High- g -factor phase-matched second harmonic generation near photonic bandgap of polar cholesteric liquid crystals

The discovery of polar liquid crystals, such as ferroelectric and helielectric liquid crystals, provides fascinating platforms for designing and modulating polarisation structures that generate strong second harmonic generation. Here, we report that the helielectric nematics, i.e. the polar cholesteric liquid crystals, realise an unprecedented phase-matching condition for the second harmonic generation in the photonic bandgap. Like the circular dichroism in the linear optical regime, the phase-matched second harmonic generation generated in a helielectric nematic medium exhibits a circular polarisation selectivity in the nonlinear optical regime. The maximum g-factor for the second harmonic generation is over ~ 1.95.