Abstract

One of the most interesting aspects related to the χ⁽²⁾ response of PBG crystals is the possibility of greatly enhancing the conversion efficiency of nonlinear processes The enhancement of second harmonic generation (SHG) is perhaps the best example that we could cite, although in general our discussion is valid for multi-wave mixing processes. The processes that we discuss owe their increased efficiency to the simultaneous availability of: (1) exact phase matching conditions, and (2) high localization of the fields with frequencies tuned at transmission resonances near the photonic band edge These conditions were first reported in ref ¹, where it was numerically demonstrated that pumping a 20-periods with a 3 micron pulse, a GaAs/AlAs multilayer stack approximately 5 microns in length could generate short, picosecond SH pulses tuned at a wavelength of 1 5 microns, with power levels enhanced by two to three orders of magnitude with respect to the output from an equivalent length of an exactly and ideally phase-matched bulk GaAs (or AlAs) substrate A necessary condition for efficient nonlinear coupling in any kind of quadratic material is the fulfilment of phase matching For bulk materials, this condition is satisfied when the phase velocities of the interacting fields arc the same In finite PBG structures, phase matching conditions for second harmonic generation have been recently addressed with the introduction of an effective index

© 2000 IEEE