Fabry-Pérot (FP) etalons are used as filters and sensors in a range of optical systems. Often FP etalons are illuminated by collimated laser beams, in which case the transmitted and reflected light fields can be calculated analytically using well established models. However, FP etalons are sometimes illuminated by more complex beams such as focussed Gaussian beams, which may also be aberrated. Modelling the response of FP etalons to these beams requires a more sophisticated model. To address this need, we present a model that can describe the response of an FP etalon that is illuminated by an arbitrary beam. The model uses an electromagnetic wave description of light and can therefore compute the amplitude, phase and polarization of the optical field at any position in the system. It can also account for common light delivery and detection components such as lenses, optical fibres and photo-detectors, allowing practical systems to be simulated. The model was validated against wavelength resolved measurements of transmittance and reflectance obtained using a system consisting of an FP etalon illuminated by a focussed Gaussian beam. Experiments with focal spot sizes ranging from 30 µm to 250 µm and FP etalon mirror reflectivities in the range 97.2 % to 99.2 % yielded excellent visual agreement between simulated and experimental data and an average error below 10% for a range of quantitative comparative metrics. We expect the model to be a useful tool for designing, understanding and optimising systems that use FP etalons.

Fabry-Perot (FP) etalons are used as filters and sensors in a range of optical systems. The reflected and transmitted fields associated with an FP etalon have traditionally been predicted by the Airy function, which assumes a plane wave illumination. FP etalons are, however, often illuminated by non-collimated beams, rendering the Airy function invalid. To address this limitation, we describe the angular Airy function which calculates the reflected and transmitted fields for arbitrary illumination beams, using angular spectrum decomposition. Combined with realistic models of the experimental illumination beams and detection optics, we show that the angular Airy function can accurately predict experimental wavelength resolved intensity measurements. Based on the angular Airy function, we show that the fundamental operating principle of an FP etalon is as an angular-spectral filter. Based on this interpretation we explain the asymmetry, broadening and visibility reduction seen on wavelength resolved intensity measurements from high Q-factor FP etalons illuminated with focused Gaussian beams.

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.

A numerical model of Gaussian beam propagation in planar Fabry-Perot (FP) etalons is presented. The model is based on the ABCD transfer matrix method. This method is easy to use and interpret, and readily connects models of lenses, mirrors, fibres and other optics to aid simulating complex multi-component etalon systems. To validate the etalon model, its predictions were verified using a previously validated model based on Fourier optics. To demonstrate its utility, three different etalon systems were simulated. The results suggest the model is valid and versatile and could aid in designing and understanding a range of systems containing planar FP etalons. The method could be extended to model higher order beams, other FP type devices such as plano-concave resonators, and more complex etalon systems such as those involving tilted components.

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Fabry-Pérot etalon-based ultrasound detectors are typically interrogated with a focused Gaussian beam in order to achieve a desired acoustic element size. However, tightly focused Gaussian beams lead to beam 'walk-off' within the etalon cavity which reduces sensitivity. In previous work, the planar geometry of the Fabry-Pérot etalon has been replaced by a curved geometry matched to the interrogation beam geometry, thus preventing walk-off. In this work we instead propose using propagation invariant Bessel beams, thus matching the beam geometry to that of the planar etalon geometry, to reduce beam walk-off and increase sensitivity. Increased sensitivity may extend the imaging depth of Fabry-Pérot ultrasound detection systems and may thus enable photoacoustic imaging to access a range of deep tissue imaging applications.

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An open source package for performing full-wave simulation of light propagation in optical systems is presented. The package includes pre-defined functions to model specific optical components. Optical systems are modelled simply by combining these functions. We outline its implementation and show examples of possible applications.