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Journal of Applied Physics

Stark effect in high-frequency fields for resonant modulation

S. H. Kim, Hae Yang Chung

Published Oct 1, 1978• 6 citations
Publisher

Abstract

We solved in closed form the resonant-modulation problem for the effect of the high-frequency electric field on the absorption spectra of the three-level system. It is shown that an electric field whose frequency is made resonant with the separation between two upper levels should give rise to the two absorption lines of equal intensity disposed symmetrically in pairs about the allowed line. The separation between these two lines is linearly proportional to the intensity of the electric field. The positions and the property of equal intensity of these lines are the same in both the laser absorption spectrum and the ordinary absorption spectrum.

DOI
10.1063/1.324453

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Canadian Journal of Physics•Dec 1, 1990•6 citations
We solved in closed form the resonant-modulation problem for the effect of the high-frequency electric field on the absorption spectra of the three-level system. It is shown that an electric field whose frequency is made resonant with the separation between two upper levels should give rise to the two absorption lines of equal intensity disposed symmetrically in pairs about the allowed line. The separation between these two lines is linearly proportional to the intensity of the electric field. The positions and the property of equal intensity of these lines are the same in both the laser absorption spectrum and the ordinary absorption spectrum.
Atomic absorption spectra of the He I plasma in the static magnetic field in the absence of laser radiation are different from spectra in the presence of laser radiation. Especially, it has been theoretically predicted that the spectral shift of the satellite line, which is seen in the latter case, does not exist in the former case. In this paper, the effect of three-dimensional high-frequency electric fields on the σ+, σ−, and π components of the allowed 1 1S0-3 1P1 transition and the forbidden 1 1S0-3 1D2 lines in atomic absorption spectra of the He I plasma in a static magnetic field in the absence of a laser beam is investigated from the coupled equations for the probability amplitudes of atomic states. It is shown that they should give rise to a spectral shift of the allowed lines and satellites about forbidden lines. The calculation reveals that the shift is proportional to the mean-square stochastic electric field, and that the ratio of the intensity of the near satellite to that of the far satellite is different from the ratio obtained by the second-order perturbation theory or the three-level rotating-wave approximation. Discussion is given for the validity of this theory.
The review systematizes the experimental material and reports the fundamental theoretical results on the study of nonlinear resonance effects in spectra of atomic systems situated in the radiation field of lasers. The theoretical part explains the topics of greatest importance and significance for understanding of the experimental studies: the Stark effect in an optical field; the nonequilibrium velocity distribution of the atoms; the shape of the spectral line for a transition adjacent to a transition combining with a strong field; the simultaneous manifestation of the Stark effect and of Doppler broadening in the form of a very sharp structure on the line contour; a brief mention of the influence of collisions, recoil, and other factors on the sharp structure in spectra. The experimental part reports the results of experiments on the observation of the Stark effect in the optical region of the spectrum, the fine structure of the profile of a Doppler-broadened line and its properties, namely the dependence on the observation direction, the anisotropy in the field of a standing wave, the polarization properties, etc. in spectra of spontaneous or stimulated emission, absorption, and generation.
We consider the interference spectra arising from the competition between a spontaneous process and two processes induced by two laser fields, which are coupled with a three-level atom in the "Λ" configuration. In the low-intensity limit of both laser fields and on two-photon resonance, the frequency profiles of the two peaks, which arise from the spontaneous and induced processes, cancel each other out completely at the center of the line for zero detuning and at the finite values of the detuning as well. At high intensities of the laser fields and on two-photon resonance, the dynamic Stark effect dominates the spectra of the excited state of the atom. Expressions for the interference spectra and correlation functions are derived, which describe the physical process of the absorption of a laser photon at two different times by the ground state of the atom. Interference spectra and correlation functions are calculated for the two-photon off-resonance and for the proces of the absorption of a photon by the ground state of the atom. In this case, the intensities of the frequency dips take negative values indicating that stimulated emission prevails for certain values of the detunings. Using values for the parameters involved close to those for Ba+, the computed two-photon resonance and off-resonance spectra are graphically presented and discussed.
We have numerically calculated the excitation spectra arising from the 3rd order mixing of the frequencies ωa and ωb of two laser fields interacting with a three-level atom, where each laser field resonantly couples the ground state with each excited state of the atom, respectively. In the limit of high photon densities, the excitation spectra near the reduced frequency X = (ω−ωa + 2ωb)/γ0 ≈ 0 are considered as a function of the reduced Rabi frequencies ηa and ηb of the two laser fields, respectively and γ0 is the spontaneous emission probability. For ηa < ηb the spectra consist of a doublet peaked at [Formula: see text] and its intensity is constant. When ηa = ηb, the spectra are composed of five pairs of bands peaked at [Formula: see text], and [Formula: see text]. When ηa < ηb the computed spectra consist of five pairs of bands, where the intensities of the peaks at [Formula: see text] and [Formula: see text] are positive indicating absorption, those at [Formula: see text] are negative implying amplification, and the two pairs of peaks at [Formula: see text] have positive and negative components describing the mixed process of absorption–amplification. The intensities of these bands are found to vary as (ηa/ηb)2 for (ηa/ηb) > 1 and, therefore, the intensities of the bands are immensely enhanced as the value of the ratio (ηa/ηb) increases. The computed spectra for a wide selection of Rabi frequencies are graphically presented and compared with those derived by analytical methods.
We have considered the interference spectra arising from the competition between a spontaneous process and one induced by a laser field in a two-level atom. Expressions for the spectral functions have been derived describing the spectra of the excited and ground states of the atom in the low- and high-intensity limit of the laser field. For the excited-state spectra in the low-intensity limit, the frequency profiles of the two peaks, which arise from the spontaneous and the induced processes, cancel each other out completely near the center of the line, while for the ground state the induced process dominates. For finite values of the detuning, the spectra of the excited state consist of two peaks, which have positive and negative frequency profiles, respectively. The computed spectra have been graphically presented and discussed. In the high-intensity limit, the dynamic Stark effect dominates the spectra of the excited and ground states of the atom. Expressions for the correlation functions have been derived that describe the emission or the absorption of a laser photon at two different times. The derived expressions for the corresponding delay functions in the low- and high-intensity limits have been found to be identical to those recently proposed in the literature. The laser field has been treated as a classical as well as a quantized entity.