Page 286 - Tunable Lasers Handbook

246 Norman P. Barnes

= lyv :
iir

where the quantity WPLf can be computed exactly. If, in addition, the offset is
small, that is, all, is smaller than unity, then

exp (- S, < 2nz + 1 >) (s, < 1 + in >)'I'
qll = forp,, > 0 . (28)
PI, !

I(
exp (-So < 2m + 1 > So < nz >)""'
1 PI, I! for p,, < 0 . (29)

In these expressions, So is proportional to the square of the offset, that is, aJ4, and

-1
<n7> = [ exp
- I]

According to this expression, the shape of the absorption and emission features
tends to be given by a Poisson distribution. In fact, emission lines can often be
approximated by such a line shape. In addition, the similarity between this
expression and the multiphonon theory can be observed. Thus, the multiphonon
theory appears to be valid when the approximations just given are valid.
Struck and Fonger also compared this derived theory to the activation
energy theory. Although the activation energy theory can approximate the pre-
ceding equations (28 and 29). in the cases of a relatively large offset, the fit was
only valid over relatively small temperature ranges. As such, the more complex
Struck and Fonger theory may be required to describe the radiative and non-
radiative decay for the large offset cases.

4. Cr:AI2O3

Cr:A1,03. a transition metal solid-state laser, was the first laser of any type
to be demonstrated [12]. Cr:A1203. commonly referred to as ruby, has several
advantages, which are currently being put to use. Its principal advantage is the
wavelength at which it is usually operated. 0.694 pm. Although this wavelength
is near the limit of the response of the human eye, it is plainly visible. Part of its
easy visibility is due to its high intensity. Most other solid-state lasers operate
further into the near infrared and are not visible to the human eye. Other desir-
able properties of ruby include wide absorption bands. a long upper laser level
lifetime, a narrow linewidth, and a high quantum efficiency.