Self-phase Modulation Effect Research Articles

An Mach-Zehnder Interferometer Refractive Index Sensor Based on Self-phase Modulation Effect in a Tapered Double-cladding Highly Nonlinear Fiber

An Mach-Zehnder interferometer (MZI) sensor based on self-phase modulation (SPM) effect in a tapered double-cladding highly nonlinear fiber (DCHNLF) was proposed and experimentally verified for refractive index (RI) measurement. The DCHNLF was tapered and the SPM spectrum generated in its untapered region acted as the broadband light source for the sensor. The integration of the SPM effect and the RI detection not only simplified the structure of the sensor, but also enhanced its long-term stability and reliability. Since the effective RI of the outer cladding mode of the tapered DCHNLF was affected by the RI variation, a spectral shift would occur in interference spectrum between the core mode and the outer cladding mode. The tapering treatment enhanced the evanescent wave on the surface of DCHNLF, making the sensor more sensitive to external RI. In the external RI range of 1.3333 ~ 1.3972, the sensor achieved an excellent sensitivity of 238.51nm/RIU. In addition, the effect of average pump power and pump wavelength on the sensor performance were experimentally discussed. The results showed that the sensitivity was not affected by the pump condition. This MZI RI sensor has advantages of excellent performance, simple structure and easy fabrication, demonstrating broad application prospects in biomedical research, marine environment monitoring, and human health detection.

State transitions for the rational solutions of Kundu equation with non-zero boundary conditions

Several novel rational solutions with nonzero boundary condition for the Kundu equation, which is an important physical model, are derived using the technique of generalized Darboux transformation. It is the first time that a systemic analysis has been conducted on such rational solutions for the Kundu equation. For the 1-order rational solutions with nonzero boundary conditions, our findings reveal that three parameters, a, b, and β, which are associated with the effects of self-steepening, self-phase modulation, and quintic nonlinearity in the Kundu equation, can result in four distinct states for case B and five distinct states for case C, all corresponding to rational solutions with nonzero boundary conditions.

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.

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.

Synergic action of linear dispersion, second-order nonlinearity, and third-order nonlinearity in shaping the spectral profile of a femtosecond pulse transporting in a lithium niobate crystal

We present a detailed theoretical and numerical analysis on the temporal-spectral-spatial evolution of a high-peak-power femtosecond laser pulse in two sets of systems: a pure lithium niobate (LN) plate and a periodically poled lithium niobate (PPLN) plate. We develop a modified unidimensional pulse propagation model that considers all the prominent linear and nonlinear processes and carried out the simulation process based on an improved split-step Fourier transformation method. We theoretically analyze the synergic action of the linear dispersion effect, the second-order nonlinearity (2nd-NL) second-harmonic generation (SHG) effect, and the third-order nonlinearity (3rd-NL) self-phase modulation (SPM) effect, and clarify the physical mechanism underlying the peculiar and diverse spectral broadening patterns previously reported in LN and PPLN thin plate experiments. Such analysis and discussion provides a deeper insight into the synergetic contribution of these linear and nonlinear effects brought about by the interaction of a femtosecond laser pulse with the LN nonlinear crystal and helps to draw a picture to fully understand these fruitful optical physical processes, phenomena, and laws.

Multiple solitons structures in optical fibers via PNLSE with a novel truncated M-derivative: modulated wave gain

This study introduces a novel truncated Mittage–Leffler (M)- proportional derivative (TMPD) and examines its impact on the perturbed nonlinear Schrödinger equation (PNLSE) that includes fourth-order dispersion and cubic-quintic nonlinearity. The TMPD-PNLSE is used to model light signals in nanofibers. In addition to dispersion and Kerr nonlinearity, which are characteristics of the NLSE, the PNLSE also exhibits self-steepening and self-phase modulation effects. The unified method is implemented to derive exact solutions for the model equation. These solutions provide a variety of phenomena; including breathers, geometric chaos, and complex solitons. The solutions also exhibit numerous structures, such as geometric chaos, where undulated M-shaped and M-shaped solitons are embedded. The modulation instability is analyzed, finding that it is triggered when the coefficient of the fourth-order dispersion surpasses a critical value.

