Advances in the Spectral Index method for the analysis of photonic integrated circuits
The prolific rate at which advances in photonics have been made in recent years has increased the need for accurate and efficient computer aided design tools. New device technologies and material systems mean the designer is faced with many more degrees of freedom with which to optimise a design. Because of this versatile techniques that yield results accurately and quickly are foremost in the designers mind. Throughout this work a well proven technique, the Spectral Index (SI) method is extended and generalised to a wide variety design situations of practical importance. The design of a novel Silicon Germanium based device was used to prove the suitability of an iterative design methodology in developing and optimising practical waveguiding components. The novel development of the SI method for the accurate analysis of waveguide losses is then presented further extending its suitability to the analysis and design of rectangular rib waveguides. Following this the generalisation of the SI method to structures of non-rectangular cross-section is presented allowing for the analysis of a wider range of optical rib waveguides. A novel implementation of the SI method is then developed for the analysis of the whispering gallery class of resonant modes supported by cylindrical dielectric disc and ring structures, allowing for the characterisation of the optical properties of this important class of devices. A 3D circuit analysis technique based upon a robust implementation of the SI method in its complex form is developed that allows for the characterisation of any waveguide system that may be represented by a number of discrete waveguide components. Finally the SI method is generalised to the full 3D exact analysis of optical waveguiding structures.