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Spin-lattice relaxation and the calculation of gain, pump power, and noise temperature in ruby

J. R. Lyons

Published Aug 15, 1989• 4 citations

Abstract

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.

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The theory of the rubidium-87 maser is described. It is shown that the maser power output is a critical function of the rubidium density, light intensity, and cavity $Q$. Fundamental parameters and constants of the maser are grouped together to define an oscillation parameter ${{\ensuremath{\Gamma}}_{m}}^{\ensuremath{'}}$ which determines the oscillation characteristics of the maser. Spin-exchange calculations in rubidium are presented. The relaxation times ${T}_{1}$ and ${T}_{2}$ due to spin-exchange interactions are related to each other, and it is shown that ${T}_{2}=(\frac{8}{5}){T}_{1}$. A method of determining the spin-exchange cross section in terms of fundamental constants and maser parameters is described. Results of experiments made to verify these calculations are given. It is found in general that the results agree with the theory, but slight discrepancies exist. Tentative explanations are given.

Physical Review•Apr 5, 1968•59 citations

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.

The computational results of a comparison of maser materials for a 32 GHz maser amplifier are presented. The search for a better maser material is prompted by the relatively large amount of pump power required to sustain a population inversion in ruby at frequencies on the order of 30 GHz and above. The general requirements of a maser material and the specific problems with ruby are outlined. The spin Hamiltonian is used to calculate energy levels and transition probabilities for ruby and twelve other materials. A table is compiled of several attractive operating points for each of the materials analyzed. All the materials analyzed possess operating points that could be superior to ruby. To complete the evaluation of the materials, measurements of inversion ratio and pump power requirements must be made in the future.

Cross relaxation between adjacent intervals may be used to secure an advantage in maser operation comparable to that obtained by ``push-pull'' pumping. Equations for the rate of change of populations in a scheme of four levels (A,B,C,D) when AC is pumped and cross relaxation takes place between BC, CD have been formulated, and the steady-state condition corresponding to various assumptions regarding lattice relaxation times is discussed. In an experimental investigation of maser operation based on this scheme and using ruby as the active material, an inversion of 0.9:1 was obtained at a signal frequency of 14.5 kMc when pumping at 24.5 kMc.

Transition probabilities of spin-lattice relaxation (RTP) based on the Kronig-Van Vleck mechanism are calculated for ruby for the orientations θ = 90 and 54° and for magnetic fields up to 15 kG. Inversion ratios are evaluated on the basis of the RTP's for various pumping modes. Experimental measurements of the inversion ratio and pumping power at a signal frequency of fs = 22.2 GHz are carried out. The Kronig-Van Vleck mechanism is shown to be the principal mechanism of spin-lattice relaxation for high magnetic fields and low concentrations of paramagnetic ions.

The theory of the rubidium-87 maser is described. It is shown that the maser power output is a critical function of the rubidium density, light intensity, and cavity

Q

. Fundamental parameters and constants of the maser are grouped together to define an oscillation parameter ${{\ensuremath{\Gamma}}_{m}}^{\ensuremath{'}}$ which determines the oscillation characteristics of the maser. Spin-exchange calculations in rubidium are presented. The relaxation times

{T}_{1}

and

{T}_{2}

due to spin-exchange interactions are related to each other, and it is shown that

{T}_{2}=(\frac{8}{5}){T}_{1}

. A method of determining the spin-exchange cross section in terms of fundamental constants and maser parameters is described. Results of experiments made to verify these calculations are given. It is found in general that the results agree with the theory, but slight discrepancies exist. Tentative explanations are given.