Development of a mathematical model of a collinear filter based on Quartz (SiO2) and its practical implementation

Purpose of the work. Development and testing of a theoretical model of an acousto-optic quasi-collinear tunable filter on crystalline quartz, operating in the spectral range of 0.25-0.4 microns with a spectral resolution of 0.2 nm. Methods. The paper analyzes the basic properties of acousto-optic tunable filters based on crystals of various classes. Based on literature analysis and calculations, an experimental AOTF model was proposed and practically implemented. The study of the physical properties of light filtration on an α-SiO2 crystal was carried out using an experimental method. Practical studies of the spectral tuning of the device at experimental optical frequencies were carried out in the proposed ultrasonic standing wave system in accordance with the tuning characteristic. Based on known experimental data, a theoretical model for describing the passband taking into account piezoelectric effects is proposed. Results. The influence of crystal anisotropy on their acoustoelectric properties is shown. The optimal crystallographic parameters for the operation of filters on a silicon oxide crystal have been determined. A computer model of AOTF has been developed, implemented on the basis of numerical calculations in the Wolfram Mathematica environment. It was experimentally revealed that in the red part of the spectrum under study, the maximum intensity of the frequencies of diffracted light is observed, which corresponds to those closest to the natural frequencies of the piezoelectric transducer, while at the same time, in the blue and violet spectra, the lowest transmission was observed. Practical studies have confirmed that the broadening of the filter passbands occurs due to an increase in the divergence of light. Conclusions. A mathematical model of an acousto-optic quasi-collinear tunable filter on crystalline quartz was substantiated and developed, on the basis of which the calculation of the AOTF operating in the spectral range of 0.25 - 0.4 μm with a spectral resolution of about 0.2 nm was performed.