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Optics and Spectroscopy

Incoherent properties of induced radiation

B. A. Veklenko

Published May 1, 2003• 2 citations
Publisher

Abstract

The evolution of a quantized electromagnetic field in a thermally excited dispersion medium is determined by two scattering channels. The coherent channel is formed exclusively by the elastic scattering of quanta. The incoherent channel, along with elastic scattering processes, necessarily contains inelastic scattering processes, including induced radiation. Interference between the channels is absent because of the orthogonality of the wave functions of the medium in its final states, which correspond to different scattering channels. Therefore, in an excited medium, interference processes that are not described by its refractive index may arise. An interference pattern of this kind can be formed, in particular, as a result of the superposition of the resonance radiation incident on an excited medium and the radiation reflected from this medium. In this case, the conventional perturbation theory proves to be inadequate.

DOI
10.1134/1.1576851

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The evolution of a quantized electromagnetic field in a thermally excited dispersion medium is determined by two scattering channels. The coherent channel is formed exclusively by the elastic scattering of quanta. The incoherent channel, along with elastic scattering processes, necessarily contains inelastic scattering processes, including induced radiation. Interference between the channels is absent because of the orthogonality of the wave functions of the medium in its final states, which correspond to different scattering channels. Therefore, in an excited medium, interference processes that are not described by its refractive index may arise. An interference pattern of this kind can be formed, in particular, as a result of the superposition of the resonance radiation incident on an excited medium and the radiation reflected from this medium. In this case, the conventional perturbation theory proves to be inadequate.
Scattering of a resonance electromagnetic field from excited atoms cannot be described by the semiclassical theory of radiation operating with nonquantized electromagnetic fields. Field quantization effects are manifested in this case on the macroscopic level and lead to evolution of statistical properties of radiation in the course of scattering. It is found that a combined process coupling elastic scattering from an atom and induced emission from the same atom, which cannot be studied by the methods of the standard perturbation theory, plays a significant role in this effect. The process of combined scattering in extended media exhibits coherent properties that cannot be described by the standard refractive index.
According to quantum electrodynamics, the cross section for resonant scattering of radiation on an aggregate of excited atoms can be written as a sum of positive definite terms. This type of structure is not consistent with the Fresnel formulas for the reflection coefficient of radiation from thermally excited media. The difference shows up on a macroscopic level and indicates that semiclassical radiation theory cannot be used. A study of the correlation between elastic scattering and stimulated emission processes clarifies the reason for the discrepancies. The resulting singularities require summing of Feynman diagrams which appear beginning in the sixth order of perturbation theory. A lower bound estimate for the reflection coefficient from a plane layer is given, including processes which violate the statistics of radiation. The contribution of stimulated emission processes caused by the initially scattered photon are examined specifically. An experiment is proposed which would settle the choice of theories.
This thesis concerns the theoretical investigation of interference phenomena related to elastic and inelastic scattering of quantized light. The presented work is naturally divided into two parts, the first is concerning elastic scattering while the second explores inelastic scattering. In the first part we use a scattering-matrix formalism combined with results from random-matrix theory to investigate the interference of quantum optical states on a multiple scattering medium. We investigate a single realization of a scattering medium thereby showing that it is possible to create entangled states by interference of squeezed beams. Mixing photon states on the single realization also shows that quantum interference naturally arises by interfering quantum states. We further investigate the ensemble averaged transmission properties of the quantized light and see that the induced quantum interference survives even after disorder averaging. The quantum interference manifests itself through increased photon correlations. Furthermore, the theoretical description of a measurement procedure is presented. In this work we relate the noise power spectrum of the total transmitted or reflected light to the photon correlations after ensemble averaging. This analysis enables us to describe an experimental observation of the quantum nature of light that survives the averaging over disorder. In the second part we investigate inelastic scattering. This we do by first treating the scattering of light on dipoles embedded in an arbitrary dielectric environment. By considering the two different models for dipole interaction known as the minimal-coupling and electric-dipole interaction Hamiltonians, we find exact relations between the electric field and the dipole operators in the Heisenberg picture, while keeping the model of the dipoles arbitrary. Due to the exact treatment of the electric-field operators, we obtain kernels known from classical scattering theory to describe the propagation of the field from the dipoles. Using the found electric field operators we derive the Heisenberg equations of motion for the dipoles while treating them as quantum two-level systems and using the Born–Markov and rotating-wave approximations. Postponing the rotating-wave approximation to the very end of the formal calculations allows us to identify the different physical parameters of the dipole evolution in terms of physical quantities known from optics. Finally, we use our Heisenberg picture formalism to treat a dilute cloud of two-level atoms, by simplifying the equations of motion using a single-scattering approximation for the interaction between the atoms. This enables us to derive expressions for the steady-state population and fluorescence spectrum, where we find cooperative effects in both the elastic and the inelastic spectra.
It is shown that coherent processes of elastic scattering of resonant radiation form a “buffer” electromagnetic field near the boundary of excited media. This part of radiation is not governed by the standard refractive index, but precisely this part of radiation forms the beams reflected and refracted by the excited medium. The presence of the “buffer” field causes the suppression of stimulated emission near the boundary and leads to the appearance of a frequency angular broadening of the beam transmitted through a thin film of excited atoms at an oblique angle.