arXiv subjects

Samudra Roy

Publications and source records attributed to Samudra Roy.

At least 19 recordsLinked to original sources

arXiv2026

Static and breathing dynamics of optical bullets in nonlinear GRIN fibers

We explore the properties of spatiotemporal solitons within nonlinear graded-index (GRIN) optical fibers, specifically addressing their formation, stability, and breathing dynamics. We solve the (3+1)-dimensional nonlinear Schr\"odinger equation employing a semi-analytical variational approach, which leads to a set of reduced coupled ordinary differential equations describing the bistable bullet dynamics. The stability of these states is assessed using the Vakhitov-Kolokolov criterion and linear stability analysis within the Kantorovich optimization framework. The breathing dynamics of the optical bullets are investigated adopting the potential formalism, revealing an oscillatory behavior and self-imaging dynamics in GRIN fibers. The analytical results demonstrate strong agreement with full numerical simulations, validating the robustness of our theoretical model. Our research enhances the understanding of stabilizing self-repeated 3D optical structures, which is beneficial for the development of advanced photonic technologies.

physics.optics↗

arXiv2026

Robust bistable vortex light bullets in graded-index multimode fibers

We explore theoretically the formation and evolution of spatiotemporal vortex bullets, pulses confined in both space and time while carrying orbital angular momentum, inside a graded-index multimode fiber. Through a two-fold approach, combining variational analysis with full numerical simulations, we establish the existence of a bistable vortex soliton family, characterized by distinct radial and azimuthal quantum numbers. These wave packets exhibit a Laguerre-Gaussian multi-ring topology in their spatiotemporal structure. We identify the experimental conditions necessary for the generation of such structured states of light. A stability analysis based on Vakhitov-Kolokolov criteria reveals an upper limit for the propagation constant, below which vortex bullets are found to be stable. Stationary and non-stationary dynamics of vortex bullets with different topological charges are analyzed fully, exploiting analytical techniques that are supported by full numerical simulations. These results enhance our understanding of self-trapped, spatiotemporal vortex solitons in a graded-index medium and may lead to potential applications in the area of classical and quantum information processing.

physics.optics↗

arXiv2026

Nondegenerate bright solitons and their interactions in the generalized coupled nonlinear Schroedinger system

It is known that the generalized coupled nonlinear Schroedinger (GCNLS) equations can be reduced to the basic vector nonlinear Schroedinger models through various symmetry reductions. By using such reductions, soliton solutions of several interesting types can be obtained for the GCNLS system. In this paper, we show how the non-degenerate soliton solutions can be derived using one such reduction and analyze the various special features associated with the resulting soliton solutions. We find that the obtained non-degenerate soliton solutions exhibit breathing behavior, characterized by a breathing frequency. We also show that the vector solitons emerging from the reduction undergo elastic collisions with the standard phase shift, similar to the non-degenerate solitons of other coupled nonlinear Schroedinger models. Further, they undergo interesting energysharing collisions when they interact with the already known bright solitons. These collision scenarios are further confirmed by an appropriate asymptotic analysis. We have also analyzed the stability of the obtained vector solitons and found that they are stable against random perturbations. The results presented here enhance the understanding of the nature and dynamics of non-degenerate vector solitons.

nlin.PS↗

arXiv2026

Optical beam propagation inside a graded-index fiber with saturable nonlinearity

We study theoretically the spatial evolution of optical beams inside a graded-index fiber exhibiting saturable nonlinearity. Utilizing an approach based on the variational principle, we identify the existence of bistable spatial solitons inside such a nonlinear medium, whose stability, analyzed through a linear stability analysis, is due to the saturating nature of the nonlinearity. Spatial solitons adhere to a specific amplitude-width relationship. Any deviation from this relationship leads to oscillating-type solutions with a period that increases with saturation level of the nonlinearity. Theoretically calculated values of this period agree well with numerical findings.

