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Design of the liquid crystal band-pass optical filter

Dispersion of the refraction indices n (λ) as well as dispersion of the imaginary part of the refection coefficient r = r0*exp(-iφR(λ)) have to be determined to design band-pass Fabry-Perot filter. In the case when liquid crystal is placed in the filter gap then both ordinary and extraordinary indices have to be determined. Consequently one must find imaginary part of the coefficient r for ordinary and extraordinary waves transmitted by the filter. Imaginary part of the refraction coefficient is called also phase of reflection. Proposed method exploits a Fabry-Perot filter to obtain examined values. It has been proved that both values, phase of reflection, and refraction indices must be determined in the same procedure from data obtained in the same measurement. The procedure consists of: determination of the transmission peaks position in the Fabry-Perot filter spectrum; nonlinear fit procedure which optimize dispersions of the n(λ), and φR(λ) to minimize the differences between theoretical and experimental transmissions of the filter; simulation of the free spectral range (FSR), and finesse of the filter spectrum in dependence on dispersions of n(λ), and φR(λ). Results have been presented in the case of four different liquid crystal substances and two different mirrors applied in the filter. The way for determination of the φR (λ) seems to be interesting as this value is really hard to measure. Presented data for the examined liquid crystals are also new.