Cross-phase Modulation Effect Research Articles

Coupled Nonlinear Schrödinger Equations for Pulse Interactions in Optical Fibers: Self- and Cross-Phase Modulation Effects

Coupled Nonlinear Schrödinger Equations for Pulse Interactions in Optical Fibers: Self- and Cross-Phase Modulation Effects

Bidirectional all-PM Er-doped fiber laser based on a self-stabilized interferometer mode-locker

We demonstrate a bidirectional all polarization-maintaining (PM) Er-doped fiber laser based on a self-stabilized interferometer mode-locker. By utilizing mechanical sharing and multiplexing propagation directions, the laser has balanced bidirectional outputs and passively suppresses common-mode noise. We also investigate the intra-cavity pulse dynamics via numerical simulations, which coincides well with experimental observations. The self-stabilized interferometer compensates for the group delay difference between the polarization components induced by linear birefringence. The cross-phase modulation effect in the self-stabilized interferometer leads to asymmetric spectra. In addition, from 10 kHz to 1 MHz frequency range, the integrated RMS phase noise in clockwise (CW) and counter-clockwise (CCW) directions are 0.124 mrad and 0.14 mrad, respectively. The integrated RMS RIN in CW and CCW directions are 439 ppm and 464 ppm. Due to passive common-mode noise cancellation, the repetition frequency difference can be stabilized near 19 Hz in 2500 s gate time. The stability of the repetition frequency difference can reach a minimum value of 4.167 × 10−4 at a gate time of 100 s. This novel bidirectional all-PM Er-doped fiber laser based on a self-stabilized interferometer mode-locker can provide a new scheme for the construction of an all-PM dual-comb system.

Stability and instability nature of solitons in an optical fiber with four wave mixing effect

The investigation into modulational instability (MI) within the Kundu-Eckhaus (KE) equation, governing optical solitons, involves a thorough examination of the effects of self-phase modulation, cross-phase modulation, and intermodal dispersion. Special attention is given to understanding the influence of the four-wave mixing effect. The KE equation, which models birefringent fiber and includes terms related to intermodal dispersion, cross-phase modulation, and self-phase modulation, serves as the fundamental framework for this analytical study. Employing conventional linear stability analysis, the gain within the KE equation is determined. To shed light on the role of four-wave mixing in various scenarios, the gain spectrum is utilized as a tool to analyze the behavior of the KE equation under different conditions. This methodology seeks to provide insightful information about the intricate interactions that impact the modulational instability of solitonic pulses in an optical systems. After that, we have investigated the soliton solution by implementing the Jacobian elliptical function approach. Finally, our focus here is on linear stability analysis, which employs eigenvalue spectra to study solitons’ stability via direct numerical simulation.

High-precision passive stabilization of a dissipative soliton resonance laser repetition rate based on optical pulse injection.

I present what is believed to be the first demonstration of using the cross-phase modulation (XPM) effect to achieve high-precision, all-optical synchronization and stabilization of the pulse repetition rate of a dissipative soliton resonance (DSR) mode-locked (ML) fiber laser working in the 1.06 µm wavelength range. Nanosecond 1.55 µm Master oscillator pulses were injected into the Slave cavity of the DSR laser to induce the XPM effect and subsequently synchronize both repetition rates. When referencing the Master laser to a rubidium frequency standard, the fractional instability of the DSR ML laser pulse repetition rate reached 1.26 × 10-12 for 1000 s integration time. The locking range and stability of the XPM synchronization are experimentally verified under varying conditions and discussed in the paper.

A Single-Shot Technique for Measuring Broadband Two-Photon Absorption Spectra in Solution.

Applications involving two-photon activation, including two-photon fluorescence imaging, photodynamic therapy, and 3D data storage, require precise knowledge of the two-photon absorption (2PA) spectra of target chromophores. Broadband pump-probe spectroscopy using femtosecond laser pulses provides wavelength-dependent 2PA spectra with absolute cross sections, but the measurements are sometimes complicated by cross-phase modulation effects and dispersion of the broadband probe. Here, we introduce a single-shot approach that eliminates artifacts from cross-phase modulation and enables more rapid measurements by avoiding the need to scan the time delay between the pump and the probe pulses. The approach uses counterpropagating beams to automatically integrate over the full interaction between the two pulses as they cross. We demonstrate this single-shot approach for a common 2PA reference, coumarin 153 (C153), in three different solvents using the output from a Yb:KGW laser. This approach provides accurate 2PA cross sections that are more reliable and easier to obtain compared with scanning pump-probe methods using copropagating laser beams. The single-shot method for broadband two-photon absorption (BB-2PA) spectroscopy also has significant advantages compared with single-wavelength measurements, such as z-scan and two-photon fluorescence.

