Fig. 3: Polarization of the fifth harmonics for the charge-neutral case and highly doped case.

a Polarization profiles of the fifth harmonics. Black circles show the fifth harmonic intensity measured after a linear polarizer as a function of polarizer angle \(\varphi\). Polarization profile of laser excitation with ellipticity \({\varepsilon }_{{{{{{\rm{exc}}}}}}}\) = 0, 0.12, 0.3, and 0.5 (left column labeled with Excitation) is plotted as a guidance. For the charge-neutral case (middle column labeled with \(2\left|\mu \right|\) = 0 eV), the harmonic polarization sensitively rotates with \({\varepsilon }_{{{{{{\rm{exc}}}}}}}\). For the highly doped case (right column labeled with \(2\left|\mu \right|\) = 1.4 eV), the harmonic polarization nearly does not rotate up to \({\varepsilon }_{{{{{{\rm{exc}}}}}}}\) = 0.5. Pink solid lines show the theoretically calculated polarization, which exhibits good agreement with experimental results. b, c Direction of harmonic polarization rotation under elliptically polarized excitation. Under laser excitation with left-handed helicity in (b) (or right-handed helicity in (c)), the polarization axis rotates in counterclockwise direction (or clockwise direction) with \({\varepsilon }_{{{{{{\rm{exc}}}}}}}\). d, e Harmonic intensity as a function of \({\varepsilon }_{{{{{{\rm{exc}}}}}}}\). Both \({I}_{{{{{{\rm{x}}}}}}}^{(5\omega )}\) (red circles) and \({I}_{{{{{{\rm{y}}}}}}}^{(5\omega )}\) (blue circles) are observed for the charge-neutral case whereas \({I}_{{{{{{\rm{y}}}}}}}^{(5\omega )}\) is nearly absent for the highly doped case. Theoretical calculation results (solid lines) show a good agreement with experimental results.