Physics of Solid-State Laser Materials by Zundu Luo & Yidong Huang

Author:Zundu Luo & Yidong Huang
Language: eng
Format: epub
ISBN: 9789813296688
Publisher: Springer Singapore

(7.21)

where HSO is the spin–orbit coupling Hamiltonian and μ denotes the operator of electric-dipole moment . It can be seen from the above matrix elements that the transition probability is inversely proportional to the square of energy separation between 2E and 4T1 or between 2E and 4T2. Owing to the fact that the separation between 2E and 4T1 is four times that between 2E and 4T2, besides the matrix element of is equal to zero; therefore, in the comparison of R line absorption intensity in different polarization direction, the contribution of the first matrix element in (7.21) can be neglected. To compare the π and σ polarized intensities of the 2E→4A2 transition induced by the 2E and 4T2 spin–orbit coupling, it is enough to compare the squares of matrix elements and .

Energy levels 4T2 and 4A2 belong to even parity states. The matrix element of electric-dipole moment μ between them is equal to zero unless their wave functions are mixed by the wave functions of the electronic configuration 3d24p introduced by odd crystal field potential Vu. In this case, the electric-dipole matrix element between 4A2 and 4T2 is

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