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# Threshold Pump Power

Definition: the pump power at which the laser threshold is reached

German: Schwellenleistung

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The threshold pump power of a laser is the value of the pump power at which the laser threshold is just reached, usually assuming steady-state conditions. At this point, the small-signal gain equals the losses of the laser resonator. A similar threshold exists for some other types of light sources, such as Raman lasers and optical parametric oscillators. Figure 1: Output versus input power for an optically pumped laser. The threshold pump power is 5 W, and the slope efficiency is 50%.

The “edge” occurring at the threshold is very slightly rounded due to the influence of amplified spontaneous emission.

For an optically pumped laser, the definition of threshold pump power may be based either on the incident or absorbed pump power. For applications, the incident pump power may be more relevant, but the threshold power with respect to absorbed power can be interesting e.g. for judging the gain efficiency of the gain medium.

A low threshold power requires low resonator losses and a high gain efficiency. The latter is achieved by using, e.g., a small laser mode area in a gain medium with a high <$\sigma -\tau$> product. The latter is fundamentally limited by the emission bandwidth. Therefore, broadband gain media tend to have higher laser thresholds.

For a simple four-level laser gain medium, we can use an equation for the gain efficiency from the corresponding article for calculating the threshold pump power:

$${P_{{\rm{p,th}}}} = \frac{{{l_{{\rm{rt}}}}}}{{\partial g/\partial {P_{\rm{p}}}}} = \frac{{h{\nu _{\rm{p}}}\;A\;\;{l_{{\rm{rt}}}}}}{{{\eta _{\rm{p}}}\;{\tau _2}\;{\sigma _{{\rm{em}}}}}}$$

where <$l_\textrm{rt}$> is the round-trip power loss of the laser resonator (taking into account the output coupler loss and parasitic losses), <$h\nu_\textrm{p}$> is the photon energy of the pump source, <$A$> is the beam area in the laser crystal, <$\eta_\textrm{p}$> is the pump efficiency, <$\tau_2$> the upper-state lifetime and <$\sigma_\textrm{em}$> the emission cross-section. It is assumed that the power losses <$l_\textrm{rt}$> per round trip and thus the round-trip gain is small (e.g. below 20% or 1 dB). The pump efficiency contains terms for the quantum defect, for possible losses of excitation in the gain medium (e.g. by quenching processes), for pump power lost outside the region covered by the laser beam, and also (if we consider the pump threshold in terms of incident pump power) for incomplete pump absorption.

## Calculator for the Threshold Pump Power

 Pump wavelength: Beam radius: Round-trip losses: (must be ≪ 100 %) Pump efficiency: Upper-state lifetime: Emission cross-section: Threshold pump power: calc (absorbed)

Enter input values with units, where appropriate. After you have modified some inputs, click the “calc” button to recalculate the output.

The optimization of the laser output power for a given pump power usually involves a compromise between high slope efficiency and low laser threshold power. In typical situations, the pump power used in normal operation is several times higher than the pump threshold power. The question of which value is most appropriate for the threshold pump power is one of the issues of laser design.

The dependence of output power on pump power of a laser is not always as simple as shown in Figure 1. For example, the onset of lasing may not be as well defined in some lasers with high resonator losses. The threshold pump power is then sometimes defined by extrapolating the approximately linear curve at higher powers down to zero.

There are some exotic types of lasers, e.g. single-atom lasers, which have no laser threshold, and are thus called thresholdless lasers.

## Questions and Comments from Users

2022-02-17

The threshold power of a laser is 20 mW and its slope efficiency is 20%. What is the pump power required for an output power of 10 mW?

It is 20 mW + 10 mW / 0.20 = 70 mW.

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