One-and two-dimensional porous silicon photonic crystals: Momentum dispersion relations and stopbands analysis

We report on a novel approach to analyze and measure the optical properties of one-and two-dimensional photonic crystals (PCs) in all spatial directions inlcluding the symmetry axis of the PCs. The analysis is based on calculating momentum dispersion relations between the ordinary and the Bloch components of the wavevector and finding momentum stop-bands of the PC. This method provides a direct way to analyze the angular dependence of the reflection and the diffraction pattern of a monochromatic optical beam approaching the PC. Measurements have been performed on 1D PCs, e.g., 1D periodic structures of micro-porous silicon and 2D periodic arrays of macro-porous silicon. The periodicity of these PCs is about 2.5 to 4 μm so that their momentum stop-bands fall in the mid-infrared (IR) wavelengths. We analyze several geometries, including slabs and prisms, to map the momentum dispersion relations and stopbands associated with guided and radiation modes. Angular reflection and diffraction measurements using a tunable CO₂ laser showed a good agreement with the calculated momentum dispersion relations. Image Presented.