Transmission of soliton for a coupled Radhakrishnan–Kundu–Lakshmanan equation in an optical fiber using the Jacobi elliptical sn function method

We examine a coupled Radhakrishnan–Kundu–Lakshmanan (cRKL) equation that includes self-phase modulation, third order dispersion, self-steepening, and cross-phase modulation effects. A propagating ultrafast pulse in nonlinear systems is described by the given equation. Utilizing the coupled Radhakrishnan–Kundu–Lakshmanan (cRKL) model, we explored the dynamics of various innovative optical solitons, such as wing-shaped, W-shaped, and brilliant solitons. We used mathematical methods like the Jacobi elliptical sn function method to get the exact analytical solution. Our results demonstrate that the self-phase modulation (SPM), self-steepening (SS), cross-phase modulation (XPM), and third order dispersion (TOD) can be effectively varied to influence the structure of the solitons. It is demonstrated that the precise balance between the self-steepening effect, the self-phase modulation, and the group velocity dispersion forms these novel W-shaped chirp-free dark solitons and dark and bright solitonic structures. By choosing appropriate settings for the physical variables, it is possible to create a graphic representation of the properties of optical solitons. The study and application of nonlinear materials with third order dispersion, cross-phase modulation, self-phase modulation effect, and self-steepening nonlinearity may take new paths as a result of our findings.

The nondegenerate solitons solutions for the generalized coupled higher-order nonlinear Schrödinger equations with variable coefficients via the Hirota bilinear method

In this paper, the generalized coupled higher-order nonlinear Schrödinger equations (GCHNLSEs) with variable coefficients, describing the propagation of femtosecond pulse with high peak power in birefringence fibers and inhomogeneous media, are researched by the Hirota bilinear method. The nondegenerate two-solitons and nondegenerate N-solitons solutions for these equations are obtained successfully for the first time. Then, we attain the v-shape, u-shape and wave-type double-hump solitons by adjusting the group velocity dispersion, cross-phase modulation and group velocity effect. Finally, through selecting the appropriate complex wave parameters, we change the distances between solitons and analyze the dynamic behaviors of the collisions.

Mode-locked large-mode-area Er/Yb-doped fiber oscillator via nonlinear polarization evolution with enhanced mode suppression

We report a mode-locked Er/Yb-doped large-mode-area (LMA) fiber oscillator based on nonlinear polarization evolution (NPE), which utilizes a linear cavity primarily composed of polarization-maintaining (PM) fibers. The oscillator operates at 1.56 µm with a fundamental repetition rate of 34.47 MHz and has two output ports. One port can deliver high-quality soliton-like pulses with a pulse duration of 325 fs and an average power of 39.5 mW (corresponding to a pulse energy of 1.15 nJ). In contrast, the other port not only generates lower-quality complex pulses but also exhibits poorer short-term and long-term stability, likely due to cross-phase modulation effects. To the best of our knowledge, this is the first implementation of the NPE mode-locked technology in a PM-LMA Er/Yb-doped fiber oscillator at 1.55 µm which often suffers from poor self-starting mode-locking capabilities. This achievement is primarily attributed to the use of endlessly single-mode photonic crystal fibers, which effectively suppress higher-order modes in PM-LMA fibers.

High-repetition-rate femtosecond "OR" gate design in a differential SOA-MZI

In this article, an experimental investigation of a combined "OR" gate design reliant on a differential semiconductor optical amplifier Mach-Zehnder interferometer (SOA-MZI) is presented. The suggested "OR" gate takes advantage of the cross-gain modulation (XGM) and cross-phase modulation (XPM) effects generated at the SOA-MZI outcome. Furthermore, the optical, electrical, and temporal categories are used for testing and analyzing the system's performance. This "OR" gate technology is very useful in numerous scenarios, especially in optical networking. Numerous factors, including extinction ratio (ER), beam quality factor, and optical and electrical spectra, are used for assessing the optical "OR" gate. With a beam propagation ratio (BPR) of less than 2.4 (M2<2.4), the "OR" gate design provides superb beam quality. The successful creation of the electrical "OR" transmission exhibits about sixteen harmonics with exceptional powers and substantial ERs. The last important phase in optical communications and network connectivity is pulse compression, which can increase the optical average power while enjoying the advantages of brief pulses. In fact, pulse compression combines the intense energy of an extensive pulse with the great accuracy of an extremely short pulse. The grating-fiber compressor approach is widely used to accomplish the pulse compressions. The combined "OR" output pulse, which has undergone pulse compression, has a duration of 50 fs at a wavelength of 1530 nm.

