Modeling and optimization of complex photonic resonant cavity circuits

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Abstract
The simple method for modeling of circuits of weakly coupled lossy resonant cavities, previously developed in quantum mechanics, is generalized to enable calculation of the transmission and reflection amplitudes and group delay of light. Our result is the generalized Breit-Wigner formula, which has a clear physical meaning and is convenient for fast modeling and optimization of complex resonant cavity circuits and, in particular, superstructure gratings in a way similar to modeling and optimization of electric circuits. As examples, we find the conditions when a finite linear chain of cavities and a linear chain with adjacent cavities act as bandpass and double bandpass filters, and the condition for a Y-shaped structure to act as a bandpass 50/50 light splitter. The group delay dependencies of the considered structures are also investigated.

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