In this paper we discuss the conditions to obtain the enhancement of second harmonic generation in a two-dimensional circular photonic crystal AlGaAs cavity. The photonic crystal circular cavity offers the possibility of having high-Q resonance modes with respect to those obtained with other types of photonic crystal lattices. The crystallographic cut of the AlGaAs provides a strong nonlinear coupling between a transverse-magnetic (TM) polarized resonant mode at the fundamental wavelength and a transverse-electric (TE) polarized resonant mode at second harmonic wavelength. The double resonance condition leads to a strong improvement of the second harmonic generation process. A preliminary linear analysis has been performed by using the finite-difference time-domain method, which includes the dispersive response of the material, modeled using the well-known one-pole pair Lorentzian function.

A two-dimensional, photonic-crystal microcavity is proposed in order to achieve efficient second-harmonic generation in the third optical communication window. The simultaneous resonance conditions of the pump beam at the fundamental frequency and second-harmonic field generated inside the structure with a defect provides a considerable enhancement of the conversion efficiency. In the configuration we propose, a transverse-magnetic (TM) polarized beam resonating at the fundamental frequency generates a second-harmonic field corresponding to a transverse-electric (TE) polarized resonant mode. The design of this doubly resonant microcavity is carried out by a linear analysis to search for the resonance frequencies and calculate their field distributions. The nonlinear analysis of the second-harmonic generation is performed using a dispersive finite-difference time-domain code.