Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Applied Optics

Transient Solutions to a Three Level Maser

M. L. Narchal, M.M. Dhawan, M. R. Monga

Published Apr 1, 1967• 1 citation
Publisher

Abstract

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.

DOI
10.1364/ao.6.000723

Related papers

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

P N Butcher

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 proceedings of the Institution of Electrical Engineers. Part B, Radio and electronic engineering, including communication engineering•May 1, 1958•0 citations

Use of Active Material in Three-Level Solid State Masers*

E. O. Schulz-DuBois, H. E. D. Scovil, R. W. DeGrasse

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.

Bell System Technical Journal•Mar 1, 1959•25 citations

Recovery technique for saturated masers

Günter Wessel

The practical application of masers is often hindered by saturation effects of the maser material. Any strong signal frequency (e.g., the transmitter pulse of a radar system leaking into the maser) will cause saturation. This paralyzes the maser for a period of time, too long for most intended applications. In this report, a method is described which has been used in desaturating a four-level ruby maser. The saturation is caused by equalizing the populations of levels one, two, and three of the maser crystal by the leakage of the transmitter pulse, in addition to the action of the maser pump. The application of a desaturation pulse between levels one and four will then desaturate the maser restoring the excess population density between levels two and one. In a cavity maser, full recovery of the amplification capabilities has been achieved within less than 1 msec after the maser has been saturated. Repetition rates up to 120 cps are tolerable.

IRE Transactions on Electron Devices•Oct 1, 1960•2 citations

Theory of a Three-Level Maser

Ali Javan

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 ${T}_{1}={T}_{2}$ 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 ${T}_{1}={T}_{2}$ 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.

Physical Review•Sep 15, 1957•258 citations

Three-Level Maser Action in Gas I. Theory of Multiple Quantum Transition and Doppler Effect in Three-Level Gas Maser

Tatsuo Yajima

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.

Journal of the Physical Society of Japan•Aug 1, 1961•31 citations

A Theory of Microwave Masers in Strong Pumping Field

Yoshio Ebina

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 \(1{\times}\hbar\) 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.

Journal of the Physical Society of Japan•Nov 1, 1964•0 citations
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.
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 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 practical application of masers is often hindered by saturation effects of the maser material. Any strong signal frequency (e.g., the transmitter pulse of a radar system leaking into the maser) will cause saturation. This paralyzes the maser for a period of time, too long for most intended applications. In this report, a method is described which has been used in desaturating a four-level ruby maser. The saturation is caused by equalizing the populations of levels one, two, and three of the maser crystal by the leakage of the transmitter pulse, in addition to the action of the maser pump. The application of a desaturation pulse between levels one and four will then desaturate the maser restoring the excess population density between levels two and one. In a cavity maser, full recovery of the amplification capabilities has been achieved within less than 1 msec after the maser has been saturated. Repetition rates up to 120 cps are tolerable.
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 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.
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.