Optical Phase Conjugation Research Articles

Optically enhanced pump-phase noise in mid-link optical parametric phase conjugation

This paper discusses the impact of pump-phase noise in the χ(2)-based optical parametric amplification process on the phase-conjugated idler. We show that the dispersive fiber propagation of the phase-conjugated idler causes the optically enhanced pump-phase noise (OEPN) effect including a group-velocity jitter. The signal penalty caused by the OEPN in the mid-link optical phase conjugation systems was quantified analytically and proved by numerical simulations. We also experimentally evaluated the OEPN with an optical parametric phase conjugator using periodically poled LiNbO3 waveguides. With a 96-Gbaud probabilistically constellation-shaped 64QAM signal, the experimental results were in good agreement with the analytically derived penalty in a standard single-mode fiber link up to 800 km.

Vector modulation of fully-polarized phase conjugate light field through scattering media

Vector modulation of the light field through scattering media holds significant scientific and application value in areas such as optical imaging, optical communications, nonlinear optics, and biomedicine. Digital optical phase conjugation (DOPC), grounded in the time reversal principle, has been extensively investigated for wavefront shaping in scattering media. Nonetheless, reports on vector modulation of phase conjugate beams via DOPC remain scarce. In this study, we propose a vector DOPC to recover and modulate the polarization state of the phase conjugate beams based on vector decomposition and superimposition of light field. First, pre-set two orthogonal polarization basis probe beams to pass through a multimode fiber and use digital holography to record the phase distribution of their orthogonal polarization components in the speckle field. Then, perform polarization-preserving phase conjugation and vector superposition of both components simultaneously. By altering the phase difference and amplitude ratio between the two, vector modulation of the synthesized phase conjugate beam can be achieved. Theoretical analysis aligns well with experimental results, demonstrating a positive impact on understanding the physical properties of scattering media and expanding the applications of the DOPC technique.

Study of a Crosstalk Suppression Scheme Based on Double-Stage Semiconductor Optical Amplifiers

An all-optical crosstalk suppression scheme is desirable for wavelength and space division multiplexing optical networks by improving the performance of the corresponding nodes. We put forward a scheme comprising double-stage semiconductor optical amplifiers (SOAs) for wavelength-preserving crosstalk suppression. The wavelength position of the degenerate pump in the optical phase conjugation (OPC) is optimized for signal-to-crosstalk ratio (SXR) improvement. The crosstalk suppression performance of the double-stage SOA scheme for 20 Gb/s quadrature phase shift keying (QPSK) signals is investigated by means of simulations, including the input SXR range and the crosstalk wavelength deviation. For the case with identical-frequency crosstalk, the double-stage SOA scheme can achieve equivalent SXR improvement of 1.5 dB for an input SXR of 10 dB. Thus, the double-stage SOA scheme proposed here is more suitable for few-mode fiber systems and networks.

High-precision alignment of optoelectronic devices for optical phase conjugation

Abstract Digital optical phase conjugation (DOPC) is considered as a promising solution to achieve optical focusing against scattering. The implementation of DOPC based on the digital micromirror device (DMD) has been proven to have great potential, supporting a large number of modulation modes and a high modulation rate. However, the accuracy of optical alignment seriously affects the focusing contrast, limiting the applications of DMD-based DOPC systems. Here we demonstrate a simple alignment protocol including a marker-assisted tuning and an embedded compensation. Our approach can realize an exact pixelwise optical conjugation between the DMD and detector, as well as a rapid compensation for aberrations and minor misalignment. Experimental results show that the proposed alignment protocol improves the focusing contrast to 66% of the highest value predicted in the theory.

STAR-FDTD: space-time modulated acousto-optic guidestar in disordered media

Abstract We developed a 2D Finite-difference time-domain (FDTD) method for modeling a space-time modulated guidestar targeting wavefront shaping applications in disordered media. Space-time modulation in general (a particular example being the acousto-optic effect) is used here as a guidestar for the transverse confinement of light around the tagged region surrounded by disorder. Together with the guidestar, the iterative optical phase conjugation (IOPC) method is used to overcome the diffusion of light due to multiple scattering. A phase sensitive lock-in detection technique is utilized to estimate the steady-state amplitude and phase of the modulated wavefronts emerging from the guidestar region continuously operating in the Raman-Nath regime. As the IOPC scheme naturally converges to the maximally transmitting eigenchannel profile, one could use the position of the guidestar within the disorder to channelize the maximal transmission through the tagged region. The associated code developed in MATLAB® is provided as an open source (The MIT License) package. The code package is referred by the acronym STAR-FDTD where STAR stands for Space-Time modulated Acousto-optic guidestaR.

