Periodic bandgap and effective dielectric materials in electromagnetics: characterization and applications in nanocavities and waveguides

The main objectives of this paper are to characterize and develop insight into the performance of photonic bandgap (PBG) periodic dielectric materials and to integrate the results into some novel applications. A powerful computational engine utilizing the finite-difference time-domain technique with periodic boundary conditions/perfectly matched layers integrated with Prony´s method is applied to provide an in-depth look at the physics of PBG/periodic bandgap structures. Next, the results are incorporated into two classes of applications in the areas of nanocavity lasers and guidance of electromagnetic (EM) waves in sharp bends. A two-dimensional PBG structure with finite thickness is presented to strongly localize the EM waves in three directions and design a high-Q nanocavity laser. It is shown that the periodic PBG/total internal reflections remarkably trap the EM waves inside the defect region. The effect of the number of periodic cells and defect´s dielectric constant on the Q of structure is investigated. It has been found that a seven-layer PBG with a dielectric impurity defect can be used in the design of a laser with a Q as high as 1050. Additionally, potential applications of the PBG structures for guiding the EM waves in sharp bends, namely, 90° and 60° channels are demonstrated. It is shown that shaping the bend by introducing small holes can noticeably improve the guidance of the waves at the bends and channel the EM waves with great efficiency. A comparative study between PBG and effective dielectric materials in controlling the EM waves is also provided and it is observed that the novel characteristics of the PBG cannot be modeled using the effective material for the frequencies within the bandgap.