Second harmonic generation in planar two-dimensional photonic crystals without out-of-plane losses

Abstract

We are making a study of the out-of-plane losses for the second harmonic generation process in planar twodimensional photonic crystals made from Al 0.3 Ga 0.7 As. We found that for the rhombic symmetry of the lattice it can be obtained a structure in which the out-of-plane losses vanish for both fundamental and second harmonic waves in conditions of very small diffraction for the second harmonic wave and a diffraction close to the one obtained in homogeneous medium for the fundamental wave. INTRODUCTIONThe light wavelength conversion is an important process that it is used in various optical engineering technologies. In general, for converting the wavelength it is used a nonlinear optical process where higher-order polarization generates new frequency components. This conversion process requires the use of highly nonlinear crystals (as Al 0.3 Ga 0.7 As, for example) and the conversion efficiency depends on the input light intensity, phase matching condition and light travelling distance. One way to obtain higher light intensity is to focus the light into a narrow beam (with spot of few light wavelengths) inside the nonlinear material. If the second harmonic (SH) wave, for example, is generated in relatively long nonlinear crystals the region where the beam has its minimum diameter (i.e. maximum intensity) is small compared with the nonlinear material length. Therefore, the efficiency of the conversion process, and in particular of the second harmonic generation (SHG) for such narrow beams is limited in the first place by the diffraction, which is responsible for the transverse spatial broadening of both fundamental wave (FW) and SH wave leading to a decreasing of their top intensities. Another mechanism which is limiting the SHG efficiency for narrow beams is the phase mismatch, as for narrow beams the spatial spectra will be broader and the Fourier components of spatial spectra can be never simultaneously phase matched. Because of these two reasons the parametric coupling between extremely narrow beams is still a challenging problem of wavelength conversion in both bulk and structures nonlinear materials. Moreover, if we are thinking at realistic structures that could be used in experiments, we should take into account also the thickness of the planar structure, which could introduce additional out-of-plane losses.The diffractive broadening of both FW and SH beams could be reduced or even avoided letting the light propagate in a subdiffractive (or self collimation [1]) regime. Subdiffractive propagation is associated with the flattening of spatial dispersion iso-frequency lines of the propagating Bloch modes. It has been shown (by a standard method of harmonic expansion) that for a particular photonic crystal (PC) of square symmetry there are wavelengths at which such flattening occurs in particular spatial directions in certain propagation band [2][3][4][5]. On the other hand the PCs can be made in nonlinear materials and thus they can be used in nonlinear optics, in particular for observation of the efficient ...