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Acta Physica Polonica A

Strong versus Weak Excitation in Frequency Mixing and Harmonic Generation by Two-Level Systems

R. Parzyński, T. Kopyciuk

Published Nov 1, 2021• 0 citations
Publisher

Abstract

In the limits of weak and strong excitation, we solve analytically the Riccati-type differential equation for a two-level system in the field of two different lasers and then use these solutions to find easy to handle formulae for the induced electric-dipole moment of the system.We apply these formulae to describe the effects of strong excitation in both the higher harmonics generation and multiphoton frequency mixing, namely the diminishing of the generation of harmonics of a given laser when an additional laser is turned on and the diminishing of the radiation at mixed frequencies with increasing strength of lasers under the condition of multiphoton excitation.

DOI
10.12693/aphyspola.140.407

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In the limits of weak and strong excitation, we solve analytically the Riccati-type differential equation for a two-level system in the field of two different lasers and then use these solutions to find easy to handle formulae for the induced electric-dipole moment of the system.We apply these formulae to describe the effects of strong excitation in both the higher harmonics generation and multiphoton frequency mixing, namely the diminishing of the generation of harmonics of a given laser when an additional laser is turned on and the diminishing of the radiation at mixed frequencies with increasing strength of lasers under the condition of multiphoton excitation.
Linearized version of the Riccati-type differential equation for the ratio of population amplitudes in a laserdriven two-level system is used to calculate analytically the induced electric dipole moment.The formula found for the dipole moment is valid for weak excitations by smooth-shape pulses of arbitrary off-resonant frequencies, i.e., those producing neither exact one-photon nor odd multiphoton resonances.For a given pulse shape, the formula allows to express the Fourier components of the induced dipole moment as functions of both laser frequency and intensity and to find the field-dependent refractive index of the system versus laser frequency.
The theory of coherent radiation emission in two-level quantum systems with permanent dipole moments at the multiphoton resonant excitation by moderately strong laser fields is presented. A simple analytic formula for the expectation value of a dipole moment operator is obtained. The spectrum corresponding to harmonic generation and low-frequency radiation on the generalized Rabi frequency is investigated both analytically and numerically. The effect of dynamic Stark shift on a dipole spectrum under direct multiphoton resonant excitation is considered.
The phase relationship between an induced atomic dipole moment and a driving laser field is an essential aspect of high harmonic generation (HHG) in a dense medium. A ``phase-matching'' criterion must be fulfilled to obtain coherent amplification of harmonic radiation, which is critical for practical HHG. We have performed numerical calculations on model atoms to survey the intensity dependence of the phase in the case of strong one- or two-frequency laser fields. The calculations show that multiphoton resonances significantly affect the yield of harmonic generation and that in the ``plateau'' regime, the phases exhibit only weak dependence upon the intensity of the driving field. \textcopyright{}1996 The American Physical Society.
Abstract We derive a compact formula for the electric dipole induced in a weakly laser-driven two-level system. The dipole is shown to oscillate at frequencies being different combinations of even multiplicities of the transition frequency and odd multiplicities of the laser frequency. Applying this formula to laser frequencies much lower than the transition frequency in the system, we explain the numerical dipole spectra reported in literature, particularly the bunches of spectral lines grouped around even multiplicities of the transition frequency. These bunches form a part of spectrum additional to the ordinary odd laser-light harmonics.
We consider harmonics generation and wave mixing by two-color multiphoton resonant excitation of three-level atoms and molecules in strong laser fields. The coherent part of the spectra corresponding to multicolor harmonics generation is investigated. The obtained analytical results on the basis of a generalized rotating wave approximation are in a good agreement with numerical calculations. The results applied to the hydrogen atoms and homonuclear diatomic molecular ions show that one can achieve efficient generation of moderately high multicolor harmonics via multiphoton resonant excitation by appropriate laser pulses.
We formulate the problem of harmonic generation by a two-level system with ionization in terms of a nonlinear Riccati-type differential equation. Different simplified forms of this equation are solved analytically and the resulting photon-emission spectra are compared with those obtained by others along different lines. For the complete-form Riccati-type equation, we give an iterative code solving this equation for arbitrary laser pulses. The code is used to study the effect of ionization and turn-on of the laser pulse on the harmonic spectrum.