physics.optics↗

arXiv2025

Bistable quartic soliton in saturable nonlinear media

This report presents a theoretical demonstration of a novel bistable quartic soliton (BQS) in saturable nonlinear media, specifically within a realistic dispersion-engineered ridge waveguide made of Lithium Niobate LiNbO3 . The study employs the variational method to establish the amplitude-width relationship, indicating the coexistence of stable solitons with the same duration but differing amplitudes. The impact of shock on the bistable soliton is examined through perturbative variational analysis, supported by numerical results. Additionally, we examine the interaction of BQS in different regimes and analyze the formation of the bound state. The robustness of the BQS under perturbations is further investigated via linear stability analysis.

physics.optics↗

arXiv2025

A comprehensive study on beam dynamics inside symmetrically chirped waveguide array mimicking the graded index media

In this article, we explore the beam dynamics within symmetrically chirped nonlinear waveguide arrays, focusing on linear and quadratic chirping schemes. We propose a practical structure for these arrays that enhances control over light propagation. By employing a continuous approximation of the discrete nonlinear Schr\"odinger equation (DNLSE), we utilize a semi-analytical variational method to analyze beam behavior under waveguide chirping. Our findings indicate that the symmetrically chirped waveguide arrays behave similarly to graded index systems, with varying coupling coefficients analogous to the refractive index in continuous media. We derive a steady-state solution and validate it against numerical simulations, alongside conducting a linear stability analysis to assess the robustness of these solutions. The results reveal that input Gaussian beams in such waveguide arrays follow an oscillatory trajectory akin to that in parabolic index media. Notably, under nonlinear conditions, these beams evolve as discrete solitons. Our rigorous investigation of the propagation characteristics in both linear and nonlinear regimes highlights the intricate dynamics of optical beams within the engineered chirped waveguide arrays, supported by comparisons to comprehensive numerical simulations.

physics.optics↗

arXiv2023

Radiation families emitted by a discrete soliton in parity-time-symmetric waveguide arrays

We investigate the dynamics of a spatial discrete soliton and the radiation families emitted by it inside a parity-time ($\mathcal{PT}$)-symmetric waveguide array with alternate gain-loss channels. A strong spatial soliton that evolves inside the waveguide array due to the balance between discrete diffraction and Kerr nonlinearity excites linear waves in the form of diffractive radiation when launched with an angle. $\mathcal{PT}$-symmetric nature of the waveguide leads to additional radiations in Fourier space that were never explored before. In our work, we mainly focus on the origin of these radiations and try to understand how to control them. Under strong $\mathcal{PT}$ symmetry, a discrete soliton launched normally to the waveguide array produces strong side-lobes which can lead to a population of field at $\pm \pi/2$ in momentum space. In addition, a strong soliton with initial phase gradient radiates unique $\mathcal{PT}$ symmetry assisted linear wave. We establish a phase matching condition to locate such radiation in momentum space. The periodic arrangement of the gain-loss channel also leads to radiations due to reflection and back-scattering, which is prominent for a weak soliton. A linear Hamiltonian analysis for such a waveguide array is provided to identify the $\mathcal{PT}$-phase transition regime and to optimize the parameter for stable discrete soliton dynamics. We thoroughly investigate the origin of all the radiations that emerged in the $\mathcal{PT}$-symmetric waveguide array and put forward the background theory which is in good agreement with the full numerical results.

physics.optics↗

arXiv2023

Beam propagation in an active nonlinear graded-index fiber

A theoretical model is developed by exploiting the variational technique to investigate the evolution of an optical beam inside an optically pumped graded-index fiber amplifier. The variational analysis is a semi-analytical method that provides us with a set of coupled ordinary differential equations for the beam's four parameters. Numerical solution of these equations is much faster compared to the underlying multidimensional nonlinear wave equation. We compare the results of the variational and full numerical simulations for the two pumping schemes used commonly for high-power fiber amplifiers. In the clad-pumping scheme, the use of a relatively wide pump beam results in a nearly uniform gain all along the fiber. In the case of edge pumping, a narrower pump beam provides gain that varies both radially and axially along the fiber's length. In both cases, the variational results are found to be in good agreement with time-consuming full numerical simulations. We also derive a single equation for the beam's width that can predict amplification-induced narrowing of the signal beam in most cases of practical interest.

