Enhancement of second harmonic generation in helical Sc liquid crystals

In a ferroelectric liquid crystal, a special type of phase-matching for optical second harmonic generation (SHG) is possible, where two counter-propagating fundamental waves create second harmonic waves at the edge of the selective reflection band. We compute the SHG intensity in such a situation and show that, at slight detuning from exact phase-matching, useful resonance enhancement can be obtained. A considerable amount of SHG also appears when the second harmonic frequency is in the reflection band, where the SHG wave is non-propagating.