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Optics Letters

Regenerative Fourier transformation for dual-quadrature regeneration of multilevel rectangular QAM

Mariia A. Sorokina, Stylianos Sygletos, Andrew D. Ellis, Sergei K. Turitsyn

Published Jun 24, 2015• 27 citations
Publisher

Abstract

We propose a new nonlinear optical loop mirror based configuration capable of regenerating regular rectangular quadrature amplitude modulated (QAM) signals. The scheme achieves suppression of noise distortion on both signal quadratures through the realization of two orthogonal regenerative Fourier transformations. Numerical simulations show the performance of the scheme for high constellation complexities (including 256-QAM formats).

DOI
10.1364/ol.40.003117

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We propose a new nonlinear optical loop mirror based configuration capable of regenerating regular rectangular quadrature amplitude modulated (QAM) signals. The scheme achieves suppression of noise distortion on both signal quadratures through the realization of two orthogonal regenerative Fourier transformations. Numerical simulations show the performance of the scheme for high constellation complexities (including 256-QAM formats).
Since Shannon derived the seminal formula for the capacity of the additive linear white Gaussian noise channel, it has commonly been interpreted as the ultimate limit of error-free information transmission rate. However, the capacity above the corresponding linear channel limit can be achieved when noise is suppressed using nonlinear elements; that is, the regenerative function not available in linear systems. Regeneration is a fundamental concept that extends from biology to optical communications. All-optical regeneration of coherent signal has attracted particular attention. Surprisingly, the quantitative impact of regeneration on the Shannon capacity has remained unstudied. Here we propose a new method of designing regenerative transmission systems with capacity that is higher than the corresponding linear channel, and illustrate it by proposing application of the Fourier transform for efficient regeneration of multilevel multidimensional signals. The regenerative Shannon limit—the upper bound of regeneration efficiency—is derived. The Shannon limit describes the limit of error-free information transmission and thus the information that can be transmitted in telecommunications. Here, the authors derive the Shannon limit for nonlinear, regenerative systems, expanding on the classical linear case.
In this paper, we propose and demonstrate simultaneous phase regeneration of four different channels of QPSK signal based on phase sensitive amplification. The configuration can be divided into two parts. The first one uses four wave mixing in high nonlinear fiber (HNLF) to generate the corresponding three harmonic conjugates precisely at the frequency of the original signals. The other one uses optical combiner to realize coherent addition which is aimed at completely removing the interaction in phase regeneration stage. The simulation results suggest that this scheme can optimize signal constellation to a large extend especially in high noise environment. Besides, optical signal to noise ratio (OSNR) can improve more than 3 dB while the bit-error-rate (BER) reaches 10 –3 with a constant white noise and 15° phase noise.
We propose a kernel-based adaptive filtering method to suppress the phase noise (PN) arising from small deviations from ideal counter-phasing in the dual-pump fibre-based optical phase conjugation (OPC) of pilot-free quadrature-amplitude modulation (QAM) signals. We demonstrate experimentally and numerically that the proposed scheme achieves signal-to-noise ratio improvement over conventional PN compensation under optimised pump dithering settings in the OPC device and features no performance penalty across a range of pump-phase mismatch values, when it is used with a 16-QAM signal in an optical back-to-back configuration. We also illustrate the applicability of the method to the 64-QAM modulation format, and evaluate its performance in a transmission setup with mid-link OPC by means of numerical simulations.
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.
This study investigates a multi-stage digital phase-encryption scheme designed for secure coherent optical communication. While the proposed method is implemented in DSP and can be modeled as a software-level stream cipher, it is explicitly co-designed with and tightly coupled to the physical-layer modulation structure. Unlike conventional XOR-based bitwise schemes, the encryption is applied to the symbol phase domain. It is integrated into the transmitter's modulation process, enabling symbol-level security evaluated in conjunction with transmission physics. By applying K-level phase-shift secret keys toM-ary quadrature amplitude modulation (QAM) signals, this method increases the number of secret-key bits per symbol without altering the signal constellation in its baseline configuration. This approach enhances encryption strength while maintaining signal integrity and reducing quantization overhead in phase-only operation. Experimental evaluations on nonlinear optical transmission channels confirm that baseline digital phase encryption preserves Q-factor stability under self-phase modulation, cross-phase modulation, and four-wave mixing. The proposed scheme ensures error-free transmission at forward error correction thresholds, effectively preventing eavesdroppers from reconstructing symbols under worst-case observation conditions. Additionally, simulations analyzing generalized mutual information and quantization errors demonstrate that the encryption scheme can minimize signal-to-noise ratio penalties, even when employing high-order QAM formats with limited digital-to-analog and analog-to-digital conversion resolutions. As an optional extension, we also analyze pseudo-quantum-noise-based IQ spreading and explicitly quantify the associated trade-off between additional noise masking and increased sensitivity to quantization. These findings position multi-stage digital phase encryption as a practical and power-efficient modulation-layer encryption technique whose behavior is systematically characterized under realistic nonlinear channel and hardware constraints, rather than as an entirely new cryptographic primitive.
We demonstrate the phase sensitive amplification of a high-order quadrature amplitude modulation (QAM) signal using non-degenerate parametric amplification in a periodically poled lithium niobate (PPLN) waveguide. The interaction between the pump, signal, and phase-conjugated idler enables us to amplify arbitrary phase components of the signal. The 16QAM signals are amplified without distortion because of the high gain linearity of the PPLN-based phase sensitive amplifier (PSA). Both the phase and amplitude noise reduction capabilities of the PSA are ensured. Phase noise cancellation is achieved by using the interaction with the phase-conjugated idler. A degraded signal-to-noise ratio (SNR) is restored by using the gain difference between a phase-correlated signal-idler pair and uncorrelated excess noise. The applicability of the simultaneous amplification of multi-carrier signals and the amplification of two independent polarization signals are also confirmed with a view to realizing ultra-high spectrally efficient signal amplification.