BER Performance for the proposed dual frame OFDM with QPSK and QAM-16 modulation schemes is also compared in this research work.

Optical Phase Conjugation Using Nonlinear SOA for Nonlinearity and Dispersion Compensation of Coherent Multi-Carrier Lightwave Systems

We study the use of nonlinear semiconductor optical amplifier (SOA) for generating optical phase conjugate towards compensation of distortions in short distance optical fiber transmission due to Kerr nonlinearity and chromatic dispersion in coherent multi-carrier lightwave signals. We experimentally demonstrate the effectiveness of the SOA-based phase conjugator to improve the link budget with a 100 km standard single mode fiber link for 20 GHz coherent OFDM signals, with QPSK and 16QAM modulations and a corresponding net bit-rate of 40 Gbps and 80 Gbps respectively. Mid-span spectral inversion scheme is employed where the optical phase conjugate is generated through a partially degenerate four-wave mixing process in a nonlinear SOA. We demonstrate a bit error rate performance within 2×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> for an average launched power of up to 12 dBm (9 dBm) for QPSK (16QAM) coherent OFDM signals, in a 100 km fiber link. We also investigate the possible improvement in link budget using numerical simulation for 16QAM and 64QAM CO-OFDM signals with the proposed scheme.

Performance Evaluation of Diverse Hybrid Pulse Width Reduction Modules in WDM systems

Long reach wavelength division multiplexing (WDM) systems are required to cater the remote locations and to cover the maximum distances. Dispersion is prominent factor for distance limitation and should be addressed with high efficiency as well as using low cost pulse width reduction (PWR) modules. In this research work, hybridization of different PWR is proposed such as FBG-DCF, OPC–DCF (optical phase conjugation), FBG-DCF-OPC to analyse the PWRE and total cost of the modules. Further, in order to get optimal hybrid PWR module and amplification unit, different optical amplifiers are also investigated at 10 Gbps over 300 km. An ultra dense WDM system with 25 GHz channel spacing using 32 channels is demonstrated and PWRE is analysed using different hybrid PWR modules. Results revealed that FBG-DCF having least cost with PWRP of 55%, OPC-DCF show PWRE of 45% with moderate cost, and FBG-DCF-OPC provide maximum PWRE of 70% with little bit higher cost. Performance sequence of investigated PWR modules is give as: FBG-DCF-OPC (70% PWRE)> FBG-DCF (55% PWRE)>OPC-DCF (45% PWRE)> and performance of amplification unit with FBG-DCF-OPC is depicted as EDFA>RFA>SOA). This module can be used in passive optical networks for long reach systems.

Optical phase‐sensitive amplification of higher‐order QAM signal with single Mach–Zehnder amplitude modulator

An optical phase-sensitive amplifier (PSA) has the potential of low-noise optical amplification. A frequency non-degenerate PSA (ND-PSA) can amplify arbitrary modulation formats including higher-order QAM. The ND-PSA requires a co-propagating phase conjugated light (idler light) that has been conventionally created with an optical phase conjugator at the transmitter side. We propose a transmitter configuration using simultaneous signal generation of both a signal and its idler by double-sideband modulation for transmission systems with ND-PSAs. The proposed scheme provides a simple configuration with a single Mach–Zehnder amplitude modulator without optically creating the idler light. We performed experiments using 16QAM, 32QAM, and probabilistically shaped 256QAM signals. As a result, a phase-sensitive amplification with each modulation format was successfully demonstrated using the proposed transmitter configuration.

Nonlinear optical properties of halide perovskites and their applications

Nonlinear optics has undergone dramatic developments in the past 60 years, which has revolutionized the photonic and optoelectronic fields with many essential applications such as electro-optic switching, frequency mixing, optical parametric oscillation, optical phase conjugation, and so forth. As one of the new and promising candidates for both next-generation photovoltaic and optoelectronic devices, halide perovskite semiconductors have attracted extensive research attention because of their excellent electrical and optical properties demonstrated in the linear optical regime. In the past five years, halide perovskites have become a new research frontier of nonlinear optical materials because their highly tunable chemical components and multiple structures provide a variety of outstanding nonlinear optical properties, which support a broad scope of nonlinear optical applications. In this review, we have summarized the nonlinear optical properties of halide perovskites categorized according to the second-, third-, and high-order processes. Aside from the more conventional nonlinear effects, such as sum and difference frequency generation, this review also pays attention to the lesser known but important nonlinear phenomena, such as linear and circular photogalvanic effects, the high-order shift current effect, and the multi-photon pumped photoluminescence. We have also reviewed and summarized the nonlinear applications of halide perovskites, including multi-photon pumped photoluminescence imaging, multi-photon pumped amplified spontaneous emission and lasing, sub-bandgap and self-powered photodetection, all-optical and electro-optic modulation, saturable absorption, optical limiting, and so on. It is our belief that halide perovskites have proven to be excellent candidates for promoting the upgrading and updating of nonlinear optical devices with greatly improved performance and novel functionalities.

