We demonstrate nondefect mid-infrared waveguides based on the self-collimation effect in photonic crystals (PhCs). Due to the spatial dispersion properties serving to confine and route light, propagation loss as low as 2.56 dB/mm is obtained in a silicon-on-insulator (SOI)-based waveguide. The efficiency, together with their ability of arbitrary and structureless routing of electromagnetic beams, of these self-collimation devices provide a potential candidate for miniaturizing devices.
Techniques for analyzing symmetric and asymmetric polarized modes in coupled photonic crystal waveguides are presented. The techniques employed include the plane wave method (PWM) and the finite-difference time-domain (FDTD) method. Two variants of a photonic crystal directional coupler consisting of air holes in silicon are discussed. Additionally, fabricated photonic crystal directional couplers are characterized and experimental results are presented. Applications for photonic crystal directional couplers include frequency-selective filters, dispersion compensators, and optical switches.
A realizable optimal weighted minimum average correlation energy (MACE) filter with arbitrary spatial light modulator (SLM) constraints is presented. The MACE filter can be considered as the cascade of two separate stages. The first stage is the prewhitener which essentially converts colored noise to white noise. The second stage is the conventional synthetic discriminant function (SDF) which is optimal for white noise, but which uses training vectors subjected to the prewhitening transformation. So the energy spectrum matrix is very important for filter design. New weight function we introduce is used to adjust the correlation energy to improve the performance of MACE filter on current SLMs. The action of the weight function is to emphasize the importance of the signal energy at some frequencies and reduce the importance of signal energy at some other frequencies so as to improve correlation plane structure. The choice of weight function which is used to enhance the noise tolerance and reduce sidelobes is related to a priori pattern recognition knowledge. An algorithm which combines an iterative optimal technique with Juday's minimum Euclidean distance (MED) method is developed for the design of the realizable optimal weighted MACE filter. The performance of the designed filter is evaluated with numerical experiments.