In Chapter 3, we move to a semiclassical treatment (quantum theory) of light absorption and scattering, specifically from atoms. We start with a description of how lidar measures Doppler shift, and the fundamental difference between the measurement when the laser is in resonance with an atomic transition (resonant) and when it is not (nonresonant). We follow with a treatment of quantum polarizability and the resulting absorption cross section, leading to the differential resonance scattering cross section and its contrast with the classical result. After quantum polarizability, we demonstrate the radiation pattern of coherently excited atoms. This takes us to an interpretation of the Hanle Effect. Following these descriptions of the phenomena that impact resonance lidar, we extend our understanding by closing the chapter with an overview of the rudimentary physics of sodium laser guide stars.
In Chapter 3, we move to a semiclassical treatment (quantum theory) of light absorption and scattering, specifically from atoms. We start with a description of how lidar measures Doppler shift, and the fundamental difference between the measurement when the laser is in resonance with an atomic transition (resonant) and when it is not (nonresonant). We follow with a treatment of quantum polarizability and the resulting absorption cross section, leading to the differential resonance scattering cross section and its contrast with the classical result. After quantum polarizability, we demonstrate the radiation pattern of coherently excited atoms. This takes us to an interpretation of the Hanle Effect. Following these descriptions of the phenomena that impact resonance lidar, we extend our understanding by closing the chapter with an overview of the rudimentary physics of sodium laser guide stars.
A laser resonant scattering process involves two steps, excitation and emission. That emission occurs spontaneously is well accepted. That the atoms involved in the emission are excited coherently by a laser beam leading to a non-isotropic angular distribution of emission (an antenna pattern) is not well known. The difference between coherent and incoherent excitation leads to the Hanle effect. In this paper, I discuss the physics of Hanle effect, and its influences on the backward scattering intensity of Na, K, and Fe atomic transitions and the associated Na and Fe resonant fluorescence lidar systems.
The problem of light scattering from a monochromatic laser beam by an ensemble of atmospheric atoms or molecules in thermal equilibrium under ambient wind and temperature is revisited with two emphases. First, the essence of and difference between laser Cabannes scattering (CS) and laser-induced resonance fluorescence (LIF), which permit atmospheric temperature and wind measurements, are simply presented. A classical model is shown to yield the same angular distribution in scattered power for both, a factor of two larger Doppler shift for the former (CS), in the backward direction with the same line-of-sight (LOS) wind, and a dramatic 17 order larger backscattering cross section for the latter (LIF). Second, the LIF process is developed from first principles, and we present the relations between absorption cross section, differential scattering cross sections, and LIF emission spectrum for atoms with hyperfine structure. By doing this, we (1) equate the decoherence rate among the mixed excited substates to half of the Einstein coefficient to comply with energy conservation, and (2) present a clear physical insight into the origin of the Hanle effect, whose quantitative evaluation for these atoms requires quantum mechanical treatment. We then derive LIF emission rates for each of the eight and 10 pathways associated with the D1 and D2 transitions, and deduce the temperature and LOS wind dependence in differential backscattering cross sections of atmospheric sodium and potassium atoms. Using these cross sections allows retrieval of atmospheric parameters in the mesopause region (80–110 km in altitude) by a metal resonance lidar.
This chapter introduces a three-level atomic model and discusses two other coherent atomic phenomena; namely, coherent Raman scattering and lasing without inversion. Lasing without inversion may take place in three-level resonant atomic systems and, like super-radiance, results from atomic coherence. Super-radiation is initiated by spontaneous fluctuations of the polarization in the medium. The semiclassical method is a powerful tool that is useful for the treatment of propagation effects in super-radiance as well as in such coherent emission processes as self-induced transparency, photon echo and others. The use of the Maxwell—Bloch equations allows one to consider these phenomena in elongated systems. Fortunately, the semiclassical approach is readily applicable to low-density systems that are to gases. However, one has to exercise greater care when applying it to coherent emission in solids. In high-density systems there is a strong mixing of the field and atomic states in the vicinity of resonance.
