Analysing the impact of non-parallelism in Fabry-Perot etalons through optical modelling

Abstract

Fabry-Perot (FP) etalons, composed of two parallel mirrors, are used widely as optical filters and sensors. In certain applications, however, such as when FP etalons with polymer cavities are used to detect ultrasound, the mirrors may not be perfectly parallel due to manufacturing limitations. As little is known about how the mirrors being non-parallel impacts upon FP etalon performance, it is challenging to optimize the design of such devices. To address this challenge, we developed a model of light propagation in non-parallel FP etalons. The model is valid for arbitrary monochromatic beams and calculates both the reflected and transmitted beams, assuming full-wave description of light. Wavelength resolved transmissivity simulations were computed to predict the effect that non-parallel mirrors have on the sensitivity, spectral bandwidth and peak transmissivity of FP etalons. Theoretical predictions show that the impact of the non-parallel mirrors increases with both mirror reflectivity and incident Gaussian beam waist. Guidelines regarding the maximum angle allowed between FP mirrors whilst maintaining the sensitivity and peak transmissivity of a parallel mirror FP etalon are provided as a function of mirror reflectivity, cavity thickness and Gaussian beam waist. This information, and the model, could be useful for guiding the design of FP etalons suffering a known degree of non-parallelism, for example, to optimize the sensitivity of polymer based FP ultrasound sensors.

Fabrication of a Low-Cost, Fiber-Coupled, and Air-Spaced Fabry-Pérot Etalon

“…The parallelism of the spacers determines the parallelism of the etalon mirrors and, hence, influences the finesse 7 . A ½ inch UVFS precision window, as provided in the Materials, with a parallelism of ≤5 arcsecs and a surface flatness of λ/10 over the clear aperture was used in this study.…”

“…The finesse of an ideal plane-parallel etalon is determined by the mirror reflectivities R 1 and R 2 only 3 : However, a real etalon is subject to many losses, which degrade the theoretically achievable finesse 4 , 5 , 6 . Deviation of the mirror parallelism 7 , non-normal incidence of the laser beam, beam shape 8 , mirror surface impurities, and scattering, among others, lead to a reduction in the finesse.…”

Effective transmittance of Fabry–Perot cavity under non-parallel beam incidence

“…[13] Marques et al employed angular spectrum analysis to establish a model and studied the effects of mirror parallelism, planarity and the ITF for Gaussian beam focusing. [14][15][16][17] However, most of these studies focused on laser applications with small divergence angles and normal incidence. [18][19][20] There is relatively limited research on the general case of non-parallel beam incidence, particularly for large divergence angles and tilted beam incidence.…”

Interrogating Fabry-Perot ultrasound sensors with Bessel beams for photoacoustic imaging

“…However, in planar FP sensor, a focused Gaussian beam, required for the small acoustic element size, naturally diverges due to the short depth of focus of focused Gaussian beam. For this reason, ITFs, using focused Gaussian beam interrogation, have reduced contrast and sensitivity when the mirror reflectivities are increased [1]. This challenge can be addressed by changing the shape of the FP cavity to refocus the Gaussian beam in a round-trip basis, as in Plano-Concave Microresonator (PCMR) [2].…”