We propose an approach for the design of resonant cavities employed in magnetophotonic crystal (MPC) circulators and isolators. Starting from the analysis of a model circularly symmetric cavity, we show how to obtain a significant splitting of the eigenfrequencies of the two counterrotating cavity modes without introducing subdomains magnetized in opposite directions. Using the multiple-scattering method extended to handle uniaxial gyrotropic materials, we demonstrate numerically an MPC circulator working in a uniform external magnetic field.

By exploiting the concepts of magnetic group theory we show how unidirectional behavior can be obtained in two-dimensional magneto-photonic crystals (MOPhC) with uniform magnetization. This group theory approach generalizes all previous investigations of one-way MOPhCs including those based on the use of antiparallel magnetic domains in the elementary crystal cell. Here, the theoretical approach is illustrated for one MOPhC example where unidirectional behavior is obtained by appropriately lowering the geometrical symmetry of the elementary motifs. One-way transmission is numerically demonstrated for a photonic crystal slice.