Nonlinear pulse compression technique based on in multi-pass plano-cancave cavity

<sec>Ultrafast femtosecond laser system with hundreds of microjoules of energy, operating at a repetition frequency of several kilohertz, has very important applications in many fields such as medicine, mid-infrared laser generation, industrial processing, and vibrational spectroscopy. The chirped pulse amplification technique provides a feasible path to obtain light sources with those parameters. However, the use of chirped pulse amplification increases the technical complexity and cost of the laser system. Recently, the proposal of a multi-pass cell (MPC) nonlinear pulse compression technique has enabled us to obtain high power ultrafast femtosecond pulses with reduced technical complexity and cost. The device requires only two concave mirrors and a nonlinear medium in between. In the past seven years, the multi-pass cell nonlinear pulse compression technique has made great progress, making it possible to obtain ultrashort pulses with average power of more than a few kW and peak power of tens to hundreds of TW.</sec><sec>In this work, we achieve nonlinear pulse compression of a 100-W picosecond laser by using an improved nonlinear pulse compression scheme that combines a hybrid of a plano-cancave multi-pass cell and multi-thin-plate. Using fused silica plates in plano-cancave cavity, the spectral bandwidth (FWHM) of input picosecond laser is broadened from 0.24 nm to 4.8 nm due to self-phase modulation effect, the pulse is compressed to 483 fs by dispersion compensation using grating pairs, which corresponds to a compression factor of 22, and the final output power of 44.2 W is obtained. Compared with traditional MPC, the plano-cancave cavity scheme we developed is a very promising solution for nonlinear compression due to its compactness, more stability and large compression ratio.</sec>

Self-Phase Modulation-Induced Instability of High-Power Narrow-Linewidth Fiber Amplifiers

In this study, we investigated the effect of self-phase modulation (SPM)-induced modulation instability (MI) on the spectral purity of high-power narrow-linewidth fiber amplifiers and established a spectral evolution model for SPM-induced MI in those amplifiers. The spectral evolution process of MI under different laser powers was simulated and analyzed. The results show that, at low power (100 W), SPM can cause a dynamic change in the spectral sideband secondary peak and the spectral wingspan. An increase in laser power led to the cascade effect of MI, forming a zigzag secondary sideband with a larger spectral width and causing the spectral main peak and spectral broadening to split. Experiments based on the fiber Bragg grating (FBG) of oscillating seed sources were carried out on high-power narrow-linewidth laser amplifiers, and the above spectral evolution phenomenon was observed. The experimental results indicate that the spectral evolution model based on SPM-induced MI can effectively explain the dynamic change in the spectral secondary peak, spectral wingspan and zigzag broadening phenomenon in the power amplification process of narrow-linewidth lasers.

Electrically coupled optomechanical cavities as a tool for quantum nondemolition measurement

We present a new model of two electrically coupled optomechanical cavities. This model is based on the recently presented proposal [Physical Review A 103 (2021) 043509]. We found that coupling two optomechanical cavities via Coulomb force leads to cross-Kerr interactions between those cavities. We show that such systems may be ideal for a protocol of quantum non-demolition measurement because it is easy to eliminate the self-phase modulation effect. Moreover, nonlinearities in our model are based on easily adjustable parameters, and therefore, given recent experimental studies, we believe that experimental realization of a cross-Kerr interaction via Coulomb force coupling is feasible.

