Page 277 - Tunable Lasers Handbook

6 Transition Metal Solid-state lasers 37

rule and the Laporte selection rule. According to the spin selection rule, a transi-
tion can only occur between levels in which the number of unpaired electrons in
the initial and final levels is the same. In cases where a single electron undergoes
a transition, the spin must be the same for the initial and final levels. According
to one formulation of the Laporte selection rule, a transition is forbidden if it
involves only a redistribution of electrons having similar orbitals v, ithin a single
quantum shell. This formulation is particularly relevant to transition metals
because transitions tend to be between different 3d levels but within the same
quantum shell. For example, transitions involving only a rotary charge displace-
ment in one plane would be forbidden by this selection rule.
Selection rules were also considered by Tanabe and Sugano. Usually the
strong interaction that allows a transition between levels with the emission of a
photon is the electric dipole interaction. However, for the 3d electrons, all transi-
tions between the various levels are forbidden since all levels have the same par-
ity. Consequently, three other transition interactions were considered: the electric
dipole interaction coupled with a vibration, the electric quadrupole interaction,
and the magnetic dipole interaction. The strengths of these various interactions
LA ere estimated. From these estimations. it was concluded that the electric dipole
transition coupled with vibration, that is, a vibronic transition, u as the strongest
interaction. Vibronic transitions involve emission or absorption of a photon and a
quantized 3mount of lattice vibrations referred to as a phonon. Vibronic interac-
tions were estimated to be about 2 orders of magnitude stronger than the nexl
strongest interaction, the magnetic dipole interaction.
McCumber [ 101 investigated the absorption and emission that results from
vibromc interactions. Terminology used in the original paper refers to phonon-
terminated absorption and emission rather than vibronic transitions. McCumber
analyzed the absorption, emission. and gain of the transition metal Ni in the ini-
tial paper. Emission spectra from Ni:MgF, were characterized by sharp emission
lines and a broad emission spectra on &e long-wavelength side of the sharp
emission lines. Sharp lines were associated nith electronic transitions, whereas
the long-wavelength emission was associated with vibronic emission. Since
then. this general analysis has been extended to many of the transition metals.
Through the use of an analysis similar to the McCumber analysis, the gain
characteristics of an active atom can be related to the absorption and emission
spectra. Relating the gain to the absorption and emission spectra is of consider-
able practical importance since the gain as a function of wavelength is a more
difficult measurement than the absorption and emission. Emission and absorp-
tion spectra often display relatively sharp electronic, or no phonon. transitions
accompanied by adjacent broad vibronic transitions associated with the emission
and absorption of phonons. General absorption and emission processes appear in
Fig. 8. At reduced temperatures only phonon emission is observed since the
average phonon population is low. In this case. the vibronic emission spectra