The rate equations of Statz and De Mars giving the time development of the inversion and photon number in a maser or laser are discussed analytically with the aid of a mechanical analogy in which a particle moves in a potential well under the influence of a viscous damping force. The coordinate of this particle is analogous to the logarithm of the light output of the laser, and the amplitude, period, and damping of the motion can be directly related to the parameters of the rate equations. Simple analytic approximations are developed for all of the quantities of experimental interest in the spiking pattern of a laser. Four relationships are given, which do not contain any of the rate equation parameters, whereby a spike pattern can be tested to determine if it is consistent with the usual rate equations. Systematic procedures are described for extracting all of the information contained in spike patterns.The rate equations of Statz and De Mars giving the time development of the inversion and photon number in a maser or laser are discussed analytically with the aid of a mechanical analogy in which a particle moves in a potential well under the influence of a viscous damping force. The coordinate of this particle is analogous to the logarithm of the light output of the laser, and the amplitude, period, and damping of the motion can be directly related to the parameters of the rate equations. Simple analytic approximations are developed for all of the quantities of experimental interest in the spiking pattern of a laser. Four relationships are given, which do not contain any of the rate equation parameters, whereby a spike pattern can be tested to determine if it is consistent with the usual rate equations. Systematic procedures are described for extracting all of the information contained in spike patterns.

Bell System Technical JournalJul 1, 196466 citations

Derivation of Rate Equations

Kluwer Academic Publishers eBooksJan 11, 20060 citations

Rate equations and their applications

Hermann Haken

Springer eBooksJan 1, 19842 citations

Rate-equation approximations in high-gain lasers

Lee W. Casperson

The rate-equation approximation is one of the most fundamental and universally employed simplifications in laser analyses. The accuracy and regions of applicability of this approximation are explored in comparisons with more rigorous semiclassical models. Higher-order rate-equation approximations are also developed, and these improved models can yield much better accuracy than conventional rate equations with little added complexity. The modified adiabatic elimination methods reported here would also be useful in reducing the mathematical models governing other physical systems.The rate-equation approximation is one of the most fundamental and universally employed simplifications in laser analyses. The accuracy and regions of applicability of this approximation are explored in comparisons with more rigorous semiclassical models. Higher-order rate-equation approximations are also developed, and these improved models can yield much better accuracy than conventional rate equations with little added complexity. The modified adiabatic elimination methods reported here would also be useful in reducing the mathematical models governing other physical systems.

Physical Review AApr 1, 199710 citations

Rate Equations

Kenichi Iga

Springer eBooksJan 1, 19940 citations

Master-equation theory of the effect of vibrational relaxation on intermolecular transfer of electronic excitation

V. M. Kenkre

A theory is developed to describe the effect of simultaneously occurring vibrational relaxation on intermolecular excitation transfer in the presence of radiative and nonradiative sinks. The basis is a master equation whose rates are combinations of the F\"orster-Dexter transfer rates and the Montroll-Shuler relaxation rates. Exact solutions are obtained for the probabilities of occupation of single vibrational levels as well as of site occupation, and for quantum yields and differential photon count rates. It is shown how phenomena exhibiting dependence of quantum yields or similar quantities on the wavelength of initial excitation can be quantitatively approached with the help of this analysis. The concept of time-dependent transfer rates is developed, and it is shown that at long times the transfer rate could tend to a value different from the thermalized F\"orster-Dexter rate. It is also shown how the relaxation process can result in an effective transfer rate (for singlets) whose dependence on the intermolecular distance $R$ is other than ${R}^{\ensuremath{-}6}$.A theory is developed to describe the effect of simultaneously occurring vibrational relaxation on intermolecular excitation transfer in the presence of radiative and nonradiative sinks. The basis is a master equation whose rates are combinations of the F\"orster-Dexter transfer rates and the Montroll-Shuler relaxation rates. Exact solutions are obtained for the probabilities of occupation of single vibrational levels as well as of site occupation, and for quantum yields and differential photon count rates. It is shown how phenomena exhibiting dependence of quantum yields or similar quantities on the wavelength of initial excitation can be quantitatively approached with the help of this analysis. The concept of time-dependent transfer rates is developed, and it is shown that at long times the transfer rate could tend to a value different from the thermalized F\"orster-Dexter rate. It is also shown how the relaxation process can result in an effective transfer rate (for singlets) whose dependence on the intermolecular distance $R$ is other than ${R}^{\ensuremath{-}6}$.

Physical Review AAug 1, 197728 citations

R

is other than ${R}^{\ensuremath{-}6}$.