The effects of periodic modulation in dielectric constants on the formation of photonic band gaps of two-dimensional arrays have been characterized. When a defect is introduced into a perfect photonic crystal, a localized effect may be found at frequencies within the photonic band gap. A line defect thus acts as a waveguide, and a point defect can behave as a resonant cavity. In this report, we investigated photonic crystal structures based on germanium (n =?4.0), silicon (n =?3.49), titanium oxide (n =?2.71), and silica (n =?1.50) materials. Both square lattice arrays and triangular lattice arrays have been studied. The two-dimensional photonic structures exhibited the Mach-Zehnder interferometer function that could be applied to optical switches or optical integrators. The beam splitter had the crossed linear defects shape, constructed by two orthogonal line defects. The ratio of defect radius to the lattice constant was 0.28, and the best moving distance has been 0.76 to achieve equal output energy.
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