Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures

We present a numerical study of second-harmonic (SH) generation in a one-dimensional, generic, photonic band-gap material that is doped with a nonlinear ${\ensuremath{\chi}}^{(2)}$ medium. We show that a 20-period, 12-\ensuremath{\mu}m structure can generate short SH pulses (similar in duration to pump pulses) whose energy and power levels may be 2--3 orders of magnitude larger than the energy and power levels produced by an equivalent length of a phase-matched, bulk medium. This phenomenon comes about as a result of the combination of high electromagnetic mode density of states, low group velocity, and spatial phase locking of the fields near the photonic band edge. The structure is designed so that the pump pulse is tuned near the first-order photonic band edge, and the SH signal is generated near the band edge of the second-order gap. This maximizes the density of available field modes for both the pump and SH field. Our results show that the ${\ensuremath{\chi}}^{(2)}$ response is effectively enhanced by several orders of magnitude. Therefore, mm- or cm-long, quasi-phase-matched devices could be replaced by these simple layered structures of only a few micrometers in length. This has important applications to high-energy lasers, Raman-type sources, and frequency up- and down-conversion schemes.