A perturbation approach for the design of coupled resonator optical waveguides (CROWs)

We propose a simple and accurate technique for the design optimization of coupled resonator optical waveguides (CROWs). The technique is based on tapering the coupling coefficients at the CROWs stages to achieve arbitrary realizable filter response. A perturbation theory is developed for the linearization of the design problem. The coupling coefficients are expanded around a known mean coupling value. By dumping the higher order perturbation terms, we ignore the effect of multiple reflections among the rings introduced by the small adjustment of the coupling coefficients. This is a first order accurate approach as it takes into account only multiple reflections introduced by the zero order terms. The design problem is then formulated as an optimization problem. The optimal filter design is achieved by solving a constrained linear least square problem. This optimization problem can be solved efficiently to get the global optimal design. Our technique is accurate and efficient compared to other nonlinear approaches. Our technique has been verified using different proposed targeted filter responses utilizing third, fifth, and tenth order coupled ring resonators. Highly selective tenth order filter with flat response is proposed. We compared our results to the existing techniques to prove its accuracy.