Page 272 - Tunable Lasers Handbook

232 Norman P. Barnes

where L denotes the total orbital angular momentum with S representing 0, P
representing 1, D representing 2, F representing 3, and so forth. In accordance
with the notation used here, S is the total spin quantum number and J is the total
angular momentum quantum number. Therefore, the superscript and subscript
are numbers, but the angular momentum is represented by a letter.
Absorption and emission from lanthanide series atoms embedded in a laser
material are characterized by line structure. Linewidths of individual transitions
are on the order of 1011 Hz wide. By way of comparison, the frequency of the
transition is on the order of 3 x 1014 Hz. Thus, unlike the transition metals
lasers. the lanthanide series lasers are tunable over a fairly narrow range. Tun-
ing can be extended in some cases. One of these cases is where the number of
energy levels within a manifold is high. An example of this is the Ho j17 to 51,
transition. Fifteen levels exist in the upper manifold; 17 in the lower manifold.
Taken in combination. this produces hundreds of possible transitions between
pairs of individual levels. Thus, as the laser is tuned off of one transition, it can
be tuned onto another, making continuous tuning possible. Vibronic transitions
in lanthanide series atoms are possible but the effect is much weaker than in
transition metal atoms.
Because the crystal field has a relatively small effect on the lanthanide
series atoms, wavelengths of the transitions are less dependent on the laser
material. By knowing the energy levels of a particular lanthanide series atom in
one laser material, the energy levels of this atom in any laser can be estimated.
This has led to a useful representation of the energy levels of all of the lan-
thanide series elements. An energy-level diagram showing the positions of the
various energy manifolds for all of the lanthanide series atoms is often referred
to as a Dieke diagram [8].

3. PHYSICS OF TRANSITION METAL LASERS

Energy levels associated with transition metal atoms in laser materials can
be interpreted in terms of a theory developed by Tanabe and Sugano [9]. Tanabe
and Sugano developed the theory for transition metal active atoms subjected to
octahedral crystal fields. Active atoms in octahedral sites are common, including
such combinations as Cr:YAG and Cr:GSGG. Active atoms in other laser materi-
als are often approximated as residing in octahedral sites. For example, Cr:A1,0,
and Ti:A1,0, are often approximated as octahedral sites having a slight trigonal
distortion. By following a procedure similar to that outlined in the initial Tanabe
and Sugano paper, energy levels of active atoms in other site symmetries can be
calculated.