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

Proceedings of the Physical Society

A simplified method for the analysis of self-cross-relaxation masers

HUANG WU-HAN, LIN FU-CHENG

Published Nov 1, 1964• 0 citations
Publisher

Abstract

A simplified method for the analysis of the effect of self-cross-relaxation on the maser performance is proposed. Calculation of any four-level system involving not more than triple cross-relaxation processes is carried out by means of this method, and some operative modes which may possibly yield improved performance are given. As illustrative examples, some typical design considerations and results are given for X band and S band ruby cavity masers.

DOI
10.1088/0370-1328/84/5/302

Related papers

Cross-Relaxation Masers

G S Bogle

A survey is made of the available ways of using ruby, spinel, rutile and emerald in masers which amplify at frequencies small compared to their zero-field splitting frequencies. Particular attention is paid to means of taking advantage of cross relaxation which, it is shown, can give typically a two-fold improvement in maser performance. Analytic expressions for the energies are given which, to a large extent, remove the need for machine computations in the design of masers of this type.

Proceedings of the IRE•Mar 1, 1961•9 citations

Cross Relaxation and Concentration Effects in Ruby

Roy W. Roberts, James H. Burgess, Harold D. Tenney

Cross relaxation effects in ruby maser crystals are treated by introduction of a cross relaxation probability in the rate equations. Detailed solutions have been obtained for several specific processes and compared to recent experiments. It is shown that cross relaxation can improve maser performance even in the absence of impurity doping. Pulse experiments at 0.06 and 0.14% chromium ion concentrations in a ruby traveling wave maser are interpreted in terms of a five-spin process in addition to a four-spin process.

Physical Review•Feb 15, 1961•8 citations

Optical and Cross Relaxation Maser Level Populations by Partial Distribution

William A. Barker, J. D. Keating

The method of partial distributions is used to calculate the population distribution of three level maser systems in which spontaneous emission and cross relaxation as well as thermal relaxation and induced absorption processes are included. The results obtained are in agreement with the solution of the relevant rate equations. The method has the advantage of speed and suggestiveness. Two examples are presented: (1) A three level optical maser is analyzed in which one spontaneous emission transition probability is included. The solution in this example does not make the linear approximation to the Boltzmann factor. (2). A three level microwave maser is analyzed in which one cross relaxation mechanism is included. The solution to this problem by the method of partial distributions does require use of the linear approximation to the Boltzmann factor.

Applied Optics•Jan 1, 1962•3 citations

Optical and Cross Relaxation Maser Level Populations by Partial Distribution

William A. Barker, J. D. Keating

The method of partial distributions is used to calculate the population distribution of three level maser systems in which spontaneous emission and cross relaxation as well as thermal relaxation and induced absorption processes are included. The results obtained are in agreement with the solution of the relevant rate equations. The method has the advantage of speed and suggestiveness. Two examples are presented: (1) A three level optical maser is analyzed in which one spontaneous emission transition probability is included. The solution in this example does not make the linear approximation to the Boltzmann factor. (2) A three level microwave maser is analyzed in which one cross relaxation mechanism is included. The solution to this problem by the method of partial distributions does require use of the linear approximation to the Boltzmann factor.

Applied Optics•May 1, 1962•3 citations

Seesaw Maser Operation

Paul Forrester, W. B. Mims

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.

Journal of Applied Physics•Feb 1, 1961•3 citations

Method for Calculating Simultaneous Resonance Conditions in a Three-Level Ruby Maser

Martin A. Garstens

In operating a three-level maser one wishes to know the external magnetic field and crystal orientation necessary to match a given pair of frequencies. In the case of Cr+++ a fourth-degree secular equation determines four energy levels for each value of external field H and crystal orientation θ. Determination of the latter two variables, given two desired frequencies of operation, ordinarily involves either the solution of a tremendous number of fourth-degree equations and extrapolation towards the required solution, or determination of the matching conditions by experimental methods. In the following a method is described, allowing direct calculation of H and θ for a three-level ruby maser.

Journal of Applied Physics•Jul 1, 1959•1 citation
A simplified method for the analysis of the effect of self-cross-relaxation on the maser performance is proposed. Calculation of any four-level system involving not more than triple cross-relaxation processes is carried out by means of this method, and some operative modes which may possibly yield improved performance are given. As illustrative examples, some typical design considerations and results are given for X band and S band ruby cavity masers.
Cross relaxation effects in ruby maser crystals are treated by introduction of a cross relaxation probability in the rate equations. Detailed solutions have been obtained for several specific processes and compared to recent experiments. It is shown that cross relaxation can improve maser performance even in the absence of impurity doping. Pulse experiments at 0.06 and 0.14% chromium ion concentrations in a ruby traveling wave maser are interpreted in terms of a five-spin process in addition to a four-spin process.
The method of partial distributions is used to calculate the population distribution of three level maser systems in which spontaneous emission and cross relaxation as well as thermal relaxation and induced absorption processes are included. The results obtained are in agreement with the solution of the relevant rate equations. The method has the advantage of speed and suggestiveness. Two examples are presented: (1) A three level optical maser is analyzed in which one spontaneous emission transition probability is included. The solution in this example does not make the linear approximation to the Boltzmann factor. (2). A three level microwave maser is analyzed in which one cross relaxation mechanism is included. The solution to this problem by the method of partial distributions does require use of the linear approximation to the Boltzmann factor.
The method of partial distributions is used to calculate the population distribution of three level maser systems in which spontaneous emission and cross relaxation as well as thermal relaxation and induced absorption processes are included. The results obtained are in agreement with the solution of the relevant rate equations. The method has the advantage of speed and suggestiveness. Two examples are presented: (1) A three level optical maser is analyzed in which one spontaneous emission transition probability is included. The solution in this example does not make the linear approximation to the Boltzmann factor. (2) A three level microwave maser is analyzed in which one cross relaxation mechanism is included. The solution to this problem by the method of partial distributions does require use of the linear approximation to the Boltzmann factor.
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.
In operating a three-level maser one wishes to know the external magnetic field and crystal orientation necessary to match a given pair of frequencies. In the case of Cr+++ a fourth-degree secular equation determines four energy levels for each value of external field H and crystal orientation θ. Determination of the latter two variables, given two desired frequencies of operation, ordinarily involves either the solution of a tremendous number of fourth-degree equations and extrapolation towards the required solution, or determination of the matching conditions by experimental methods. In the following a method is described, allowing direct calculation of H and θ for a three-level ruby maser.