Abstract
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.
Highlights
Photonic crystals (PCs) are periodic structures of dielectric material that can reflect light with high efficiency due to optical interference effects; this allows PCs to bend and control light with high precision
PCs can be designed to have forbidden optical frequency bands that are known as photonic band gaps (PBGs)
The results are compared to the photonic band structure calculated through a finite difference frequency domain (FDFD) model to compare the reflectivity spectrum with the photonic band structure
Summary
Photonic crystals (PCs) are periodic structures of dielectric material that can reflect light with high efficiency due to optical interference effects; this allows PCs to bend and control light with high precision. Others have made use of semi-infinite models to study PC properties, but none of these investigates the precise effect on the number of periods relative to reflection spectra.[41,42,43] This work introduces a useful model to calculate the reflectivity spectrum for a 2-D PC with a finite number of periods in one dimension and an infinite periodicity in the perpendicular direction. The effects of varying the situational parameters (polarization, material properties, number of periods, and so on) can be investigated, as demonstrated in this work. The results are compared to the photonic band structure calculated through a FDFD model to compare the reflectivity spectrum with the photonic band structure
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