Nonlinear mechanism of multiphonon relaxation of the energy of electronic excitation in optical crystals doped with rare-earth ions

Intensities of 4f-4f transitions in glass materials

“…In many compounds with Pr 3+ it is found that the phenomenological Ω 2 parameter is negative, what, from the definition of the Ω λ [equation (21)], is not acceptable. It has been argued 9 that for this ion the lowest excited configuration of opposite parity, 4f 5d, is too close (~ 50000 cm -1 ) to the ground configuration (4f 2 ), invalidating the approximation made on the energy denominators in equation (15).…”

“…The state φ′〉 has a similar expression. The matrix element in equation (13), abbreviated as ed m r , is consequently given by: (15) An interesting estimation of the 4f-4f oscillator strengths can be made from equation (15). For an electric dipole allowed transition the oscillator strength can be as high as 1.…”

“…The advantage is that one has to deal with a single average energy difference in equation (15). It has been shown that the predicted values of the so-called intensity parameters …”

“…An alternative way of performing the summation in equation (15) has been the use of the average energy denominator method, introduced by Bebb and Gold 28 . The advantage is that one has to deal with a single average energy difference in equation (15).…”

“…In our days, the theoretical background for the rationalization of these intraconfigurational transitions, both radiative and non-radiative, is well established [7][8][9][10][11][12][13][14][15][16][17] . The standard Judd-Ofelt theory 7,8 has been used to evaluate absorption and emission cross-sections in the great majority of the works on these rare earth doped glasses.…”