The effect of variation of the refractive index and thickness of layers in thin-layer interference filters on their optical parameters

Changes in the refractive index of a medium to be matched and in the matching wavelength upon variation of the refractive indices and thicknesses of layers in thin-layer interference filters (TIF) were studied theoretically (the optical thickness of the layers is smaller than a quarter wavelength) for TIF with two and three layers in a period. New properties of such filters were discovered, in particular, the invariance of these changes with respect to the number of periods when the refractive indices of the layers vary. Simple analytical expressions were obtained that allow an adequate determination of the shift in the parameters under consideration. A computer-aided numerical analysis confirmed the theoretical predictions.