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arXiv:1912.09175 · Physical Review A

Modeling of quasi-phase-matched cavity-enhanced second-harmonic generation

Carlos Mas Arabí, Pedro Parra‐Rivas, Charles Ciret, Simon-Pierre Gorza, François Léo

Published Apr 14, 2020• 5 citations
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Abstract

We propose a mean-field model to describe second-harmonic generation in a resonator made of a material with zinc-blende crystalline structure. The model is obtained through an averaging of the propagation equations and boundary conditions. It considers the phase-mismatched terms, which act as an effective Kerr effect. We analyze the impact of the different terms on the steady state solutions, highlighting the competition between nonlinearities.

DOI
10.1103/physreva.101.043818

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We propose a mean-field model to describe second-harmonic generation in a resonator made of a material with zinc-blende crystalline structure. The model is obtained through an averaging of the propagation equations and boundary conditions. It considers the phase-mismatched terms, which act as an effective Kerr effect. We analyze the impact of the different terms on the steady state solutions, highlighting the competition between nonlinearities.
Cascaded nonlinear phase shifts via second-harmonic generation are theoretically studied for quasi-phase-matched (QPM) structures. Both the effective phase mismatch and the structure itself contribute to the resultant nonlinear phase shift. Depending on the sign of the effective phase mismatch, structural contribution may enhance or depress the nonlinear phase shift. The fundamental wave will experience a nonlinear phase shift even if the effective phase matching is satisfied. By properly designing the effective phase mismatch, QPM structures with large material-based phase mismatch may provide large nonlinear phase shifts before saturation.
The effect of saturable absorption on second-harmonic generation in a quasi-phase-matched structure is studied, including both plane-wave and diffractive coupling of the fields and detuning of the pump field from resonance. In the regime of large Fresnel numbers, the main effect of saturable absorption is to suppress the parametric instability, which limits the efficiency of the second-harmonic generation and places a bound on the device length in order to fit sufficient harmonic power. The optical limiting nature of resonance absorption places an upper bound on the gain that quasi-phase-matching can achieve. In the diffractive regime, a variety of output transverse structures may be initiated by modulation of the relative phase and mutual displacement between the input beams of the pump and seeding harmonic signal. In particular, second-harmonic dragging, i.e., the asymmetric interaction between initially overlapping pump and second-harmonic beams propagating at different angles, is observed such that a pump beam can drag a second-harmonic one out a spatial aperture, thereby implementing a colored logical switch with gain.
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Both static and dynamical analyses of quasi-phase-matched second-harmonic generation by backward propagating interaction, where the second-harmonic wave is generated in reflection, are presented. It is shown that bistability appears in the generated second-harmonic power if the amount of phase mismatch is suitably chosen. The bistability also appears in the output fundamental wave, since the cascaded second-order nonlinear process gives rise to the effective self-modulation of the fundamental wave, which can be applied to all-optical signal processing. The output second-harmonic and fundamental powers can be switched between two bistable states by controlling the intensity or phase of the input fundamental wave.>