Quantum Defect
Author: the photonics expert Dr. Rüdiger Paschotta (RP)
Definition: energy difference between pump and laser photons
Category: 
Related: quantum efficiencyphotonsslope efficiencyStokes shift
Units: %
Formula symbol: ($q$)
Page views in 12 months: 1333
DOI: 10.61835/2l0 Cite the article: BibTex BibLaTex plain textHTML Link to this page! LinkedIn
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What is a Quantum Defect?
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:
($q = h{\nu _{{\textrm{pump}}}} - h{\nu _{{\textrm{laser}}}} = h{\nu _{{\textrm{pump}}}} \cdot \left( {1 - \frac{{h{\nu _{{\textrm{laser}}}}}}{{h{\nu _{{\textrm{pump}}}}}}} \right) = h{\nu _{{\textrm{pump}}}} \cdot \left( {1 - \frac{{{\lambda _{{\textrm{pump}}}}}}{{{\lambda _{{\textrm{laser}}}}}}} \right)$)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.
In the same way, the quantum defect can be calculated for an optical amplifier.
Examples
As an example, consider the quantum defect of a Nd:YAG laser, which is pumped at 808 nm and lases at 1064 nm; the quantum defect is 0.368 eV or 24.1%.
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 demanding, and may even make it more difficult to achieve a high wall-plug efficiency.
There are special cases, for example upconversion lasers, where the definition of the quantum defect needs to be adapted, e.g. because multiple pump photons are involved.
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. There are cases with high quantum efficiency but large quantum defect, or vice versa.
Frequently Asked Questions
This FAQ section was generated with AI based on the article content and has been reviewed by the article’s author (RP).
What is the quantum defect in a laser?
The quantum defect is the energy difference between a pump photon and a laser photon. Because the laser wavelength is usually longer than the pump wavelength, each laser photon has less energy than the absorbed pump photon, and this difference is the quantum defect.
How does the quantum defect affect laser efficiency?
The quantum defect sets a fundamental upper limit on the power efficiency of a laser. The energy lost per photon is converted into heat within the gain medium, which limits the overall efficiency and can cause thermal problems in high-power lasers.
Is the quantum defect related to the quantum efficiency?
No. The quantum defect concerns the energy loss per photon, while the quantum efficiency refers to the fraction of pump photons that generate a laser photon. A laser can have a high quantum efficiency but still a large quantum defect, or vice versa.
Which lasers have a small quantum defect?
Lasers based on ytterbium-doped gain media are known for their particularly small quantum defect. This feature contributes to their high power efficiency and makes them well-suited for high-power applications.