Page 280 - Tunable Lasers Handbook

240 Norman P. Barnes

section can be readily deduced from a single fluorescence spectrum if the laser
material is isotropic or fluorescence spectra if the material is not isotropic.
McCumber's theory yields a practical method of deducing the emission
cross section from the emission spectrum or spectra. To establish this relation, a
function fp(k,v) is introduced. When multiplied by an incremental solid angle
dokp and a unit frequency interval dv, this function represents the average
intensity of emitted photonslsecond in the direction k, with frequency v, and
with polarization p. One of the prime values of this function is that it can be
easily measured and normalized. Normalization can be obtained through
another easily measured quantity, the radiative lifetime of the upper manifold,
T, by the relation

Using this function. the stimulated emission cross section can be expressed as

In this expression, c is the speed of light and II is the refractive index. In general,
the refractive index will depend on the direction of propagation k, as well as the
polarization. Combining these equations leads to the primary result of the
McCumber analysis,

That is, the gain can be related to the measurable quantities, the fluorescence
spectrum or spectra, and the radiative lifetime.
Although McCumber's theory laid the foundation for the determination of
the gain, most experimental measurements are made in terms of watts per unit
wavelength interval rather than photons per second per unit frequency interval.
However, the change can be made in a straightforward manner. To change from
fp(k,v) in units of photons per second per unit frequency interval to g,(k,v) in
units of watts per unit wavelength interval,