On the use of generalized telegrapher's equations in the synthesis of electro-optic modulators

Abstract

ABSTRACT This paper considers the application of the Generalized Telegraphers Equations (GTE) to the electromagnetic modelling and designing of integrated electro-optical devices. This approach allows to eliminate the restrictions introduced by others models, as: weakly guiding condition and isotropic unperturbed medium and to value the modulator time response for a generic modulating signal. The presence of small dielectric perturbations and the large difference between the optical and modulating signal frequencies are the hypotheses considered in deriving the model. The analysis has been applied to a GaAs phase modulator in order to validate the equations and to evidence the effects of the induced anisotropy on the time-domain response. The model can be extended to the analysis of multimode dielectric waveguides, such as independent polarization and directional coupler modulator. Keywords: Electro-optic modulation, anisotropic waveguide, Telegraphers Equations. 1. INTRODUCTION The development of high-speed digital transmission systems (high rates Time Domain Multiplexing systems) are stimulating a renewed demand for broad band optical devices [2], where electro-optic devices have a considerable role [2]. In this work we analyze, by means of a novel and rigorous approach, the effect induced by a microwave field on a propagating optical signal; the microwave field modulates the refractive index of the dielectric waveguide. The theory of electro-optic traveling wave modulator has been widely considered in the past. The theoretical approach of [1] is based on the fact that the modulating field induces coupling between the optical propagating modes; in order to obtain an analytical solution, a slowly varying envelope along the propagation direction and an isotropic medium in absence of modulating field, are assumed. The theory of the electro-optic modulation can also be derived by means of an improved coupled mode theory, as in [3], where the model is applied to an arbitrary anisotropic dielectric waveguide, under some constraints on the propagating constants and on the longitudinal optical field components. The model presented in this paper starts from Maxwells equations in order to derive the Generalized Telegraphers Equations for a time and space varying anisotropic media. Small dielectric variations on the permittivity tensor are assumed (