Terahertz wave dispersion in two-dimensional photonic crystals

Square and triangular lattice photonic crystals were fabricated by drilling holes in a methylpentene polymer. The amplitude and phase shift of transmission spectra were independently measured by terahertz time-domain spectroscopy. As the frequency is tuned across a transmission band, it is found that the transmitted wave’s phase changes by $\pi$ for each crystal plane, that is, when there exist n crystal planes along the direction of the incident wave the phase should change by $n\pi$ across the band. The dispersion curves estimated from the phase shifts show good correspondence with those calculated by a plane-wave expansion method. It should be noted that only bands for which the main component of the eigenfunction has wave vector parallel to that of the incident wave are observed by time-domain measurements.