Numerical modeling of nanophotonic crystal waveguides and waveguide devices - Khoo, Eng Huat (2010)
The objective of this thesis is to construct numerical models for various characteristics of nanophotonic crystals (PCs) waveguide based on its geometrical variation and surface perturbation. The first major work of this thesis is to improve the coupling efficiency to the narrow single mode PC waveguide (PCWG) by using PC tapered waveguide (PCTW). The tapered curvature is designed to have either linear or nonuniform shape. The curvature of the PCTW is varied by a parameter, alpha. For alpha > 1 (and alpha < 1), concave (and convex) PCTW is solved respectively whereas alpha = 1 gives the linear structure. A numerical model based on the modified step-theory is developed to calculate the transmission efficiency of the various PCTW curvatures. This numerical model is computationally efficiency and sophisticated enough to include the essential field physics for the simulation of field propagation in PCTW. The numerical results show that an average coupling efficiency of greater than 97 % at alpha = 0.5 is obtained for a short taper length of 36a, where a is the lattice constant. The coupling efficiency is higher and the shorter length is much shorter compared to the previous PCTW designs. The coupling mechanisms and loss characteristics in various tapered curvatures are also discussed. To have an in-depth understanding of the coupling mechanism and the behavior of the interaction between the modes in the tapering section, a set of coupling equations is derived from the Maxwell's equation based on the step theory. The newly developed theory, called the exact step-coupling-theory can describe the coupling mechanism and modal interaction behavior between the propagating modes occurred in waveguide structures with geometrical variation. The exact step-coupling-theory is better than the modified step-theory and other previous semi-analytical model because it allows flexibility in the mode characterization as well as in-depth understanding of the modal behavior in the tapering section. The coupling equations are analyzed in detail to obtain a comprehensive knowledge of the mode coupling and interaction behavior in the tapering section.