Record bandwidth waveband-shift-free optical phase conjugation in nonlinear fiber optical loop mirror

We present a novel configuration for broadband, wavelength-shift-free optical phase conjugation (OPC) utilizing four-wave mixing in a nonlinear fiber optical loop mirror (NOLM). In the proposed configuration, the input signals and the pump wave return to the input port of the NOLM whereas the phase-conjugated signals generated in the NOLM loop are transmitted through the output port. This allows the phase-conjugated copies to occupy the same wavelength band as the input signals, in line with the requirements for practical deployment of OPC in communication links. The demultiplexing of the phase conjugates from the input signals sharing the same band is achieved by imparting an asymmetric phase shift on the pump via a fiber Bragg grating. We experimentally demonstrate waveband-shift-free OPC with an extinction ratio between signals and conjugated copies at the NOLM output of 17 dB to 25 dB across a band of 35 nm. Whilst a 7-nm wide performance gap exists in the middle of the band, this is the record bandwidth for waveband-shift-free OPC in an all-fiber setup. We compare the experimental results with numerical simulations of the OPC-NOLM, identify the reason for the observed performance gap, and justify the route for further performance improvement.

Hybrid optical-electronic compensation of fiber nonlinearity for long-haul coherent optical transmission

Abstract From the concepts of the dispersion-folded digital backward propagation (DBP) and optical phase conjugation (OPC), a hybrid optical-electronic nonlinearity-compensation scheme is proposed to enhance the system performance of the dispersion-managed transmission. The computational complexity of the proposed scheme, compared with that of the conventional DBP method, is reduced significantly while the performance penalty is negligible. The compensation efficiency of the proposed scheme has been validated in a 5 (and 9)-channel PM-16QAM system at 256 Gbit/s.

Color-switching in an optical parametric oscillator using a phase-conjugate mirror

We construct a phase-conjugate resonator which passively produces stable pulses that alternate between the probe and the conjugate colors. The requisite phase-conjugate mirror inside the resonator is constructed using non-degenerate four-wave mixing (4WM) in rubidium vapor. The glancing-angle phase-conjugate mirror is a 100% output coupler, and therefore this resonator is unusual in that no light circulates the cavity more than once. Without the gain of the phase-conjugate mirror, the cavity boundary conditions, and thus resonant modes, are not defined and therefore can be tuned by the pump. The output of the optical parametric oscillator that is formed above threshold can passively mode-lock. The phase-conjugate mirror removes thermal or acoustic instabilities that are on a MHz or slower timescale. This work provides a new method for stable pulsing using phase-conjugate optics, and suggests a platform for producing mode-locked pulses with squeezed light, as the 4WM process has already demonstrated quantum correlations.

All-optical phase conjugation using diffractive wavefront processing

Optical phase conjugation (OPC) is a nonlinear technique used for counteracting wavefront distortions, with applications ranging from imaging to beam focusing. Here, we present a diffractive wavefront processor to approximate all-optical phase conjugation. Leveraging deep learning, a set of diffractive layers was optimized to all-optically process an arbitrary phase-aberrated input field, producing an output field with a phase distribution that is the conjugate of the input wave. We experimentally validated this wavefront processor by 3D-fabricating diffractive layers and performing OPC on phase distortions never seen during training. Employing terahertz radiation, our diffractive processor successfully performed OPC through a shallow volume that axially spans tens of wavelengths. We also created a diffractive phase-conjugate mirror by combining deep learning-optimized diffractive layers with a standard mirror. Given its compact, passive and multi-wavelength nature, this diffractive wavefront processor can be used for various applications, e.g., turbidity suppression and aberration correction across different spectral bands.

Control of structured light beams focusing through anisotropic multiple-scattering media via multi-focus-based digital optical phase conjugation

A framework to focus structured light beams through an anisotropic multiple-scattering medium (AMSM) with multi-focus-based digital optical phase conjugation is proposed. In this work, the measured full vector transmission matrix (VTM) in conjunction with a well-designed multifocal target field can be used to calculate the required input field, which consists of two orthogonally linear polarization components. The polarization, amplitude and phase of the light before and after the AMSM are then shaped and controlled by encoding the input field into a double-channel computer generated hologram that is displayed on a vector spatial light modulator. The desired output field composed of multifocal spots can be obtained through the AMSM. We demonstrated several examples, generating vector beams, array vector beams and vortex beams, to experimentally validate the feasibility of our approach. Additionally, the peak to background ratio (PBR) of the generated multifocal structured light can be predicted theoretically by introducing the idea of critical focus number. The simulated and experimental results show that the generated structured light with a clear optical ring and high PBR can be realized through the AMSM. Consequently, our method provides an effective way to control and optimize structured light beams focusing through the AMSM.

Single-shot digital optical fluorescence phase conjugation through forward multiple-scattering samples.

