Simple optimization technique for optical filters synthesis
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Abstract
A recent analytical approach to synthesis is employed to arrive at a simple optimization scheme. The approximate solution of the synthesis problem is derived in terms of the Fresnel amplitudes at each boundary. The set of dielectric materials to be used in the design defines the set of possible Fresnel amplitudes. These values are matched to the approximate solution and the necessary distribution of the materials and their thicknesses are deduced. The approach can be done graphically by plotting the analytic (ideal) solution (Fresnel amplitudes vs thickness) and then draw horizontal lines corresponding to the available Fresnel amplitudes. The intersection of the two curves yields the appropriate Fresnel amplitudes and film thickness. Once the Fresnel amplitudes are known, the refractive indices can be easily deduced.