Flexible All-Optical 8QAM Signal Format Conversion Using Pump Assisted Nonlinear Optical Loop Mirror

A flexible all-optical format interconversion scheme based on a pump assisted nonlinear optical loop mirror (NOLM) is proposed and numerically simulated for the first time to our knowledge. In this scheme, input multi-Gbps 8QAM signals are divided into clockwise (CW) and counter-clockwise (CCW) components by a 3-dB optical coupler (OC), which also couples light from the input pump into the NOLM from the CCW direction. The numerical model of the pump assisted NOLM with CW and CCW optical paths is simplified using a nonlinear Mach-Zehnder interferometer (MZI). Optical signals in the upper MZI arm will be mainly affected by the self-phase modulation (SPM) effect when traversing the highly nonlinear fiber (HNLF) and those in the lower MZI arm are impacted by cross-phase modulation (XPM) in addition to SPM when they experience the HNLF with the input pump light. When the upper-arm optical signal with SPM phase shift and the lower arm optical signal with SPM and XPM phase shifts are coherently mixed, a new converted 8QAM signal can be obtained. The power transfer function (PTF) of the pump assisted NOLM and the relative phase shift (RPS) between the input and the output optical signals are theoretically provided and verified. By only changing the input power of the 8QAM signal and the pump light, all-optical format interconversion of square-, standard- and star-shaped 8QAM signals can be achieved. Furthermore, the proposed scheme can achieve format conversion from the 30 Gbps square-shaped 8QAM signal to a 20 Gbps quadrature phase shift keying (QPSK) signal. The scheme performance is analyzed via constellation diagrams, eye diagrams, the error vector magnitude (EVM) and the bit error rate (BER) of the optical signals. The scheme developed can be deployed in optical gateways to connect different optical networks by dynamically selecting their appropriate modulation formats.

Implicit Quiescent Optical Solitons for the Dispersive Concatenation Model with Nonlinear Chromatic Dispersion by Lie Symmetry

The primary purpose of this paper is to investigate and recover implicit quiescent optical solitons in the context of the dispersive concatenation model in nonlinear optics. Specifically, the study focuses on a model that incorporates nonlinear chromatic dispersion and includes Kerr and power-law self-phase modulation effects. The objective is to identify and characterize these soliton solutions within this complex optical system. To achieve this purpose, we employ the Lie symmetry analysis method. Lie symmetry analysis is a powerful mathematical technique commonly used in physics and engineering to identify symmetries and invariance properties of differential equations. In this context, it is used to uncover the underlying symmetries of the nonlinear optical model, which in turn aids in the recovery of the quiescent optical solitons. This method involves mathematical derivations and calculations to determine the solutions. The outcomes of the current paper include the successful recovery of implicit quiescent optical solitons for the dispersive concatenation model with nonlinear chromatic dispersion, Kerr, and power-law self-phase modulation. The study provides mathematical expressions and constraints on the model’s parameters that yield upper and lower bounds for these solutions. Essentially, this paper presents a set of mathematical descriptions for the optical solitons that can exist within the described optical system. The present paper contributes to the field of nonlinear optics by exploring the behavior of optical solitons in a model that combines multiple nonlinear effects. This extends our understanding of complex optical systems.

Ultrafast laser pulse stretching via dispersive materials including high dispersion orders

Ultrafast laser systems typically employ complicated systems for varying their pulse length (duration) such as an ultrafast IR mode-locked laser used at the Schlesinger Compact Accelerator Center at Ariel University. The laser is an Astrella manufactured by Coherent generating an 800nm pulse. The pulse duration can be varied from 10 ps to 35 fs using a remote-controlled grating-based compressor. In order to measure the time duration of the pulse, an automated compact autocorrelator was designed and developed. The laser is mainly used to extract electrons from a photo-cathode using dual BBO frequency tripling system, providing a UV (266nm) ultra-short pulse. The electrons are formed into a beam, which is used to generate a THz FEL. Using an fs-level UV pulse, the extracted electron beam is unstable, resulting in high space-charge effects, high emittance values, and lowered radiation power dramatically. For this reason, we aim to stretch the UV pulse to a ps level. We study here an applicative method that uses dispersive materials. This method is convenient, compact, and can be easily installed. However, ultrafast lasers can suffer from high dispersion orders. Therefore, we study the contribution of the third and fourth orders of dispersion using analytical and numerical methods. Furthermore, our analysis takes into account the self-phase modulation effect when intense lasers are used. An experimental measurement is executed to confirm our numerical results, and a comparison between the experimental and simulation results is presented.

