Molecules in Bichromatic Circularly Polarized Laser Pulses: Electron Recollision and Harmonic Generation

Abstract

High-order harmonic generation (HHG), the highly nonlinear nonperturbative response of atoms and/or molecules to ultrafast intense laser pulses of femtosecond (\(1\text { fs}=10^{-15}\) s) duration, can be modeled as a recollision process after tunneling ionization of an electron in linear polarization. In general, recollision is suppressed at high intensities with monochromatic circularly polarized pulses. Combinations of bicircular pulses with frequencies \(\omega _1/\omega _2=n_1/n_2\) where \(n_1\) and \(n_2\) are integers, induce recollisions and HHG, seen in a rotating frame Hamiltonian. Molecules are preferred systems for circularly polarized HHG due to lower rotational symmetry as compared to infinite symmetry in atoms where emission selection rules dominate. We simulated HHG spectra from numerical solutions of time-dependent Schrodinger equations for linear and cyclic one and two electron molecular models by intense circularly polarized pulses with both co-rotating and counter-rotating components. Simulations show that the bicircular HHG spectrum is universal, with a cut-off at \(N_m=(I_p+3.17U_p)/\hbar \omega \), where \(I_p\) is the molecular ionization potential and the ponderomotive energy \(U_p=e^2E^2/4m_e\omega ^2\) for maximum electric field amplitude E. The rotating frame Hamiltonian model predicts the recollision (ponderomotive) frequency \(\omega =(\omega _1+\omega _2)/2\). The simulated HHG spectra confirm the recollision model in a rotating frame at frequency \(\bar{\omega }=(\omega _2-\omega _1)/2\). The results show that the circularly polarized HHG with definite helicity occurs efficiently when the total electric field E(t) rotational symmetry \(C_n\) of bicircular pulses is the same as the symmetry of the molecule. A mismatch of symmetry produces a random HHG spectrum, thus confirming the role of field-molecular symmetry in molecular HHG with circularly polarized pulses.