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Journal of Optoelectronics·laser

The Absorption of Pumping Light in Four-level Solid State Medium Pumped with a Long Pulse

Qin Hua

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

The theoretical solution of the pump light absorption in a 4-level solid state gain medium was presented by solving light transport and coupled rate equations of pump process in gain medium.It is shown that the absorption of pump light with respect to the depth in the solid medium is not simply a exponential function,when pump photon density is high enough,this absorption becomes a linearity with the absorption depth in the gain medium.The rule of the pump light absorption changing from expeonential to linearity was discussed.The simulation results for YAG crystal show that a rule of the pump light absorption is simplified to Beers formula only under the condition of I_0≤1.0×10~4 J·s~(-1)·cm~(-2),while I_0≥1.0×10~5 J·s~(-1)·cm~(-2) within absorption depth of 0.7 cm this rule is a linear function.

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The theoretical solution of the pump light absorption in a 4-level solid state gain medium was presented by solving light transport and coupled rate equations of pump process in gain medium.It is shown that the absorption of pump light with respect to the depth in the solid medium is not simply a exponential function,when pump photon density is high enough,this absorption becomes a linearity with the absorption depth in the gain medium.The rule of the pump light absorption changing from expeonential to linearity was discussed.The simulation results for YAG crystal show that a rule of the pump light absorption is simplified to Beers formula only under the condition of I_0≤1.0×104 J·s(-1)·cm~(-2),while I_0≥1.0×105 J·s(-1)·cm~(-2) within absorption depth of 0.7 cm this rule is a linear function.
In the n-type four-level atomic system, we have studied the nonlinear theory of electromagnetically induced absorption. The results show that the probe light Rabi frequency and the attenuation distribution coefficient A affect the nonlinear absorption and then the absorption of a medium. When the probe light intensity is weak, the absorption of the medium and the linear absorption are the same, showing the characteristics of electromagnetic induction absorption. When the probe light intensity is increased, the absorption of the medium and the linear absorption are no longer the same, and now the medium absorption curve will show hole burning phenomenon, and then it will show the gain phenomenon. At the same time, the nonlinear absorption is affected by the value of A. Even if the probe light is weak, the medium absorption will change the electromagnetic induction absorption into the gain phenomenon with the A value decreasing.
According to the analysis of gain theory, the absorption or gain of medium depends on pump power. The coherent population oscillation leads the pulse to experience absorption saturation and propagation delay in a medium with absorption. This effect induces the pulse to experience gain saturation and propagation advance in a medium with gain. Making use of the transition rate equation of metastable state poplation, we develop the model of fast light in erbium-doped optical fiber and obtain the analytic expression of time advance. We demonstrate that there is a saturation effect of fast light in low frequency region, but the fast light is enhanced with pump power increasing in high frequency region.
Abstract A semiclassical algorithm is explored to a four-energy level model, aiming to find out the factors that affect the dynamics behavior during the pump process. The impacts of pump intensity Ω p , non-radiative transition rate γ 43 and decay rate of electric dipole δ 14 are discussed in detail. The calculation results show that large γ 43 , small δ 14 , and strong pumping Ω p are beneficial to the establishing of population inversion. Under strong pumping conditions, the entire pump process can be divided into four different phases, tentatively named far-from-equilibrium process, Rabi oscillation process, quasi dynamic equilibrium process and ‘equilibrium’ process. The Rabi oscillation can slow the pumping process and cause some instability. Moreover, the duration of the entire process is negatively related to Ω p and γ 43 whereas positively related to δ 14 .
Theoretical treatment of the effects of external pulse field on the emission and absorption of two impurity centers has been attempted. Good overlapping of emission band of one center (donor of energy) with the absorption band of another center (acceptor of energy) is assumed, so that radiative and non-radiative energy transfer may take place. Mathematical model is based on the system of reduced Maxwell equations for magnitudes of field components and Bogolubov's equations for elements of multiparticle density matrix of donor-acceptor complex. Numerical solution is obtained for NaCl:Cu, Mn and KCl:Pb,Eu crystals. These materials are differing in the value of transition dipole moment of acceptor absorption. It is low for the first medium while for KCl:Pb,Eu it is comparable to that one for the donor emission. It turns out that in the case of low value of transition dipole moment the luminescence of both components of donor-acceptor pair takes place. On the contrary, only acceptor emission exists in the case of high value of transition dipole moment of acceptor when the pump intensity is low. Simultaneous luminescence of donor and acceptor occurs when pump intensity is enough. So, in the systems of such kind the emission may be changed over from one frequency to another through the power level of pump radiation.