arXiv subjects

Anuj P. Lara

Publications and source records attributed to Anuj P. Lara.

9 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 Schrödinger 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

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

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 Schrödinger 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 $\pm π/2$ 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{ansätz} 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↗

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↗