PHYSICAL REVIEW A VOLUME 48, NUMBER 5 NOVEMBER 1993 High-order harmonic-generation cutoff Anne L'Huillier, M. Lewenstein, ' P. Salieres, and Ph. Balcou Service des Photons, Atomes et Molecules, Centre d'Etudes de Saclay, 91191 Gif sur Y-vet-te, France M. Yu. Ivanovt National Research Council of Canada, M 2$A, -Ottawa, Ontario, Canada K1A OR0 J. Larsson and C. G. Wahlstrom Department of Physics, Lund Institute of Technology, S-22 100 Lund, Sweden (Received 19 February 1993) We have experimentally determined the harmonic-generation cutofI' as a function of the laser intensity in neon using an intense, short-pulse Ti:sapphire laser. The experimental cutoff is lower than that obtained in single-atom calculations. Using a simple quantum-mechanical approach to harmonic generation valid at high intensity, we show that the difI'erence is due to the effect of propagation. PACS uumber(s): 42. 65. Ky, 32.80.Rm High-order harmonic generation has recently become one of the major topics of multiphoton physics. The spec- trum of such radiation falls ofF for the first few harmon- ics, then exhibits a plateau extending sometimes to more than 150 eV [1, 2]. The plateau ends up by a rather sharp cutoff One of t. he most intriguing questions concerns the nature and location of this cutoff. Numerical calculations of Krause, Schafer, and Kulander, [3] have shown that the maximum energy at the end of the plateau, which we call the cutog energy, is well approximated by the sim- ple formula I„+3U„, where Ip is the atomic ionization potential, while U„= E' /4co is the ponderomotive en- ergy in the laser Geld of strength E' and &equency u. Some insight into the physical meaning of this formula has recently been given by Schafer, Kulander, and Krause [4] and by Corkum [5], using a two-step quasiclassical ap- proach. In this model, electrons first tunnel through the barrier formed by the atomic potential and the laser Geld [6,7]. Their subsequent motion in the field is treated clas- sically. Only those electrons that return to the nucleus can emit harmonics by recombining to the ground state. The maximum kinetic energy acquired by the electrons from the Geld at the time they return to the nucleus is 3. 2U„, so that the maximum emitted energy is Ip+3 2Up, in accord with the prediction of [3]. The aim of this Rapid Communication is to discuss the harmonic-generation cutoff from experimental data to calculations involving the response of a single atom and of the macroscopic medium. We have performed sys- tematic measurements of the harmonic-generation yields in neon using a short-pulse low-frequency laser. The ex- perimental cutofF energy is found to be approximately I„+2U„and is therefore lower than that predicted in single-atom theories [3, 8]. To understand the difFerence, we have investigated the influence of propagation [9] and in particular of focusing on the location of the cutoff. We use single-atom dipole moments obtained from a simple (and new) quantum-mechanical theory of harmonic gen- eration valid in the tunneling limit. The results obtained for the response of the macroscopic medium agree well I I I I I I I I op poopp ooo ooo oo pp ~ o'oooo 00 oooo ~ oo o p ~ ~ oo pp ~ o oooo 0 ~ Qpoo ooo ~ o ~ 0 oO Qpp oOO 00 ~ p OO OQOO oo ~ op ~ p 0 ~ opopo 0 O 00 ~ 00 OQ p oo 0 ~ oo o oo p ~ 0 ~ 0 obo 0 0 o 0 ~ ~ o 0 0 ~ o 0 0 p ~ 0 0 10 — o' ~ 79 29 69 Neon l/l 10 o CL. 0 0 &9 49 59 10 10~4 Laser Intensity (W/cm ) 2 10 FIG. 1. 19th, 29th, 39th, 49th, 59th, 69th, and 79th har- monics in neon as a function of the laser intensity with the experimental data. The experiments have been carried out with a 100-m3 Ti:sapphire laser operating at a wavelength of 794 nm and a pulse width of 250 fs. The laser is loosely focused by a f = 2 m lens into a 1-mm 20-Torr atomic beam pro- vided by a pulsed gas jet. The confocal parameter (b) is measured to be 1. 3 cm. The 10-Hz repetition rate allows us to perform systematic measurements of the harmonic- generation yields as a function of the laser intensity from 20 eV (the 13th harmonic) to about 130 eV (the 83rd harmonic, the highest observed with significant dynam- ical range). In Fig. 1, we present the results for seven of these harmonics. The harmonics appear successively as the intensity increases. They vary first rather rapidly with the laser intensity, in the cutoff region. Then, they reach the plateau, where all of the harmonics have ap- proximately the same strength, exhibiting a slow depen- dence with the laser intensity. As the harmonic order in- creases, the variation in the cutoff region becomes more rapid and the variation in the plateau slower. The loca- 1050-2947/93/48(5)/3433(4)/$06. 00 48 R3433 1993 The American Physical Society