Aberrations and multiple scattering in biological tissues critically distort light beams into highly complex speckle patterns. In this regard, digital optical phase conjugation (DOPC) is a promising technique enabling in-depth focusing. However, DOPC becomes challenging when using fluorescent guide stars for four main reasons: the low photon budget available, the large spectral bandwidth of the fluorescent signal, the Stokes shift between the emission and the excitation wavelength, and the absence of reference beam preventing holographic measurement. Here, we demonstrate the possibility to focus a laser beam through multiple-scattering samples by measuring speckle fields in a single acquisition step with a reference-free, high-resolution wavefront sensor. By taking advantage of the large spectral bandwidth of forward multiply scattering samples, digital fluorescence phase conjugation is achieved to focus a laser beam at the excitation wavelength while measuring the broadband speckle field arising from a micrometer-sized fluorescent bead.

Toward optimal performance of systems for digital optical phase conjugation

Toward optimal performance of systems for digital optical phase conjugation

Signal Impairments Compensation Based on Wavelength-Shift-Free Optical Phase Conjugation

Signal Impairments Compensation Based on Wavelength-Shift-Free Optical Phase Conjugation

Focusing scattering light field with different states based on iterative algorithm

Transmitting optical information through scattering medium has broad application prospects in biomedical, aerospace and other fields. However, the light passing through the scattering medium will cause wavefront distortion and optical information blurring. Wavefront shaping technology uses a mathematical matrix to characterize the characteristics of scattering medium, which can achieve refocusing and imaging after light propagation through the scattering medium. It mainly includes optical phase conjugation, optical transmission matrix and wavefront shaping based on iterative optimization. However, the iterative wavefront shaping is considered to be a cost-effective method. Based on the wavefront amplitude modulation technology, the wavefront amplitude of the incident light is continuously adjusted by using the optimization algorithm to find the corresponding wavefront amplitude distribution that can maximize the light intensity in the target area. The system generates binary patterns implemented with digital-micromirror device (DMD) based on on-off state of micromirror, where “on” represents 1 and “off” refers to 0. The DMD has a high refresh rate and can achieve high speed wavefront amplitude modulation by using the iteration algorithm. In the experiment, the scattering medium is prepared with TiO<sub>2</sub>, water and gelatin, whose persistence times are controlled with the water-gelatin ratio (WGR). In addition, the Pearson correlation coefficient (Cor) curve obtained through 300-s-measurement under different WGR conditions, which shows that the greater WGR, the shorter the persistence time is. The experiment mainly studies the focusing of the spatial light through scattering media by wavefront amplitude modulation, and discusses the ability of point guard algorithm (PGA) and genetic algorithm (GA) to control the scattered light field with different persistence times in 64 × 64 segments. The experimental results show that the PGA can achieve higher enhancement factor and more uniform multi-point focusing than the GA after 1000 iterations in the scattering medium with the same persistence time. The relative standard deviation value is inversely proportional to the WGR value when multi-point focusing can be completed. We also demonstrate that GA can only achieve single-point focusing when WGR = 40, and it cannot accomplish multi-point focusing in self-made scattering medium. This study not only verifies a method to achieve focusing scattering light field, but also provides a new scheme for testing the performance of the iterative wavefront shaping.

Performance enhancement in wavefront shaping of multiply scattered light: a review.

In nonballistic regime, optical scattering impedes high-resolution imaging through/inside complex media, such as milky liquid, fog, multimode fiber, and biological tissues, where confocal and multiphoton modalities fail. The significant tissue inhomogeneity-induced distortions need to be overcome and a technique referred as optical wavefront shaping (WFS), first proposed in 2007, has been becoming a promising solution, allowing for flexible and powerful light control. Understanding the principle and development of WFS may inspire exciting innovations for effective optical manipulation, imaging, stimulation, and therapy at depths in tissue or tissue-like complex media. We aim to provide insights about what limits the WFS towards biomedical applications, and how recent efforts advance the performance of WFS among different trade-offs. By differentiating the two implementation directions in the field, i.e., precompensation WFS and optical phase conjugation (OPC), improvement strategies are summarized and discussed. For biomedical applications, improving the speed of WFS is most essential in both directions, and a system-compatible wavefront modulator driven by fast apparatus is desired. In addition to that, algorithm efficiency and adaptability to perturbations/noise is of concern in precompensation WFS, while for OPC significant improvements rely heavily on integrating physical mechanisms and delicate system design for faster response and higher energy gain. Substantial improvements in WFS implementations, from the aspects of physics, engineering, and computing, have inspired many novel and exciting optical applications that used to be optically inaccessible. It is envisioned that continuous efforts in the field can further advance WFS towards biomedical applications and guide our vision into deep biological tissues.

Optimized receiver design for entanglement-assisted communication using BPSK.

