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Physical Review A

Semiclassical theory of gaseous dipolar media with application to the gas laser

A. S. Acampora, P. Serafim

Published Jun 1, 1980• 0 citations
Publisher

Abstract

A new semiclassical model of the active medium of a gas laser and a description of its interaction with a classical electromagnetic field are reported. The model is based upon an exact microscopic formulation of the density of the active medium in a suitably defined semiclassical state space. Field-medium interaction mechanisms are studied by coupling the equation describing the dynamics of this density with Maxwell's field equations and the Schr\"odinger wave equation. Coupled stochastic nonlinear equations are formulated and quasilinear techniques are employed to effect their solutions. Wave-dipole correlations, the dominant nonlinearity, is shown to effect stability, produce the phenomena of hole burning, mode coupling, and frequency conversion, and to provide the mechanism whereby nonresonant pump field energy is converted into resonant laser oscillations.

DOI
10.1103/physreva.21.1991

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A new semiclassical model of the active medium of a gas laser and a description of its interaction with a classical electromagnetic field are reported. The model is based upon an exact microscopic formulation of the density of the active medium in a suitably defined semiclassical state space. Field-medium interaction mechanisms are studied by coupling the equation describing the dynamics of this density with Maxwell's field equations and the Schr"odinger wave equation. Coupled stochastic nonlinear equations are formulated and quasilinear techniques are employed to effect their solutions. Wave-dipole correlations, the dominant nonlinearity, is shown to effect stability, produce the phenomena of hole burning, mode coupling, and frequency conversion, and to provide the mechanism whereby nonresonant pump field energy is converted into resonant laser oscillations.
The semiclassical Lamb theory of gas lasers is extended to the case of lasers operating simultaneously on two coupled transitions. The theory is formulated in terms of the density-matrix equations for a three-level gaseous laser medium interacting with the field through electric-dipole transitions, so that there are two allowed transitions and one two-photon transition. It is assumed that there is a single resonator mode near each of the transition frequencies. Previous treatments of such three-level gas lasers either have used simple rate equations or have solved the density-matrix equations in an approximate fashion valid only for low intensities. Thus the numerical approach developed herein represents, to our knowledge, the first semiclassical theory of three-level gas lasers which is accurate for arbitrary detuning and intensity. Significant deviations from earlier, approximate treatments are found.
In this paper a completely classical model for laser action is discussed. An active medium consisting of classical anharmonic oscillators interacts with a classical electromagnetic field in a resonant cavity. Comparison with the case of a medium consisting of harmonic oscillators shows the significance of nonlinearities for producing self-sustained oscillations in the radiation field. The results for the classical model are found to be similar to those for a semiclassical model of the ammonia-beam maser. The conclusion is that laser action is not intrinsically a quantum-mechanical effect. The classical-laser theory as given in this paper can also be applied to the case of the electron-cyclotron maser.
This chapter explains a semi classical model in terms of a self consistent theory. An electric field present within the medium produces microscopic dipole moments; these moments added together in a many-atom system lead to a macroscopic polarization. This polarization acts as a source in the Maxwell's equations producing a reaction field. The electric field produces a dipole moment that can be explained by using the quantum mechanical model of the interaction of the classical electromagnetic field with an atom having quantized energy levels. Principles of statistical mechanics are used by considering the medium as an ensemble and density matrix is used to facilitate the process of calculating the macroscopic polarization. The semi classical model can apply to the lasers bounded by Brewster windows in a cavity that can sustain oscillation of a linearly polarized field. Two-mode operation of a laser is the simplest case of multimode operation.
A stochastic, semiclassical model is developed for a multimode, homogeneously broadened laser with rapid-dipole dephasing (e.g., semiconductor or dye lasers). The theory is valid for systems with a free spectral range that is large compared to the decay rates of the population inversion and the field. Population dynamics including temporal beating effects and relaxation oscillations, spatial-hole burning, coherent-wave mixing, and quantum noise are all included self consistently. A principal restriction of the model, when applied to coupled-cavity systems, is that the modes satisfying the boundary conditions of the gain medium must form a subset of the modes defined by the cavity and that only modes in this subset are above threshold. For typical systems, the model is valid for pump rates up to several times threshold. The effects on the emission linewidth of coherent-wave mixing and the number of modes included in the simulation at various pump rates are discussed.
Active media are materials that consist of quantum systems, such as atoms, impurities, or quantum dots, and are characterized by strong resonant absorption and re-emission of radiation. In this article, we present a general framework for the numerical simulation and analysis of time-dependent radiation-induced phenomena in active media. The formulation used is based on the solution of semiclassical Maxwell–Bloch equations describing the evolution of each quantum element under the effect of external and re-emitted radiation. Within these Maxwell–Bloch equations, the coupling of quantum systems to classical Maxwellian fields poses computational challenges due to the strong nonlinearities involved. In contrast to traditional mesh-based solvers, we adopt an electric field integral-operator approach that can reliably account for near-field effects—including self-radiation—and is scalable to large systems. We then focus on media based on large numbers of quantum dots and demonstrate various physical effects arising from the near-field coupling, including polarization modulations and superradiance.
We study the general problem of matter-laser interaction within the framework of nonrelativistic quantum electrodynamics, with particular emphasis on strong laser field effects. Consequently, we formulate a well-defined approximation leading in a straightforward manner toward the conventional semiclassical mode of description. Namely, we arrive naturally to two coupled equations of motion: (i) the Schr\"odinger equation which governs the quantum dynamics of an atomic system driven by classically described radiation field (composed of an incoming laser pulse plus radiation emitted from the atom), and (ii) the classical Maxwell wave equation which describes the emission of radiation from the mentioned atomic source. Employing the formalism of adiabatic Floquet theory, we derive a simple criterion of validity of the just described semiclassical approach. It shows that the semiclassical treatment is justified in most situations. On the other hand, it turns out that the semiclassical approximation breaks down completely in certain special but realistic cases, regardless of the fact that the incoming laser pulse contains a huge number of photons. Under such special circumstances, we anticipate new effects arising due to the quantized nature of the radiation field, to be observable, for example, in harmonic generation spectra. Our considerations are illustrated more explicitly using a simple model of a two-level atom strongly driven by a laser. The quantum dynamics of this model problem is resolved within the framework of quantum electrodynamics while adopting well-defined and physically justifiable approximations. As an outcome, analytic formulas are found serving as a quantitative criterion of (non)applicability of the semiclassical approach and demonstrating the breakdown of semiclassical theory under well-defined conditions. An illustrative numerical calculation is provided.