Angular Airy function: a model of Fabry-Perot etalons illuminated by arbitrary beams

Area of Science:

• Optics and Photonics
• Optical Engineering
• Spectroscopy

Background:

• Fabry-Perot (FP) etalons are crucial optical components used as filters and sensors.
• Traditional analysis using the Airy function assumes plane wave illumination, which is often not experimentally valid.
• Non-collimated or focused beams lead to inaccuracies with the standard Airy function.

Purpose of the Study:

• To develop a model for predicting the performance of FP etalons under arbitrary illumination conditions.
• To introduce the angular Airy function for accurate optical system modeling.
• To provide a new interpretation of FP etalon operating principles.

Main Methods:

• Angular spectrum decomposition was employed to analyze non-collimated beams.
• The novel angular Airy function was derived to calculate reflected and transmitted fields.
• Experimental illumination beams and detection optics were realistically modeled.
• The angular Airy function was validated against experimental wavelength-resolved intensity measurements.

Main Results:

• The angular Airy function accurately predicts experimental measurements for FP etalons with arbitrary illumination.
• The fundamental operating principle of an FP etalon is identified as an angular-spectral filter.
• The model explains asymmetry, broadening, and reduced visibility in high Q-factor FP etalons under focused Gaussian beams.

Conclusions:

• The angular Airy function provides a more accurate and versatile tool for FP etalon analysis.
• Understanding FP etalons as angular-spectral filters offers new insights into their behavior.
• This work enhances the design and application of FP etalons in optical systems with non-ideal illumination.