Optical single-angle plane-wave transmittances/reflectances from Schwarzschild objective variable-angle measurements

Abstract

Photonic crystal structures and other nanoscale and microscale optical structures are centrally important to future device technology. The fundamental infrared single-angle plane-wave experimental characterization of these structures is needed to evaluate the analysis, design, and fabrication progress on these devices. The very small sizes of these devices necessitates focusing the infrared probe light typically with a Schwarzschild reflecting objective. The small spot size inherently requires the large range of incident angles associated with the objective. In this work, a variable-angle measurement method is presented for obtaining the optical single-angle plane-wave transmittances/reflectances. The primary steps in this method are (1) calculating the reference sample single-angle plane-wave transmittance/reflectance, (2) measuring the composite transmittances/reflectances of a reference sample over a range of objective angles of incidence, (3) calculating the intensity-angular-weighting coefficients for the objective using the Moore–Penrose (overdetermined linear equations) matrix inversion technique, (4) measuring the composite transmittances/reflectances of a sample-under-test over a range of objective angles of incidence, and (5) calculating the single-angle plane-wave transmittances/reflectances using the Moore–Penrose matrix inversion technique.