A quantum statistical theory of resonant optical phenomena is developed for the case when the fluctuations of the laser, used for exciting transitions, are important. The general equations describing the dynamics of a relaxing two-level atom (TLA) are solved exactly for different types of mean values and the two-time amplitude and intensity correlations. The phase-diffusion model is adopted for laser fluctuations. The exact results are used to analyze the effect of laser fluctuations on a number of optical effects-optical free-induction decay, adiabatic following, the spectrum of the scattered light from a relaxing TLA, the energy-absorption spectrum from a weak field, Hanle resonances, etc. In each case, the laser fluctuations are found to affect in an important way the characteristics of the above optical-resonance phenomena. For example, the spectrum of scattered radiation from a TLA has the usual three-peak structure for fields at resonance and with strengths $\ensuremath{\alpha}$ above the threshold and for $\ensuremath{\alpha}\ensuremath{\gg}{\ensuremath{\gamma}}_{c}$; however, now the peak heights (widths) are in the ratio 3x (3x2), $x=\frac{[{\ensuremath{\gamma}}_{c}+\frac{({T}_{1}^{\ensuremath{-}1}+{T}_{2}^{\ensuremath{-}1})}{3}]}{[2{\ensuremath{\gamma}}_{c}+{T}_{2}^{\ensuremath{-}1}]}$, where ${\ensuremath{\gamma}}_{c}^{\ensuremath{-}1}$ is the correlation time for laser phase fluctuations. For ${\ensuremath{\gamma}}_{c}\ensuremath{\gg}\ensuremath{\alpha}$, one gets a single-peak spectrum. The laser field is treated as a second-quantized field with excitation in either a coherent state or a Fock state. The results, obtained by straightforward perturbation theory, but valid for arbitrary values of the relaxation parameters, detuning, and the laser correlation time, are also presented.
Although the primarily phenomenological theory of absorption and refraction of light by matter, based on classical models as presented in Chapter 4, is very useful, it is incomplete and often inadequate. A more complete and accurate picture of electrodynamics is given by the theory of quantum optics, and that is the topic of this chapter. The models developed in this chapter are more detailed and therefore more complicated than the phenomenological models of Chapter 4. The most robust models, which are applied in Part II, are presented in this chapter. The quantum models accurately represent experimental data and allow extrapolation and interpolation of such data. Many practical computer based models concerning optical propagation are based on this theory. The theory of elastic scatter as presented in Chapter 4 is consistent with quantum optics and is not presented again. (However, inelastic scatter must address the quantum nature of the scattering medium.) Quantum optics is not completely covered in this chapter. Entire textbooks are devoted to this diverse and comprehensive topic covering optics (see Refs. 5.1–5.3). The emphasis of this book is on absorption and reflection spectroscopy. Now details of internal structure of the medium impacting light–matter interaction are examined. The classical oscillator model is upgraded by semiclassical radiation theory and a quantum oscillator model is developed. Semiclassical radiation theory is based on a quantized medium coupled to a classical field. It is often applied to laser theory, where near-line-center stimulated emission dominates. The quantum oscillator model again utilizes the quantized medium and classical field, but with more attention to detailed balance between absorption and emission. It satisfies causality and the fundamental symmetry relationships established in Chapter 2. These quantum optics models are more complete formalisms and provide solutions to the shortcomings of classical electrodynamics. Of particular interest to propagation in gaseous media is the line shape in the far wing. To achieve long path lengths, propagation near line center of a resonance must be avoided. Line shape models in quantum optics accurately represent much of the frequency and temperature dependence observed in experimental data.
We investigate in this chapter the general problem of the interaction of an atom (or a molecule) and a classical electromagnetic field. Its importance derives firstly from the fact that a large part of our knowledge of atoms is obtained from a study of the radiation they absorb or emit (we shall consider equally visible radiation and radio-frequency and X-rays) and, secondly, that the interaction with matter modifies the propagation of the electromagnetic field itself, notably through absorption, refraction or scattering. The interactions of atoms with light therefore encompass a vast range of physical effects that we could not hope to cover adequately in a single chapter. In this chapter we shall therefore present the fundamental features of the interaction of an atom, which will be treated quantum mechanically, with a classical electromagnetic field, that is an electromagnetic field described by real electric and magnetic vectors obeying Maxwell's equations. A rigorous description of the atom–light interaction would have to take into account the quantum nature of light. This we shall leave to Chapter 6. It turns out, nevertheless, that many important results can be obtained from the semi-classical viewpoint adopted here (although it is perhaps more appropriate to refer to this treatment as ‘semi-quantized’).