ABSTRACT
This chapter summarizes the modeling techniques that are in widespread used for the analysis of optical waveguide devices. Modeling techniques for optical guided-wave propagation could be classified into two groups: time-harmonic and time-dependent modelings. The most fundamental guiding properties of optical waveguides are expressed in terms of waveguide modes that can propagate in longitudinally invariant structures. In the finite difference method, a waveguide cross-section is divided with a rectangular grid of points which may be of constant or variable spacing, and the Helmholtz equation is discretized by the usual five-point Taylor series formula. The beam propagation method (BPM) is the most widely used propagation technique for modeling integrated and fiber-optic photonic devices. The BPM automatically includes effects of both guided and radiation fields as well as mode coupling and conversion. The finite-difference time-domain method is a widely used propagation solution technique in integrated optics, especially in photonic crystal device simulations.
