In most lasers, the laser wavelength is longer than the pump wavelength (exception: upconversion lasers). This means that the energy of the laser photons is smaller than that of the pump photons – there is a so-called Stokes shift. As a consequence, the power efficiency of the laser could not be 100% even if every pump photon could be converted into a laser photon. The quantum defect is defined as the difference in photon energies:
It is also often specified as a percentage of the pump photon energy, effectively using only the parentheses in the equation above. In any case, it sets a lower limit to the loss in the conversion from pump power to laser power, i.e. an upper limit to the power efficiency.
The quantum defect is not related to the quantum efficiency. The latter refers to the average number of output photons per pump photon, rather than to the photon energies.
Some laser crystals (e.g. those doped with ytterbium) have a particularly small quantum defect of only a few percent of the pump photon energy, leading to potentially very high power efficiency. However, a small quantum defect also leads to quasi-three-level behavior of the gain medium, which makes certain aspects of laser design more sophisticated, and may even make it more difficult to achieve a high wall-plug efficiency.