S. Konar

Introduction to non-Kerr Law Optical Solitons

INTRODUCTION History Optical Waveguides THE NONLINEAR SCHRODINGER EQUATION Introduction Traveling Waves Integrals of Motion Parameter Evolution Quasi-Stationary Solution KERR LAW NONLINEARITY Introduction Traveling Wave Solution Inverse Scattering Transform Integrals of Motion Variational Principle Quasi-Stationary Solution Lie Transform POWER LAW NONLINEARITY Introduction Traveling Wave Solution Integrals of Motion Quasi-Stationary Solution PARABOLIC LAW NONLINEARITY Introduction Traveling Wave Solution Integrals of Motion Quasi-Stationary Solution DUAL-POWER LAW NONLINEARITY Introduction Traveling Wave Solution Integrals of Motion Quasi-Stationary Solution SATURABLE LAW NONLINEARITY Introduction The NLSE Bistable Solitons Arbitrary Pulse Propagation SOLITON-SOLITON INTERACTION Introduction Mathematical Formulation Quasi-Particle Theory STOCHASTIC PERTURBATION Introduction Kerr Law Power Law Parabolic Law Dual-Power Law OPTICAL COUPLERS Introduction Twin-Core Couplers Multiple-Core Couplers Magneto-Optic Waveguides OPTICAL BULLETS Introduction 1 + 3 Dimensions EPILOGUE HINTS AND SOLUTIONS BIBLIOGRAPHY INDEX

Propagation of an elliptic Gaussian laser beam in a medium with saturable nonlinearity

We present an analysis for self-focusing of an elliptic Gaussian laser beam in a saturable nonlinear medium. It is shown that stationary self-trapped propagation is forbidden in a saturable medium. Though self-trapped propagation does not occur, a virtual threshold power for self-focusing can be defined. Above this threshold power value, but not far from it, the beam focuses. Below this threshold the beam defocuses. It is also shown that the effective beam radius never reaches zero, which is a property of a Gaussian laser beam.

HIGH BIT RATE DENSE DISPERSION MANAGED OPTICAL COMMUNICATION SYSTEMS WITH DISTRIBUTED AMPLIFICATION

In this paper we have investigated optical pulse propa- gation in a dense dispersion managed (DM) optical communication system operating at a speed of 100 Gb/s and more taking into account of the effects of third order dispersion, intra-pulse Raman scattering and self steepening. Using perturbed variational formulation, we have obtained several ordinary differential equations for various pulse pa- rameters. These equations have been solved numerically to identify launching criteria in the first DM cell of the system. Full numerical simulation of the nonlinear Schrodinger equation has been employed to identify effects of higher order terms on pulse propagation and to in- vestigate the intra-pulse interaction. The roles played by these higher order linear and nonlinear effects have been identified. It has been found that the shift of the pulse centre due to intra-pulse Raman scat- tering increases with the increase in the distance of propagation and average dispersion. We have noticed that for higher value of average dispersion pulses travel less distance before collision than for lower average dispersion.

QUASI-STATIONARY OPTICAL SOLITONS IN NON-KERR LAW MEDIA WITH FULL NONLINEARITY

In this paper, the governing equation for optical solitons, namely the nonlinear Schrodingers equation, is studied with non-Kerr law nonlinearity in the presence of perturbation terms with full nonlinearity. The quasi-stationary optical soliton is obtained after applying the multiple-scale perturbation analysis. The forms of nonlinearity that are studied in this paper are Kerr law, power law and the log law.

Index Guiding Photonic Crystal Fibers With Large Birefringence and Walk-Off

This paper presents the design of an index guided photonic crystal fiber which promises to yield very large birefringence (~2.22 ×10- 2). Important optical properties, such as birefringence, single modeness, optical confinement, fiber dispersion, walk-off, etc., have been studied employing numerical simulation through finite difference time domain scheme. The fiber also promises a very small walk-off near optical communication wavelength.

