The four-wave mixing generates the polarization on the additional frequency under the interaction of the two-level system with polychromatic field. The absorption profiles of side-back harmonic have the subradiation structure in the case of excitation of system by the symmetric trichromatic field with the intense central component and weak (or equal to central) side-back harmonics. The resonances of the absorption coefficient on the subradiation frequencies have the specific dispersion features.
The four-wave mixing generates the polarization on the additional frequency under the interaction of the two-level system with polychromatic field. The absorption profiles of side-back harmonic have the subradiation structure in the case of excitation of system by the symmetric trichromatic field with the intense central component and weak (or equal to central) side-back harmonics. The resonances of the absorption coefficient on the subradiation frequencies have the specific dispersion features.
An analytic expression of the polarization induced by a polychromatic weak probe field in a two-level medium, driven by a strong polychromatic pumping field, is obtained. This expression allows one to obtain both the absorption and dispersion spectra at any frequency of a probe field. The numerically calculated graphs of the central-component probe-field absorption and dispersion spectra, depending on the pumping-field amplitude in the cases of the one-, two- three-, four-, and five-component pumping field, are presented. It is shown that when the probe-field detuning is close to the strong-field Rabi frequency, the absorption spectrum changes to the dispersionlike form, while the dispersion spectrum changes to the absorptionlike one.
Let us consider preliminary two situations. In the first of them the monochromatic radiation is absorbing. The increase of its intensity leads to the diminution of an absorption down to zero in a limiting case, i.e. to the effect of saturated absorption. In the second case an absorption of test radiation with a small intensity is observing, while two—level atom is strongly interacting with a perturbing field. This case is characterized by asymmetric dependence of absorption on the frequency difference w- w = A, where w and w are the frequencies of two light waves. As it was shown by Rautian and Sobelman in 19611, the amplification of test radiation arises in a certain range of frequency offsets A instead of the absorption, and the energy transfers from a strong wave to a weak one. In this paper we study the problem which appears from the above situation, when the intensity of test radiation increases. Such an increase leads to new maxima in absorption spectra of test radiation at frequencies A = i n = 2, 3 4 . . . which are additional to the main maxima at n R A = where R the Rabi frequency. These new resonances were observed by Bonch-Bruevich, Vartanyan, and Chigir in 19792 and cal led the subradiat ive structure. We have the following simple approximate expression for R obtained in the case of interaction with two fields: Q =d(?+E2)1"2/h. (1) R 0 1 There are two essential effects in the described situation: the saturation of absorption and the nonlinear interference effect. The last causes the redistribution of an absorbed energy between radiation components, the negative absorption (amplification) without population inversion, and the multiphoton parametric resonances at difference frequencies. The laser generation on the base7of the negative absorption without population inversion was obtained in 1989. The following problems arise from the facts reviewed above: 1. The calculation of absorption coefficients for individual components of a strong polychromatic radiation with an equidistant spectrum. 2. Determining of a generalized Rabi frequency and verification of the simple formula A = In for maxima of resonances. n R The aim of this paper is to solve these problems.
When a two-level system interacts resonantly with a saturating pump laser, the absorption profile of a probe wave in the Rabi sidebands resembles two separate dispersion profiles. At sufficiently high probe intensity this effect is accompanied by a dispersive profile in the pump-wave absorption, considered as a function of the probe-wave frequency, and also by a dip in the population of the upper state of the two-level system. The relative stabilization of the ground state is interpreted in terms of two-laser-photon processes where absorption of a pump (probe) photon is followed by stimulated emission of a probe (pump) photon. The dispersive absorption profile is attributed to the competition between three- and four-photon scattering processes.
