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Nonlinear Optics

Radiative Renormalization Analysis of Optical Double Resonance

Paul L. Kelley, O. Blum, T. Kenneth Gustafson

Published Jan 1, 1992• 1 citation
Publisher

Abstract

The problem of optical double resonance as shown in the Figure is a familiar one in optics.[1-3] In this case, a near-resonant field at frequency ν l connects level 1 with level 2 while a near resonant field at frequency v u connects level 2 with level 3. When level 2 is below level 3, the excitation of level 3 involves two photon absorption; if level 2 is above level 3, the excitation of level 3 is a Raman process.

DOI
10.1364/nlo.1992.tud4

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The problem of optical double resonance as shown in the Figure is a familiar one in optics.[1-3] In this case, a near-resonant field at frequency ν l connects level 1 with level 2 while a near resonant field at frequency v u connects level 2 with level 3. When level 2 is below level 3, the excitation of level 3 involves two photon absorption; if level 2 is above level 3, the excitation of level 3 is a Raman process.
A complete and detailed treatment of a three-level atom interacting with two near-resonant monochromatic fields is presented. It is assumed that the only damping mechanism is radiative damping, and that the atoms all have the same resonance frequencies, as is the case in an atomic beam. Detailed analytic solutions as well as numerical examples are determined from quantum-electrodynamic equations of motion. In addition, approximation techniques are presented which allow one to get accurate quantitative predictions for strong applied fields from simple rate-equation-like arguments. Absorption and emission spectra are determined, as are the transient and steady-state response of the atom. Two of the more interesting predictions are an emission spectrum containing up to seven components and a prediction of steady-state populations larger than 0.5 in the second excited state.
The nonlinear interaction of two intense optical waves with three energy levels of an atomic system is analyzed theoretically. The frequencies of the applied fields are assumed to be on or near two of the resonances involving the three levels. Particular attention is given to the generation of power at the difference frequency of the two applied fields where their frequency separation lies in the far-infrared range of the spectrum. In the limit of large input fields where atomic transitions are driven to saturation, the generated difference-frequency power is no longer proportional to the product of the two input powers. It is shown that, in this limit, the total rate of emission of photons at the difference frequency may, in principle, approach a value given by rNT\frac{\mathrm{rN}}{T}TrN​, where NNN is the total number of atoms, TTT is the average time of coherent interaction of atoms and the radiation field, and rrr is a factor which in favorable cases approaches unity at low temperatures. Also, a number of additional effects are encountered due to coherent double-quantum transitions among various levels which may be ignored only for weak input powers. These effects are highly dependent on the modes of relaxations of atomic levels and the details of the line shape. The results are applied to several cases, in which the resonance condition yields large efficiency in nonlinear frequency mixing.
Abstract If and only if spontaneous resonance Raman scattering is excited by irradiation upon a single, discrete and non‐degenerate energy level sufficiently distant from other levels can it be interpreted as resonance fiuorescence, i.e. a sequence of two independent one‐photon processes, an absorption and an emission in definte order of succession. This decomposition of the resonance scattering process is independent of the bandwidth of the exciting radiation relative to the widths of the combining levels. These widths however determine quantitatively the temporal decay of the resonance scattering (= resonance fluorescence) probability given explicitly in the paper.
We have calculated the excitation spectra of a single electron in the excited state of a three-level atom interacting with two off-resonant laser fields at high intensities. We have also considered the process where one laser photon is absorbed by the ground state, as well as a Raman-type process where one photon of one of the laser fields is emitted while another photon of the other laser field is absorbed simultaneously by the second excited state of the atom. The net excitation spectra of the three processes in question consist of two peaks having always positive intensities indicating induced absorption (attenuation) and a third peak which has positive, zero and negative intensities for values of the Rabi frequencies , and , respectively. When , the Raman-type process prevails over the other two, and the resulting peak has a negative intensity indicating that significant amplification is likely to occur at the corresponding frequency.
The resonant Raman scattering in a three level system produces an optical pumping of molecules from the initial to the final states which are radiatively coupled to the intermediate resonant state. We consider the pumping that is produced by an intense, pulsed, monochromatic radiation field that is near-resonant with the initial resonance frequency. The Heitler–Ma damping theory is solved exactly for the case when the resonance fluorescence is weak compared to the Raman scattering, or any other processes which might cause irreversible decay of the resonant state. In particular, we examine the usefulness of dressed states to describe the intense field limit. The spectral line shape for the Raman scattering is obtained. The transient behavior following the onset of the laser pulse is examined and a careful analysis of the pumping rate and its relationship to both weak and strong field theories is presented.