Fourier transform infrared transmission microspectroscopy of photonic crystal structures

The detailed microscopic characterization of photonic crystal (PC) structures is challenging due to their small sizes. Generally, only the gross macroscopic behavior can be determined. This leaves in question the performance at the basic structure level. The single-incident-angle plane-wave transmittances of one-dimensional photonic crystal (PC) structures are extracted from multiple-incident-angle, focused-beam measurements. In the experimental apparatus, an infrared beam is focused by a reflecting microscope objective to produce an incident beam. This beam can be modeled as multiple, variable-intensity plane waves incident on the PC structure. The transmittance of the structure in response to a multiple-incident-angle composite beam is measured. The composite beam measurement is repeated at various incident angle orientations with respect to the sample normal so that, at each angular orientation, the included set of single-angle plane-wave components is unique. A set of measurements recorded over a range of angular orientations results in an underspecified matrix algebra problem. Regularization techniques can be applied to the problem to extract the single-angle plane-wave response of the structure from the composite measurements. Experimental results show very good agreement between the measured and theoretical single-angle plane-wave transmittances.