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This paper explores an analytical approach for obtaining multiple solutions for a three-wave interaction system in ( 1 + 1 ) dimensions. We introduce a novel approach that expresses wave solutions in terms of Jacobi elliptic functions and explores specific cases involving hyperbolic functions. Additionally, this paper focuses on analyzing the linear stability of two kinds of solutions: (a) periodic and (b) one or two-hump bright solitons influenced by group velocity and group velocity dispersion. The method of separation of variables along with the ansatz method is employed to derive extract analytical solutions of this model. For linear stability analysis, the eigenvalue problem is solved using the Fourier collocation method, where Fourier coefficients are defined analytically and validated numerically. Moreover, linear stability is verified through direct numerical simulations using the pseudospectral method with special derivatives in the temporal direction ( t ) and the 4th-order Runge–Kutta method in the spatial direction ( z ), further confirmed by the Crank-Nicholson finite difference method. All these investigations within the framework of our current model yield novel insights and present breakthrough research opportunities in the realm of nonlinear optics. A key finding of this study is the discovery of stable analytical solutions, which are presented here for the first time. Furthermore, we introduce a special case known as constant magnitude wave solution and examine its modulational instability in the presence of group velocity dispersion. We also investigate the influence of group velocities and wave vector mismatches. All the results obtained are new and interesting, and the concept opens new possibilities for results in the field of nonlinear optics and nonlinear dynamics.

Silicon nitride photonics is on the rise owing to the broadband nature of the material, allowing applications of biophotonics, tele/datacom, optical signal processing and sensing, from visible, through near to mid-infrared wavelengths. In this paper, a review of the state of the art of silicon nitride strip waveguide platforms is provided, alongside the experimental results on the development of a versatile 300 nm guiding film height silicon nitride platform.

This work outlined the integrated role between vertical cavity surface emitting laser diodes with Gaussian pulse generators and Ideal erbium doped fiber amplifier (EDFA) for the self-phase modulation instability management, as well as the signal/NP level (Power level [PL]) with the spectral frequency is simulated after wavelength division multiplexing (WDM) fiber at length of 10 km based third order Gaussian pulse generators. The light power variations against temperature after WDM fiber is also studied at length of 10 km based various order Gaussian pulse generators. Electrical received power (ERP) variations against temperature is clarified after avalanche photo diode (APD) photodetectors based various order Gaussian pulse generators. The study emphasis the bad effects of the increase of the temperature, and higher Gaussian pulse generators order on the signal power levels.

Parametric down-conversion in a nonlinear crystal is a widely employed technique for generating quadrature squeezed light with multiple modes, which finds applications in quantum metrology, quantum information and communication. Here we study the generation of temporally multimode femtosecond pulsed squeezed light in a synchronously pumped optical parametric oscillator (SPOPO) operating below the oscillation threshold, while considering the presence of non-compensated intracavity group-velocity dispersion. Based on the developed time-domain model of the system, we show that the dispersion results in mode-dependent detuning of the broadband supermodes of the pulsed parametric process from the cavity resonance due to temporal Gouy phase, as well as linear coupling between these supermodes. With perturbation theory up to the second order in the coupling coefficients between modes, we obtained a solution for the amplitudes of multiple supermodes given an arbitrary sub-threshold pump level. The dispersion affects the quantum state of the supermodes by influencing their squeezing level and the rotation of the squeezing ellipse. It also affects the entanglement among the supermodes, leading to reduced suppression of shot noise level as measured in the balanced homodyne detection scheme. Furthermore, our study highlights the potential of SPOPO with group-velocity dispersion as a testbench for experimental investigations of multimode effects in linearly evanescent coupled parametric oscillators.

In this work, a dispersion compensating photonic crystal fiber (DC-PCF) is proposed in which dispersion, dispersion slope, second order dispersion, third order dispersion, nonlinearity, effective mode area, parameter are investigated. The suggested structure is very effective for compensating of chromatic dispersion about −951 to −3075.10 ps/(nm.km) over 1340–1640 nm wavelength bandwidth. With perfectly matched layer boundary condition, guiding properties are inspected applying finite element method (FEM). The investigated results conform the opportunity of large negative dispersion and high group velocity dispersion (GVD) of −2367.10 ps/(nm.km) and 3018.55 ps /km respectively, at 1550 nm operating wavelength. The offered fiber also shows low third order dispersion about −637.88 ps /km, high nonlinearity of 91.11 W  km . From overall simulation results, it can be expected that the suggested PCF will be an effective candidate in high bit rate long haul optical communication system as well as sensing applications.

Fiber optics telecommunication is the currently established backbone infrastructure for most of the information flow across the world. New services and applications are causing an exponential increase in Internet traffic, increasing transmission rate, and high bandwidth-demanding applications have been propelling the data rate per wavelength to approach the speed limit of electronics. In a few years, the current fiber optic communication system infrastructure will not be able to meet this demand because fiber nonlinearity dramatically limits the information transmission rate. Also, the dispersion phenomenon is a problem for high bit rates and long-haul optical communication systems. An easy solution to this problem is optical solitons pulses that preserve their shape over long distances. An optical soliton is formed by balancing nonlinearity (self-phase modulation) and dispersion phenomenon (group velocity dispersion). In this review article, a detailed study of optical solitons is presented along with its recent progress. Advanced numerical methods such as Darboux transform (DT), digital back propagation, split step Fourier, and forward–backward methods are also discussed in this paper which is used for solving higher-order solitons.

