Four-level and Three-level Gain Media | previous | next | feedback |
Definition: laser gain media without/with reabsorption from the lower laser level
Optical amplification in the gain medium of a laser or laser amplifier arises from stimulated emission, where the input light induces transitions of laser-active ions from some excited state to a lower state.
Three-Level Systems
In a three-level system, the laser transition ends on the ground state. The unpumped gain medium exhibits strong absorption on the laser transition. Only by pumping more than half of the ions (or atoms) into the upper laser level do a population inversion and consequently net laser gain result; the threshold pump power is thus fairly high.
The population inversion can be achieved only by pumping into a higher-lying level, followed by a rapid radiative or non-radiative transfer into the upper laser level, because in this way one avoids stimulated emission caused by the pump wave. (For transitions between only two levels, simultaneous pump absorption and signal amplification can not occur.)
An example of a three-level laser medium is ruby (Cr3+:Al2O3), as used by Maiman for the first laser.
Figure 1: Left: a three-level system, where the laser transitions ends on the ground state. Middle: a four-level system, where the laser transition ends on a level above the ground state, which is quickly depopulated e.g. via phonons. Right: a quasi-three-level system, where the lower laser level has some population in thermal equilibrium.
Four-Level Systems
A lower threshold pump power can be achieved with a four-level laser medium, where the lower laser level is well above the ground state and is quickly depopulated e.g. by multiphonon transitions. Ideally, no appreciable population density in the lower laser level can occur even during laser operation. In that way, reabsorption of the laser radiation is avoided (provided that there is no absorption on other transitions). This means that there is no absorption of the gain medium in the unpumped state, and the gain usually rises linearly with the absorbed pump power.
The most popular four-level solid-state gain medium is Nd:YAG. All lasers based on neodymium-doped gain media, except those operated on the ground-state transition around 0.9-0.95 μm, are four-level lasers.
Neodymium ions can also be directly pumped into the upper laser level, e.g. with pump light around 880 nm for Nd:YAG. Even though effectively only three levels are involved, the term three-level system would not be used here.
Quasi-Three-Level Systems
A quasi-three-level laser medium is one with a kind of intermediate situation, where the lower laser level is so close to the ground state that an appreciable population in that level occurs in thermal equilibrium at the operating temperature. As a consequence, the unpumped gain medium causes some loss at the laser wavelength, and transparency is reached only for some finite pump intensity. For higher pump intensities, there is gain, as required for laser operation.
Examples of quasi-three-level media are all ytterbium-doped gain media (e.g. Yb:YAG, or Yb:glass as used in optical fibers), neodymium-doped media operated on the ground state transition (e.g. 946 nm for Nd:YAG), thulium-doped crystals and glasses for 2-μm emission, and erbium-doped media for 1.5 or 1.6-μm emission, such as erbium-doped fiber amplifiers.
An important fact is that the spectral shape of the optical gain in a quasi-three-level laser medium depends on the excitation level, because this affects the balance between emission and reabsorption. As a consequence, the laser wavelength obtained may depend on the resonator losses: high losses require a higher gain, and thus a higher excitation level, and consequently a shorter wavelength of maximum gain.
Figure 2: Gain and absorption (negative gain) of erbium (Er3+) ions in germano-alumino-silicate glass for excitation levels from 0 to 100% in steps of 10%. Strong three-level behavior (with transparency reached only for >50% excitation) occurs at 1530 nm. At longer wavelengths (e.g. 1580 nm), a lower excitation level is required for obtaining gain, but the maximum gain is smaller.
There can actually be a smooth transition from three-level to four-level gain characteristics with increasing laser wavelength. For example, erbium-doped glass (see Figure 2) shows strong three-level behavior around 1535 nm but nearly four-level behavior for long wavelengths of e.g. 1600 nm. Similarly, ytterbium-doped glass exhibits pronounced three-level characteristics for wavelengths below ∼1040 nm, and the same holds for Yb:YAG lasers at 1030 nm and for lasers based on many other rare earth crystals. For operation at such wavelengths, a large inversion density is required for overcoming the reabsorption loss. For longer wavelengths, as sometimes used particularly in fiber lasers, there is hardly any reabsorption, and in a long fiber only a very low excitation density may be required to obtain sufficient gain.
Pronounced three-level behavior is inevitable for gain media with a very small quantum defect, because this enforces a small energy spacing between the lower laser level and the ground state, so that thermal population of the lower laser level is significant.
Note that the gain media of semiconductor lasers actually also behave like three-level lasers, exhibiting losses in the unpumped state, an asymmetric gain region, etc.
Common Errors
In the literature, a profound misunderstanding of various aspects related to three-level gain media is very widespread:
- It is sometimes not understood that the reabsorption does not constitute a real loss of energy, because it excites ions into the upper level, so that stimulated emission can again occur at a later time. Nevertheless, three-level characteristics tend to decrease the laser efficiency for other reasons: they require higher excitation densities, leading to higher losses through fluorescence, and they usually do not permit the gain medium to be made long enough for complete pump absorption, because reabsorption would dominate in weakly pumped regions.
- Another frequent mistake is to believe that (according to Einstein's original simple model) there are equal cross sections for stimulated emission and reabsorption, although this does not hold for effective cross sections of transitions between level manifolds with non-degenerate Stark levels, as often occur in solid-state gain media.
- The saturation fluence is often not calculated correctly: it is the photon energy divided by the sum of emission and absorption cross sections.
- It is not true that reabsorption in a three-level gain medium (whether in an unpumped region or not) acts like a saturable absorber, tentatively leading to Q-switching effects and the like. For such effects, the cross sections of the absorber would have to be larger than those of the gain medium.
Bibliography
| [1] | P. P. Sorokin and M. J. Stevenson, "Stimulated infrared emission from trivalent uranium" (the first four-level laser), Phys. Rev. Lett. 5 (12), 557 (1960) |
| [2] | W. P. Risk, "Modeling of longitudinally pumped solid-state lasers exhibiting reabsorption losses", J. Opt. Soc. Am. B 5 (7), 1412 (1988) |
See also: gain media, ytterbium-doped gain media, rare-earth-doped gain media, solid-state lasers, reciprocity method, effective cross sections, Spotlight article 2006-08-12
This encyclopedia is authored by Dr. Rüdiger Paschotta, the founder and executive of RP Photonics Consulting GmbH. Contact this distinguished expert in laser technology, nonlinear optics and fiber optics, and find out how his technical consulting services (e.g. product designs, problem solving, independent evaluations, or staff training) could become very valuable for your business!
