Parameters for Quantitative Comparison of Two-, Three-, and Four-Level Laser Media, Operating Wavelengths, and Temperatures

Several parameters are proposed for describing the statistical thermodynamic component of the exchange of photons between a pump and a laser beam. They are based on the occupation probability of absorbing and emitting, pump and laser levels, and are complementary to the optical cross sections. The ldquooccupation factor,rdquo
f

₀
, is appropriate for describing an optical amplifier in the small signal regime.
f

₁
is appropriate for describing an amplifier in the large signal regime, e.g., a laser. They serve to facilitate a quantitative comparison of laser gain media, operating temperatures, and choice of pump and laser wavelengths. After a simple scaling, both occupation factors have a numerical value that coincides well, in most cases, with conventional usage of the terms two-, three-, and four-level laser. They can thus serve as an unambiguous, quantitative alternative to the quasi-two-, quasi-three-, and quasi-four-level terminology. The proposed definitions are general enough to apply to many types of gain media, but are particularly useful for comparing systems with discrete levels, pumped with a narrowband source, in near-resonance with the laser wavelength. Several low-quantum-defect combinations of pump and laser wavelengths are analyzed for Er
³⁺
, Nd
³⁺
, Yb
³⁺
, and Ho
³⁺
in YAG, as a function of temperature.