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

Circularly polarized (CP) 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 (800 + 400 nm wavelengths), counter-rotating CP laser pulses into gas targets (Fleischer et al 2014 Nat. Photonics 8 543). 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 non-linear, one-dimensional fluid model and particle-in-cell simulations, showing good agreement with both.