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Theory of Resonant Absorption.

Thomas Speziale

Published Jan 1, 1978• 0 citations
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Calculations of cross sections of resonant two-photon transitions to the second excited 4f5d state in Pr3+:Y3Al5O12using density matrix theory

Zhenwen Dai, Jing‐yao Liu, Siyuan Zhang

The density matrix resonant two-photon absorption (TPA) theory applicable to laser crystals doped with rare earth ions is described. Using this theory, resonant TPA cross sections for transitions from the ground state to the second excited state of the 4f5d configuration in Pr3+:Y3Al5O12 are calculated. The peak value of TPA cross section calculated is 2.75 × 10-50 cm4 s which is very close to the previous experimental value 4 × 10-50 cm4 s. The good agreement of calculated data with measured values demonstrates that the density matrix resonant TPA theory can predict resonant TPA intensity much better than the standard second-order perturbation TPA theory.

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A theory of resonance two-photon absorption, which describes this effect as a combination of two-stage and two-photon processes, is developed in a unified mathematical formalism. Expressions for the transition probabilities and kinetic equations are derived, the absorption coefficient is determined for different and identical frequencies, and the shift of the maximum of the resonance two-photon absorption line is obtained. Investigations are made of the intensity dependences of these expressions and of the kinetics of resonance two-photon transitions. The results are compared with available experimental data.

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Springer eBooks•Jan 1, 1984•1 citation
The density matrix resonant two-photon absorption (TPA) theory applicable to laser crystals doped with rare earth ions is described. Using this theory, resonant TPA cross sections for transitions from the ground state to the second excited state of the 4f5d configuration in Pr3+:Y3Al5O12 are calculated. The peak value of TPA cross section calculated is 2.75 × 10-50 cm4 s which is very close to the previous experimental value 4 × 10-50 cm4 s. The good agreement of calculated data with measured values demonstrates that the density matrix resonant TPA theory can predict resonant TPA intensity much better than the standard second-order perturbation TPA theory.
A theory of resonance two-photon absorption, which describes this effect as a combination of two-stage and two-photon processes, is developed in a unified mathematical formalism. Expressions for the transition probabilities and kinetic equations are derived, the absorption coefficient is determined for different and identical frequencies, and the shift of the maximum of the resonance two-photon absorption line is obtained. Investigations are made of the intensity dependences of these expressions and of the kinetics of resonance two-photon transitions. The results are compared with available experimental data.