Abstract

The successful three-micron laser emission between the levels ⁴I_11/2 and ⁴I_13/2 in highly-concentrated Er³⁺ systems,^[1] despite of the unfavourable ratio of lifetimes of these levels, is essentially determined by several energy transfer processes that affect all the levels (pump, emitting, terminal) involved in the laser generation: (1) two-and three-ion processes^[2] (globally characterized by rate W4) that deactivate the pump level ⁴S_3/2 and populate equally the levels ⁴i_13/2 and ⁴I_13/2; (ii) up-conversion process W₁ [(⁴I_13/2 ⁴I_15/2) + (⁴I_13/2→⁴i_9/2 ~> ⁴I_11/2)] that depopulates the terminal level and Tepumps the emitting level and (iii) upconversion W₂[(⁴I_11/2→⁴I_15/2) + (⁴I_11/2→⁴I_7/2)] that reduces the emission efficiency. The three-micron laser emission can be satisfactorily described by rate equations involving these processes.^[3] In the case of stationary regime analytical expressions for the photon flux density and population inversion are obtained showing explicitly the role of the various physical properties of the laser crystal and of the pump wavelength. A crucial role is played by the figure of merit $\text{p}\text{=}\frac{\text{β}}{\text{α}}\sqrt{\frac{{\text{w}}_2}{{\text{w}}_1}}$ (first introduced in^[4]), α and β being the Boltzmann population factors for the actual crystal field sublevels of ⁴I_13/2 and ⁴I_11/2 involved in emission. A positive pump effect implies $\text{p}<\sqrt{2}$, a condition that selects the possible laser transitions and therefore the wavelength range of emission.

© 1992 IQEC