An Automatic Optimized Method for a Digital Optical Phase Conjugation System in Focusing through Scattering Media

In this paper, a reliable automatic optimized method for a digital optical phase conjugation (DOPC) system based on a multipopulation genetic algorithm (MPGA) is proposed for improving the compensation quality of DOPC. The practical implementation and compensation quality of DOPC in focusing through scattering media are greatly limited by imperfect pixel alignment, optical aberration, and mechanical error in the DOPC system. For comprehensively solving the above problems, the concept of global optimization is introduced by Zernike polynomials (Zernike modes) to characterize overall imperfections, and MPGA is used to search for the most optimal Zernike coefficient and compensate for the overall imperfections of the DOPC system. The significant optimization ability of the proposed method is verified in DOPC-related experiments for focusing through scattering media. The peak-to-background ratio (PBR) of the OPC focus increases 174 times that of the initial OPC focus. Furthermore, we evaluated the optimization results of the proposed method with a fitness function of intensity fitness and correlation coefficient fitness in MPGA. The results show that the optimized capability is excellent and more efficiently used than the correlation coefficient fitness function in the Zernike modes.

High-fidelity off-axis digital optical phase conjugation with transmission matrix assisted calibration.

The spatial information carried by light is scrambled when it propagates through a scattering medium, such as frosted glass, biological tissue, turbulent air, or multimode optical fibres. Digital optical phase conjugation (DOPC) is a technique that 'pre-aberrates' an illuminating wavefront to compensate for scatterer induced distortion. DOPC systems act as phase-conjugate mirrors: they require a camera to holographically record a distorted wavefront emanating from the scatterer and a spatial light modulator (SLM) to synthesize a phase conjugate of the measured wavefront, which is sent back through the scatterer thus creating a time-reversed copy of the original optical field. High-fidelity DOPC can be technically challenging to achieve as it typically requires pixel-perfect alignment between the camera and SLM. Here we describe a DOPC system in which the normally stringent alignment criteria are relaxed. In our system the SLM and camera are placed in-line in the same optical path from the sample, and the SLM is used in an off-axis configuration. This means high-precision alignment can be achieved by measurement of the transmission matrix (TM) mapping optical fields from the SLM to the camera and vice-versa, irrespective of their relative position. The TM also absorbs and removes other aberrations in the optical system, such as the curvature of the SLM and camera chips. Using our system we demonstrate high-fidelity focussing of light through two ground glass diffusers with a peak-intensity to mean-background ratio of ∼700. We provide a step-by-step guide detailing how to align this system and discuss the trade-offs with alternative configurations. We also describe how our setup can be used as a 'single-pixel camera' based DOPC system, offering potential for DOPC at wavelengths in which cameras are not available or are prohibitively expensive.

Probabilistic Shaping for the Optical Phase Conjugation Channel

Probabilistic constellation shaping is studied and developed for optical phase conjugation (OPC)-based nonlinearity compensation of Kerr nonlinearities in optical fiber links. The mid-link OPC scenario is considered for dispersion compensated systems. It is demonstrated in simulations and experimentally that transmission strategies optimal for classical additive white Gaussian noise (AWGN) channels can be sub-optimal for these systems without nonlinearity compensation. On the contrary, when nonlinearity compensation is applied with mid-link OPC, the channel noise is demonstrated to be Gaussian and AWGN-like transmission strategies thus remain effective. A channel-agnostic probability mass function (PMF) optimization algorithm is proposed for the input constellation in order to further improve the shaping gains in both scenarios. Operating arbitrary PMFs on arbitrary channels is enabled by a channel-agnostic digital signal processing (DSP) chain. After ≈2000 km of transmission, mid-link OPC is demonstrated to provide ≈1 dB of gain in effective SNR, which translates to ≈0.4 bits/QAM symbol of gain in achievable information rate. The gain is then increased by an extra 0.2 bits/QAM symbol by applying probabilistic shaping.