Department of Physics

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# Higher Harmonics Generation: Transition from bound to unbound dynamics

## Transition from bound to unbound dynamics

Frequency spectrum of the Lienard-Wiechert radiation field produced at the retarded time due to an initially bound electron, in the ground hydrogen state, moving under the influence of a traveling laser field is displayed. The direction of the observation (z) is parallel to the magnetic component and perpendicular to the electric component (x) of the laser field. The relativistic but classical equations of motion of the electron has been solved numerically. The spectrum is computed at 200 peak electric field strengths and displayed with increasing values (indicated by the figure as well as the moving color bar near top of the frame). Spectrum is seen to grow with laser intensity and peaks are well matched by the formula w(L,M) = L w_l + M w_a, with L, M = ... -2, -1, 0, 1, 2... Here w_l is the laser frequency and w_a = 0.927 a.u. is the field dressed atomic frequency that is slightly red-shifted by dw = 0.068 a.u. from the field free value. The absence of any even harmonics (L + M = even) is due to the inversion symmetry of the Coulomb potential. Towards the end of the movie as peak field strength exceeds 0.33 a.u. the ionization occurs which has effectively remove the atomic lines. The field is not strong enough to show multiples of laser frequency either.

Computation parameters associated with this movie are as follows. Laser field strength is varied linearly within 0.01 a.u. < E0 < 0.4 a.u., laser frequency w_l = 0.15 a.u., laser pulse is turned on and off in 2 laser cycles and maintained at its peak value for 30 cycles. The initial position of the electron is at origin with Vx0=0.1 a.u. bound by the screened Coulomb potential V(r) = -1 / [r^2+1]^(1/2).