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

Journal of the Physical Society of Japan

A Theory of Microwave Masers in Strong Pumping Field

Yoshio Ebina

Published Nov 1, 1964• 0 citations
Publisher

Abstract

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.

DOI
10.1143/jpsj.19.2195

Related papers

Solid-state masers without inversion: Theoretical prediction for high-efficiency oscillators or phase-sensitive detectors

F. F. Popescu

Analytic steady-state solutions of the density-matrix equation are derived by means of a formalism suitable for multilevel spin systems in dilute paramagnetic solids at high temperature and subjected to several strong fields. It is shown that solid-state masers without inversion may be obtained in the presence of one, two, or three quasimonochromatic strong fields at resonance. In the usual cases of two fields, the maser action with or without inversion cannot achieve high-efficiency microwave generation or detection, since for strong emitted fields, the saturating and nonlinear effects are strong too. On the contrary, whenever three frequency-correlated fields fulfill the ``spectroscopic bridge'' conditions, the saturating effects do not occur, and linear effects prevail, even when all these fields are strong. In this case, high-efficiency microwave generations or phase-sensitive detections may be achieved.

Physical review. B, Condensed matter•Nov 1, 1993•9 citations

General Analysis of Optical, Infrared, and Microwave Maser Oscillator Emission

J. R. Singer, S. Wang

The equations are generalized governing coherent emission from quantum mechanical amplifiers (microwave, infrared, and optical masers) using either electric or magnetic dipole transitions. Earlier analyses by Gordon, Zeiger and Townes, Feynman, Vernon and Hellworth, and Wang and Singer, are incorporated in this generalization. The principal new result of this analysis is that an amplitude modulation of the output is to be expected from all maser oscillators excepting those in which excited atoms are supplied at a notably greater rate than the depopulation rate due to coherent induced emission. This analysis also suggests that an energy population inversion of electric dipole moments can be performed using coherent light sources in the same manner as with magnetic dipole moments. It appears therefore that modulation of an optical or infrared maser (e.g., for communication purposes) may be easily accomplished by varying the population of excited states through control of the pumping energy. This modulation may be both by absorption and amplification. (Author)

Physical Review Letters•Apr 1, 1961•21 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

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

Quantum Mechanical Effects in Stimulated Optical Emission

Roscoe C. Williams

An analysis of a three-level system using time-dependent perturbation theory shows that two distinct photon-emission processes take place within such a system when stimulated optical emission occurs: one-and two-photon transitions. The two-photon transition consists of the emission of a stimulated photon followed by the absorption of a coherent pump photon. In three-level systems which possess a narrow pump level, two-photon transitions are dominant at high pump powers while the maser line is split into two lines due to the modulation of the wave function at an angular frequency determined by the rate of pumping. This might lead to the possibility of frequency-modulating the maser line. These results are extended qualitatively to include optical masers which possess broad pump-bands.

Applied Optics•Jan 1, 1962•0 citations

Quantum Mechanical Effects in Stimulated Optical Emission

Roscoe C. Williams

An analysis of a three-level system using time-dependent perturbation theory shows that two distinct photon-emission processes take place within such a system when stimulated optical emission occurs: one-and two-photon transitions. The two-photon transition consists of the emission of a stimulated photon followed by the absorption of a coherent pump photon.In three-level systems which possess a narrow pump level, two-photon transitions are dominant at high pump powers while the maser line is split into two lines due to the modulation of the wave function at an angular frequency determined by the rate of pumping. This might lead to the possibility of frequency-modulating the maser line. These results are extended qualitatively to include optical masers which possess broad pump-bands.

Physical Review•May 1, 1962•6 citations
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.
Analytic steady-state solutions of the density-matrix equation are derived by means of a formalism suitable for multilevel spin systems in dilute paramagnetic solids at high temperature and subjected to several strong fields. It is shown that solid-state masers without inversion may be obtained in the presence of one, two, or three quasimonochromatic strong fields at resonance. In the usual cases of two fields, the maser action with or without inversion cannot achieve high-efficiency microwave generation or detection, since for strong emitted fields, the saturating and nonlinear effects are strong too. On the contrary, whenever three frequency-correlated fields fulfill the ``spectroscopic bridge'' conditions, the saturating effects do not occur, and linear effects prevail, even when all these fields are strong. In this case, high-efficiency microwave generations or phase-sensitive detections may be achieved.
The equations are generalized governing coherent emission from quantum mechanical amplifiers (microwave, infrared, and optical masers) using either electric or magnetic dipole transitions. Earlier analyses by Gordon, Zeiger and Townes, Feynman, Vernon and Hellworth, and Wang and Singer, are incorporated in this generalization. The principal new result of this analysis is that an amplitude modulation of the output is to be expected from all maser oscillators excepting those in which excited atoms are supplied at a notably greater rate than the depopulation rate due to coherent induced emission. This analysis also suggests that an energy population inversion of electric dipole moments can be performed using coherent light sources in the same manner as with magnetic dipole moments. It appears therefore that modulation of an optical or infrared maser (e.g., for communication purposes) may be easily accomplished by varying the population of excited states through control of the pumping energy. This modulation may be both by absorption and amplification. (Author)
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.
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.
An analysis of a three-level system using time-dependent perturbation theory shows that two distinct photon-emission processes take place within such a system when stimulated optical emission occurs: one-and two-photon transitions. The two-photon transition consists of the emission of a stimulated photon followed by the absorption of a coherent pump photon. In three-level systems which possess a narrow pump level, two-photon transitions are dominant at high pump powers while the maser line is split into two lines due to the modulation of the wave function at an angular frequency determined by the rate of pumping. This might lead to the possibility of frequency-modulating the maser line. These results are extended qualitatively to include optical masers which possess broad pump-bands.
An analysis of a three-level system using time-dependent perturbation theory shows that two distinct photon-emission processes take place within such a system when stimulated optical emission occurs: one-and two-photon transitions. The two-photon transition consists of the emission of a stimulated photon followed by the absorption of a coherent pump photon.In three-level systems which possess a narrow pump level, two-photon transitions are dominant at high pump powers while the maser line is split into two lines due to the modulation of the wave function at an angular frequency determined by the rate of pumping. This might lead to the possibility of frequency-modulating the maser line. These results are extended qualitatively to include optical masers which possess broad pump-bands.