Spectral characteristics of the Fabry-Perot interferometer transmission upon illumination by an arbitrary light beam

TL;DR

This paper develops a comprehensive method to analyze how the spectral transmission of a Fabry-Perot interferometer varies with arbitrary incident light beams by decomposing the incident field into angular spectra and deriving related transfer functions.

Contribution

It introduces a general approach to account for the incident beam's spatial characteristics in FPI spectral analysis, including formulas relating coherence functions and angular power spectra.

Findings

Derived expressions for FPI transfer functions and point-spread functions.

Showed how beam divergence affects FPI transmission properties.

Validated results with calculations for Gaussian and conical beams.

Abstract

It is known that spectral properties of the Fabry - Perot interferometer (FPI) depend on the spatial characteristics of the incident radiation. This paper proposes a general method for taking this dependence into account, based on the decomposition of the incident field into the angular spectrum of plane waves, which are the FPI eigenfunctions. In the scalar approximation, the angular-frequency transfer function and the point-spread function (Green function) of the FPI are calculated, which enables to relate the spatial coherence functions of the incident and transmitted radiation and to derive an expression for the output intensity I(r, k) and for the integral transmittance P(k) depending on the wavenumber of the incident monochromatic radiation k. In the resulting expressions, I(r, k) is completely determined by the Fourier transform of the input coherence function, and P(k) is determined by the angular power spectrum (APS) of the incident radiation. For beams of small divergence and high-quality FPIs, simplified formulas have been obtained that allow, in the first approximation, for the dependence of the FPI parameters on the angle of incidence and on the radiation wavelength. Analysis of the expressions obtained makes it possible to clarify an exact meaning of the well-known regularities in the distortions of the FPI transmission band associated with the incident beam deviation from the plane wave (shift to the shortwave region, broadening, reduction of the maximum transmittance and the appearance of asymmetry). As examples, calculations of the integral transmittance for three types of APS, corresponding to Gaussian and conical beams, and the output intensity distribution I(r, k) for the input beam with a Gaussian APS are performed. Results are consistent with other theoretical and experimental works.