Definition of a laser threshold

Björk, Gunnar; Karlsson, Anders; Yamamoto, Yoshihisa

doi:10.1103/physreva.50.1675

Cited by 198 publications

(162 citation statements)

References 14 publications

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“…Defining the threshold is a non trivial issue, which sparks off interesting discussions [1,2]. Classically, the threshold is defined as the operating point for which the unsaturated gain equals the a Present address: Institut de Physique de Rennes, UMR CNRS-Université de Rennes I 6251, 35042 Rennes Cedex, France losses.…”

Section: Introductionmentioning

confidence: 99%

Experimental study of the delayed threshold phenomenon in a class-A VECSEL

Amili

Gredat

Alouini

et al. 2012

Eur. Phys. J. Appl. Phys.

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Abstract. An experimental study of the delayed threshold phenomenon in a Vertical Extended Cavity Semiconductor Emitting Laser is carried out. Under modulation of the pump power, the laser intensity exhibits a hysteresis behavior in the vicinity of the threshold. The temporal width of this hysteresis is measured as a function of the modulation frequency, and is proved to follow the predicted scaling law.A model based on the rate equations is derived and used to analyze the experimental observations. A frequency variation of the laser around the delayed threshold and induced by the phase-amplitude coupling is predicted and estimated.

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Section: Introductionmentioning

confidence: 99%

Experimental study of the delayed threshold phenomenon in a class-A VECSEL

Amili

Gredat

Alouini

et al. 2012

Eur. Phys. J. Appl. Phys.

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“…Most of present work on the intensity noise in high β lasers has been applied to standard semiconductor laser diodes, embedding quantum wells as gain material. These models predict that if β is small, the peak-to-valley difference of the relaxation oscillations is very large and it decreases with increasing β [19,20]. However, all these models are based on standard rate equations used in quantum well lasers and very few studies have been carried out in this field when switching from quantum well lasers to quantum dot lasers.…”

Section: Bad-cavity Regimementioning

confidence: 99%

Quantum theory of a single-emitter nanolaser

Larionov

Kolobov

2013

Phys. Rev. A

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Using two equivalent approaches, Heisenberg-Langevin and density operator, we investigate the properties of nanolaser: an incoherently pumped single two-level system interacting with a singlecavity mode of finite finesse. We show that in the case of good-cavity regime the HeisenbergLangevin approach provides the analytical results for linewidth, amplitude fluctuation spectrum, and intracavity Mandel Q-parameter. In the bad-cavity regime we estimate the frequency at which the peak of relaxation oscillations appears. With the help of the master equation for density operator written in terms of coherent states we obtain approximated expression for Glauber-Sudarshan P function. This solution can be used in the case of good-cavity regime and allows us to investigate in more detail the thresholdless behaviour of the nanolaser. All two approaches are in a very good agreement with each other and numerical simulations.

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“…Two competing ideas can be invoked: either this is a thresholdless laser [85] or we can define the threshold in any reasonable way, for example when the population of the mode exceeds unity [84]. In any case, the laser (stimulated emission) action happens at very low pump powers, which is where the industrial interest in microlasers may come from.…”

Section: Microlasersmentioning

confidence: 99%

“…(5) we findṖ = γβN (P + 1) − κP where the terms in parentheses make clear the roles of stimulated (P ) and spontaneous (+1) emission. This model neglects re-absorption by the fluorescent medium, non-radiative loss, saturation of excited state population and fluctuations but still captures the essential behaviours [79][80][81][82][83][84][85].…”

Section: Microlasersmentioning

confidence: 99%

Bose-Einstein condensation of photons from the thermodynamic limit to small photon numbers

Nyman

Walker

2017

Journal of Modern Optics

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Photons can come to thermal equilibrium at room temperature by scattering multiple times from a fluorescent dye. By confining the light and dye in a microcavity, a minimum energy is set and the photons can then show Bose-Einstein condensation. We present here the physical principles underlying photon thermalization and condensation, and review the literature on the subject. We then explore the 'small' regime where very few photons are needed for condensation. We compare thermal equilibrium results to a rate-equation model of microlasers, which includes spontaneous emission into the cavity, and we note that small systems result in ambiguity in the definition of threshold. FOREWORDThis article is written in memory of Danny Segal, who was a colleague of one of us (Rob Nyman) in the Quantum Optics and Laser Science group at Imperial College for many years. The topic of this article touches on the subject of dye lasers, the stuff of nightmares for any AMO physicist of his generation, but a stronger connection to Danny is that he was very supportive of my application for the fellowship that pushed my career forward, and funded this research. One of Danny's quirks was a strong dislike of flying. As a consequence, I had the pleasure of joining him on a 24 hour, four-train journey from London to Italy to a conference. That's a lot of time for story telling and forging memories for life. Danny was one of the good guys, and I sorely miss his good humour and advice.This article presents a gentle introduction to thermalization and Bose-Einstein condensation (BEC) of photons in dye-filled microcavities, followed by a review of the state of the art. We then note the similarity to microlasers, particularly when there are very few photons involved. We compare a simple non-equilibrium model for microlasers with an even simpler thermal equilibrium model for BEC and show that the models coincide for similar values of a 'smallness' parameter.

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Definition of a laser threshold

Cited by 198 publications

References 14 publications

Experimental study of the delayed threshold phenomenon in a class-A VECSEL

Experimental study of the delayed threshold phenomenon in a class-A VECSEL

Quantum theory of a single-emitter nanolaser

Bose-Einstein condensation of photons from the thermodynamic limit to small photon numbers

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