Arbitrary Nonlinear Media Research Articles

Pulse Propagation in a Non-Linear Medium

Abstract This paper considers a novel approach to solving the general propagation equation of optical pulses in an arbitrary non-linear medium. Using a suitable change of variable and applying the Adomian decomposition method to the non-linear Schrödinger equation, an analytical solution can be obtained which takes into accountparameters such as attenuation factor, the second order dispersive parameter, the third order dispersive parameter and the non-linear Kerr effect coefficient. By analysing the solution, this paper establishes that this method is suitable for the study of light pulse propagation in a non-linear optical medium.

Pseudospectral mode solver for analyzing nonlinear optical waveguides

Numerical mode solver using a pseudospectral scheme is developed for solving various nonlinear dielectric and plasmonic waveguides with arbitrary nonlinear media. Two nonlinear iterative approaches that use this scheme are implemented; these approaches assign the mode power and effective index as extracted eigenvalues. However, to obtain the complete power dispersion curve including the stable and unstable modal solutions, assigning the mode power as an eigenvalue for a given effective index is required. Moreover, the biaxial feature of the nonlinear refractive index is considered for solving the transverse magnetic (TM) modes in materials of practical interest. Furthermore, the proposed scheme solves the problem of nonlinear surface plasmons guided by a thin metal film with nonlinear cladding, and the mode characteristics of long- and short-range surface plasmon polaritons are analyzed. We also apply the proposed scheme to a 2D strip waveguide with a nonlinear saturation substrate.

Quantum field entropy and entanglement of a three-level atom two-mode system with an arbitrary nonlinear medium

Abstract In this paper, we use the quantum field entropy to measure the degree of entanglement in the time development of a three-level atom interacting with two-mode fields including all acceptable kinds of nonlinearities of the two-mode fields. This model describes a very general situation in which the system admits two detuning parameters and includes an arbitrary form of the nonlinearity of the two modes. It is shown that when the individual modes of the field are detuned far from the intermediate atomic level, the dynamic Stark shift is induced by the nonlinear medium. The results show that the non-linearity effect yields the superstructure of atomic Rabi oscillations and changes the quasiperiod of the field entropy evolution and entanglement between the atom and the field. The general conclusions reached are illustrated by numerical results.

Quantum field entropy and entanglement of a three-level atom two-mode system with an arbitrary nonlinear medium

In this paper, we use the quantum field entropy to measure the degree of entanglement in the time development of a three-level atom interacting with two-mode fields including all acceptable kinds of nonlinearities of the two-mode fields. This model describes a very general situation in which the system admits two detuning parameters and includes an arbitrary form of the nonlinearity of the two modes. It is shown that when the individual modes of the field are detuned far from the intermediate atomic level, the dynamic Stark shift is induced by the nonlinear medium. The results show that the non-linearity effect yields the superstructure of atomic Rabi oscillations and changes the quasiperiod of the field entropy evolution and entanglement between the atom and the field. The general conclusions reached are illustrated by numerical results.

Diagnostics of nonlinearities using scattered field disturbances

We formulated an integral equation for finding the field in an arbitrary nonlinear medium. In the case of a localized nonlinearity, this equation is effectively solved using the iteration technique. It is shown that the inverse problem of recovering current-voltage characteristics of arbitrary nonlinearities by scattered field disturbances can be solved on this basis.

Optical components induced by repelling solitons

By colliding either bright or dark solitons, one can induce idealized lossless (linear) optical components in a nonlinear medium. We provide the first reported analytical method, to our knowledge, for determining the transmission properties of these components when they are induced in an arbitrary nonlinear medium. Components induced from colliding bright solitons behave qualitatively the same regardless of the nonlinear material, unlike components induced from colliding dark solitons.

Analysis of nonlinear MQW waveguides: a simple numerical approach

A simple numerical procedure for analysing the modes of nonlinear MQW waveguides with any arbitrary nonlinear media is presented here. The method can be used for any non-Kerr-type nonlinearity and can be extended to estimate losses in nonlinear MQW waveguides.

