Analytic theory of high-order-harmonic generation by an intense few-cycle laser pulse

Abstract

Frolov, M. V.; Manakov, N. L.; Popov, A. M.; Tikhonova, O. V.; Volkova, E. A.; Silaev, A. A.; Vvedenskii, N. V.; and Starace, Anthony F., "Analytic theory of high-order-harmonic generation by an intense few-cycle laser pulse" (2012 We present a theoretical model for describing the interaction of an electron, weakly bound in a short-range potential, with an intense, few-cycle laser pulse. General definitions for the differential probability of abovethreshold ionization and for the yield of high-order-harmonic generation (HHG) are presented. For HHG we then derive detailed analytic expressions for the spectral density of generated radiation in terms of the key laser parameters, including the number N of optical cycles in the pulse and the carrier-envelope phase (CEP). In particular, in the tunneling approximation, we provide detailed derivations of the closed-form formulas presented briefly by M. V. Frolov et al. [Phys. Rev. A 83, 021405(R) (2011)], which were used to describe key features of HHG by both H and Xe atom targets in an intense, few-cycle laser pulse. We then provide a complete analysis of the dependence of the HHG spectrum on both N and the CEP φ of an N -cycle laser pulse. Most importantly, we show analytically that the structure of the HHG spectrum stems from interference between electron wave packets originating from electron ionization from neighboring half-cycles near the peak of the intensity envelope of the few-cycle laser pulse. Such interference is shown to be very sensitive to the CEP. The usual HHG spectrum for a monochromatic driving laser field (comprising harmonic peaks at odd multiples of the carrier frequency and spaced by twice the carrier frequency) is shown analytically to occur only in the limit of very large N , and begins to form, as N increases, in the energy region beyond the HHG plateau cutoff.

Scaling laws for high-order-harmonic generation with midinfrared laser pulses

“…In this paper, we present an analytic description of the λ dependence of the HHG yield based on an analysis of the (near-) universal properties of the returning EWP [30,31]. Our results confirm the main conclusions concerning the λ scaling of HHG represented in Ref.…”

“…[30,31]. They are based upon a quantum-mechanical treatment of an exactly solvable model for an electron in both a short-range potential and a strong laser field [33] and form the starting point of the present investigation of the λ scaling for short low-frequency midinfrared pulses.…”

“…Within the classical three-step scenario for HHG, the EWP can be expressed in terms of a coherent superposition of contributions from returning closed classical orbits j of electrons escaping from and recombining with the atoms as [31] …”

Harmonic generation spectroscopy with a two-colour laser field having orthogonal linear polarizations

“…For a linearly polarized field, this factorization was proposed phenomenologically, based on numerical solutions of the time-dependent Schrödinger equation [3,4]. It has now been justified theoretically for a monochromatic field [5,6], for a short laser pulse [7][8][9], and for a two-colour field with collinearly polarized components [10].…”

“…Using the solution of the system (9), (10) as the zeroorder iteration of the system (6), (8), one can find the first-order quantum corrections to the classical times from the next iteration of the system (6), (8). We introduce dimensionless definitions for the laser field, f(t ) = F(t )/F 1 , the electron's momenta q(t, t i ) = K(t i ; t, t i )/( κ ) and p(t, t i ) = K(t; t, t i )/( κ ) and the time τ = ωt.…”