6 - Solid state and gas laser amplifier and oscillator

Summary

Rate equation and population inversion

In a material which has only two energy levels, χ″ is always positive because ρ₁₁ > ρ₂₂ for E₁ < E₂ at thermal equilibrium. Prior to the invention of lasers, there was no known method to achieve ρ₂₂ > ρ₁₁. However, we now know that a negative χ″ in Eq. (5.41a) (i.e. ρ₂₂ > ρ₁₁) can be achieved by pumping processes that are available in materials that have multiple energy levels, as described in the following.

Let there be many energy levels in the material under consideration, as shown in Fig. 6.1. Let there be a mechanism in which the populations at E₁ and E₂, i.e. N₁ = Nρ₁₁ and N₂ = Nρ₂₂, are increased by pumping from the ground state at pump rates R₁ and R₂. In solid state lasers, the pumping action may be provided by an intense optical radiation causing stimulated transition between the ground state and other higher energy states, where the particles in the higher energy states relax preferentially into the E₂ state. In gas lasers, the molecules in the ground state may be excited into higher energy states within a plasma discharge; particles in those higher energy states then relax preferentially to the E₂ state. Alternatively, collisions with particles of other gases may be utilized to increase the number of particles in the E₂ state. Various schemes to pump different lasers are reviewed in ref. In order to obtain amplification, it is necessary to have R₂ ≫ R₁.