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Journal of Applied Physics

Analysis of the Emissive Phase of a Pulsed Maser

H. H. Theissing, F. A. Dieter, P. J. Caplan

Published Dec 1, 1958• 4 citations
Publisher

Abstract

The operation of a pulsed solid-state Maser consists essentially of alternate periods of spin inversion and stimulated spin emission. Inversion can be accomplished by a short driving pulse or an adiabatic rapid passage. In the emission phase a weak signal field causes the spin system to spiral back coherently and radiate. The emissive phase can be treated by equations which for finite relaxation times can not be solved in closed form, but which are amenable to machine computation. Such numerical solutions giving the transverse moment, output field, output power, and power gain as a function of time were computed for various relaxation times, input fields, and values of the oscillation parameter. The results are interpreted with respect to applications of both regenerative and superregenerative modes of operation.

DOI
10.1063/1.1723022

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The operation of a pulsed solid-state Maser consists essentially of alternate periods of spin inversion and stimulated spin emission. Inversion can be accomplished by a short driving pulse or an adiabatic rapid passage. In the emission phase a weak signal field causes the spin system to spiral back coherently and radiate. The emissive phase can be treated by equations which for finite relaxation times can not be solved in closed form, but which are amenable to machine computation. Such numerical solutions giving the transverse moment, output field, output power, and power gain as a function of time were computed for various relaxation times, input fields, and values of the oscillation parameter. The results are interpreted with respect to applications of both regenerative and superregenerative modes of operation.
The transient behavior of a two-level spin system coupled to an electric circuit is investigated by using the equations of Bloembergen and Pound. The equations are solved, in the limit where the circuit ringing time is very short compared with all other characteristic times, for two cases: 1) the spin-lattice and spin-spin relaxation times both infinite, with an externally applied driving field, and 2) the spin-lattice relaxation time infinite but the spin-spin relaxation time finite, in the absence of an external field. In case 1), it is shown that the motion of an initially inverted magnetization under the action of an applied signal consists roughly of two stages: in the first stage, the effect of radiation damping is unimportant and the motion of the system is determined principally by the applied signal via the ordinary Bloch equations, whereas in the second stage, the motion is essentially the same as if the applied signal had been turned off and only radiation damping were present. In case 2), it is shown that a delayed peak in the emitted radiation should be observed under certain conditions. The delayed peak condition is identical with that derived by Bloom. Curves are presented showing the peak power and the time at which the delayed peak occurs as functions of the relevant parameters. In connection with the ordinary maser behavior of a two-level spin system, it is shown that for values of the parameters typical of steady-state maser amplification, the effects of radiation damping should be unimportant. Finally, systems are examined for which the radiation damping time is much shorter than all other characteristic times (super-regenerative systems). It is indicated how such systems might be operated as one-shot multivibrators or as linear amplifiers. For the latter type of operation, an expression for the gain is derived which is found to be similar to that encountered in ordinary circuit theory.
A change in the character of maser generation in a two-level system is found when the initial population inversion exceeds some threshold value proportional to the square root of the total number of atoms. Above this threshold, the number of photons begins to grow exponentially with time and the pulse with short leading edge and broadened trailing edge is generated. In this work, we attempt to explain the nature of this threshold. Coherent pulse duration estimated by its half-width increases significantly with increasing inversion, if all other parameters are fixed and the absorption is neglected. The inclusion of the energy loss of photons leads to the fact that the duration of coherent pulse is almost constant with increasing inversion, at least well away from the threshold. If there is exist a recovery mechanism for the population inversion, the pulsating mode of stimulated emission generation becomes possible. The integral radiation intensity at this may be increased several times. This approach can be used for analysis of the cosmic radiation that might help explain a great variety of pulsating radiation sources in space.
The spectrum of power radiated by a solid-state optical maser in steady-state operation is obtained by considering each atomic system to be a source of randomly fluctuating dipole moment which drives every mode of the cavity. The nonlinear behavior of the collection of atomic systems is treated in such a way that a detailed examination of the distribution of power in the various modes is possible. A number of examples are considered which show how critically dependent on the relative loss rates of the various modes are the characteristics of the output from a multimode oscillator. An interesting result of this calculation is the appearance in some cases of an abrupt transition as the pumping power is increased: above this point a large fraction of energy goes into the mode which is resonant with the atomic transition and which has the lowest loss rate. Another case is studied which does not have this feature, but which could be useful in analyzing the behavior of solid-state optical masers which have substantial scattering due to crystal imperfections.
To treat the laser in a realistic way, we need the density matrix concepts and formalism given in Chap. 7. This material makes it possible to incorporate dipole phase decays due, for example, to collisions and to treat multimode electric fields in a straightforward way. Nevertheless, it is gratifying to find that we can already determine the field intensity for a simplified model of the ammonia beam maser, the first device of the maser-laser genre. The maser was originally conceived in 1951 by Townes, who noted his thoughts on the back of an envelope during a period of contemplation on a bench in Franklin Park, Washington, DC.T The device was realized experimentally by Gordon, Zeiger, and Townes (1954). In this chapter, we treat the maser along the lines given by Lamb (1960). The analysis is not complicated by atomic (molecular) lifetimes, because they are long compared to the Rabi flopping time, which is the optimal transit time for molecules in the maser cavity. Furthermore, by considering single-mode, steady-state operation, we can assume by energy conservation (1) that the energy given up by the atoms due to stimulated emission is gained by the field, and (2) that this energy flow balances the cavity losses.
The interaction between an electromagnetic (em) pulse and a maser medium is described by a general set of five equations, under the assumption of a homogeneously broadened electric-dipole transition with two Bloch relaxation times T2and T1and of a linear broadband loss mechanism. When the equations are specialized at resonance, their solutions include the results of the previous treatments on the amplifier problem obtained under particular assumptions. The steady-state pulse (S. S. P.) introduced by Wittke and Warter forT_{2}/T_{1} = 0is here generalized forT_{2}/T_{1} \neq 0and it is shown to propagate at the same velocity of the light in the medium. In the caseT_{2}/T_{1} = 0the steady state is described by exact analytical relations. For times short in comparison to the relaxation times, a solution is given which generalizes the usual interaction formula between an em field and a two-level system by introducing propagation effects. In the general case out of resonance, it is shown that an S. S. P. exists, and that its frequency coincides with the frequency of the atomic transition, independent of the frequency of the input field.