Optimum phase for rugate filter synthesis by Fourier transforms

An optimum phase is developed for the synthesis of rugate reflectors by a simple Fourier transform. This phase belongs to a complex function of the desired spectral characteristics and is usually a free parameter. In general, it receives much less attention than the function magnitude, which is not known exactly. The current work shows that phase shaping alone produces surprisingly good results and has other advantages in rugate filter synthesis. In addition, the operating mode of this design procedure is quite unusual and interesting in itself.