Spatially inhomogeneous field induced harmonic radiation in solids

TL;DR

This paper introduces a new inhomogeneous coefficient equation that accurately models harmonic radiation in solids driven by spatially inhomogeneous fields, outperforming the traditional semiconductor Bloch equation.

Contribution

The paper develops a novel theoretical equation for inhomogeneous fields, enabling better analysis of harmonic generation mechanisms in solids like graphene.

Findings

Even-order harmonics increase with field inhomogeneity.

Second harmonic intensity aligns with perturbation theory predictions.

Wavelength dependence helps distinguish intraband and interband contributions.

Abstract

By theoretical derivation, we constructed an inhomogeneous coefficient equation to correctly describing harmonic radiation in solids induced by a spatially inhomogeneous field, where the widely used semiconductor Bloch equation fails. This equation has superiority over the semiconductor Bloch equation with good applicability to both homogeneous and inhomogeneous fields. Using graphene as an example, it is found that under inhomogeneous field driving, even-order harmonics occur with an enhancing tendency as the field inhomogeneity increases. As for the second-order harmonic, its intensity dependence is consistent with the prediction from the perturbation theory, and its wavelength dependence can use to directly distinguish the relative contribution of intraband and interband transitions. The inhomogeneous coefficient equation provides a direct theoretical analysis tool for elucidating the physical mechanism of inhomogeneous field induced harmonic radiation in solids.