Modal Methods for Modeling and Simulation of Photonic

Abstract

Optical waveguide structures and devices are the fundamental basic building blocks of photonic cireuits which play important roles in modern telecommunication and sensing systems. With the fast development of fabrication technologies and in response to the needs of miniaturization and fast increased functionality in future integrated photonic chips, various structures based on high-index contrast waveguides, surface plasmonic polaritons structures, etc., have been widely proposed and investigated. Modeling and simulation methods, as efficient and excellent cost performance tools comparing to costly facilities and time-consuming fabrication procedures, are demanded to explore and design the devices and circuits before their finalization. This thesis covers a series of techniques for modeling, simulation and design of photonic devices and circuits with the emphasis of handling of radiation wave and the related power couplings. The fundamental issue in optical waveguide analysis is to obtain the complete mode spectrum. In principle, we need the radiation modes to expand the arbitrary fields of an open waveguide. In practice, however, the continuum nature of the radiation modes makes them hard to use. The discrete leaky modes may approximately represent a cluster of radiation modes under some circumstance and can be utilized in mode expansion together with guided modes to significantly simplify the analysis of mode coupling problems in optical waveguides. However, the leaky modes are unbounded by nature and hence lack the usual characteristics of normal guided modes in terms of normalization and orthogonality. Recently a novel scheme for handling of radiation optical fields was proposed and demonstrated by applying perfectly matching layers (PML) terminated with a perfectly reflecting boundary (PRB) condition. In this scheme, the radiation fields are represented in terms of a set of complex modes, some of which resemble the conventional leaky modes and others associated with the interaction between the PML media and the reflecting numerical boundaries. The mode spectrum is therefore split into the guided modes and complex modes which possess the normal mode features such as normalization and modal orthogonality. The seemingly paradoxical application of both the PML and PRB in the new method has in fact overcome one of the main challenges assoiated with this traditional method, i.e., the desire for discrete, orthogonal, and normalized modes to represent radiation fields and the need for elimination and reduction of spurious reflections from the edges of the finite computation window. With the understanding of mode spectrum, a full vector mode matching method and a complex coupled mode method for analyzing the wave propagation in optical waveguides under the framework of PRL and PRB computation model have been proposed. The methods have been validated through various structures such as waveguide facet, polarization rotators, long/short period gratings etc. Then the proposed techniques have been utilized to design a series of waveguide structures based on surface plasmonic polaritons, slot waveguides etc.