Theoretical And Applicational Study Of One And Two Dimensional Photonic Crystals

In this report, theoretical calculations and computational simulations are both used to study the properties and applications of photonic crystals. The methods include the Transfer Matrix Method, Plane Wave Expansion technique, and Finite Difference Time Domain method, et al. The main research results consist of three parts as listed below:1. The effect of waveguide width on the propagation of self-collimated beams in photonic crystals is studied using the finite-difference time-domain method. It is shown that, to obtain good transmission, it would be better to keep the waveguide width above a minimum value. It is also shown that, waveguide intersections based on the effect of self-collimated beams can provide high throughput and low cross talk simultaneously within a relatively wide bandwidth.2. We propose a method to construct omnidirectional reflectors withwide band gaps by one dimensional photonic crystals, and the main notion is the direct tailor of the projected band structures. Based on our method, much wider omnidirectional band gap can be obtained comparing to the results reported earlier. Furthermore, a general criterion is derived for this method that does not require materials with large indices.3. A Wavelength Division Multiplexer is designed based on one dimensional photonic crystals. When a light beam incidents on a one dimensional photonic crystals with a defect layer, the transmission efficiency of different wavelengths will reach the maximum at different incident angles. By using two of this kind of photonic crystals as reflecting mirrors, it is possible to separate light beams with different wavelengths.