THEORY OF INTEGRATED OPTIC WAVEGUIDES

THEORY OF INTEGRATEDOPTIC WAVEGUIDES

Integrated photonics devices are based on the processing of light confined in optical

structures called optical waveguides. In this chapter we will describe the theory of

optical waveguides using the electromagnetic theory of light previously discussed. We

start by describing the basic geometries found in waveguide structures: planar waveguides,

channel waveguides, optical fibres and photonic crystals. Then, we introduce

the concept of optical mode, and discuss the types of modes that can be supported by

a planar structure. Using the Maxwell’s equations we will obtain the wave equation

for planar waveguides, and then we will solve it for the simplest case of step-index

planar waveguides, considering TE and TM polarised modes separately. In particular,

we will see that for confined radiation the wave equation admits a discrete number of

solutions, called guided modes. Based on the results obtained for guided modes in stepindex

waveguides, we describe the different approaches to solving graded-index planar

waveguides, examining the advantages and disadvantages of each method. Finally,

the guided modes in channel waveguides are studied, and the solutions provided by

Marcatili’s method and the effective index method are presented. Several examples of

mode calculations are given for the different optical waveguide structures using the

methods and algorithms.