Photonic band gap engineering in two-dimensional photonic crystals and iso-frequency contours

Abstract

We have theoretically investigated photonic band structures of two-dimensional (2D) photonic crystals (PCs) in air background. The lattices consist of the rotated and modified square dielectric rods. The influence of opto-geometric parameters of designed unit-cell structures are analyzed in terms of opening frequency gaps and appearing tilted band graphs by applying plane wave expansion method. Optimum structures with large photonic band gaps are notified. In order to get “gap maps”, the gaps as a function of the size and the rotation angle of the square rods are calculated. So, the band gaps of transverse magnetic and transverse electric polarization modes indicate symmetry in point of the rotation angle and these band gaps overlap. Thus, the smallest width of the narrow air veins is founded as 0.06a. The results show almost 40 nm complete width of the air veins for mid-gap wavelength λ = 1.55 μm. This result shows the fabrication capability of these optimized PC structures.