Harnessing XPM effects in non-linear directional couplers for 4-bit gray code conversion and even parity verification

Abstract The all-optical switching phenomena in the non-linear directional coupler using cross-phase modulation (XPM) effect have been proposed. It is designed to generate an all-optical XOR functionality, considering the XOR logic gates as a basic module the design and analysis of an efficient all-optical 4-bit binary to gray code converter and 4-bit even parity checker circuit is proposed. The design methodology includes the switching of a weak continuous-wave (CW) signal, which is controlled by the combination of two controlled pump signals. In this paper, mathematical analysis of the coupled mode theory associated with optical directional couplers has been discussed. The switching characteristics of XPM effect based All-optical directional couplers have been examined for appropriate values of the controlled pump signals. Appropriate values of extinction ratio and corresponding controlled pump signal levels are investigated for an efficient generation of XOR logic gates. Further, the detailed analysis of layout generation and design aspects of All-optical 4-bit binary to gray code converter and 4-bit even parity checker circuits have been carried out. The proposed methodology is verified by the appropriate simulation results, which include the transmittivity, extinction ratio (Xratio) curve variation and dynamic time domain plot associated with proposed units.

Terahertz Replica Generation of Ultra-High Data Rate Transmission in an Electro-Optical Semiconductor Optical Amplifier Mach–Zehnder Interferometer System

This article presents an analysis of an electro-optical up-converter relying on a semiconductor optical amplifier Mach–Zehnder interferometer (SOA-MZI). The pulsed control signal is generated by an optical pulse clock (OPC) with a repetition rate of fs= 19.5 GHz. The intermediate frequency (IF) signal, which carries the modulation format known as quadratic phase shift keying (QPSK) at a frequency fIF, is shifted at the output of the SOA-MZI to high outlet mixing frequencies nfs±fIF, where n represents the harmonic order of the OPC. To examine the characteristics of the sampled QPSK signals, we employ the Virtual Photonics Inc. (VPI) emulator and evaluate them using significate metrics like error vector magnitudes (EVMs), conversion gains, and bit error rates (BERs). The up-mixing process is mainly achieved through the cross-phase modulation (XPM) effect in the SOA-MZI, which operates within a 195.5 GHz ultrahigh frequency (UHF). The electro-optical SOA-MZI up-converter demonstrates consistent uplifting conversion gains across the scope of the output mixing frequencies. The simulated conversion gain deteriorates from 38 dB at 20 GHz to 13 dB at 195.5 GHz. The operational efficiency of the electro-optical SOA-MZI design, employing the standard modulation approach, is also evaluated by measuring the EVM values. The EVM attains a 24% performance level at a data rate of 5 Gbit/s in conjunction with the UHF of 195.5 GHz. To corroborate our results, we compare them with real-world experiments conducted with the UHF of 59 GHz. The maximum frequency range of 1 THz is attained by increasing the OPC repetition rate. Ultimately, through elevating the control frequency to 100 GHz, the generation of terahertz replicas of the 4096-QAM (quadrature amplitude modulation) compound signal becomes achievable at heightened UHF, extending 1 THz, while maintaining a data transmission rate of 120 Gbit/s and upholding exceptional performance characteristics.

Slot-Waveguide Based All-Optical RF Spectrum Analyzer

All-optical radio-frequency spectrum analyzers (AORFSAs) with ultrabroad bandwidth break the electronic bottleneck and provide an efficient frequency analysis means for ultrafast optical signals in communications, signal generation and processing systems. Here, we propose and experimentally demonstrate an AORFSA built on the cross-phase modulation effect in a 50 cm long CMOS-compatible photonic slot-waveguide. The waveguide has a 100 nm thick thin-film core of fused silica that is sandwiched by two 750 nm thick cladding layers of high-index doped silica, which shows optimized dispersion and comparable nonlinear characteristics. The measured 3 dB bandwidth of the proposed slot-waveguide-based AORFSA has a three-fold increase over the conventional channel waveguide having the same dimension and length. The sensitivity and wavelength- and polarization-dependence properties are investigated, confirming the proposed waveguide as a versatile platform for frequency analysis of ultrafast optical signals, such as Kerr microcombs with hundreds of GHz or even THz mode spacing.

