Understanding the contribution of mode area and slow light to the effective Kerr nonlinearity of waveguides

V. Shahraam Afshar,T. M. Monro,C. Martijn de Sterke

doi:10.1364/oe.21.018558

Abstract

We resolve the ambiguity in existing definitions of the effective area of a waveguide mode that have been reported in the literature by examining which definition leads to an accurate evaluation of the effective Kerr nonlinearity. We show that the effective nonlinear coefficient of a waveguide mode can be written as the product of a suitable average of the nonlinear coefficients of the waveguide's constituent materials, the mode's group velocity and a new suitably defined effective mode area. None of these parameters on their own completely describe the strength of the nonlinear effects of a waveguide.

Highlights

The nonlinear Schrodinger equation (NSE) describes pulse propagation in Kerr nonlinear dispersive media both for bulk and waveguides [1, 2]
Based on the full vectorial NSE developed by Afshar et al [27], we develop a new and general form of the effective nonlinear coefficient and explicitly show that in the form developed here, γ depends on the contribution of three physical parameters; the distribution of nonlinearity of the waveguide’s constituent materials over the waveguide cross section and its overlap with the field, the area of the propagating mode represented by the effective area Aeff, and the group velocity of the mode
To understand the contribution of the effective area on the effective nonlinear coefficient γ in both the strong and weak guidance regimes, we consider A(e2ff) and A(e3ff) and other definitions of Aeff reported in the literature

Summary

Introduction

The nonlinear Schrodinger equation (NSE) describes pulse propagation in Kerr nonlinear dispersive media both for bulk and waveguides [1, 2]. Based on the full vectorial NSE developed by Afshar et al [27], we develop a new and general form of the effective nonlinear coefficient and explicitly show that in the form developed here, γ depends on the contribution of three physical parameters; the distribution of nonlinearity of the waveguide’s constituent materials over the waveguide cross section and its overlap with the field, the area of the propagating mode represented by the effective area Aeff, and the group velocity of the mode. This is followed by the results Section, 3, in which we compare the behavior of different definitions of effective areas and effective nonlinear coefficients of the HE11, TE01 and TM01 modes of a step-index, glass-air fiber as a function of core radii. We present the conclusion and a brief discussion of our results

Theory

Factorization based on effective area

Factorization based on slow light

Results

Discussion and conclusion