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Physical Review A

Enhancement of many high-order harmonics via a single multiphoton resonance

Mette B. Gaarde, Kenneth J. Schäfer

Published Jun 13, 2001• 83 citations
Publisher

Abstract

In the strong-field regime a single multiphoton resonance can enhance many harmonics of the fundamental laser frequency simultaneously. We demonstrate that an alkali-metal atom driven by an intense, ultrafast midinfrared pulse is an ideal system for observing this effect by calculating the response of potassium atoms to radiation that is nearly three or five photon resonant with the $4s\ensuremath{-}4p$ transition. We find that all the harmonics through at least the 17th are enhanced over a wide range of intensities, and that the resonance width of the enhanced harmonics is governed by the lifetime of the multiphoton resonance.

DOI
10.1103/physreva.64.013820

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Physical Review A•Feb 11, 2008•19 citations
In the strong-field regime a single multiphoton resonance can enhance many harmonics of the fundamental laser frequency simultaneously. We demonstrate that an alkali-metal atom driven by an intense, ultrafast midinfrared pulse is an ideal system for observing this effect by calculating the response of potassium atoms to radiation that is nearly three or five photon resonant with the 4s\ensuremath−4p4s\ensuremath{-}4p4s\ensuremath−4p transition. We find that all the harmonics through at least the 17th are enhanced over a wide range of intensities, and that the resonance width of the enhanced harmonics is governed by the lifetime of the multiphoton resonance.
We develop a Floquet based formalism which describes a process of the generation harmonics of in an atom driven by a laser field. Using this formalism, we show that several harmonics are strongly enhanced in the spectrum when the laser frequency is such that a multiphoton resonance occurs between the initial state and a quasienergy state. We illustrate these findings by a numerical calculation of the harmonics generation in the potassium and rubidium atoms driven by a laser in the near-infrared energy range. The present formalism is also applicable when the initial state is a coherent superposition of several field-free atomic states.
We study the interplay between resonant multiphoton population transfer and strong field ionization in potassium atoms, by calculating their response to intense, midinfrared (MIR) radiation. We use wavelengths close to the three or five photon resonance between the ground 4s4s4s state and the first excited 4p4p4p state, and find that the amount of population transferred to the excited state as a function of wavelength and intensity shows clear signatures of these resonances. The ionization yield also shows moderate resonant enhancement for intermediate intensities. We can further distinguish between population transfer to and ionization of the 4p4p4p state by using a chirped laser pulse to temporally separate the two processes. We find that the amount of population remaining in the 4p4p4p state at the end of the pulse shows a pronounced sensitivity to the sign of the chirp whereas the total amount of ionization does not. From this we conclude that direct, nonresonant ionization of the ground state competes strongly with the resonant process.
This work examines the use of higher order multiphoton resonances in higher harmonic generation together with judicious exploitation of coherent interaction properties to achieve efficient harmonic generation. A detailed experimental study on third harmonic generation in two photon resonant coherent interaction and a theoretical study on four photon resonant coherent interaction have been conducted. Two photon resonant coheren propagation in lithium vapor (2S-4S and 2S-3D interaction) has been studied in detail as a function of phase and delay of the interacting pulse sequence. Under coherent lossless propagation of 90 phase shifted pulse pair, third harmonic generation is enhanced. A maximum energy conversion efficiency of 1% was measured experimentally. This experiment shows that phase correlated pulse sequence can be used to control multiphoton coherent resonant effects. A larger two photon resonant enhancement does not result in more efficient harmonic generation, in agreement with the theoretical prediction. An accurate (to at least 0.5 A°) measurement of intensity dependent Stark shift has been done with the newly developed "interferometric wavemeter." Stark shifts as big as several pulse bandwidths (of picosecond pulses) result in a poor tuning of multiphoton resonance and become a limiting factor of resonant harmonic generation. A complete theory has been developed for harmonic generation in a four photon resonant coherent interaction. A numerical application of the theory to the Hg atom successfully interprets the experimental observations in terms of the phase dependent stimulated Raman scattering. With the intensity required for four photon resonant transition, the calculation predicts a dramatic Stark shift effect which completely destroys the resonance condition. This model provides a basis for the development of future schemes for efficient higher order coherent upconversion.
An analytic study is presented of the efficient multiphoton excitation and strong harmonic generation in three-level systems specified by a pair of nearly degenerate, strongly dipole-coupled excited states. Such systems are physically formed by the three lowest states in, e.g., the hydrogen atom or evenly charged homonuclear diatomic molecular ions under reasonably chosen laser intensities. As a detailed analytic result, we found that the laser pulse of photon energy 2.05eV2.05\text{eV}2.05eV, duration 0.23ps0.23\text{ps}0.23ps, and intensity $5\ifmmode\times\else\texttimes\fi{}{10}^{13}\frac{\mathrm{W}}{{\mathrm{cm}}^{2}}$ is able to produce complete inversion of the initial population in the hydrogen atom through the five-photon excitation. At the same photon energy, the pulse of duration 0.41ps0.41\text{ps}0.41ps and intensity $3.44\ifmmode\times\else\texttimes\fi{}{10}^{14}\frac{\mathrm{W}}{{\mathrm{cm}}^{2}}$ was found to produce the same effect in the molecular ion but through the nine-photon excitation. We show that the accompanying scattering of light has very rich spectrum differing substantially from that of the two-level system.
The present paper applies the method of high-intensity quantum electrodynamics developed earlier to several problems of current experimental interest. In this paper the intensitydependent shifts and widths of atomic levels are calculated and applied to a given transition near resonance. The technique is demonstrated with three examples: the multiphoton ionization of atomic cesium and hydrogen in atomic beams and third-harmonic production in an atomic vapor. It is found that the multiphoton-ionization rate in a relatively weak laser beam (of order 108{10}^{8}108 W/cm2{\mathrm{cm}}^{2}cm2) is determined by the intensity-dependent level width (6f6f6f configuration) as well as the interference of the fine-structure states, and that the rates for hydrogen, in a much more intense beam (of order 1012{10}^{12}1012 W/cm2{\mathrm{cm}}^{2}cm2) are determined by both the intensity-dependent widths and shifts as‘\stackrel{\mathrm{`}}{\mathrm{s}}s‘ well as the wave-function renormalization constants. The agreement of these two examples of calculations with the experiments done recently is satisfactory. For third-harmonic production the role of two-photon resonance is emphasized, and the dependence of the generated third-harmonic intensity on the intensity and frequency of the fundamental is discussed. Near resonance, the ratio of third-harmonic intensity to fundamental intensity saturates.
The coherent scattering spectrum of a three-level atom driven by an intense laser field with multiphoton resonant excitation is considered. The spectrum corresponding to harmonic generation is investigated both analytically and numerically for different initial atomic states. The analytical calculations are based on the generalized rotating wave approximation, which allows one to explain obtained spectra containing in general both even and odd harmonics. The results applied to the hydrogen atom show that one can achieve efficient generation of moderately high harmonics using multiphoton resonant excitation by appropriate laser pulses.