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Mode Competition

Definition: the phenomenon that different resonator modes experience laser amplification in the same gain medium, leading to cross-saturation effects

German: Modenkonkurrenz

Categories: optical resonators, laser devices and laser physics, physical foundations

Author: Dr. Rüdiger Paschotta

Cite the article using its DOI: https://doi.org/10.61835/twz

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A frequently used (and very valuable) concept is to describe the light circulating in an optical resonator in terms of resonator modes. The light in each mode can then be characterized with few parameters, e.g. electric field amplitude (or total power) and optical phase, apart from optical frequency and polarization. When only a few modes participate e.g. in the lasing process, the overall number of parameters is small, and various physical phenomena can be described on that simple basis.

The modes of a laser resonator all experience optical amplification in the same gain medium, e.g. a laser crystal, in which they spatially overlap to a significant extent. This leads to the phenomenon of mode competition or gain competition. Unfortunately, the terms are not precisely defined, and different meanings appear to be used in the literature:

the fact that different modes experience amplification in the same gain medium, and that this leads to cross-saturation effects, where stimulated emission by one mode causes gain saturation not only for itself (self-saturation), but also for the other modes
the phenomenon that the power distribution over several modes is unstable

Of course, the last-mentioned phenomenon can be a consequence of the former condition.

In the case of the former meaning of the term, mode competition can in principle be quantified: it is complete if the intensity distributions of the modes are identical, so that self- and cross-saturation are equally strong (assuming that the emission cross-sections are also identical). Mode competition is then reduced if the overlap of the intensity distributions is incomplete. Two simple examples are:

In a linear resonator, each resonator mode forms a standing-wave pattern in the gain medium, which differs for modes with different frequencies. Therefore, if one mode acquires a large power and strongly saturates its gain, another mode may see a reduced amount of gain saturation, as its standing-wave pattern has its anti-nodes at different positions (→ spatial hole burning).
If a laser resonator contains a dispersive prism, modes with different optical frequencies may obtain a relative transverse offset in the gain medium.

In a situation with strong mode competition (in the sense of strong overlap of mode intensity distributions), which may occur, e.g., in a unidirectional ring laser, a single mode may be excited in the steady state (→ single-mode operation, single-frequency lasers): the mode with the highest net gain will saturate the gain so that it exactly balances its losses, and any other mode will then experience a negative net gain, which causes its power to fade away.

Situations with reduced mode competition can be more complicated: a strong lasing mode can not saturate the gain for the others to a level which prevents them from lasing. One then has a situation with complicated nonlinear dynamics, often dominated by cross-saturation effects, but possibly also influenced even by tiny mode coupling effects. Depending on various details, a stable distribution of optical power over several modes may occur, or (more frequently) an unstable power distribution, which causes additional laser noise.

The discussion has shown that strong mode overlap can lead to a stable situation. Depending on the definition of terms, this may be considered as a situation with strong mode competition ( because of the strong overlap), or on the contrary as a situation with weak competition (as the situation is stable, not exhibiting explicit signs of competition).

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Bibliography

[1]	R. L. Fork and M. A. Pollack, “Mode competition and collision effects in gaseous optical masers”, Phys. Rev. 139 (5A), A1408 (1965); https://doi.org/10.1103/PhysRev.139.A1408
[2]	G. Stephan et al., “Competition effects in the polarization of light in a quasi-isotropic laser”, J. Opt. Soc. Am. B 4 (8), 1276 (1987); https://doi.org/10.1364/JOSAB.4.001276
[3]	I. Leyva, E. Allaria and R. Meucci, “Polarization competition in a quasi-isotropic CO₂ laser”, Opt. Lett. 26 (9), 605 (2001); https://doi.org/10.1364/OL.26.000605
[4]	M. Ahmed and M. Yamada, “Influence of instantaneous mode competition on the dynamics of semiconductor lasers”, IEEE J. Quantum Electron. 38 (6), 682 (2002); https://doi.org/10.1109/JQE.2002.1005419
[5]	M. Gong et al., “Numerical modeling of transverse mode competition in strongly pumped multimode fiber lasers and amplifiers”, Opt. Express 15 (6), 3236 (2007); https://doi.org/10.1364/OE.15.003236
[6]	M. Ahmed, “Longitudinal mode competition in semiconductor lasers under optical feedback: Regime of short-external cavity”, Optics and Laser Technol. 41 (1), 53 (2009); https://doi.org/10.1016/j.optlastec.2008.04.005

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