It is shown that the theory of the maser can be simply presented in terms of the concept of the radiation reaction field. This is the radiation field produced in a cavity or wave guide by the presence of the sample's electromagnetic moment. Its reaction back on the sample causes coherence effects such as those called ``superradiance'' by Dicke. Two amplifiers using the radiation reaction field in different ways from the usual solid-state maser are discussed. One of them takes advantage of the nonlinearity of the equations of motion to make a modulated coupling between two cavity modes by means of a sample with three energy levels such as is used in Bloembergen's maser. The resulting amplifying mixer behaves the same as (but is different in principle from) Suhl's ferromagnetic amplifier. A second type of amplifier employs the reaction field to destroy the circular polarization of a paramagnetic resonance. It is then possible to make an amplifier from this using the principle of the subharmonic generator.
It is shown that the theory of the maser can be simply presented in terms of the concept of the radiation reaction field. This is the radiation field produced in a cavity or wave guide by the presence of the sample's electromagnetic moment. Its reaction back on the sample causes coherence effects such as those called ``superradiance'' by Dicke. Two amplifiers using the radiation reaction field in different ways from the usual solid-state maser are discussed. One of them takes advantage of the nonlinearity of the equations of motion to make a modulated coupling between two cavity modes by means of a sample with three energy levels such as is used in Bloembergen's maser. The resulting amplifying mixer behaves the same as (but is different in principle from) Suhl's ferromagnetic amplifier. A second type of amplifier employs the reaction field to destroy the circular polarization of a paramagnetic resonance. It is then possible to make an amplifier from this using the principle of the subharmonic generator.
Masers exhibit interesting transient behavior that cannot be completely understood on the basis of the rate equations. The use of the rate equations in most transient analyses is usually justified on a more or less intuitive basis and the implied assumptions are not always clear. In this paper, the macroscopic maser rate equations are derived systematically from the Boltzmann equation for the density matrix of the atomic systems and Maxwell's equations for the radiation fields. When the coherence linewidth (T2−1) of the atomic systems is much larger than the cavity linewidth and the natural linewidth (T1−1) of the atomic emission, and with a WKB approximation, in the lowest order of approximation one obtains the two widely used, coupled first-order nonlinear rate equations of Statz and deMars. On the other hand, if the cavity linewidth is much larger than the atomic linewidths (T1−1 and T2−1), one can use the so-called ``reaction-field principle'' of Anderson and obtain, again, two coupled first-order rate equations; however, only one of the equations is nonlinear. The ranges of validity of both approaches are discussed in some detail.
A simple maser model consisting of a single-mode field coupled to N identical two-level atoms is presented. The assumption of negligible statistical correlation between the atoms and the field, permits the Heisenberg equations of motion to be replaced by a self-consistent set of ordinary nonlinear differential equations. Relaxation terms and an energy source are introduced phenomenologically. The resulting equations exhibit a threshold, stable and unstable steady states, relaxation oscillations and, sometimes, spiking. The dynamic equations for the hydrogen maser and the rate equations of laser theory are derived as special cases. Also discussed are the maser amplifier, locking of a maser to an external signal, and the effects of cavity thermal noise.
Since the demonstration of the possibility of achieving very low noise amplification of signals in the centimetric wavebands, a great deal of work has been carried out in various laboratories with a view to producing and testing devices. The major part of the present article focuses attention on one particular device, the three-level solid-state maser. The physical principles underlying the process of stimulated emission of radiation are in many cases unfamiliar to electronic engineers, and study of the growing literature on the subject can be confusing without a clear understanding of the physics involved. The present article outlines the general theory of emission and radiation processes, particularly as they apply to the microwave spectrum. A quantum mechanical description is employed throughout, and a brief and not very rigorous account is given of the relevant portions of this theory as it applies to the investigation of transistors between energy levels. Well-known expressions are derived for the operating characteristics of a three-level maser, particular attention being given to the significance of the various factors involved and their relationship to easily measured quantities. Little information is included concerning practical maser amplifiers; at the time of writing, few practical devices had been constructed. A survey of recent literature indicates the rapid progress which has since been made, and shows the interest in the development of masers.
A theoretical model is developed for the behavior of an optical maser medium in a static magnetic field of arbitrary strength in the Z direction and an electromagnetic field which is composed of traveling waves with both states of polarization and with both +z and $\ensuremath{-}z$ directions. An integral formulation of a truncated phenomenological density matrix is introduced to treat the degeneracy of the atomic energy levels within the natural width. This integral is an exact solution of the phenomenological differential equation for the density matrix which was introduced by Wilcox and Lamb. The inherent degeneracy in the electromagnetic field is included by treating the field in a classical manner. The integral formulation is iterated to yield the first- and third-order contributions to the electric polarization vector P in a spatial element dr, and the electric field and the electric polarization are made self-consistent in this spatial element by using coefficients in Maxwell's equations which are slowly varying functions of position and time. Atomic motion, hyperfine, isotope, and other line-broadening effects are included in the polarization vector P. The general linear-amplifier, linear-oscillator, and closed-path-oscillator or photon-rate-gyroscope problems are formulated and in the simplest case require the analysis of eight nonlinear equations. These reduce to four equations for the linear oscillator with an axial magnetic field, and these examples are discussed in detail and compared with experiment. An anomalous situation arises for the ja=jb or Fa=Fb linear amplifiers or linear-oscillator masers, and the development indicates that these systems are stable near line center only for either right or left circular polarization in zero or weak magnetic fields. A magnetic field "dip" near line center is discussed. Special examples which require four or fewer nonlinear equations are discussed.
It is shown that spontaneous emission of an excited atom is suppressed, and electromagnetic instability of the ground state is possible, if an atom is located in the vicinity of an active medium which amplifies the propagating radiation. The effect is due to a modified and phase-shifted near field of an oscillating atomic dipole, which prevails over the usual radiation reaction field related to the wave zone. The necessary conditions for the reversal of the total electromagnetic back reaction are found, and possible experimental realizations are discussed.