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Füchtbauer–Ladenburg Equation

The Füchtbauer–Ladenburg equation is used for calculating the stimulated emission cross-sections of the laser gain medium. This equation is derived from the fluorescence analysis carried out based on the electronic transition of the laser medium.

The fluorescence intensity, dependant on the emission wavelength, is proportional to the fifth power of the optical frequency.

In the Füchtbauer–Ladenburg method, the quantum efficiency of a laser transition is approximately equal to unity, which means that the lifetime of an upper electron state is close to the radiative lifetime.

This is determined by the cross sections of emissions during transition to any lower energy level, which is represented by the following equation:

where n is the refractive index, ν is the optical frequency, σem(ν) is the emission cross sections dependant of emission frequency, and c is the velocity of light.

The above equation is considered as a derivative of the relation between the Einstein A and B coefficients. It can be described for a narrow emission bandwidth as:

where the dominator includes the mean wavelength of the considered transition. The Füchtbauer–Ladenburg equation is obtained based on the fact that the fluorescence intensity is a function of the emission cross section, as follows:

The denominator can be taken as the effective emission bandwidth, if the intensity is normalized to be 1 at the peak of the optical spectrum.

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