We propose a structure for ideal 3-dB splitters –combiners in photonic crystals. In photonic crystals, ideal 3-dB splitters based on a three-port system are achievable in principle, but it is impossible to achieve ideal 3-dB combiners based on the three-port system because there is no path for a loss, owing to strong confinement of photons. The proposed structure is based on a four-port system in which the concept of a microwave circuit, the so-called rat-race circuit is adopted. Design conditions for two-dimensional photonic-crystal-based rat-race circuits have been investigated by use of the coupled-mode theory in time. With the proposed structure, a 3-dB splitter–combiner has been designed. The performance of the device was numerically calculated by the finite-difference time-domain method.
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