By numerically integrating the three-dimensional Maxwell equations in the time domain with reference to a dispersive quadratically nonlinear material, we study second harmonic generation in planar photonic crystal microresonators. The proposed scheme allows efficient coupling of the pump radiation to the defect resonant mode. The out-coupled generated second harmonic is maximized by impedance matching the photonic crystal cavity to the output waveguide.In the early sixties the very first experiments in nonlinear optics were Frankens investigations of traveling-wave second harmonic generation.1 It took a number of years to realize that guided-wave optics and resonators could dramatically enhance phenomena requiring high intensities and tuning of critical parameters.2-4 Since then, both the advent of nano-optics and the technological advances have made new solutions available. Among them, microresonators can certainly be considered among the best candidates for nonlinear optics and frequency generations. [5][6][7][8] In the past few years, photonic crystal (PC) microcavities, i. e. periodic (bandgap) structures hosting a resonant defect, have attracted attention for some of their unique properties.9, 10 In particular, in PC microresonators it is possible to obtain extremely high quality factors (Q) in reduced volumes while tailoring their dispersive features, 11, 12 characteristics which can be exploited to achieve efficient frequency generation with various schemes. [13][14][15][16] The advantages inherent to a high confinement, however, are partially counterbalanced by a difficult energy coupling into the resonators: well isolated resonant states, in fact, correspond to large (external) quality factors of the cavity.
17To this extent, impedance matching has been proposed based on a properly designed coupling to/from the microcavities. 18,19 In this Letter we propose and investigate an efficient outsourcing scheme to maximize frequency doubling from a PC defect. Resorting to a second-order nonlinearity in a large Q photonic crystal microcavity, an optical pump is up-converted to a resonant crosspolarized harmonic signal. Since the device is designed to be nearly transparent to the pump wavelength, input coupling losses are minimized while the out-coupled second harmonic can be maximized by impedance matching. The temporal evolution of the resonant mode at the second-harmonic (SH) can be described and related to the cavity parameters by coupled mode theory in the time domain (CMT-TD):where a SH is the mode amplitude at the SH frequency ω SH , τ SH takes into account both internal (1/τ o ) and external (1/τ e ) losses (1/τ SH = 1/τ o + 1/τ e ), κ is the (three-dimensional) overlap integral between the sus-1