Paraxial theory of sum-frequency generation by side-walk alignment and phase-matching in uniaxial crystals

TL;DR

This paper develops a paraxial formalism using Hertz potentials to analyze sum-frequency generation in uniaxial crystals, focusing on side-walk propagation and phase-matching, especially for second harmonic generation.

Contribution

It introduces a novel formalism for sum-frequency generation in uniaxial crystals, emphasizing side-walk alignment and phase-matching within a simplified paraxial framework.

Findings

Derived simplified paraxial equations for sum-frequency generation

Analyzed the role of side-walk propagation in phase-matching

Focused on second harmonic generation mechanisms

Abstract

A formalism in terms of Hertz potentials is presented describing sum-frequency generation in a uniaxial non-linear crystal. A scheme is proposed consisting in aligning the side-walk propagation of extraordinary waves in combination with phase-matching. Simplified paraxial equations describing this situation are obtained. Particular attention is paid to the generation of second harmonics.