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Physical review. B, Condensed matter

Theory of second-harmonic generation from atom pairs in solids

Jacira C. B. Freitas, F. A. M. de Oliveira, S. S. Vianna, Cid Bartolomeu de Araujo

Published Sep 1, 1994• 0 citations
Publisher

Abstract

We present a theoretical study of the second-harmonic generation from pairs of two-level atoms in solids. The density-matrix formalism is used to obtain the nonlinear polarization governing the process. The second-harmonic polarization depends on the laser frequency, the interaction potential between the atoms, and the laser intensity. The signal line shape may exhibit power broadening and shift of resonances.

DOI
10.1103/physrevb.50.6620

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We present a theoretical study of the second-harmonic generation from pairs of two-level atoms in solids. The density-matrix formalism is used to obtain the nonlinear polarization governing the process. The second-harmonic polarization depends on the laser frequency, the interaction potential between the atoms, and the laser intensity. The signal line shape may exhibit power broadening and shift of resonances.
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We theoretically study intensity-saturation effects in resonant harmonic generation and multiphoton ionization. A first laser excites a two-photon resonance which is coupled by a second laser to an autoionizing state. Starting from an effective Hamiltonian for the three resonant atomic states, we derive a set of equations for the density matrix of the gaseous medium and the electromagnetic field within a semiclassical framework. We present and discuss analytical and numerical solutions of these equations which show a variety of line profiles depending critically on the intensities of the incident laser pulses.
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.
Understanding the processes underlying the optical excitation of atomic vapor in the vicinity of solid surfaces is of interest both from physical and technical points of view. Selective reflection spectra of laser light from an interface of a transparent dielectric material and resonant vapor are known to be Doppler-free and to provide important spectroscopic information about the atom-wall interaction. On the other hand, atomic vapors have such a large and fast nonlinear response on or near resonances that they are capable of processing signals and images with milliwatt lasers at a time scale of submicroseconds. In the present paper we investigate linear and nonlinear optical properties of a thin film of atomic vapor confined between two solid surfaces. Assuming two-level atoms, we solve the Maxwell- Bloch equations for light reflection from resonant atoms. The interaction between the resonant atoms and the wall is accounted for through the boundary conditions for all elements of density matrix. The transient polarization is shown to make an important contribution not only to the field structure in the vicinity of the wall but also to the interference pattern of the reflected field. It is found that the spectrum of reflection depends remarkably on the film thickness. Strong enhancement of signal is also found from this study and possible devices for the detection are discussed.
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.