A model for the analysis of nonlinear interactive problems between TE and TM waves based on the resonance technique

A simple and easily programmable approach based on the resonance method has been developed for analysing the nonlinear interaction between TE and TM waves. The model is oriented to be applicable to complicated nonlinear interactive problems, such as multilayer dielectric structures with arbitrary nonlinear media, two-dimensional nonlinear guides, nonisotropic nonlinear media, etc. In this paper, the five-layer waveguiding configuration containing two nonlinear media, along with a linear film of arbitrary refractive index profile, is treated.

FINITE ELEMENT ANALYSIS OF TE AND TM MODES IN NONLINEAR PLANAR WAVEGUIDES

A general approach based on the finite element method for analyzing optical waves guided by dielectric planar waveguides with arbitrary nonlinear media and with arbitrary refractive index distribution is considered. A complete transverse-electric and transverse-magnetic mode analysis is presented and TM polarization solutions are obtained without approximations on the biaxial nature of the nonlinear refractive index. Solution convergence and stability is discussed and both film-guided and surface-guided modes are presented for symmetrical and asymmetrical structures. Bistability and hysteresis phenomena have been investigated for TE as well as for TM modes.

Finite-element solution of nonlinear TM waves in multiple-quantum-well waveguides

Intensity-dependent characteristics for TM-polarized optical waves guided by multiple-quantum-well (MQW) waveguides with arbitrary nonlinear media are numerically analyzed by the finite element method. In this approach, self-consistent solutions are obtained through a simple iterative procedure. The power-dependent dispersion relations and magnetic-field (H/sub x/) as well as two electric-field (E/sub y/ and E/sub z/) profiles for nonlinear TM waves in MQW waveguides with three different nonlinear mechanisms are presented. It is shown that, for the waveguides with molecular orientational mechanism, a distinct power limiting action for nonlinear TM modes exists. >

Calculation of nonlinear modes guided by multilayer dielectric structures using the resonance technique

A simple and easily programmable approach based on the resonance method has been developed for analysing optical waves guided by complicated configurations such as multilayer dielectric structures with arbitrary nonlinear media. In this formulation both TE and TM polarizations are considered. In the present paper, as an example of the resonance technique application, the five-layer waveguiding configuration, including two arbitrary nonlinear media along with a linear film of arbitrary profile, is treated. Numerical results are presented in the form of guided power versus propagation constant for various parameters of the problem.

Numerical modeling of nonlinear TE waves in multiple-quantum-well waveguides

A computer-aided technique, based on the finite element method, has been developed for analyzing intensity-dependent properties of TE waves guided by multiple-quantum-well (MQW) waveguides with arbitrary nonlinear media. Self-consistent solutions are obtained by a simple iterative procedure. The numerical results for TE power-dependent modes are presented for waveguides with either linear or nonlinear cladding regions. They reveal that, for values of total optical power above a certain threshold, the effect of nonlinear cladding regions on the propagation characteristics can be ignored. The power-dependent behavior of a non-Kerr-like case is also examined. >

Finite-element formalism for nonlinear slab-guided waves

A unified computer-aided numerical approach, based on the finite-element method, is developed for analyzing optical waves guided by dielectric slab waveguiding structures with arbitrary nonlinear media. In the formulations, both TE and TM polarizations are considered. For the TM case, the biaxial nature of nonlinear refractive index is considered without any approximation. Numerical results are presented for nonlinear TE and TM waves propagating in symmetric slab waveguides. The dependence of dispersion relations on the refractive-index profile of the film is examined.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Nonlinear polarization dynamics. I. The single-pulse equations.

We consider the polarization dynamics of a pulse propagating through an arbitrary nonlinear medium, in the limit of small nonlinearities, anisotropies, and dispersion, using the full SO(3) covariance of the Stokes parameters. The invariants of the motion are discovered and physically interpreted, a complete analogy with the ``airplane-and-rotor'' problem of rigid-body dynamics is established, and a full classification of the solutions for parity-invariant and non-parity-invariant media, with all propagation-axis rotation symmetries, is presented. In all cases, the problem is reduced to quadrature; in most cases, we find analytic solutions in terms of well-known functions.