Second-harmonic generation from 2D photonic crystal waveguide with simultaneous near-flat dispersions at fundamental frequency and second harmonic

Photonic crystal waveguides (PCW) have shown great potential to generate second harmonic (SH), but the available schemes with cavity or defect suffer from a lack of multiple wavelengths operation and excessive phase -matching requirement. Here we propose a 2D PCW structure comprised of a modulated single line defect, which is capable of independently controlling the fundamental frequency (FF) and SH modes. Therefore, two near -flat group velocity dispersions can be achieved for these modes, and they simultaneously satisfy phase matching conditions. Based on multiply scattering method, we theoretically demonstrate that the SH resonant modes originated from the nonradiative near -flat dispersion have high quality factors (nearly 6 .5 x 10(4) for the maximum value). And the maximum SH conversion efficiency for these resonant modes are 2 orders of magnitude higher than that of off -resonant modes. In addition, benefitting from the matching of the group velocities of the second harmonic and the fundamental, the central wavelength of SH can be modulated within wavelength range similar to 3 nm . These results can provide potential applications in on -chip integration of photonics and quantum optics.