Proceedings of the Royal Society of London A Mathematical and Physical Sciences

Excitation of transitions between atomic or molecular energy levels by monochromatic laser radiation. IV. Transient excitation of Doppler-broadened transitions — effect of detuning

Robert A. L. Smith

Published Jun 30, 1980• 6 citations

Abstract

Abstract The effect of detuning from the centre of the Doppler-broadened profile of a transition is studied by use of the rate of change of a modified density matrix. The variation of population density of the two energy levels involved in the transition is obtained under transient conditions. Two values of the ratio of the damping parameters 2γ and γ' for the on-diagonal and off-diagonal matrix elements are considered; γ' = γ corresponds to very low gas pressures and y' = 10y to conditions for which phase-destroying collisions predominate. While these considerations apply both in the visible and infra-red spectral regions, and equally to atoms and molecules, they are at present of special interest in connection with excitation of transitions of importance in laser photochemistry.

DOI: 10.1098/rspa.1980.0083

Related papers

Excitation of transitions between atomic or molecular energy levels by monochromatic laser radiation IV. Transient excitation of Doppler-broadened transitions-

Robert A. Smith

The effect of detuning from the centre of the Doppler-broadened profile of a transition is studied by use of the rate of change of a modified density matrix. The variation of population density of the two energy levels involved in the transition is obtained under transient conditions. Two values of the ratio of the damping parameters 2y and T' for the on-diagonal and off-diagonal matrix elements are considered; y' = y corresponds to very low gas pressures and ' = 10y to conditions for which phase-destroying collisions predominate. While these considerations apply both in the visible and infra-red spectral regions, and equally to atoms and molecules, they are at present of special interest in connection with excitation of transitions of importance in laser photochemistry.

Jan 1, 20160 citations

Excitation of transitions between atomic or molecular energy levels by monochromatic laser radiation III. Effect of Doppler broadening when phase-destroying collisions predominate

Robert A. L. Smith

Abstract The treatment of transient excitation of transitions between two atomic or molecular energy levels by monochromatic laser radiation under conditions in which phase-destroying collisions predominate is treated by means of numerical and approximate analytical solutions of the equations giving the rate of change of a modified density matrix. The analytical solutions are then used to obtain the transient values of the population of the excited state when Doppler broadening is taken into account. Numerical calculations are carried out for the ratio γ'/γ = 10, where 2γ is the damping constant for diagonal and γ' for non-diagonal elements of the density matrix. This extends the treatm ent given in two previous papers for the situation when γ' = γ, corresponding to very low pressures for which phase-destroying collisions are relatively unimportant.

Proceedings of the Royal Society of London A Mathematical and Physical SciencesOct 29, 19799 citations

Excitation of transitions between atomic or molecular energy levels by monochromatic laser radiation - II. Excitation under conditions of strictly inhomogeneous line broadening and mixed homogeneous and inhomogeneous broadening

Robert A. L. Smith

Abstract The development with time of the excitation of a transition between two atomic or molecular energy levels under the influence of monochromatic laser radiation is examined under conditions of strictly inhomogeneous line broadening due to such causes as doppler shift arising from translational velocity. The ratio of the number of molecules, N2, in an excited state to the total number, N, is calculated for various ratios of the intensity parameter β ═ E0μ/ħ to the half line-width ∆, where E0 is the amplitude of the electric field in the incident radiation and is the dipole moment matrix element for the transition. Excitation functions obtained in a previous paper (I) for various values of the ratio γ/β, where γ is the half line-width in the absence of inhomogeneous broadening, are used to obtain the variation of N2/N with time under conditions of mixed broadening for various values of the ratio γ/∆ and γ/β, when the exciting radiation is in exact resonance with the central frequency of the transition.

Proceedings of the Royal Society of London A Mathematical and Physical SciencesJun 30, 197812 citations

Excitation of transitions between atomic or molecular energy levels by monochromatic laser radiation - I. Excitation under conditions of strictly homogeneous line broadening

Robert A. L. Smith

Abstract The development with time of the excitation of a transition between two atomic or molecular energy levels under the influence of monochromatic laser radiation is examined under conditions of strictly homogeneous line-broadening. The ratio of the number of atoms or molecules, N2, in an excited state to the total number, N, is calculated for various ratios of the intensity parameter β ═ E0μ/ħ to the half line-width γ. E0 is the amplitude of the electric field in the incident radiation and the dipole moment matrix element for the transition. Exact expressions for N2/N as a function of time are given for the situation when the frequency ω/2π of the radiation is exactly equal to that of the transition ω0/2π. Numerical calculations are made for the situation when the ‘detuning’ δ ═ ω — ω0 is not equal to zero. Approximate expressions are also derived in terms of δ for use in a later paper which deals with mixed homogeneous and inhomogeneous line-broadening.

Proceedings of the Royal Society of London A Mathematical and Physical SciencesJun 30, 197817 citations

Photoprocesses with the sub-Doppler Spectral Selectivity Excited by the Monochromatic Optical Pulse in a Thin Gas Cell 1

H. Javid

The method of sub-Doppler spectroscopy is theoretically elaborated, which is based on the specific dynamics of a number of optically excited atomic particles (atoms or molecules) of a rarefied gas medium in a thin cell after the action of the resonance pulse of the monochromatic radiation. Corresponding calculations are carried out on the basis of density matrix equations for the resonance optical transition between Zeeman degen- erate ground and excited quantum levels of particles in case of the linear polarization of the laser pulse at its normal incidence on the cell. The situation is considered when the radiative lifetime of the excited level is much more than the characteristic transit time of particles between nearest plane-parallel walls of the cell. Then the distribution of a number of excited particles versus the pulse frequency detuning narrows in the process of par- ticles collisions with walls of the cell after action of the laser pulse. The factor of such a narrowing (in compar- ison with the Doppler broadening of the spectral line of the resonance transition) may be more than the ratio of the characteristic transverse size of the thin gas cell to its inner thickness. We discuss possible use of given sub- Doppler resonances (of the number of excited particles) in the high-resolution spectroscopy and also in high- selective processes of photo-ionization and photo-dissociation, especially, for isotope (or isomer) separation and detection of rare (in particular single) atoms or molecules of a gas medium.

Jan 1, 20090 citations

Collisional effects in gas lasers

Ashish Agarwal, Rupamanjari Ghosh

The effects of phase-interrupting and velocity-changing collisions between active and perturber atoms on the spectral profile of a gas laser are studied. Exact analytical results for the density matrix are presented for the case of strong collisions in a unidirectional ring laser, and the laser intensity is then evaluated in the Doppler limit under the condition of self-consistency. The washout of the hole burning in the steady-state population difference and the broadening of the laser line shape are discussed. The results of the third-order perturbation theory are compared with the exact calculations valid for an arbitrarily intense pump.

Physical Review AFeb 1, 19932 citations