This work involves the development of a finite-element method model to examine the optical properties of two-dimensional photonic crystals (PCs). The model is capable of studying the effect of a finite number of periods in a PC structure. The new design minimizes computational resources by modeling a PC with one infinite dimension with periodic boundary conditions while modeling the second with finite dimensions. This allows for calculation of transmission and reflection spectra across the PC structure. A finite difference frequency domain (FDFD) model has been created for calculation of the photonic band structure. This is compared with the reflection spectra obtained through the reflection model and is found to closely match. The reflection model capabilities are demonstrated by calculating the reflection spectrum for various parameters: period length, number of periods, incident light polarization, and material properties. Effects of varying these parameters are demonstrated. For example, the reflectivity of a GaAs/Air PC was found to reach greater than 95% when the PC has 10 periods; it exceeds 99% with 13 periods and reaches 99.9% at 15 periods.
This work investigates the significance of the number of periods in two-dimensional photonic crystals. Models have been developed to study various photonic crystal properties (Reflection, Photonic crystal band gap). The numbers of photonic crystal periods, length of periods, and material properties have been investigated to determine their effect on the losses in the waveguide. The model focuses on a square period and has been designed to study transmission properties and the effects of period length. A finite difference frequency domain (FDFD) model has also been created to calculate the photonic band structure. Additionally, a simplified study focuses on the transmission of light through photonic crystal layers.
Diatom algae are single-celled, photosynthetic organisms with a cell wall called a frustule—a periodically patterned
nano-structure made of silica. Throughout the last decade, diatom frustules have been studied for their potential uses as
photonic crystals and biomimetic templates for artificially developed metamaterials. A MATLAB program
characterizing their pore structure as a function of angle was developed, potentially giving insight into how their
geometric characteristics determine their optical properties.