Amplification of maser radiation involves an interaction between the radiation and the response function of the molecules that exhibit the population inversion. If the molecular response is taken to be quantum-mechanical, it is shown that the matter–radiation interaction must involve both amplitude and phase if a correct treatment of saturation of the population inversion is to be determined. The semi-classical treatment is compared with a fully quantum-mechanical approach, in which the radiation field is also quantized. Amplification and saturation of the maser radiation are accompanied by a partial locking of the phase across the lineshape. Significant variation of the phase under strongly saturated conditions occurs only over frequency intervals much larger than the homogeneous linewidth. The fully quantum-mechanical treatment of the radiation may have important consequences for the initiation of maser action.
Amplification of maser radiation involves an interaction between the radiation and the response function of the molecules that exhibit the population inversion. If the molecular response is taken to be quantum-mechanical, it is shown that the matter–radiation interaction must involve both amplitude and phase if a correct treatment of saturation of the population inversion is to be determined. The semi-classical treatment is compared with a fully quantum-mechanical approach, in which the radiation field is also quantized. Amplification and saturation of the maser radiation are accompanied by a partial locking of the phase across the lineshape. Significant variation of the phase under strongly saturated conditions occurs only over frequency intervals much larger than the homogeneous linewidth. The fully quantum-mechanical treatment of the radiation may have important consequences for the initiation of maser action.
Amplification of maser radiation involves an interaction between the radiation and the response function of the molecules that exhibit the population inversion. If the molecular response is taken to be quantum-mechanical, it is shown that the matter-radiation interaction must involve both amplitude and phase if a correct treatment of saturation of the population inversion is to be determined. The semi-classical treatment is compared with a fully quantum-mechanical approach, in which the radiation field is also quantized. Amplification and saturation of the maser radiation are accompanied by a partial locking of the phase across the lineshape. Significant variation of the phase under strongly saturated conditions occurs only over frequency intervals much larger than the homogeneous linewidth. The fully quantum-mechanical treatment of the radiation may have important consequences for the initiation of maser action.
ABSTRACT We consider the radiation properties and processes of a gas with a population inversion using the formalism based on the Maxwell–Bloch equations. We focus on the maser action and Dicke’s superradiance to establish their relationship in the overall radiation process during the temporal evolution of the system as a function of position. We show that the maser action and superradiance are not competing phenomena but are rather complementary and define two distinct limits for the intensity of radiation. Masers characterize the quasi-steady state limit, when the population inversion density and the polarization amplitude vary on time-scales longer than those of non-coherent processes affecting their evolution (e.g. collisions), while superradiance defines the fast transient regime taking place when these conditions are reversed. We show how a transition from a maser regime to superradiance will take place whenever a critical threshold for the column density of the population inversion is reached, at which point a strong level of coherence is established in the system and a powerful burst of radiation can ensue during the transient regime. This critical level also determines the spatial region where a transition from the unsaturated to the saturated maser regimes will take place; superradiance can thus be seen as the intermediary between the two. We also quantify the gain in radiation intensity attained during the superradiance phase relative to the two maser regimes and show how the strong coherence level during superradiance is well suited to explain observations that reveal intense and fast radiation flares in maser-hosting regions.
Using semiclassical radiation theory, a formalism similar to that used by Lamb in his Theory of an Optical Maser is developed for studying the amplification of vector traveling waves in a laser-type medium. The effect of the medium on the waves is given in terms of space (or time) dependent field amplitudes and phases and a nonlinear index of refraction. With particular emphasis on typical gaseous media, the effects of Doppler broadening are treated in detail for arbitrary ratios of natural to Doppler linewidths. Polarization and propagation vectors in various directions are considered, and the nonlinear effects are found to make an isotropic medium effectively anisotropic.
Lowest order nonlinear effects (due to a polarization cubic in the field amplitudes) are studied extensively, and the frequency dependence of several of these processes is presented in graphical form. In particular, the introduction of fields at new frequencies and polarization effects are considered. The characteristics of these nonlinear processes peculiar to Doppler broadened lines are discussed, and the processes are interpreted in terms of saturation and coherent modulation of the population inversion density.
Strong nonlinear effects are considered in a more approximate way and are found to consist of saturation of the various linear and nonlinear processes previously considered. These strong nonlinear effects should occur at low enough intensities to be easily observed in practice on a CW basis. With the present formalism, the analytical results of Gordon, White and Rigden regarding gain saturation in laser amplifiers are obtained, and the extension is made to include frequencies away from line center and the effects of multiple spectral components. Again, the introduction of fields at new frequencies is considered in detail. These results are also discussed in terms of saturation and coherent modulation of the populations and hole burning.
This paper has two purposes: 1) to clarify the relationship between the quantum theory of radiation, where the electromagnetic field-expansion coefficients satisfy commutation relations, and the semiclassical theory, where the electromagnetic field is considered as a definite function of time rather than as an operator; and 2) to apply some of the results in a study of amplitude and frequency stability in a molecular beam maser. In 1), it is shown that the semiclassical theory, when extended te take into account both the effect of the field on the molecules and the effect of the molecules on the field, reproduces almost quantitatively the same laws of energy exchange and coherence properties as the quantized field theory, even in the limit of one or a few quanta in the field mode. In particular, the semiclassical theory is shown to lead to a prediction of spontaneous emission, with the same decay rate as given by quantum electrodynamics, described by the Einstein A coefficients. In 2), the semiclassical theory is applied to the molecular beam maser. Equilibrium amplitude and frequency of oscillation are obtained for an arbitrary velocity distribution of focused molecules, generalizing the results obtained previously by Gordon, Zeiger, and Townes for a singel-velocity beam, and by Lamb and Helmer for a Maxwellian beam. A somewhat surprising result is obtained; which is that the measurable properties of the maser, such as starting current, effective molecular Q, etc., depend mostly on the slowest 5 to 10 per cent of the molecules. Next we calculate the effect of amplitude and frequency of oscillation, of small systematic perturbations. We obtain a prediction that stability can be improved by adjusting the system so that the molecules emit all their energy h Ω to the field, then reabsorb part of it, before leaving the cavity. In general, the most stable operation is obtained when the molecules are in the process of absorbing energy from the radiation as they leave the cavity, most unstable when they are still emitting energy at that time. Finally, we consider the response of an oscillating maser to randomly time-varying perturbations. Graphs are given showing predicted response to a small superimposed signal of a frequency near the oscillation frequency. The existence of "noise enhancing" and "noise quieting" modes of operation found here is a general property of any oscillating system in which amplitude is limited by nonlinearity.
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’).
The effect of thermal photons on the radiative properties of a one-atom maser is investigated. Stationary P and Q distribution functions are determined analytically in the approximation of strong interaction between an atom and a cavity field mode. The generation conditions are found for a one-atom maser. It is shown that taking into account thermal photons leads to a decrease in the threshold value of incoherent pumping. It is demonstrated that generation may occur in the absence of population inversion in the atomic subsystem and when losses exceed the intensity of incoherent pumping. A formula is proposed for the Fano factor of a one-atom maser in the form of the sum of the Fano factors of the microcavity radiation in the absence of thermal photons and the thermal radiation.