Optical Bullets and Domain Walls with Cross Spatio-Dispersion and Having Kudryashov’s form of Self-Phase Modulation

In this paper, we investigate the retrieval of optical bullets and domain walls in a novel context, considering the interplay of cross spatio-dispersive effects and employing Kudryashov' s proposed form of self-phase modulation. The integration of these two key elements represents a significant advancement in the field of nonlinear optics, enabling the recovery of optical structures with enhanced precision and control. We propose an enhanced Kudryashov’s approach, which overcomes the limitations of conventional methods and facilitates the retrieval of optical bullets and domain walls even in the presence of cross spatio-dispersive effects. Kudryashov' s self-phase modulation mechanism has proven to be a powerful tool in controlling the nonlinear dynamics of optical systems, offering unique opportunities to manipulate light waves through phase variations induced by the medium' s response to intense optical fields. The results presented herein offer new insights into the intricate interplay between self-phase modulation and spatio-dispersive effects in nonlinear optical systems. Moreover, our findings provide a promising avenue for developing novel applications in ultrafast all-optical signal processing, such as the manipulation of light bullets for high-speed data transmission and storage. The enhanced retrieval and control of optical bullets and domain walls are expected to have a profound impact on the advancement of nonlinear optics and its practical implications.

Effect of dispersion and nonlinearity on ultrashort optical pulse propagation in long-period fiber grating: An analytical investigation

Long-period fiber grating is widely used as an optical component in photonics communication technology. The optical pulse propagation in grating has been studied mostly numerically and some number of studies carried out experimentally. The detailed analytical investigation has not been reported due to the complexity of the mathematical equations. Here, we have investigated analytically the effect of dispersion and nonlinearity on ultrafast optical pulse propagation in long-period fiber grating and derived the expression for transmitted optical pulses because the detailed analytical investigation has not been reported by any authors. The results of the study show how grating-induced overall dispersion and nonlinearity-induced self-phase modulation (SPM) modify the shape of the ultrashort optical pulses when it’s propagating through a length of the grating. The combined effects of dispersion and SPM on the optical pulse evaluation are also analyzed. From the plotted graphs it is investigated that the dispersion of the grating distorted the pulse shape whereas SPM shifts the pulse towards the higher time scale. It is also investigated that the distorted optical pulse due to dispersion is reshaped by the nonlinearity introduced in the medium due to the combined effect of dispersion and SPM. Optical pulse compression, optical limiting and pulse reshaping are also illustrated as a function of excitation intensity.

A Wide Spectrum Yb-Doped All-Fiber-Integrated Chirped Pulse Amplification System Based on Parabolic Shaping

Nonlinear effect in an ultrafast fiber laser has always been a major obstacle in realization of laser with narrow pulse width and high energy. To achieve higher peak power, we herein introduce pre-chirping management and pre-amplification before the chirped pulse amplification (CPA) system. The self-phase modulation effect is used to effectively stretch the spectrum when the pulse reaches a high peak power, and then the parabolic pulse and spectrum are obtained in a fiber amplifier. This parabolic pulse effectively reduces the impact of nonlinear effect in subsequent fiber amplifier and realizes the amplification of chirped pulse with a higher peak power compared with conventional CPA system. We finally achieved a mode-locked pulse with 143 fs pulse duration, 8.57 W average power, 85.7 μJ single pulse energy, M2 < 1.10 beam quality, and without obvious pulse degeneration. The reported pulse energy is the highest among all-fiber CPA systems based on nonlinear amplification technology.

Wafer-scale inverted gallium phosphide-on-insulator rib waveguides for nonlinear photonics.