physics.optics↗

arXiv2023

Spatial beam dynamics in graded-index multimode fibers under Raman amplification:a variational approach

We investigate the spatial beam dynamics inside a multimode graded-index fiber under Raman amplification by adopting a semi-analytical variational approach. The variational analysis provides us with four coupled ordinary differential equations that govern the beam's dynamics under Raman gain and are much faster to solve numerically compared to the full nonlinear wave equation. Their solution also provides considerable physical insight and allows us to study the impact of important nonlinear phenomena such as self-focusing and cross-phase modulation. We first show that the variational results corroborate well with full numerical simulations and then use them to investigate the signal's dynamics under different initial conditions such as the initial widths of the pump and signal beams. This allows us to quantify the conditions under which the quality of a signal beam can improve, without collapse of the beam owing to self-focusing. While time-consuming full simulations may be needed when gain saturation and pump depletion must be included, the variational method is useful for gaining valuable physical insight and for studying dependence of the amplified beam's width and amplitude on various physical parameters in a faster fashion.

physics.optics↗

arXiv2022

Collision dynamics of discrete soliton in uniform waveguide arrays

We investigate the collision dynamics of discrete soliton (DS) pair in a realistic semi-infinite nonlinear waveguide array (WA) in the context of \textit{diffractive resonant radiation} (DifRR). Depending on the initial amplitude ($A_0$) and wavenumber ($k_0$), a co-moving pair of identical DSs either collide elastically or merge to form a discrete \textit{breather}. For large amplitude and small wavenumber, DSs form a bound state and do not interact . We map the domain of interaction by iterative simulation and present a phase plot in ($A_0$-$k_0$) parameter space. A variational technique is developed where the interaction term is considered as perturbation. A proper choice of Lagrangian density and the \textit{ans\"{a}tz} function followed by the Ritz optimization leads us to a set of ordinary differential equations that describe the collision mechanism. The analytical result corroborate well with numerical data. We further investigate the role of initial phase detuning between two identical DS and observe a periodic energy exchange during their interaction. Varied degree of energy exchange occurs when two DS with different wavenumbers collide which results in three distinct output states accompanied by DifRR generation. Extending our investigation to a more generalized condition by taking different amplitudes and wavenumber of DS pair, we find an unique secondary radiation in $k$-space which is originated due to the collision of solitons. The nature of this collision mediated secondary radiation is found to be different from usual DifRR. Our results shed light on the interesting aspects of the collision dynamics of DS pair in nonlinear WA and useful in understanding the complex mechanism.

physics.optics↗

arXiv2022

Spatial dissipative solitons in graphene-based active random metamaterials

We investigate dissipative nonlinear dynamics in graphene-based active metamaterials composed of randomly dispersed graphene nano-flakes embedded within an externally pumped gain medium. We observe that graphene saturable nonlinearity produces a sub-critical bifurcation of nonlinear modes, enabling self-organization of the emitted radiation into several dissipative soliton structures with distinct topological charges. We systematically investigate the existence domains of such nonlinear waves and their spatio-temporal dynamics, finding that soliton vortices are unstable, thus enabling self-organization into single dissipative structures with vanishing topological charge, independently of the shape of the graphene nano-flakes. Our results shed light on self-organization of coherent radiation structures in disordered systems and are relevant for future cavity-free lasers and amplifier designs.

physics.optics↗

arXiv2021

Free-carrier-induced nonlinear dynamics in hybrid graphene-based photonic waveguides

We develop from first principles a theoretical model for infrared pulse propagation in graphene-covered hybrid waveguides. We model electron dynamics in graphene by Bloch equations, enabling the derivation of the nonlinear conductivity and of a rate equation accounting for free-carrier generation. Radiation propagation is modeled through a generalized nonlinear Schr\"{o}dinger equation for the field envelope coupled with the rate equation accounting for the generation of free carriers in graphene. Our numerical simulations clearly indicate that unperturbed Kerr solitons accelerate due to the carrier-induced index change and experience a strong self-induced spectral blueshift. Our numerical results are fully explained by semianalytical predictions based on soliton perturbation theory.

