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Abstract
The relationship between the spatial-frequency parameters of a rough surface with a random profile, which has a Gaussian form of the correlation function, and the amplitude-frequency characteristics of the electric field created by this surface is determined. The numerical determination of the evanescent field optimal configuration formed near the quartz rough surface in the gaseous medium saturated with chlorine molecules when illuminated from the quartz side has been considered. The finite-element approach is used to solve the Helmholtz two-dimensional vector equation. It was found that at the initial stage of photochemical polishing different electrodynamic conditions are created for the etching process depending on the profile height standard deviation value. In particular, when the standard deviation is less than 1 nm, all surface protrusions, for which the spatial spectrum harmonics of the profile are located in the region of the maximum slope of the spectral function, are most actively etched. This leads to a decrease in the effective width of the spatial spectrum of a rough quartz surface and an increase in its correlation length. Therefore, simultaneously with decreasing the height of the protrusions, the surface becomes flatter. The paper shows the different character of quartz surface nano-polishing process conditions depending on the initial standard deviation of the profile height.
Highlights
Optics progress in such areas as fiber optics, holography, and integrated optics and photonics leads to a constant increase in requirements for both the quality of materials and the accuracy of the optical elements manufacture
Us, the objectives of this work are (1) determination of the conditions for the formation of the optimal electric field, at which the most effective local photochemical etching of the sinusoidal surface protrusions will occur, leading to a decrease in its roughness level; (2) calculation of the field contrast directly above the surface of the sinusoidal profile depending on its spatial frequency and the height of the protrusions; and (3) finding the regularities of the influence of the parameters of a random quartz surface described by a Gaussian correlation function on the contrast value of the field formed by these irregularities, depending on the spatial frequency of the surface under consideration
The maxima of the electromagnetic field strength are formed exclusively above the surface protrusions, and the field minima are formed in the troughs, which makes the surface polishing process as efficient as possible, since only the surface protrusions are etched
Summary
Optics progress in such areas as fiber optics, holography, and integrated optics and photonics leads to a constant increase in requirements for both the quality of materials and the accuracy of the optical elements manufacture. Us, the objectives of this work are (1) determination of the conditions for the formation of the optimal electric field, at which the most effective local photochemical etching of the sinusoidal surface protrusions will occur, leading to a decrease in its roughness level; (2) calculation of the field contrast directly above the surface of the sinusoidal profile depending on its spatial frequency and the height of the protrusions; and (3) finding the regularities of the influence of the parameters of a random quartz surface described by a Gaussian correlation function on the contrast value of the field formed by these irregularities, depending on the spatial frequency of the surface under consideration. Where E1 and E2 are the amplitudes of the evanescent field in the regions of protrusions and troughs
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