Low-threshold laser oscillation due to group-velocity anomaly in a two-dimensional photonic crystal

Because of the periodic modulation of their dielectric constants, the dispersion relations of electromagnetic eigenmodes in photonic crystals are quite different from those in uniform materials. For example, extremely small group velocities can easily be realized at the band edges of the dispersion curves. Then, we can expect an enhancement of stimulated emission for those eigenmodes with small group velocities because the interaction time between radiation field and matter is long. Sakoda (1998) previously presented an analytical expression for the enhancement factor and reported that the enhanced stimulated emission takes place more efficiently for those eigenmodes characterized by their group-velocity anomaly, that is, a phenomenon that the group velocity of a band becomes small over its entire spectral range irrespective of the degree of the spatial modulation of the dielectric constant. The group velocity anomaly is peculiar to two- and three-dimensional photonic crystals and absent for one-dimensional ones. Because quite a large enhancement of stimulated emission is expected even for specimens with very small thickness, the experimental observation of the enhancement does not seem difficult. Here, we show that the threshold of laser oscillation is quite low for those eigenmodes with the group-velocity anomaly in comparison with ordinary eigenmodes.