Pulse energy exchange of vector solitons in a fiber laser

The energy exchange between orthogonal polarization components is crucial for the build-up of vector solitons (VSs). Unlike previous observations of energy exchange in the frequency domain, our experiments analyzed pulse energy flows in the time domain. We provide evidence to demonstrate the influence of the four-wave mixing (FWM) and cross-phase modulation (XPM) effect on VSs build-up in passive mode-locked fiber lasers through a perspective of pulse energy exchange. The results indicate that the energy exchange of PRVS caused by FWM and XPM is stronger than that of PLVS. The liner energy exchange caused by the birefringence of fiber and PC influences the period of energy exchange. After stabilization, the intra-cavity energy evolution period is one roundtrip for PLVS while serval roundtrips for PRVS. In the future, we can achieve PLVS by adjusting the linear energy exchange through cavity birefringence, thereby meeting the industrial demand for stable and uniform pulse trains.

Solitons in a coupled system of fractional nonlinear Schrödinger equations

Interest in physical systems with fractional derivatives has exploded in the 21st century. Similarly, interest in the localized excitations of nonlinear dynamical systems continues to grow significantly in recent times. In this work, we demonstrate the existence of localized solutions in the nonlinear system of three coupled Schrödinger equations with fractional dispersion, linear coupling, and cubic nonlinearities. We then check the stability of these localized solutions, i.e., solitons, by utilizing the linear stability analysis method and by propagating the perturbed solutions using the split-step fast-Fourier beam propagation method. We also prove that the solitary solutions can be stabilized in this system, thanks to the confining influence of the cross-phase modulation effect. The system is set with the same cross-phase modulation parameter but different self-phase modulation coefficients. We further find that the Lévy index (LI), the propagation constant, and the cross-phase modulation effect markedly affect the profiles and the stability domains of the solitons in the three-coupled system. Furthermore, the amplitude of the component with the strongest self-phase modulation is the largest among the three components, and the variation of the LI, the propagation constant, or the cross-phase modulation coefficient does not affect much this result. Besides the common perturbed propagation, the propagation with modulated LI is also investigated in this work, displaying increased instability when the LI is modulated suddenly, as opposed to stable propagation when the change in the LI is gradual.

Coherent pulse generation based on noise-like-pulse pumped Raman amplification

The coherent Raman pulse generation based on the noise-like-pulse (NLP) pumped Raman amplification is numerically investigated in the cases with weak and strong walk-off effects between the pump and Stokes pulses. In the former case, the amplified Stokes pulse suffers from the temporal and spectral distortions because the random time-varying intensity profile of the NLP can be transferred to the Stokes pulse through combined effects of cross-phase modulation (XPM), stimulated Raman scattering (SRS), and spontaneous Raman scattering. In the latter case, the heavily germanium-doped fiber with large normal dispersion is firstly used as the Raman gain medium to improve the walk-off effect and Raman gain. As a result, the Stokes pulse can be amplified undistorted and possess linear frequency chirp and conversion efficiency of up to 82.4 %. Further, it is important to note that the NLP-pumped Raman fiber laser based on the large normal dispersion fiber can generate the Stokes pulse with linear frequency chirp, narrow temporal duration, and dissipative-soliton-like spectrum with steep edges, even though the saturable absorber is not introduced into the Raman fiber cavity.

Simultaneous OSNR and chromatic dispersion monitoring based on optical tones power ratio

A novel technique is proposed for simultaneous monitoring of optical signal-to-noise ratio (OSNR) and chromatic dispersion (CD). The scheme is based on the cross-phase modulation effect in a highly nonlinear fiber, which induces a change in the optical tones according to the impairments. The power ratio of the optical tones at two separate frequencies is utilized for monitoring. Improvements in the maximum measurable OSNR, CD and dynamic range can be obtained using only the clock tone for the non-return-to-zero, return-to-zero with a 50% duty cycle differential quadrature phase-shift keying, differential phase-shift keying and on-off keying signals at 80 Gb/s. For the return to zero differential quadrature phase shift keying (RZ-DQPSK) system, the OSNR of 4–40 dB can be monitored with a 36.73 dB dynamic range, and a chromatic dispersion of 0–117 ps/nm can be monitored with a 48.68 dB dynamic range. A correlation is built to describe the relationship of the power ratio with the OSNR and chromatic dispersion which has a root-mean-squared error of 1.41. The delay group dispersion insensitivity, the impact of the input signal power, and the filter selection are investigated. The design enables accurate monitoring, simple operation and may be used in a wide range.

Ultra-compact all-optical plasmonic switch for three telecommunication windows using a nonlinear Kerr material and Fano resonance.

