Abstract

The infinite square lattice of coupled microring optical resonators is studied for what we belive to be the first time. Using the standard matrix formalism and the classical Bloch’s theorem for propagation in periodic optical media, the dispersion equation and the amplitudes of propagating Bloch modes are derived analytically. It is found that the dispersion equation $\omega (k_x,k_y)$ of this 2D microring array is expressed as the sum of two independent dispersion equations of the 1D microring array with wavenumbers $k_x$ and $k_y$. As a result, the width of the passband is twice that of a microring coupled-resonator optical waveguide and there are no stop bands for an interresonator power coupling ratio greater than $1∕2$. The evanescent modes that are important to the analysis of lattices with interrupted periodicity are also studied. The reported analysis is the prerequisite to the future study of superresonators consisting of large finite microring arrays.

© 2008 Optical Society of America

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