Second Harmonic Generation and Nonlinear Frequency Conversion in Photonic Time-Crystals

TL;DR

This paper investigates second harmonic generation in photonic time-crystals, revealing conditions for enhanced nonlinear conversion without phase matching, leading to exponential growth of harmonics driven by temporal modulation.

Contribution

It introduces a phase matching condition for SHG in time-crystals and demonstrates exponential harmonic growth without the need for resonance or thresholds.

Findings

Enhanced second harmonic generation occurs without phase matching.

Exponential growth of higher order harmonics is observed.

The process is robust and driven by temporal modulation.

Abstract

We study the nonlinear process of second harmonic generation in photonic time-crystals, materials with refractive index that varies abruptly and periodically in time, and obtain the phase matching condition for this process. We find conditions for which the second harmonic generation is highly enhanced even in the absence of phase matching, governed by the exponential growth of the modes residing in the momentum gap of the photonic time crystal. Additionally, under these conditions, a cascade of higher order harmonics is generated at growing exponential rates. The process is robust, with no requirement for phase-matching, the presence of a resonance or a threshold, drawing energy from the modulation.