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A method for designing optical-waveguide band-rejection filters is presented that allows side-lobe levels to be reduced by several orders of magnitude while the rolloff rate of the response characteristics is not appreciably degraded. The method is based upon the control of the shape of the perturbation-amplitude envelope. We discuss in detail the particular case where the coupling coefficient of the waveguide filter takes the form of a modified raised cosine function along the length of the waveguide. Side-lobe level and rolloff can be traded off by appropriately choosing the index p of the function. Design curves are included that allow the optimization of filter responses for side-lobe levels or rolloff characteristics.
Matsuhara et al. (1974) studied this question.