Wave-mixing with high-order harmonics in extreme ultraviolet region

Abstract

We report studies of the wave-mixing process in the extreme ultraviolet region with two near-infrared driving and controlling pulses with incommensurate frequencies (at 1400 nm and 800 nm). A non-collinear scheme for the two beams is used in order to spatially separate and to characterise the properties of the high-order wave-mixing field. We show that the extreme ultraviolet frequency mixing can be treated by perturbative, very high-order nonlinear optics; the modification of the wave-packet of the free electron needs to be considered in this process.

Perturbative wave-mixing and amplification in the extreme ultraviolet region

“…When the interaction of the 800 nm pulse is very weak or absent (for delay < -80 fs) the harmonic spectrum consists of odd harmonic orders of the 1400 nm pulse, as expected. For a negative delay time < -40 fs other peaks can be seen between the odd orders of 1400 nm which are caused by frequency mixing with the 800 nm pulse [7]. A quasi-continuum spectrum with a large bandwidth of ~ 35 eV is detected around zero delay time.…”

“…In this case a quasi-continuum XUV spectrum is obtained. This indicates that other mixing processes of the two fields [7,8] need to be considered and the symmetry of the total field is broken. A minimum in the spectrum can be seen at ~ 51 eV (24 nm) where a Cooper minimum caused by destructive interference of the 5s and 4d transition dipole moments is expected [12].…”

“…The spectrum exhibits distinguishable peaks which indicate the position of the wave-mixing radiation. To emit a single XUV photon, parity conservation requires that for a dipole transition the wave function of the continuum electron and the ion together must be in a state of different parity to that of the original ground state [6,7]. Therefore only the net absorption of an odd total number of photons n = n 1 + n 2 can lead to photon emission.…”

“…of SPIE Vol. 9835 98350U-4 = 2 + 2 ; 2 = 1 2 ( * + * ) (7) γ is the nonlinear coupling coefficient between the idler and signal field. The γ s,i are determined by the amplitudes of the corresponding nonlinear atomic dipole moments which depend on the intensity of the driving field A p and the optical properties of the medium.…”

“…Bertrand et al [6] have shown that when two intense fundamental laser pulses of frequency ω and 2ω are crossed non-collinearly in a gas-jet target the emission spectrum can be described simply in terms of conservation of energy and momentum. We realised the optical wave-mixing [7] and amplification [8] in HHG which suggests the possibility to treat the physics in the XUV range with a perturbative nonlinear optics theory.…”