Model of THG and EFISH using the SBHM

TL;DR

This paper presents a comprehensive theoretical study of the tensors governing third harmonic generation and EFISH in centrosymmetric materials, introducing a simplified model that aligns well with experimental data and offers new insights into symmetry breaking.

Contribution

It introduces the SBHM approach to model the fourth rank tensor for THG and EFISH, simplifying the tensor to fewer independent elements and providing a classical explanation of EFISH.

Findings

The fourth rank tensor for THG and EFISH can be reduced to two independent elements.

SBHM reproduces EFISH experimental results accurately.

EFISH tensor can be further simplified to a third rank tensor with a classical symmetry-breaking explanation.

Abstract

We report for the first time a comprehensive study of the fourth rank tensor describing third harmonic generation (THG) and electric field induced second harmonic (EFISH) in centrosymmetric material from two different viewpoints: Group Theory (GT) and the Simplified Bond Hyperpolarizability Model (SBHM). We show that the fourth rank tensor related to THG and direct current (DC) EFISH can be reduced to two independent elements whereas SBHM always gives only one, reproducing perfectly well EFISH experimental results in Metal Oxyde Semiconductor (MOS). We argue that it is possible to reduce the fourth rank tensor describing EFISH to a third rank tensor and further deliver a classical explanation of EFISH regarding symmetry breaking where the term containing $r^3$ in the potential immediately leads to second harmonic generation (SHG).