Stochastic Interpretation of Inhomogeneous Spectroscopic Line Shapes

P. R. Berman

A. S. Bankovskii, Pavel A Apanasevich

E. I. Neimark, Inna Nikolayevna Nurutdinova, A. B. Roǐtsin

Abani K. Bhuyan

It has been postulated that the state function can be expressed as a linear superposition of eigenstates of Hermitian operators. When a system is subjected to an external impulse in the form of radiation, the probability of finding the system in different eigenstates of the state function changes. The total probability is always unity, which means the change in probabilities for different states occurs at the expense of each other. This change in probability of finding the system in different eigenstates brought about by system-radiation interaction is called the spectroscopic transition. Here, we use a two-level system to develop the details of a general spectroscopic transition, and work further to examine the effects of interruption in the coherent evolution of the state function. The physical meaning of absorption coefficient is discussed in detail. We derive the general forms of relaxation of the excited state, spectral line shape, and line broadening. The origin and the meaning of homogeneous and inhomogeneous line broadening are discussed. We describe the Doppler effect and its use in the interpretation of inhomogeneous line shape.

Milton Birnbaum

Fluorescence studies of the R-line emission of ruby laser rods over the temperature range of 77 to 300 K have disclosed several new features. In particular, for most of the ruby rods, the fluorescent decay time, τ, was not strictly exponential. Effects of this kind have been observed in the fluorescent decay of the 4F3/2 level of Nd3+ in YAG (yttrium aluminum garnet) and in Nd-doped glasses. In both cases, the nonexponential decay was interpreted as evidence for inhomogeneous line broadening effects, among which are strains, ion clustering, and other defects that modify the crystal field at the ion site. Our observations of nonexponential fluorescent decay in ruby are indicative of inhomogeneous line broadening effects in lightly doped (0/05%) ruby. In fact, inhomogeneous line broadening was observed in ruby at liquid helium temperatures, in the spectroscopic studies of A. L. Schawlow.

Lewis S. Klein