We have recently introduced a novel method to calculate local dispersion relation based on the Finite-Difference Time-domain
and filter diagonalization method, which is suitable for local study of dispersion in optical waveguide, especially
for the cases of non-periodic, curvilinear, and finite waveguides. In this paper, this approach is applied to study the
photonic crystal waveguides at interfaces and double hetero-structure waveguides. We also studied the stretching effect,
which is increasing the lateral distance between neighboring rods along guiding direction on band gap. Hybrid modes at
interface are results of superposition of existing modes in adjacent waveguides. The results present a clear picture of
localization mechanism of cavity modes and the transmission in the double-hetero-structures.
The Local Density of photonic States (LDOS) and Multiple Multipole Expansion technique (MME) are powerful tools in the study of spontaneous emission and calculation of photon confinement as well as efficient calculation of stationary field in planar photonic crystals. We bridge between optimization of Purcell factor and Q-factor in photonic crystal micro-cavities on one hand, and cavity power loss on the other hand. The quality factor calculated through a pulse response technique based on Finite Difference Time Domain (FDTD) simulations are compared with quality factor calculated by other approaches of LDOS and power loss. It turned out that the latter methods are more accurate and computationally less expensive. The cavity power loss is defined as the surface integration of energy density flow projected toward outside of the effective cavity volume. It is shown that size changes and shifting the neighboring rods or holes have a large impact on the mode volume and confinement. The quality factor optimization is performed for a H1- photonic crystal cavity, and mode volume investigations carried out for high Q factor arrangements. These investigations are resulted in effective structural design rules and geometrical freedom contour plots for the neighboring rods in the vicinity of the micro-cavity. These generalized design rules are suitable for further studies in other photonic micro-cavities.