physics.optics↗

arXiv2020

Intra-cavity field dynamics near avoided mode crossing in concentric silicon nitride ring resonator

Understanding the intra-cavity field dynamics in passive microresonator systems has already been intriguing. It becomes fascinating when the system is complex, such as a concentric dual microring resonator that exhibit avoided mode crossing (AMC). In this work, we present a systematic study of intra-cavity oscillatory field dynamics near AMC in a concentric silicon nitride microring resonator with the help of the coupled Lugiato-Lefever equation (LLE). We identify two regions viz. weakly coupled region (WCR) and strongly coupled region (SCR) based on eigenfrequency separation of the two-hybrid modes, which originate from mode coupling near AMC. In WCR, the mode coupling effect is dominant, leading to intra-cavity power oscillation between these two modes in a periodic manner and non-identical variation of their phases. In SCR, the mode coupling effect reduces gradually with nearly identical characteristics of both the modes. We further verify our numerical findings with the semi-analytical variational method, leading to an in-depth understanding of the mode coupling induced dynamics. We finally analyze the polarization evolving state, and the polarization locked state with the help of Stokes parameters and Jones vectors in WCR and SCR, respectively.

physics.optics↗

arXiv2020

Dynamic diffractive resonant radiation in a linearly chirped nonlinear waveguide array

We theoretically and numerically investigate the evolution of discrete soliton in a 1D linearly chirped nonlinear waveguide array (WA). The discrete soliton is self-accelerated inside the transversely chirped WA and emits a \textit{dynamic diffractive resonant radiation} (DifRR). The radiation appears when soliton wave-number matched with linear radiation wave. Unlike uniform WA, the DifRR can be excited even for zero wave-number of input soliton when the waveguide channels are chirped. The transverse modulation due to chirp conceptually imposes a linear potential which acts as a perturbation to soliton dynamics and leads to a monotonous wave-number shift of the propagating wave. Exploiting perturbative variational analysis we determine the equation of motion of soliton wave-number and use it to establish a modified phase-matching condition which takes into account the soliton wave-number shift and efficiently predicts the dynamic DifRR. A startling effect like generation of dual DifRR occurs as a result of the interplay between self-accelerated soliton and its initial wave-number. We exploit the modified phase matching relation to understand this unique phenomenon of dual radiation and find a satisfactory agreement with numerical result in radiation wave-number calculation.

physics.optics↗

arXiv2020

Dynamics and selective temporal focusing of a time truncated Airy pulse in varying dispersive medium

We theoretically investigate the dynamics of a time truncated Airy pulse under longitudinally varying dispersion. The realistic waveguide geometry is proposed that offers linear or oscillating dispersion profile. By solving the dispersion equation, we theoretically investigate how a linear variation of the group-velocity dispersion (GVD) over space affects the parabolic trajectory of an accelerating finite energy airy pulse (FEAP). It is demonstrated that, suitable adjustment of GVD can lead to unusual quasi-linear trajectory of the accelerating airy pulse. The impact of the periodic GVD on airy dynamics is more interesting where FEAP exhibits oscillatory trajectory with periodic peak power modulation. We theoretically estimate optimized length of the waveguide delivering maximum power at the output by solving the transcendental relation between GVD modulation strength and period. The effect of oscillatory higher order dispersion is dramatic for optical airy pulse where it experiences singularity points during propagation. At singularity points airy pulse loses its identity and flips over in time. The rich dynamics of FEAP near singular point is carefully investigated by solving the propagation equation analytically. In this report we provide detail theoretical analysis to achieve selective temporal focusing of FEAP which may be useful for application. All theoretical predictions are verified numerically and the agreement is found to be excellent.

physics.optics↗

arXiv2019

Trajectory manipulation of an Airy pulse near zero dispersion wavelength under free carrier generated linear potential

