# Threshold Pump Power

Author: the photonics expert Dr. Rüdiger Paschotta

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

Categories: nonlinear optics, laser devices and laser physics

DOI: 10.61835/c1e Cite the article: BibTex plain textHTML Link to this page LinkedIn

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.

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.

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*.

## More to Learn

Encyclopedia articles:

Blog articles:

- The Photonics Spotlight 2009-09-27: “Lasers with Short Upper-state Lifetime”

## Questions and Comments from Users

2023-09-13

A particular laser, oscillating in a single longitudinal mode, when operated separately at two different pump powers of <$P_{x {\rm pump}}$> and <$P_{y {\rm pump}}$> gives steady-state output intensities of <$I_x$> and <$I_y$>, respectively. In steady state, the gain coefficients are given by <$\gamma_x$> and <$\gamma_y$>. If <$P_{x {\rm pump}} > P_{y {\rm pump}} > P_{\rm th pump}$> (threshold pump power), what is the relationship between the output intensities and gain coefficients at the lasing wavelength?

The author's answer:

Above threshold, the gain must be constant, since the round-trip gain must be zero in steady state. With more pump power, you just get more output power, but not more internal gain.

2023-12-01

Can you think of reasons why the threshold would actually be lower than calculated? A prototype reaches threshold at roughly half of the calculated threshold power, even when only considering quantum defect and incomplete absorption for pump efficiency but not imperfect spatial overlap.

The author's answer:

Sure, there can be various reasons, for example:

- not properly considered spatial profiles – for example, Gaussian beams instead of top-hat beams in a simple model
- inaccurate spectroscopic data
- inaccurate data on your optical components, e.g. concerning the reflectance of mirrors

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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?

The author's answer:

It is 20 mW + 10 mW / 0.20 = 70 mW.