We analyze phase matching with reference to frequency doubling in nanosized quadratic waveguides encompassing form birefringence and supporting cross-polarized fundamental and second harmonic modes. In an AlGaAs rod with an air-void, we show that phase-matched second-harmonic generation could be achieved in a wide spectral range employing state-of-the-art nanotechnology. c 2017 Optical Society of America OCIS codes: 190.4360, 190.4390 Since the pioneering work by Franken et al., 1 frequency doubling has been among the most studied nonlinear processes in optics. Conversion efficiency in second harmonic generation (SHG) relates to spatio-temporal overlap of waves at fundamental (FF) and second harmonic (SH) frequencies, as well as to their group and phase velocity matching. For the latter, in order to compensate material and waveguide dispersion, several approaches have been proposed and demonstrated, 2 including birefringent phase-matching (PM), non-critical PM, quasi-PM (QPM) 3 in co-or counter-propagating geometries, including vertical QPM for surface-emitted SHG.
4-7More recently, novel PM schemes for SHG include random quasi-PM, 8 photonic crystals and microcavities,
9, 10as well as form-birefringence in waveguides. 11-14 Formbirefringence conjugates the large intensities and interaction distances of guided-waves with the possibility of tailoring the dispersion of cross-polarized waves even in isotropic crystals such as GaAs and its composites.
12-14It consists in alternating layers with different refractive indices orthogonally to the direction of propagation, such that the harmonics experience distinct eigen-values for TE (quasi-TE) and TM (quasi-TM) polarizations. As in photonic crystals, the degree of birefringence, its dispersion and the achievable PM line-width are directly linked to the index contrast between alternating films and their thicknesses, 15 making film growth a formidable task.14 For these reasons, a nano-sized structure encompassing form-birefringence but realizable with just one nonlinear material should provide significant advantages and versatility over standard approaches for parametric mixing and frequency generation. In this Letter we propose and investigate SHG in a suspended rod-waveguide with a nanometric void, implementing form-birefringence and large modal overlap for efficient upconversion. To achieve the highest index contrast between a quadratically nonlinear semiconductor (AlGaAs) and air (or vacuum), we consider the basic geometry sketched in Fig. 1, with the electric field of the FF mode parallel to the void (i.e., quasi-TM with respect to the top surface) and a cross-polarized (i.e., quasi-TE) SH tightly confined in the air-gap owing to the discontinuity in the electric field normal to the interfaces, the latter separated by v. Fig. 1 also displays the calculated FF and SH lowest-order eigen-profiles of such a slot waveguide, similar to the one recently studied by Xu et al. for ringresonators in SiO 2 . 16 We consider cubic Al 0.3 Ga 0.7 As with indices n F F and n SH...