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CRC Press eBooks

Effects of diffraction upon super-radiance

M. G. Benedict, A. M. Ermolaev, Viktor A. Malyshev, I. V. Sokolov, Evgenii Dmitrievich Trifonov

Published Mar 29, 2018• 0 citations
Publisher

Abstract

This chapter investigates both diffraction and fluctuation effects on super-radiance within the framework of two models. Firstly, the two-dimensional theory of super-radiance of an extended system is developed. Secondly, the chapter considers the super-radiance of a 'sheet of paper' volume. However, quantum fluctuations of the initial polarization give rise to transverse inhomogeneity of atomic and field characteristics, which manifests itself in a change in the shape of the pulse and in the radiation polar diagram. The ringing of the envelope, which is typical of the one-dimensional model, becomes smoother. The super-radiance polar diagram has a ray structure, of which the angular size of individual components (rays) is of the order of the diffraction angle. The angular size of the ray is close to the diffraction angle, and its form changes relatively little from one realization of the initial polarization distribution to another.

DOI
10.1201/9780203737880-9

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Journal of Physics B Atomic Molecular and Optical Physics•Nov 14, 1993•4 citations
This chapter investigates both diffraction and fluctuation effects on super-radiance within the framework of two models. Firstly, the two-dimensional theory of super-radiance of an extended system is developed. Secondly, the chapter considers the super-radiance of a 'sheet of paper' volume. However, quantum fluctuations of the initial polarization give rise to transverse inhomogeneity of atomic and field characteristics, which manifests itself in a change in the shape of the pulse and in the radiation polar diagram. The ringing of the envelope, which is typical of the one-dimensional model, becomes smoother. The super-radiance polar diagram has a ray structure, of which the angular size of individual components (rays) is of the order of the diffraction angle. The angular size of the ray is close to the diffraction angle, and its form changes relatively little from one realization of the initial polarization distribution to another.
This chapter focuses on the relation between quantum and semiclassical approaches in super-radiance theory. The semiclassical solution can be regarded only as an ingredient of a convenient scheme for calculating quantum mechanical expectation values. Indeed, at the earliest stages, when the electric field and the polarization have not yet risen above the level of quantum fluctuations, the radiative process is not a classical one and would be greatly disturbed by measurements. The chapter presents some statistical characteristics of the linear stage of super-radiance. Super-radiance may be treated as an amplification of the field generated by quantum fluctuations of the polarization. Another aspect of super-radiance evolution is a build up of coherence both of the radiation field and the atomic polarization. Initially tiny, it grows to a macroscopic size and exhibits the statistics of super-radiance pulses. The parameters characterizing the shape of the pulse vary strongly enough within the ensemble for their root mean square deviations.
This introduction presents an overview of the key concepts discussed in the subsequent chapters of this book. The book discusses the main features of super-radiance using some simplified models. It presents a review of experimental work on super-radiance. The book also presents a generalization of the Wigner–Weisskopf approach to the N -atom system using a diagram method of non-stationary perturbation theory. It discusses several correlation functions for the field and the polarization, which characterize the coherence properties of super-radiation. The book uses the semiclassical approach to investigate the influence of de-phasing processes on radiation efficiency, or in other words, the influence of homogeneous and inhomogeneous broadening of the spectral line on the dynamics and spectrum of super-radiance. It considers the boundary value problem for the transmission and reflection of short pulses, taking into account the local field correction. Two effects are of special interest: the population-dependent frequency shift and the possibility of mirror-less bistability of ultra-short electromagnetic pulses.
We study here level-degeneracy effects in super-radiance, using the quantum "small-system" model whose interest and limitations are discussed. First, we show that this model allows one to understand the physical origin of these effects and to describe their qualitative influence on the properties of the emitted light. We also present and analyze numerical results obtained for the case of a dipole transition between two degenerate levels of angular momenta \textonehalf{}. We show that in this particular case one can define a basis of collective states which is well adapted to the invariance properties of the master equation. It is then possible to solve the master equation and to compute expectation values for the radiated field (intensity radiated with a given polarization, quantum fluctuations of this intensity) for various initial conditions and for small but already significant values of the number of individual systems. A detailed analysis of these results and a comparison with analogous calculations in the case where the degeneracy is supposed to be removed allows us to estimate the individual influence of the different types of effects (interference effects and the two sorts of competition effects, inhibition and initiation). We also compare the total intensity radiated to the intensity radiated by the same number of two (nondegenerate) level atoms. This comparison can be simply understood if one studies the partition of the population of the collective energy levels between the different states of these levels, and it appears that the most populated states are these which are able to radiate the most. Finally, it is shown how level degeneracy affects the quantum fluctuations of the intensity.
This chapter considers super-radiance on an elementary level in the sense that the main notions and concepts of the phenomenon will be treated as they evolved in the course of the early studies starting with the classical works by R. H. Dicke. It considers super-radiance from a system with dimensions small compared with the wavelength of the emission that is the Dicke model. The chapter discusses the results to be obtained are also applicable to the single-mode super-radiance of an extended system. It then considers mainly the cooperative spontaneous emission of a collection of N identical atoms confined within a small volume. If the audience wish to investigate the super-radiance of an extended system, the dimensions of which exceed the emission wavelength, the semiclassical method is more convenient. In essence, the semiclassical approach discussed in the chapter combines the quantum mechanical treatment of the atomic system that uses the density matrix formalism with the classical treatment of the radiation field.
The influence of the dipole–dipole inter-atomic coupling on collective spontaneous emission has been considered by many authors using both semiclassical and quantum theories. Specific results have been obtained for simple cases of regular atomic systems with a finite number of atoms. For disordered systems it has been found that the dipole–dipole coupling causes relaxation of the polarization phase (the effect of de-phasing), thus suppressing super-radiance. The main object of this chapter will be a regular linear chain of identical two-level atoms fully excited in the initial moment of time. The chapter considers the super-radiance of a regular linear chain of atoms. Such a system is the limiting case of a multi-atomic system characterized by a small Fresnel number. The dipole–dipole inter-atomic coupling modifies the super-radiance dynamics only slightly, but has a strong effect on the shape and width of the spectrum.
The polarization properties and the temporal shapes of the super-radiance pulses formed on degenerate levels are studied theoretically in a semiclassical approximation. The dependence of the super-radiance pulse polarization on the values of the total angular momenta of resonant levels and on the polarization and area of the pumping pulse is examined in detail. Non-linear equations describing the temporal shapes of the super-radiance pulses with different polarizations are obtained. Some examples with low values of angular momenta of the levels are discussed. It is shown that, in general, the temporal shape of the super-radiance pulse differs from hyperbolic secant.