Abstract
We investigate the initial buildup characteristics of the wave propagation in waveguides made of sonic crystals or photonic crystals, whose rising time-constant is an important factor for high speed signal processing and also for wave control by such functional wave guides. A sonic crystal made of air circular-cylinders in agar-gel host is shown to have novel and preferable properties for such waveguides. We compare three typical artificial crystals for waveguides, namely sonic crystal A made of an array of acrylic-resin circular-cylinders in air, sonic crystal B of air circular-cylinders in agar-gel, and photonic crystal C of GaAs circular-cylinders in air. Longitudinal acoustic waves alone are assumed to contribute to the guided waves in these sonic crystals. Using the FDTD method for numerical simulations of the wave propagations in these artificial crystals, we have obtained different characteristic behavior among these crystals. For buildup to a steady-state wave propagation in the straight waveguide, (1) sonic crystal A needs about 5 periods, (2) sonic crystal B needs less than a period, and (3) photonic crystal about 3 periods. Sonic crystal B is shown to have novel preferable properties, namely not only quick establishment of the steady-state wave propagation, but also fine confinement of the guided wave in the wave guide with a -133 dB leaky wave outside the crystal, highly decaying evanescent waves, weak Bragg-reflection and small dispersion in the wave guide.
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