The use of pre-shared entanglement in entanglement-assisted communication offers a superior alternative to classical communication, especially in the photon-starved regime and highly noisy environments. In this paper, we analyze the performance of several low-complexity receivers that use optical parametric amplifiers. The simulations demonstrate that receivers employing an entanglement-assisted scheme with phase-shift-keying modulation can outperform classical capacities. We present a 2x2 optical hybrid receiver for entanglement-assisted communication and show that it has a roughly 10% lower error probability compared to previously proposed optical parametric amplifier-based receivers for more than 10 modes. However, the capacity of the optical parametric amplifier-based receiver exceeds the Holevo capacity and the capacities of the optical phase conjugate receiver and 2x2 optical hybrid receiver in the case of a single mode. The numerical findings indicate that surpassing the Holevo and Homodyne capacities does not require a large number of signal-idler modes. Furthermore, we find that using unequal priors for BPSK provides roughly three times the information rate advantage over equal priors.

Entanglement assisted communication over the free-space optical link with azimuthal phase correction for atmospheric turbulence by adaptive optics.

To improve the reliability of entanglement-assisted (EA) communication over turbulent FSO channels we propose to perform the optical phase-conjugation on idler photons rather than turbulence affected signal photons and use adaptive optics. We experimentally demonstrate that reliable EA communication over outdoor 1.45 km FSO link, established at University of Arizona campus, is possible in strong turbulence regime.

PMD tolerant transmission using multiple optical phase conjugators in the discretely amplified systems

Abstract In this paper, the impact of polarization mode dispersion (PMD) on system performance in coherent optical transmission assisted by optical phase conjugation (OPC) technique is numerically investigated for a 9-channel PM-4QAM system at 128Gbit/s. The OPC-aided transmission, amplified with lumped erbium doped fiber amplifier (EDFA), is a variation of the conventional dispersion-managed link, which is also called dispersion-inverted link. We demonstrate that introducing more OPCs along the link can partly suppress the PMD-induced impairments and thus improve the system performance significantly. Results of 960-km dispersion-managed transmission show that PMD effect will cause a performance penalty of 1.8 dB when using mid-link OPC (i.e., only 1-OPC), while this penalty will decrease to about 0.4 dB when employing 6-OPCs along the link. Comparing with conventional digital back-propagation (DBP) technique, a performance improvement of about 3.1 dB is observed with multi-OPCs when fiber PMD is equal to 0.1ps/ k m $\sqrt{km}$ .

Enhanced Pre/Post Compensation of Fiber Link Nonlinear Distortion by a Stepwise Parameter Profiled Fiber and Phase Conjugation Module

Compensation of nonlinear distortion in long distance communication links from the power induced Kerr effect is demonstrated at the transmitter or receiver by the combination of optical phase conjugation (OPC) and propagation in a stepwise parameter profiled fiber (SPF). The SPF tailored with an increasing nonlinearity and decreasing dispersion parameter on average with distance as well as Raman gain induces a distortion more closely matching that of the link to improve propagation symmetry for enhancing overall distortion cancellation by OPC. Measurements show for a module inserted at the transmitter or receiver with a 60 km long SPF comprising of three different fibers, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q²</i> -factor is improved by 2.3 and 1.7 dB, respectively, compared to without for transmitting 5 channel WDM dual polarization 12 Gbaud 16-QAM signals in 2×160 km fiber spans that both include dispersion compensation. Similarly, recirculating loop transmission of the same signal over 18×80 km (1440 km) shows improved <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q²</i> -factors of 1.9 and 1.3 dB, respectively. This corresponds to extending the transmission reach by 125 and 80%, respectively, for matched performance at equal launch power, highlighting the greater nonlinear distortion tolerance achievable with advanced OPC designs.

Compensation of the Distorted WDM Signals by Symmetric Dispersion Map with Nonuniform Zero-Crossing Place of Accumulated Dispersion in Midway-OPC System

The nonlinear Kerr effect and chromatic dispersion are the fundamental causes of optical signal degradation in single-mode fiber (SMF) and erbium-doped fiber-amplification (EDFA)-based wavelength division multiplexing (WDM) transmission. Dispersion management combined with a midway optical phase conjugator among the technologies for compensating for such optical signal distortion is known to not be limited by the modulation format and multiplexing technology. Optimization of the dispersion map can partially alleviate the capacity and maximum transmission distance limitations of the SMF and EDFA system. In this paper, we propose various types of symmetric dispersion maps in which the position of zero-crossing place of the cumulative dispersion is not constant, and analyze the effect of each dispersion map configuration on 40 Gb/s × 24-channel WDM signal distortion compensation. When designed with the residual dispersion per span (RDPS) around 400 ps/nm, it is confirmed that most of the proposed dispersion maps are more effective in compensating the distorted WDM signal than conventional dispersion map. In particular, we confirm that, among the proposed dispersion maps, the dispersion map in which the RDPS is designed uniformly for all fiber spans can increase the power margin of WDM channel and expand the range of the total residual dispersion in the dispersion-managed link.