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.
Highlights
Ideal Fabry-Perot (FP) etalons are composed of two parallel mirrors which form an optical cavity [1]
The model was used to perform a series of parametric studies to provide insight about the impact that an angle between the FP mirrors has on the Interferometer Transfer Function (ITF)
We have presented a full wave model for calculating the propagation of arbitrary optical fields inside non-parallel FP etalons
Summary
Ideal Fabry-Perot (FP) etalons are composed of two parallel mirrors which form an optical cavity [1]. The model was used to compute the effect of the angle between mirrors on the ITF from a single FP design This model has the advantage of being valid for arbitrary incident beams, but requires the evaluation of a two-dimensional Fourier transform to switch between angular spectrum and spatial field representations, for each simulated light round trip inside the cavity. The field is always described as an angular spectrum and no two-dimensional Fourier transforms are evaluated in the iterative stage of the algorithm This significantly reduces the computation time of our model compared to that of Lee et al. By using an angular spectrum description, the model remains valid for arbitrary incident beams, and the mirrors may be described based on their layered refractive index distribution and thickness, or as idealised interfaces with a specified reflectivity. Guidelines about the maximum angle between the FP mirrors which can be tolerated, whilst still achieving high peak transmissivity and sensitivity, are presented, as a function of mirror reflectivity, cavity thickness and the Gaussian beam waist
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