Light pulse propagation in three-dimensional photonic crystals
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Light pulse propagation in three-dimensional photonic crystals H.Kitano, F.Minami, T.Sawada1, S.Yamaguchi2 and K.Ohtaka2 Department of Physics, Tokyo Institute of Technology, Meguro-ku, Tokyo 152-8551, Japan 1 National Institute for Materials Science, Tsukuba, Ibaraki 305-0044, Japan 2 Center for Frontier Science, Chiba University, Chiba 263-8522, Japan ABSTRACT The phase characteristics of transmitted optical pulses in three-dimensional photonic crystals were investigated in the frequency and time domain by using the spectrally resolved cross-correlation technique. The temporal evolution of femtosecond pulses passing through polystyrene colloidal crystals exhibits a large phase distortion near the stop bands. The phase discontinuity around the band gap was observed in the frequency-domain. The phase of the transmitted pulses is found to change by π across the band gap. The dispersion curve estimated from the phase shift shows good correspondence with those calculated from a photonic band calculation. The group velocity significantly slows down near the stop bands. A large change of the group velocity dispersion is also observed near the band edges. These results are in good agreement with the band theory.
INTRODUCTION Photonic band gap (PBG) or photonic crystals are artificially manufactured periodic dielectric structures with lattice constants of the order of the wavelength of light [1]. Their periodicity gives rise to photonic band structures, analogous to electronic band structures, and does not allow propagation of electromagnetic waves for a certain range of frequencies, forming stop bands. The propagation of electromagnetic waves is strongly modified when the frequency of the waves is close to the stop bands. In particular, information on the phase distortion of transmitted electromagnetic waves is important because the dispersion relation ω(k) between frequency ω and wave vector k of propagating wave is directly connected to the frequency dependence of the phase shift [2-5]. In this paper, we present the intensity and the phase of light propagating through a three-dimensional optical photonic crystal fabricated from a colloidal suspension of polystyrene microspheres. The colloidal crystal, which has a lattice spacing comparable to the wavelength of light, does not exhibit a complete photonic band gap, because the concentration and the index of refraction of the polystyrene spheres relative to water are not sufficiently high. However, this crystal is very useful in studying PBG effects seen only in particular directions [6]. The experiments were based on a new phase-sensitive spectroscopic method: the frequency-resolved optical gating (FROG) which was recently developed to characterize phase properties of the laser pulses [7]. In the FROG method, a nonlinear auto-correlation signal is spectrally resolved, and from this datum both of the phase and the intensity of the light field are reconstructed. We applied this technique to a spectrally resolved second harmonic cross-correlation (SHG-cross FROG). We determ
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