Quadratic phase matching in slot waveguides

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 $\mathrm{AlGaAs}$ 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.