This study aims to determine the 1D deep S-wave velocity structure for Çanakkale Province and the surrounding area (Biga Peninsula, NW Turkey) using the moderate (M ≥ 4.0) earthquakes from the last decade. A total of 540 velocity seismograms with a high S/N ratio are obtained from 218 three-component acceleration records of the 10 earthquakes (4.0 ≤ Mw ≤ 5.3) that occurred in the areas of Ayvacık, Saros, and Çan between 2010 and 2018. A total of 34 strong ground motion stations operated by AFAD are grouped in 27 azimuthal directions, and fundamental mode surface wave group velocity dispersion curves are obtained using the multiple-filter method. First, the observed dispersion curves are utilized for the inversion application to define the 1D deep Vs model. Then they are compared with the theoretical curves of the tuned 1D deep Vs models with the trial-and-error forward method after inversion. The RMS misfits between observed and calculated surface group velocities decrease from 0.6 to 0.2 on average. The dispersion analyses allow for improved seismic velocities and thicknesses of especially the uppermost 4–5 km. The defined 1D deep Vs model of 202 source-station paths are also inferred to obtain an average pseudo-3D deep Vs model. In addition, the velocity models are verified with 1D numerical ground motion simulations for 0.05–1 Hz, including the characterized source models of the earthquakes and 1D shallow soil amplifications. The simulation results are quantitatively evaluated with goodness-of-fit measures considering different frequency bands. Fairly good agreement for waveform first arrival and spectral amplitude (0.05–1 Hz) is achieved. However, the later wave packages at the sites located on thick sediment basins cannot be modeled because of the reverberations in the sediment overlying the engineering bedrock. The test of the pseudo-3D Vs model using broadband (0.05–10 Hz) simulation of the 2017 Lesvos mainshock (Mw 6.3) also indicates that both the phase arrival times (< 1 Hz) and the amplitude spectral decay in the high-frequency range of 1–7 Hz are well modeled.

Between 2017 and 2019, the CSIR-NGRI, Hyderabad, Telangana, established a broad-band seismic-network with fifty-five 3-component broadband seismometers in the Himalayan region of Uttarakhand, India. Out of 55 three component broadband seismic (BBS) networks, we chose 17 for the present study. Using digital waveform data from twenty-one (21) regional Indian earthquakes of Mw 5.0–6.2 that were recorded in the 17 broadband seismometer, we compute fundamental mode group-velocity dispersion (FMGVD) characteristics of surface waves (Love and Rayleigh waves) and the average one-dimensional regional shear-wave velocity ( V s) structure of the Uttarakhand Himalayan region. First, we compute FMGVD curves for Love waves (6–73 s) and Rayleigh waves (at 6.55–73 s) period, and then, we finally invert these dispersion curves to compute the final average one-dimensional regional crustal & sub-crustal shear-wave velocity ( V s) structure below the Uttarakhand Himalaya. Our best model in Uttarakhand Himalayan region, India, reveals the 8-layered crust with a mid-crustal low velocity layer (MC-LVL) (approximately a drop of 1.5–2.3% in V s ) between 8 and 20 km depth in the proximity of MCT (Main Central Thrust). In the upper crustal part (0–20 km depths), our modelling suggests shear velocities ( V s) varies from 3.1 to 3.9 km/sec while shear velocities ( V s) in the lower crustal part (20–45 km depth) are modelled to be varying from 3.7 to 4.69 km per sec. The Moho-depth is calculated to be 45 km deep below the K-G Himalaya, and the shear-velocity ( V s) in the sub-crustal sector is 4.69 km/sec. Our estimated mid-crustal low-velocity layer (MC-LVL) could be linked to the presence of metamorphic fluids in the fractured Main Himalayan Thrust (MHT), resulting from the weakening of the crustal material at the interface between the overriding Eurasian plate and upper part of the underthrusting Indian plate.

The polarization difference between neighboring channels in WDM systems causes various nonlinear fiber impairments such as self-phase modulation (SPM), cross-phase modulation (XPM), polarization mode dispersion (PMD), and polarization-dependent loss (PDL), resulting in a deterioration of signal quality. PMD limits the distance and the transmission speed in high bit rate optical link. PDL varies the state of polarization of light in adjacent channels to travel at slightly different speeds in the optical fiber, leading to signal distortions and increased bit error rate. This research investigates cutting-edge strategies that make use of the synergy of optical phase conjugation (OPC) and dispersion compensation module (DCM) suited for differently polarized adjacent channels in a wavelength-division multiplexing link to compensate these numerous limitations. The precise reversal of optical phase and amplitude distortions that a signal experiences during optical phase conjugation efficiently mitigates nonlinearities like SPM and XPM. The influence of chromatic dispersion, which can otherwise cause signal broadening and unfavorable inter-symbol interference, is rigorously countered by dispersion adjustment modules. The applicability of this new approach is validated by numerical simulations. For uniformly varying polarization angles between different channels, it has been found that the quality factor is highest for orthogonal polarization at 90 degrees and lowest for parallel polarization at either zero or 180 degrees. Additionally, random polarization fluctuation raises the quality factor by up to 2 dB. When using the OPC and DCM together, random polarization provides significantly greater performance. In DWDM networks, this study seeks to simultaneously mitigate nonlinear effects, dispersion-induced impairments, and polarization-dependent anomalies. By doing this, it aims to increase the network’s robustness and reduce bit error rate, allowing for the smooth and reliable transmission of high-capacity optical communications across long distances.