On the possibility of the generation of high harmonics with photon energies greater than 10 keV upon interaction of intense mid-IR radiation with neutral gases

High harmonic interferometry of the Lorentz force in strong mid-infrared laser fields

“…However, this programme runs into a surprising limitation in that the dipole approximation breaks down in the long wavelength regime: as the wavelength increases, the electron has progressively longer times to accelerate in the field, and the magnetic Lorentz force =F v B m becomes significant [7]. This pushes the electron along the laser propagation direction and, when strong enough, makes the electron wavepacket completely miss its parent ion, quenching all recollision phenomena, including in particular high harmonic generation [8][9][10][11][12][13][14][15].Multiple schemes have been proposed to overcome this limitation, both on the side of the medium, from antisymmetric molecular orbitals [16] through relativistic beams of highly charged ions [17] to exotic matter like positronium [18] or muonic atoms [19] , and on the side of the driving fields, including counter-propagating mid-IR beams [20,21], the use of auxiliary fields propagating in orthogonal directions [22], fine tailoring of the driving pulses [23], counter-propagating trains of attosecond pulses [24] in the presence of strong magnetic fields [25], and collinear and non-collinear x-ray initiated HHG [26,27].…”

“…However, this programme runs into a surprising limitation in that the dipole approximation breaks down in the long wavelength regime: as the wavelength increases, the electron has progressively longer times to accelerate in the field, and the magnetic Lorentz force F m = v/c × B becomes significant [7]. This pushes the electron along the laser propagation direction and, when strong enough, makes the electron wavepacket completely miss its parent ion, quenching all recollision phenomena, including in particular high harmonic generation [8][9][10][11][12][13][14][15].…”

“…To choose the appropriate initial condition, we note that the linear walk-off represents a secular term [44] in these solutions, and we minimize the effect of this secular term by choosing an explicit reference time at the moment of ionization: (15) This then trickles down to the action, and similarly to the harmonic dipole. This harmonic dipole is sufficient to evaluate the harmonic emission from arbitrary beam configurations, and it can be further simplified by the use of the saddle-point approximation for the momentum integral, and the uniform approximation [45,46] for the temporal integrations.…”

“…15 W/cm 2 (b) 1.6 µm, 3.2 × 10 14 W/cm2 (c) 1.6 µm, 10 15 W/cm 2 Harmonic spectra (• odd and • even harmonics) produced in helium in the non-dipole regime for intensities of 3.2 × 10 14 and 10 15 W/cm 2 and monochromatic fields of 800 nm and 1.6 µm at a beam half-angle of θ = 4 • , on arbitrary scales and eliminating z-polarized harmonics. The intensity ratio between even and odd harmonics varies from ∼10 −3 for 800 nm drivers to ∼10% for strong mid-IR fields at 1.6 µm and 10 15 W/cm 2 , which are still accessible with current technology.…”

Control of the photoelectron dynamics for the effective conversion of short-pulse, frequency-modulated optical radiation into X-ray radiation

“…It is known from the literature [38,39] that the widely used formula for the tunnelling ionisation rate [40], at large values of |E| (of interest to us in this problem), greatly overestimates its value. Therefore, following [37], in the present study we calculate v(t) by using an analytical formula for the tunnelling ionisation rate of an atom in a static field, corrected for above-barrier regime proposed in [39]: …”