Modelling of transmission for a stack of two Fizeau wedges with matched parameters

Abstract

A conventional Fizeau wedge (FW) is built of two flat reflecting surfaces inclined at a small angle. They form a gap with linearly increasing thickness normally to the wedge ridge. Such FWs with apex angles of 5–100 microradians and 5– 1000 micrometers thickness find application in optical metrology, spectroscopy and laser spectral control. The apex angle, the reflection coefficients and the refractive index in the gap form a unique interference pattern on both FW’s sides. To benefit from a large free spectral range of thin wedges and high spectral resolution of thick wedges, recently we proposed a stack of two FWs with matched parameters. Matching provides the same change of the resonant wavelength at the same lateral displacement of both wedges. The aim of this study is to develop a technique for calculation of the resultant transmission of the stack of two matched wedges at plane wave illumination that is based on determination of the number and optical path differences of the rays leaving the stack at a given point on its rear surface. Only rays with non-negligible contribution as an amplitude are taken into account. Numerical simulation and experimental verification are provided.