Abstract
Impact Statement: The classification of lasers in three- or four-level schemes is of fundamental importance for describing their operational characteristics. From solid state and fiber lasers, it is well known that the observed characteristics does not coincide with the number of physical levels, and typically even intermediate behavior is observed, which can be described by a continuous quasi-level parameter. Here we generalize the quasi-level concept so that it can be applied to a wide range of laser media. Abstract: A parameter is proposed which classifies the laser operating characteristics according to the quasi-level terminology, i.e., as intermediate behavior between that of an ideal two- and three-level or three- and four-level laser scheme. Since the quasi-level parameter is purely based on a generic rate equation description of the laser, no inherent assumptions about gain medium properties or the pumping process are required. The validity of the quasi-level parameter is verified for various prototypical laser schemes. As a specific example of a nonideal laser, the operating behavior of an experimental quantum cascade laser is classified, which constitutes a quite generic laser type since the active region properties can be custom-engineered by quantum design.
Highlights
The distinction of lasers in three- and four-level schemes is of general importance for characterizing and understanding their operational behavior [1]
As a defining criterion for three-level vs. four-level behavior of lasers, we use the change in population difference associated with an optical transition from the upper to the lower laser level: For three-level-type lasers, the upper and lower laser level occupations, n2 and n1, change by δn2 = −1 and δn1 = 1, and the population difference reduces by δn2 − δn1 = −2, while ideal four-level behavior is characterized by an empty lower laser level, yielding δn2 = −1, δn1 = 0 and δn2 − δn1 = −1 [5], [8]
We have introduced a general quasi-level parameter for classifying the laser operating characteristics by comparison to prototypical four, three- and two-level behavior. This parameter can capture intermediate behavior and is applicable to any laser which can be described by a generic rate equation model for the level populations
Summary
The distinction of lasers in three- and four-level schemes is of general importance for characterizing and understanding their operational behavior [1]. By dividing the energy states into an upper absorbing level manifold, comprising all the potential upper pump and laser levels, and a lower emitting one containing the lower pump and laser levels [see Fig. 1(d)], a quasi-level coefficient can be calculated based on the thermal population of the pump and laser levels within the corresponding manifolds [4], [5] This concept is targeted at low-quantum-defect, narrowband optically pumped lasers with discrete levels, especially solid-state lasers doped with transition metal or rare earth ions where for a given pump and lasing wavelength, the levels involved are clearly specified [4]. Typically several levels are involved in the pumping process, and more than one optical transition might contribute to lasing
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