ILP Theory Unit

Movie captions of High Harmonic Generations

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).

Relativistic ionization 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). Even though the electron is initially bound ionization would occur for all the peak laser fields chosen in this movie. Spectrum is seen to grow with laser intensity and peaks are well matched by the formula w(L) = L w_l^s with L = integer. Here w_l^s is related to the laser frequency w_l via w_l^s = (1-a) w_l with a = E0^2 / (E0^2 + 4*w_l^2*c^2). Both even and odd order harmonic peaks are present due to relativistic electron motion. Redshift in the laser frequency here may be attributed laboratory manifestation of the Doppler effect by an ExB drifted electron.

Computation parameters associated with this movie are as follows. Laser field strength is varied linearly within 1 a.u. < E0 < 40 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).

Relativistic ionization of magnetically dressed atoms

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 and a uniform magnetic field is displayed. The direction of the observation (x) is parallel to the laser electric component and perpendicular to the laser as well as the static magnetic components (z). The relativistic but classical equations of motion of the electron has been solved numerically. The spectrum is computed at 200 magnetic field strengths and displayed with increasing values (indicated by the figure as well as the moving color bar near top of the frame). Before ionization spectrum peaks are well matched by the formula w(L, M, N) = L w_l + M w_+ + N w_-, with L, M, N = ..., -2, -1, 0, 1, 2... Here w_l is the laser frequency and w_+ = [(W/2)^2+w_a^2]^(1/2) + (W/2) and w_- = [(W/2)^2+w_a^2]^(1/2) - (W/2) a.u. are the magnetic field (with cyclotron frequency W) dressed atomic frequency w_a. The absence of any even harmonics (L + M + N = even) is due to the inversion symmetry of the Coulomb potential. The enhancement of the scattered light spectrum is most significant on resonance when ionization occurs and (scaled) magnetic field W is multiples of laser frequency wL or reversely when laser frequency wL is multiples of the (scaled) magnetic field W. It is worth to note that near the non-relativistic resonance wL ~ W the spectral enhancement due to relativistic calculations show an irregular (chaotic) pattern.

Computation parameters associated with this movie are as follows. Static magnetic field with (scaled) strength varied logarithmically within 0 a.u. < W < 0.7 a.u. Laser field strength is fixed at E0 = 5 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).

Return to Movies of High Harmonic Generation page.