Two-dimensional photonic bandgap reflectors for free-propagating beams in the mid-infrared

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Abstract
We present a detailed study of a 2D photonic bandgap reflector for free-propagating beams in the mid-infrared. The photonic crystal made from macroporous silicon is a triangular lattice of cylindrical holes in bulk silicon. The reflection spectra are measured from ~2.5 to ~14 µm by using a Fourier transform spectrometer equipped with a microscope. A very high reflectivity is measured for the first-order forbidden bands, reaching 98% between 6 and 8 µm in the TE polarization and -M direction. Smaller performances are obtained at short wavelengths. Different causes of degradation are separately considered. The influence of the beam divergence is first analysed by using a 3D plane wave model. We show that the shapes, widths and positions of the higher-order forbidden bands are modified with a divergent beam, but the reflector performances are not degraded too much at short wavelengths. Diffraction losses at the interface are then estimated using a finite-difference time domain model. The crystal termination and orientation is found to have a critical influence, but diffraction losses only manifest themselves at the shortest investigated wavelengths. Finally, a comparative analysis of differently cleaved samples shows that the small roughness of the interface or the hole radius dispersion are actually the prime cause of degradation as long as diffraction effects remain weak.