Optimization and phase matching of fiber-laser-driven high-order harmonic generation at high repetition rate Amélie Cabasse,* Guillaume Machinet, Antoine Dubrouil, Eric Cormier, and Eric Constant University of Bordeaux, Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Centre national de recherche scientifique (CNRS), Centre Lasers Intenses et Applications (CELIA), Unité mixte de recherche (UMR) 5107, Talence F-33400, France *Corresponding author: cabasse@celia.u‑bordeaux1.fr Received August 3, 2012; revised September 25, 2012; accepted October 4, 2012; posted October 8, 2012 (Doc. ID 173841); published November 6, 2012 High-repetition-rate sources are very attractive for high-order harmonic generation (HHG). However, due to their pulse characteristics (low energy, long duration), those systems require a tight focusing geometry to achieve the necessary intensity to generate harmonics. In this Letter, we investigate theoretically and experimentally the optimization of HHG in this geometry, to maximize the extreme UV (XUV) photon flux and improve the conversion efficiency. We analyze the influence of atomic gas media (Ar, Kr, or Xe), gas pressure, and interaction geometries (a gas jet and a finite and a semi-infinite gas cell). Numerical simulations allow us to define optimal conditions for HHG in this tight focusing regime and to observe the signature of on-axis phase matching. These conditions are implemented experimentally using a high-repetition-rate Yb-doped fiber laser system. We achieve optimization of emission with a recorded XUV photon flux of 4.5 × 10 12 photons ∕s generated in Xe at 100 kHz repetition rate. © 2012 Optical Society of America OCIS codes: 140.3510, 140.7240. High-order harmonic generation (HHG) in gases is a well-established technique to produce short coherent and directional extreme UV (XUV) radiation. Initially de- veloped using long-pulse lasers [ 1, 2], HHG required a tight focusing geometry to reach sufficient intensity to generate harmonics (>10 13 W∕cm 2 ). The development of ultrashort amplified systems (Ti:sapphire) enabled us to use a looser focusing geometry, which helped to im- prove the harmonic yield. However, their limited average power [ 3] limits the repetition rate of these systems. Performing efficient HHG at high repetition rate [ 4] is the next experimental challenge that will allow drastic improvements in statistics and signal-to-noise ratio and open new experimental domains such as time-resolved coincidence detection. The low pulse energy associated to this high repetition rate requires a tight focusing geo- metry. Phase matching is then strongly influenced by the atomic and geometrical phases [ 5, 6]. Nowadays, several approaches allow us to reach high enough intensity to generate high harmonics at such high repetition rate. Sev- eral groups have demonstrated the promising approach of cavity-enhanced HHG, leading to the generation of few kilowatts of intracavity average power [ 7]. It is then pro- blematic to extract the harmonics from the cavity and also to control HHG without perturbing the cavity [ 8, 9]. Femtosecond fiber technologies are another promising tabletop source to achieve high average power compati- ble with HHG at a controllable high repetition rate. In- deed, Yb-doped fiber chirped-pulse amplification (FCPA) systems can generate high harmonic at a repetition rate up to 1 MHz [ 10, 11]. In this Letter, we study and define conditions for optimizing conversion efficiency to maximize the XUV photon flux in the tight focusing regime. We numerically analyze the harmonic signal as a function of several para- meters that control the efficiency of HHG at various or- ders: atomic gas media (Ar, Kr, or Xe), gas pressure, and interaction geometries (a gas jet and a finite or a semi-infinite gas cell). We optimize HHG with the gas cell at low gas pressure and achieve on-axis phase matching. An experimental campaign allows us to both maximize the harmonic signal and observe the signature of on-axis phase matching with a 100 kHz repetition rate system at 1030 nm. We performed a numerical analysis with a three- dimensional (3D) code [ 4, 6, 12] that calculates the far-field harmonic intensity and spatial profile by consid- ering the spatial profile of the fundamental Gaussian beam in the gas medium. We use a simple model har- monic dipole with amplitude d I ∕I cutoff  1.5 when I>I cutoff , and d I ∕I cutoff  5 when I<I cutoff (I being the intensity and I cutoff the minimum intensity required for a given harmonic order to be generated). Note that no gas-dependent amplitude factor was considered here. The dipole phase is q times the fundamental phase plus the atomic phase αI with α  2.5 × 10 14 cm 2 ∕W[ 5, 13], as only the short trajectory is considered here since the tight focusing prevents us from detecting the contribu- tion of the widely diverging long trajectory. The collec- tive effects that impact HHG are also considered. The coherence length, L coh , is calculated by considering the geometrical phase of the fundamental beam, the atomic dispersion for both the fundamental and the XUV light, and the single-atom dipole phase. The absorption length, L abs , is defined as 1∕σρ (σ the absorption cross section and ρ the atomic density of the gas). In our simulation, ionization of the medium is neglected. This condition is valid at low intensity and at 1030 nm as the high pon- deromotive energy associated to this field allows us to generate moderate harmonic orders at low intensity even without significant ionization (at 800 nm, generating such harmonics would imply high ionization). The harmonic signal is calculated using a constant laser intensity I  6 × 10 13 W∕cm 2 and a confocal parameter b  610 μm (w 0  10 μm). Figure 1 presents the harmonic signals for the harmonic orders 25 and 27 (noted H25 and 4618 OPTICS LETTERS / Vol. 37, No. 22 / November 15, 2012 0146-9592/12/224618-03$15.00/0 © 2012 Optical Society of America