Propagation of a Mixture of Modes of a Laser Beam in a Medium with Saturable Nonlinearity

Propagation of a mixture of modes of a laser beam through a saturable nonlinear medium has been studied using JWKB method and the paraxial ray approximation. Two second order nonlinear coupled differential equations for the beam width parameters resembling equations of coupled nonlinear oscillators of unit mass are obtained. A scalar potential of the system has been formulated whose analysis yields some valuable information like existence of two critical values of the potential within which bound state of the system exists. From the stability analysis it has been found that the stable beam propagation depends on the ratio of intensities of the two modes. A threshold of power is defined. When beam power is above the threshold value the propagation is stationary.

SUPPRESSION OF SOLITON INSTABILITY BY HIGHER ORDER NONLINEARITY IN LONG HAUL OPTICAL COMMUNICATION SYSTEMS

The results of the numerical simulation of the propagation characteristics of periodically amplified solitons in a long nonlinear fiber have been reported. The roles played by both Kerr and saturable nonlinearities have been examined. The possibility of occurrence of instability and loss of solitons are also explored. This instability is found to be sensitive to the initial chirp, fiber loss rate and amplifier spacing. Symmetrical splitting of solitons is also reported. The inhibition of instability and splitting can be possible through saturable optical nonlinearity.

Steady-state self-focusing of rippled laser beams in plasmas: arbitrary nonlinearity

This paper presents an analysis of the self-focusing of a rippled Gaussian laser beam in a plasma when the nonlinear part of the effective dielectric constant is arbitrarily large. Considering the nonlinearity to arise from ponderomotive, collisional or thermal-conduction phenomena and following the approach of Akhmanov, Sukhorukov and Khokhlov (which is based on the WKB and paraxial-ray approximation) the phenomenon of self-focusing of rippled laser beams is studied for arbitrary magnitude of nonlinearity. For ponderomotive and collisional nonlinearities, the present theory leads to two values of the critical power for self-focusing of the beam, P crl and P cr2 , which depend on the amplitudes and phase difference of the main beam and the ripple. When the beam power P lies between the two critical values (i.e. P cr1 P P cr2 ), the medium behaves as an oscillatory waveguide; the beam first converges and then diverges, again converges, and so on. For P cr2 , the beam first diverges, then converges, then diverges, and so on. When thermal conduction is the dominant mechanism of nonlinearity of the dielectric constant, only one value of the threshold critical power P cr for self-focusing of the beam exists. When the beam power P P cr , the medium behaves as an oscillatory waveguide.

THEORY OF DISPERSION-MANAGED OPTICAL SOLITONS

THEORY OF DISPERSION-MANAGED OPTICALSOLITONSA. BiswasDepartmentofPhysicsandMathematicsCenterofExcellenceinISEMTennesseeStateUniversityNashville,TN37209-1561,USAS. KonarDepartmentofAppliedPhysicsBirlaInstituteofTechnologyMesra,Ranchi-835215,IndiaAbstract—The variational principle is employed to study chirpedsolitonsthatpropagatethroughopticalfibersandisgovernedbythedispersion-managed nonlinear Schr¨odinger’s equation. Here, in thispaper,thepolarization-preservingfibers,birefringentfibersaswellasmultiple channels have been considered. The study is extended toobtain the adiabatic evolution of soliton parameters in presence ofperturbationtermsforsuchfibers. BothGaussianandsuper-Gaussiansolitonshavebeenconsidered.1 Introduction2 Governing Equations3 VariationalPrinciple4 PolarizationPreservingFibers4.1 IntegralsofMotion4.2 VariationalFormulation4.2.1 GaussianPulses4.2.2 Super-GaussianPulses

Soliton-soliton interaction with kerr law nonlinearity

The intra-channel collision of optical solitons, with Kerr law nonlinearity, is studied in this paper by the aid of quasi-particle theory. The perturbation terms that are considered in this paper are all of Hamiltonian type. The suppression of soliton-soliton interaction, in presence of these perturbation terms, is acheived. The numerical simulations support the theory.