We present a filter design formalism for the synthesis of coupled-resonator optical waveguide (CROW) filters. This formalism leads to expressions and a methodology for deriving the coupling coefficients of CROWs for the desired filter responses and is based on coupled-mode theory as well as the recursive properties of the coupling matrix. The coupling coefficients are universal and can be applied to various types of resonators. We describe a method for the conversion of the coupling coefficients to the parameters based on ring resonators and grating defect resonators. The designs of Butterworth and Bessel CROW filters are demonstrated as examples.
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