We report a gallium phosphide-on-insulator (GaP-OI) photonic platform fabricated by an intermediate-layer bonding process aiming to increase the manufacture scalability in a low-cost manner. This is enabled by the "etch-n-transfer" sequence, which results in inverted rib waveguide structures. The shallow-etched 1.8 µm-wide waveguide has a propagation loss of 23.5 dB/cm at 1550 nm wavelength. Supercontinuum generation based on the self-phase modulation effect is observed when the waveguides are pumped by femtosecond pulses. The nonlinear refractive index of GaP, n2, is extracted to be 1.9 × 10-17 m2/W, demonstrating the great promise of the GaP-OI platform in third-order nonlinear applications.

Coherent optical gyroscope on the basis of the bidirectional ultra-short pulse Erbium ring fiber laser

A gyroscopic effect has been studied in the bidirectional ultra-short pulse erbium-doped fiber ring laser hybridly mode-locked with a co-action of a Single-Walled Carbon Nanotube-based saturable absorber (SWCNT-SA) and Nonlinear Polarization Evolution introduced by means of the short-segment polarizing fiber. Owing to the Kerr nonlinearity contribution through self-phase modulation and self-steepening effects to the carrier-to-envelope phase slip of both clockwise (CW) and counterclockwise (CCW) solitons, wideband controllable tuning of a gyroscope bias point has been demonstrated by means of an appropriate adjustment of either intracavity polarization or pump power. Angular velocity detected ranges from 0.12 deg/s to 360 deg/s while the highest rotation sensitivity reaches 7 kHz/(deg/s) for 0.79 m2 single-coil ring gyroscope being in agreement with the calculated scale factor value. The gyroscope dead band with upper limit of ≈5.15 deg/s corresponding to the beat-note frequency of ≈15 kHz has been detected during clockwise rotation of the gyroscope. The highest gyroscope resolution of ≈0.01 deg/s=38 deg/h has been estimated on the basis of the bias point drift measurement.

350-2500 nm supercontinuum white laser enabled by synergic high-harmonic generation and self-phase modulation

Supercontinuum white laser with large bandwidth and high pulse energy would offer incredible versatility and opportunities for basic science and high technology applications. Here, we report the generation of high-efficiency 2.8-octave-spanning ultraviolet-visible-infrared (UV-Vis-IR) (with 350-2500 nm 25 dB bandwidth) supercontinuum white laser from a single chirped periodically poled lithium niobate (CPPLN) nonlinear crystal via synergic high-harmonic generation (HHG) and self-phase modulation (SPM). The CPPLN exhibits multiple controllable reciprocal-lattice bands to simultaneously support the quasi-phase matching (QPM) for simultaneous broadband 2nd-10th HHG via cascaded three-wave mixing against a broadband fundamental pump laser. Due to the efficient second-order nonlinearity (2nd-NL) up-conversion and significant 3rd-NL SPM effect both in the pump and HHG laser pulses, 350-2500 nm supercontinuum white laser is eventually obtained with 17 μJ per pulse under pump of 45 μJ per pulse mid-infrared femtosecond laser corresponding to an average high conversion efficiency of 37%. Our work opens up a route towards creating UV-Vis-IR all-spectrum white lasers through engineering the synergic action of HHG and SPM effects in nonlinear crystals for applications in ultrafast spectroscopy, single-shot remote sensing, biological imaging, and so on.

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.

Non-linear propagation effects of intense femtosecond pulses on below bandgap harmonics in solids

The non-linear propagation of the intense near-infrared (NIR) driving field in crystals poses a challenge and can offer an opportunity to control the spectral properties of harmonics in solids. Here, we have investigated the non-linear propagation effects in wide bandgap dielectrics such as Magnesium Oxide (MgO), Chromium (Cr) doped MgO (Cr: MgO), Sapphire (Sa) crystals, and fused silica (FS). Furthermore, we have generated second and third harmonics (TH) and measured the linear polarization dependence of harmonics in these thin solids to explore the non-linear response at a strong field. We observe spectral shifts and broadening of the driving field spectrum which is imprinted on the harmonics. We attribute these effects to the strong photoionization, generation of free-carrier density, and self-phase modulation effects. This work shows the sensitivity to control the spectral profile of harmonics by manipulating the driving field, showing the possibility of new tailored solid-state ultraviolet sources for optical diagnostics.