Modeling of Actively $Q$-Switched Intracavity Raman Lasers

The normalized space-dependent rate equations are deduced assuming the intracavity photon densities and initial population-inversion density to be of Gaussian spatial distributions in the diode-pumped actively $Q$-switched intracavity Raman lasers. Numerical calculations are carried out to investigate the influences of these normalized variables on the pulse parameters of the first Stokes. The rate equations under the planewave approximation are also normalized and solved numerically, and the results show the obvious discrepancies from those of the space-dependent theory. The spontaneous Raman scattering factor in rate equations are deduced in detail for the first time, and the oscillating threshold of the first Stokes inside the resonator is deduced analytically. A sample calculation for an actively $Q$-switched self-Raman laser is presented to demonstrate the use of the curves and related formulas.