Guiding Light by and beyond the Total Internal Reflection Mechanism

Photonics plays an important role in modern technologies, e.g. in telecommunications and sensing systems. Waveguiding structures with microand nano-meter scale features are the basic building blocks of photonic circuits. Large varieties of structures have been used by scientists and engineers. These range from the conventional planar and channel waveguides, which work on the basis of the total-internal-reflection (TIR) mechanism, to the more advanced structures that utilize the anti-resonance-reflection, leaky-defect-resonance, and photonic-band-gap principles to (quasi-)confine and control the light. More and more complicated structures are emerging along with the development of both theory and fabrication technologies, leading to the improvement of existing applications and enabling access to many new application areas. As the fabrication of these devices usually involves costly facilities and time-consuming procedures, modeling tools are indispensable to explore new ideas, characterize and design the devices before their realization, as well as to understand the experimental results. This thesis reports a series of techniques the author has developed to model various waveguiding structures, including the conventional planar and channel waveguides working by, and the advanced structures working beyond the TIR mechanism. Hence, this thesis contains both the methods and their applications to model and study the standard guided-wave and the advanced leaky-wave structures. The methods include mode solvers based on finite difference method (FDM) and finite element method (FEM), furnished with transparent boundary conditions (TBCs) for both guided and leaky modes. Based on the developed techniques, structures as simple as planar waveguides up to as complicated as photonic crystal fibers (PCFs) can be modeled rigorously. For structures with 1-D cross-section, both FDM and FEM mode solvers have been developed. For the FDM, a special discretization scheme that takes into account both the permittivity gradients and discontinuities at interfaces between different graded-index anisotropic materials of planar structures, has been developed and applied to structures with complicated index profiles like the titanium-indiffused proton-exchanged LiNbO3 waveguides. For the FEM, either the one based on the variational or Galerkin approaches, simple high-order schemes capable to give 4or