Vibrational-Rotational Population Inversion

Abstract

A general theory of partial and complete vibrational-rotational population inversion is developed. The requirement for stimulated emission in the R-branch is that the rotational quantum number J shall exceed a minimum value which depends in a simple fashion on the ratio of the rotational to the vibrational temperature (T_r/T_υ), both of which may be positive (partial inversion). Stimulated emission in the Q and R branches is only possible if T_υ < 0 (complete inversion). Features peculiar to a vibrational-rotational laser are discussed in terms of the equation for net gain. Rough upper limits are set on the power output from a chemical laser. The equations governing partial inversion are illustrated for the example of HCl. Processes (electric discharge, chemical reaction) which have produced partial population inversion are discussed. The problem of maintaining complete population inversion is set out in terms of a hypothetical process forming CO continuously in level υ = 7 only. Physical processes which might excite a molecule into a high vibrational state either by way of an electronically excited state (through fluorescence) or within the ground electronic state (through electronic → vibrational transfer, or through energetic impacts) are discussed. Chemical processes which might result in a greater probability for reaction into a higher vibrational state than a lower one, k_υ′ ≫ k_υ, are considered under three headings: attractive, mixed, and repulsive reactions. (a) In attractive reactions it is supposed that the reagents attract but the products do not repel (significantly); the heat of reaction is trapped as vibration in the new bond. (b) In the mixed reactions it is argued that there is a tendency for the repulsion to be dissipated while the new bond is still extended; as a result, both repulsion and attraction could be converted to vibration in the new bond. (c) The repulsive reactions only appear likely to give k_υ′ ≫ k_υ in special circumstances; if the central atom is light or the repulsion impulsive. Examples are suggested in each category: (a) association reactions; (b) covalent → ionic reactions (e.g., alkali metal atom plus halogen or halide); (c) covalent reactions. The second category shows particular promise of providing reactions suitable for use in a chemical laser.