Using the well-known quasi-three level kinetics model of Beach1,2 and Bourdet3 an exact analytical solution of the
coupled medium and geometric, plane-wave optical propagation equations for a longitudinally or face-pumped CW laser
is obtained. Although the quasi-three level kinetics model ignores all medium losses, e.g. amplified spontaneous
emission, upconversion, and excited state absorption, it is applicable to Yb:YAG devices. The optical extraction model,
which accounts for both laser wave amplification and pump wave absorption saturation coupling, treats both one- and
two-face pumping as well as single-, double-, and multiple-reflections of the pump wave between the faces of the disk.
Analytical expressions for the laser output power, the absorbed pump power, the threshold pump power, as well as the
pump absorption, optical-to-optical, optical extraction, and slope efficiencies are obtained. With a suitable modification
of the pump absorption efficiency, multiple-pass pumping via pump beam reinjection as achieved with a parabolic reflector
by Stewen et al4 can also be treated. Explicit equations for determining the spatial distributions of the pump and
laser intensities along the optic axis of the resonator are presented. Finally, explicit transcendental equations to determine
the resonator outcoupling fraction which maximizes either the optical-to-optical or the optical extraction efficiency
as a function of mirror loss, gain per pass, and pump power are derived. As an example the theory is applied to
the Yb:YAG gain medium.