We analyze the fluorescence and absorption spectra of a two-level atom driven by a bichromatic field with frequencies ${\mathrm{\ensuremath{\omega}}}_{1}$ and ${\mathrm{\ensuremath{\omega}}}_{2}$, separated by ${\mathrm{\ensuremath{\omega}}}_{2}$-${\mathrm{\ensuremath{\omega}}}_{1}$=2\ensuremath{\delta}, and Rabi frequencies (at resonance) 2${\mathrm{\ensuremath{\Omega}}}_{1}$ and 2${\mathrm{\ensuremath{\Omega}}}_{2}$ such that their ratio \ensuremath{\alpha}=${\mathrm{\ensuremath{\Omega}}}_{2}$/${\mathrm{\ensuremath{\Omega}}}_{1}$1. We focus on the case of ${\mathrm{\ensuremath{\omega}}}_{1}$ close to the atomic frequency ${\mathrm{\ensuremath{\omega}}}_{0}$ and ${\mathrm{\ensuremath{\omega}}}_{2}$ near the Rabi sideband frequency ${\mathrm{\ensuremath{\omega}}}_{1}$+2${\mathrm{\ensuremath{\Omega}}}_{1}$; the detunings are denoted by ${\mathrm{\ensuremath{\Delta}}}_{1}$=${\mathrm{\ensuremath{\omega}}}_{0}$-${\mathrm{\ensuremath{\omega}}}_{1}$ and ${\mathrm{\ensuremath{\Delta}}}_{2}$=${\mathrm{\ensuremath{\omega}}}_{1}$+2${\mathrm{\ensuremath{\Omega}}}_{1}$-${\mathrm{\ensuremath{\omega}}}_{2}$. We find that the spectra depend critically on the detuning ${\mathrm{\ensuremath{\Delta}}}_{2}$: For large ${\mathrm{\ensuremath{\Delta}}}_{2}$, the fluorescence spectrum consists of the well known Mollow triplet, centered at ${\mathrm{\ensuremath{\omega}}}_{1}$; for smaller (but nonzero) ${\mathrm{\ensuremath{\Delta}}}_{2}$, the spectrum is composed of a triplet at ${\mathrm{\ensuremath{\omega}}}_{1}$ together with doublets near the sideband frequencies ${\mathrm{\ensuremath{\omega}}}_{1}$\ifmmode\pm\else\textpm\fi{}2${\mathrm{\ensuremath{\Omega}}}_{1}$. However, when ${\mathrm{\ensuremath{\Delta}}}_{2}$=0 (and \ensuremath{\alpha}\ensuremath{\ll}1), the spectrum consists of a doublet centered at ${\mathrm{\ensuremath{\omega}}}_{1}$ and triplets at ${\mathrm{\ensuremath{\omega}}}_{1}$\ifmmode\pm\else\textpm\fi{}2${\mathrm{\ensuremath{\Omega}}}_{1}$: there is then no fluorescence at ${\mathrm{\ensuremath{\omega}}}_{1}$. As \ensuremath{\alpha} increases, additional triplet structures appear in the spectrum at frequencies ${\mathrm{\ensuremath{\omega}}}_{1}$\ifmmode\pm\else\textpm\fi{}2n${\mathrm{\ensuremath{\Omega}}}_{1}$ with intensities proportional to ${\mathrm{\ensuremath{\alpha}}}^{2(\mathit{n}\mathrm{\ensuremath{-}}1)}$, n\ensuremath{\gtrsim}1, and a line reappears at ${\mathrm{\ensuremath{\omega}}}_{1}$, with intensity proportional to ${\mathrm{\ensuremath{\alpha}}}^{4}$. The absorption by the system of a weak probe beam is also strongly dependent on the detuning, and the spectrum is composed of emission-dispersion-absorption features located near ${\mathrm{\ensuremath{\omega}}}_{1}$ and ${\mathrm{\ensuremath{\omega}}}_{1}$\ifmmode\pm\else\textpm\fi{}2n${\mathrm{\ensuremath{\Omega}}}_{1}$. An analysis in the dressed-atom picture is presented which explains the physical origin of all these features, in both fluorescence and absorption. \textcopyright{} 1996 The American Physical Society.
In the previous chapter we examined nonlinear propagation in a two-level medium, which leads to amplification or absorption of the radiation field. As we will see further on in this volume, when the medium is placed in an optical cavity one realizes a laser in the case of amplification or an optically bistable system in the absorptive configuration. On the other hand, the nonlinear response of the atomic polarization to the electric field leads to further fascinating scenarios [29, 51–60]. For example, a field with central ω 0 can generate harmonic components with central frequencies 2 ω 0 , 3 ω 0 etc., processes that are called second-harmonic generation, third-harmonic generation etc. Furthermore, the interaction of two fields with central frequencies ω 1 and ω 2 , with ω 1 > ω 2 , can generate components with central frequency ω 1 + ω 2 (sum-frequency generation) and ω 1 − ω 2 (difference-frequency generation). Such phenomena have not yet appeared in this volume because we have assumed that the electric field corresponds to a narrow frequency band around a central frequency ω 0 only, whereas to describe them it is necessary to assume that the electric field is the superposition of a number of frequency bands. In this chapter we will provide a description of the basic elements which are necessary to describe these phenomena and we will discuss a small number of them for the case of materials with a quadratic nonlinearity, referring to textbooks in nonlinear optics for the description of other phenomena. The following chapter is devoted, instead, to the case of materials with cubic nonlinearities. The starting point of nonlinear optics is the expansion of the atomic polarization in powers of the electric field, when the electric field is not too intense. In our treatment in Chapter 5 we saw that the expansion of the nonlinear susceptibility contains only even powers of the electric field (see Eq. (5.27)), and therefore the expansion of the polarization includes only odd powers.