Effective-index-based matrix method: a computationally simpler alternative to BPM for integrated optics design

The 2D and 3D beam propagation method (BPM) which is now widely used for the design of fiber-optic and integrated-optic components is highly computer-intensive. The matrix method, which is computationally much simpler and faster, was used to analyze 2D planar multi-layer structures. The method has now been applied to 3D channel waveguides by transforming the 2D refractive index profile over the cross-section of the channel waveguide to a 1D effective index profile and discretizing the profile into thin layers. The effective index based matrix method (EIMM) has been used to compute the guided-mode propagation constants, the coupling length of directional couplers and the bending loss in curved waveguides for Ti- indiffused LiNbO3 channel waveguides. The computed results agree closely with available experimental results. The method may also be used to compute field profiles in single and coupled waveguides. A versatile computer software is being developed to implement the above method for the design of optical waveguides and related components/devices on different substrates realized by in-diffusion, ion exchange and other techniques.