In this study, an all-optical plasmonic switch based on a metal-insulator-metal (MIM) waveguide coupled to two rectangular cavities that are perpendicularly connected to each other through a vertical stub is proposed and analyzed both theoretically and numerically. Rectangular cavities are filled with a nonlinear Kerr material, and the switching operation is achieved by applying a high-intensity pump input into the MIM waveguide to obtain nonlinear cross-phase modulation (XPM) effect. The proposed structure is designed so that it can realize the switching operation at each of the three telecommunication windows of 850, 1310, and 1550nm. Realizing the switching operation at these three wavelength bands is accomplished by the Fano resonance. In fact, the Fano resonance is utilized to create a band-stop area that is crucial for building a suitable OFF state for the switching operation at two of the three telecommunication windows of 1310 and 1550nm. The theoretical and numerical results are obtained using the transmission-line model (TLM) and the finite difference time domain (FDTD) method, respectively, the results of which comply well. The proposed ultra-compact all-optical switch has significant applications in photonic integrated circuits (PICs).

All-optical aggregation and de-aggregation between OOK, QPSK and 8QAM signals based on nonlinear effects

An all-optical aggregation and de-aggregation scheme between on–off keying (OOK) signals, quadrature phase shift keying (QPSK) signals and 8-ary quadrature amplitude modulation (8QAM) signals is proposed and numerically simulated based on nonlinear effects in the high nonlinear fiber (HNLF). In the de-aggregation processing, the input 30 Gbit/s 8QAM signal is firstly de-aggregated into one 20 Gbit/s QPSK signal and one 10 Gbit/s binary phase shift keying (BPSK) signal by deploying self-phase modulation (SPM), cross-phase modulation (XPM), four-wave mixing (FWM) and parameter amplification (PA) effects. One continuous optical carrier can be extracted from the converted BPSK signal by designing a feed-forward based modulation stripping configuration. The converted OOK signal can be obtained through vector superposition between the extracted optical carrier and the converted BPSK signal. In the aggregation processing, the converted 20 Gbit/s QPSK signal and the 10 Gbit/s OOK signal are fed to another HNLF and aggregated into one 30 Gbit/s 8QAM signal again by utilizing XPM and PA effects. Moreover, the aggregated 8QAM signal keeps the same wavelength and information integrity as the input 8QAM signal. the Error vector magnitude (EVM) and the bit error ratio (BER) for the 8QAM signal before and after aggregation and de-aggregation are measured to evaluate the scheme performance. The proposed all-optical aggregation and de-aggregation scheme for the advanced and simple modulation formats can be applied at the intermediate network node (INN) to solve the network traffic aggregation and de-aggregation with different modulation formats.

All-Optical Format Conversion for Star-8QAM Signals Based on Nonlinear Effects in Elastic Optical Networks

An all-optical format conversion (AOFC) scheme for star-octal quadrature amplitude modulation (star-8QAM) signals is proposed and numerically simulated based on nonlinear effects in the high nonlinear fiber (HNLF). In the first stage AOFC processing, the input 30 Gbit/s star-8QAM signal is firstly de-aggregated into one 20 Gbit/s quadrature phase shift keying (QPSK) signal and one 10 Gbit/s typical on-off keying (OOK) signal by deploying the self-phase modulation (SPM), cross-phase modulation (XPM) and parametric amplification (PA) effects. In the second stage AOFC processing, the 20 Gbit/s QPSK signal and the 10 Gbit/s typical OOK signal are aggregated into one 30 Gbit/s star-8QAM signal again by utilizing the XPM and PA effects. Moreover, the amplitude ratio (AR) between the outer ring and inner rings of the aggregated star-8QAM signal can be adjusted flexibly by changing the QPSK and OOK signals power. Other octal modulation formats can also be generated through changing the QPSK and OOK signals power, including the rectangular 8QAM signals, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\pi$</tex-math></inline-formula> /4-8QAM signals and 8-ary phase shift keying (8PSK) signals. Error vector magnitude (EVM) and bit error ratio (BER) for star-8QAM signals before and after AOFC are measured to analyse the scheme performance. The AOFC scheme provides the flexibility to adopt the appreciate modulation formats at the optical nodes to connect different optical networks.

Some Features of the Formation of Quantum Ghost Imaging Considering the Effects of Self-Phase Modulation, Cross-Phase Modulation, and Phase-Mismatch

Some Features of the Formation of Quantum Ghost Imaging Considering the Effects of Self-Phase Modulation, Cross-Phase Modulation, and Phase-Mismatch