Perturbative wave-mixing and amplification in the extreme ultraviolet region

Abstract

ABSTRACT We report the investigation of the wave-mixing and amplification process with two multiple-cycle pulses with incommensurate frequencies (at 1400 nm and 800 nm). With a non-collinear configuration of the two beams, a different extreme ultraviolet mixing field can be created at low intensity of the 800 nm field. When a very high intensity 800 nm pulse is applied we are able to amplify the coherent extr eme ultraviolet radiation in the photon energy range around 80 eV. Keywords: Laser applications, nonlinear optics, high order harmonic generation 1. INTRODUCTION The high-order harmonic generation (HHG) process provides me thods to produce short pulses of coherent radiation in the extreme ultraviolet (XUV) and soft X-ray region. This source opens up new applications such as in time-resolved studies of atoms and molecules [1], and coherent diffractive imaging [2]. High-order harmonic generation involving the interaction of atoms or molecules with strong laser fields is an example of nonlinear physic s, where simple pictures can be used to describe strongly non-perturbative processes with the time-dependent Schroedinger equation. This can be conceptually understood classically in the so-called three-step model [3] where an electron is first liberated from an atom through strong field ionization, then is accelerated by the laser field, and finally is recombined with the parent ion, emitting any excess energy as a high-energy photon. When matter interacts with a strong laser field the response of the medium can be expanded in many orders in the perturbative approach [4], expressed as linear and nonlinear terms in which high orders of response are taken into account. Several nonlinear phenom ena appear in the regime of extreme inter actions. With the consideration of second- and third-order nonlinearity, optical parametric generation and optical parametric amplification play an important role in the generation of ultrashort laser pulses in the infrared and visible range [5]. The detailed response of a single atom or molecule to an intense electromagnetic field is quite complex, but the fundamental underlying physics can be unexpectedly simple in many cases. Bertrand et al. [6] have shown that when two intense fundamental laser pulses of frequency Z and 2Z 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. In this paper we study the wave-mixing and amplification process with two multiple-cycle pulses with incommensurate frequencies (at 1400 nm and 800 nm). With a non-collinear configuration of the two beams and low intensity of the 800 nm field, different extreme ultraviolet mixing field can be created and separated spatially. When a very high intensity 800 nm pulse (> 7.10