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The proceedings of the Institution of Electrical Engineers. Part B, Radio and electronic engineering, including communication engineering

Theory of three-level paramagnetic masers. Part 1: Quantum theory

P N Butcher

Published May 1, 1958• 0 citations
Publisher

Abstract

The density matrix describing a paramagnetic ion subjected to both pump and signal fields is calculated. It is used to determine the fractional population differences, magnetic polarization densities, susceptibility tensors and power dissipation densities at both the pump and signal frequencies. There are six relaxation parameters of prime significance: the spin-spin relaxation times, the spin-lattice relaxation times and the Overhauser parameters for both the pump and signal transitions. The spin-spin relaxation times control the low-level absorption. The spin-lattice relaxation times control the completely saturated absorption. The Overhauser parameters control the absorption by one transition when the other transition is partially or completely saturated.

DOI
10.1049/pi-b-1.1958.0154

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Journal of the Physical Society of Japan•Aug 1, 1961•31 citations
The density matrix describing a paramagnetic ion subjected to both pump and signal fields is calculated. It is used to determine the fractional population differences, magnetic polarization densities, susceptibility tensors and power dissipation densities at both the pump and signal frequencies. There are six relaxation parameters of prime significance: the spin-spin relaxation times, the spin-lattice relaxation times and the Overhauser parameters for both the pump and signal transitions. The spin-spin relaxation times control the low-level absorption. The spin-lattice relaxation times control the completely saturated absorption. The Overhauser parameters control the absorption by one transition when the other transition is partially or completely saturated.
The transient behavior of three-level paramagnetic masers is investigated theoretically. Exact solutions to three-level maser rate equations are developed and their significance discussed. The results indicate the possibility of obtaining enhanced maser action at low saturation by pulsed pumping. A new method for the measurement of spin-lattice relaxation times for a three-level maser is proposed. The method, in addition to certain well-known static measurements, requires the observation of the decay of the signal strength when the pumping field is switched off.
In a three-level maser, a transition between two energy levels is saturated in order to produce an induced emission of power at a lower frequency corresponding to a transition between an intermediate energy level and one or the other of the two saturated levels. In this paper, certain effects are discussed which cannot be predicted from a theory in which the population differences alone are considered in this process. For instance, it is shown that, in some cases it is possible to obtain for the same system an induced emission of power at two frequencies given by the resonances between the intermediate energy level and both of the saturated levels. Also, it is shown that, even in the absence of inhomogeneous broadening of the spectral line, one can obtain a net induced emission at some portions of a resonant line and a net absorption at other frequencies within the line widths. Such effects become important even in early stages of saturation in cases where T1=T2{T}_{1}={T}_{2}T1​=T2​ which is true for ordinary gaseous systems and individual spin systems in a majority of very dilute paramagnetic solids. A complete theory is discussed for a gaseous system and extended to two limiting cases of paramagnetic materials with T1=T2{T}_{1}={T}_{2}T1​=T2​ and ${T}_{2}\ensuremath{\ll}{T}_{1}$ for each individual spin system. Furthermore, it is shown that for a saturating field of fixed frequency, the integral of induced power over the entire line is in full agreement with the results of a semiclassical treatment in which the population differences alone are considered. Some remarks are made as to the practicability of certain systems of this type.
The three-level excitation method for solid state masers, including some background material on paramagnetic resonance, is reviewed. With respect to the experimental application of the maser material, two cases can be distinguished, In the first, maser action is based mainly on a favorable relaxation time ratio in signal and idler transitions. It is shown that the relaxation time ratio can be changed artificially by a doping technique. Experimental evidence is presented for two such doping techniques, one self-doping, the other impurity doping. In the second case, maser action is based primarily on a favorable frequency ratio of signal and idler transitions. Maser experiments using this approach are described. In addition, excitation of unidirectional gain and attenuation by circular polarization is discussed. Properties of practical isolator materials are surveyed; they include high-concentration paramagnetic and polycryslolline ferrimagnetic materials.
The use of a quantitative analysis of the dominant source of relaxation in ruby spin systems to make predictions of key maser amplifier parameters is described. The spin-lattice Hamiltonian which describes the interaction of the electron spins with the thermal vibrations of the surrounding lattice is obtained from the literature. Taking into account the vibrational anisotropy of ruby, Fermi's rule is used to calculate the spin transition rates between the maser energy levels. The spin population rate equations are solved for the spin transition relaxation times, and a comparison with previous calculations is made. Predictions of ruby gain, inversion ratio, and noise temperature as a function of physical temperature are made for 8.4-GHz and 32-GHz maser pumping schemes. The theory predicts that ruby oriented at 90 deg will have approximately 50 percent higher gain in dB and slightly lower noise temperature than a 54.7-deg ruby at 32 GHz (assuming pump saturation). A specific calculation relating pump power to inversion ratio is given for a single channel of the 32-GHz reflected wave maser.
Maser action due to a mixing between unperturbed spin states, which is produced by a strong coherent pumping field at an angular frequency ω, is investigated by using rate equations of a spin density matrix referred to a rotating coordinate system. The relaxation of each state, which was introduced usually by phenomenological considerations, is obtained from an interaction Hamiltonian of the spin moments with local fields. The induced oscillating fields at 2ω±ω s and ω s , which are proportional to a small signal field at a frequency ω s , have the possibility of power emission (or absorption) by choosing suitably the pumping field. The components at 2ω±ω s are responsible for a frequency mixing between ω and ω±ω s occuring in the rotating coordinates. The emitted (or absorbed) line shape is not a simple Lorentzian in the case of the spin moment 1×ℏ1{\times}\hbar1×ℏ and considered to be a quantum affect in the three level scheme. The frequencies of the emitted (or absorbed) fields are expected to be shifted by varying the magnitude, or the frequency of the pumping field, or the static magnetic field.
The multiple quantum process in the off-resonant condition of the three-level gas maser is discussed. The intensity of the emission produced by this process is calculated by a perturbation theory and also by a more general treatment which is the application of Javan's theory to the off-resonant case. Some graphical representations of the signal line under off-resonant pumping are given for the purpose of comparison with experiment. The Doppler effect in three-level maser action is analyzed from both semiclassical and quantum mechanical points of view under the presence of collision relaxation. It was shown that in a saturation process between two levels, Doppler effect behaves as to contribute to both line-width and relaxation time for the transition, and that under strong pumping, Doppler effect in pumping transition has a marked influence on both intensity and shape of the signal line through the effect of multiple quantum transition.