Photonic crystal is widely used in optical communication. Waveguide is one of important components used in optical communication. The performance of right-angular, cross, and Y shapes photonic crystal waveguide used in optical communication is investigated. Material used for photonic crystal is GaAs. Shape of photonic crystal rod is cylindrical rod. These rods are arranged to become matrix with constant distance. In the photonic crystal matrix, some rods are removed to form waveguide channel. Three shapes of waveguides are discussed. They are right-angular, cross, and Y shapes. The relationship between distances of circular photonic crystals and wavelength in propagation is discussed. Due to coupling of multi physical phenomena and complex geometry, a finite element method software called COMOSL is used to analyze performance of waveguide under different wavelength of light. It is found under different distance of photonic crystal rods array and wavelength, light could propagate along waveguide successfully or lost energy and decay. From results analyzed by COSMOL software, numerical data are obtained to classify light being able to pass waveguide successfully or not. By neural network method, equations between crystal rods array distance and wavelength to decide whether light can propagate through waveguide successfully or not are derived. They can be used to determine performance of light propagating in waveguide. For Y shape waveguide, bifurcation phenomena of light propagate in different channel of Y shape branch is found. It is found under different crystal pillar distance the light of different wavelength would propagate in one of the branch of the Y shape channel. The longer wavelength lights pass the upper channel and the shorter pass the lower. The results show that the bifurcation happens at the tendency if pillar distance increases the bifurcation wavelength also increases. From neural network method, equations to decide light propagate to upper or lower branch of Y shape waveguides are also obtained.

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