Efficient Third-Harmonic Generation by Inhomogeneous Quasi-Phase-Matching in Quadratic Crystals

We investigate the generation of optical third-harmonic frequency in quadratic crystals with a nonlinear domain lattice optimized with the aid of a random number generator. In the developed Monte Carlo algorithm and numerical experiments, we consider domain thicknesses to be taking either the values <i>d</i>₁ or <i>d</i>₂, with <i>d</i>₁ and <i>d</i>₂ being the coherence lengths for the cascaded parametric interactions <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><mrow><mi mathvariant="sans-serif">ω</mi><mo>=</mo><mi mathvariant="sans-serif">ω</mi><mo>+</mo><mi mathvariant="sans-serif">ω</mi></mrow></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3</mn><mrow><mi mathvariant="sans-serif">ω</mi><mo>=</mo><mn>2</mn></mrow><mrow><mi mathvariant="sans-serif">ω</mi><mo>+</mo><mi mathvariant="sans-serif">ω</mi></mrow></mrow></semantics></math></inline-formula>, respectively. We focus on the cases with single segments formed by equal and/or different domains, showing that frequency tripling can be achieved with high conversion efficiency from an arbitrary input wavelength. The presented approach allows one to accurately determine the optimized random alternation of domain thicknesses <i>d</i>₁ and <i>d</i>₂ along the propagation length.