Theory of circularly polarized harmonic generation using bi-colour lasers in underdense plasmas

Abstract

Circularly-polarized extreme ultraviolet- and X-ray radiation is an essential tool for analyzing the magnetic properties of materials. Elliptically polarized high harmonic generation (HHG) has been demonstrated by focusing bi-chromatic (800nm + 400nm wavelengths), counter-rotating circularly polarized (CP) laser pulses into gas targets [Fleischer etal, Nature Photonics 8, 543 (2014)]. More recent theoretical studies indicate that a bi-circular laser driver can also work in both under- and overdense plasmas with analogous selection rules to those in gases: for example, every third harmonic is suppressed and adjacent harmonics have opposite helicity for counter-polarized CP ω₀ and 2ω₀ pumps. In this work, an analytical theory of bi-circular HHG from underdense plasmas is formulated which provides quantitative predictions of harmonic efficiency scaling, selectivity and helicity for both co- and counter-polarized drivers of arbitrary frequency ratio. This is compared to a fully nonlinear, one-dimensional fluid model and PIC simulations, showing good agreement with both.