We investigate the dynamics of an Airy pulse that experiences free carrier generated optical linear potential in the vicinity of zero group velocity dispersion (GVD) wavelength inside a Si based waveguide. The optically induced potential can be realized by an inhomogeneous medium which possesses a time dependent refractive index. We propose a pump-probe scheme in Si-based waveguide where a strong continuous wave (CW) pump excites free carriers that leads to a linear potential through a time dependent refractive index change which is experienced by the finite energy Airy pulse (FEAP) (probe). The linear potential significantly manipulate the dynamics of a FEAP and leads to a monotonous spectral shift. We mathematically model the dynamics of the Airy pulse using linear dispersion equation containing an optical potential term and establish the general solution of the pulse for non-vanishing third order dispersion (TOD). We derive the expression of the trajectory of FEAP which deviates significantly from its usual ballistic nature and can be tailored with the strength of the linear potential. For positive TOD, the propagating Airy pulse experiences a singularity and flips in time domain. We theoretically derive that for a specific potential strength the flipping region is squeezed to a point and revives thereafter. We propose an exact analytical solution beyond flipping region for this specific case. Our theoretical analysis corroborates well with the numerical results. The present study may be useful in applications related to pulse reshaping and trajectory manipulation

physics.optics↗

arXiv2019

Variational approach to study soliton dynamics in a passive fiber loop resonator with coherently driven phase-modulated external field

We report a detailed semi-analytical treatment to investigate the dynamics of a single cavity soliton (CS) and two co-propagating CSs separately in a Kerr mediated passive optical fiber resonator which is driven by a phase-modulated pump. The perturbation is dealt with by introducing a Rayleigh's dissipation function in the framework of variational principle that results in a set of coupled ordinary differential equations describing the evolution of individual soliton parameters. We further derive closed-form expressions for quick estimation of the temporal trajectory, drift velocity and the phase shift accumulated by the CS due to the externally modulated pump. We also extend the variational approach to solve two solitons interaction problem in the absence as well as in the presence of the externally modulated field. In absence of phase modulated field, the two copropagating solitons can attract, repulse or can propagate independently depending on their initial delay. The final state of interaction can be predicted through a second-order differential equation which is derived by the variational method. While in presence of the phase modulated field, the two solitons interaction can result in annihilation, merging, breathing or two soliton state depending on the detuning frequency and the pump power. Variational treatment analytically predicts these states and portrays the related dynamics that agrees with full numerical simulation carried out by solving the normalized Lugiato-Lefever equation. The results obtained through this variational approach will enrich the understanding of complex pulse dynamics under phase modulated driving field in passive dissipative systems.

physics.optics↗

arXiv2019

Stability and variational analysis of cavity solitons under various perturbations

We theoretically investigate the dynamics and stability of a temporal cavity soliton (CS) excited inside a silicon-based microresonator that exhibits free-carrier generation as a result of two-photon absorption (TPA). The optical propagation of the CS is modeled through a mean-field Lugiato-Lefever equation (LLE) coupled with an ordinary differential equation accounting for the generation of free carriers owing to TPA. The CS experiences several perturbations (like intrapulse Raman scattering (IRS), TPA, free-carrier absorption (FCA), free-carrier dispersion (FCD), etc.) during its round-trip evolution inside the cavity. We develop a full variational analysis based on a Ritz optimization principle which is useful in deriving simple analytical expressions describing the dynamics of individual pulse parameters of the CS under perturbation. TPA and FCA limit the efficient comb generation and modify the stability condition of the CS. We determine the critical condition of stability modified due to TPA and derive closed-form expressions of the saturated amplitude and width of stable CS. We perform detailed modulation-instability analysis and obtain stability condition against perturbations of steady-state solution of LLE. The CS experiences FCD which leads to a temporal acceleration resulting in spectral blueshift. Exploiting the variational analysis, we estimate these temporal and spectral shifts. We also include IRS in our perturbation theory and analytically estimate the frequency redshifting. Finally, we study the effect of pump-phase-modulation on a stable CS. All our analytical results are found to be in good agreement with the data obtained from the full numerical solution of LLE.

physics.optics↗