A "simple" rateequation model for twophoton lasers

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A "simple" rate-equation model for two-photon
lasers

• An analysis of an article by
• Hope M. Concannon and Daniel J. Gauthier
• Presented by
• Kyle Falbo

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Why Lasers?

• Lasers are a modern device used frequently in the
  military, medical, retail, telecommunication, and
  consumer electronics industries.

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Why Lasers?

• Lasers are a modern device used frequently in the
  military, medical, retail, telecommunication, and
  consumer electronics industries.
• Lasers are an essential device used in modern
  optical storage devices such as CDs, DVDs, and
  the more recent storage media Blu-ray.

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Why Lasers?

• Lasers are a modern device used frequently in the
  military, medical, retail, telecommunication, and
  consumer electronics industries.
• Lasers are an essential device used in modern
  optical storage devices such as CDs, DVDs, and
  the more recent storage media Blu-ray.
• A recent study explores the usefulness of lasers
  in the field of quantum cryptography.

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• A recent study explores the usefulness of lasers
  in the field of quantum cryptography.

http//www.nature.com/nature/journal/v447/n7143/im
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Simple rate-equation model for two-photon lasers
In a two-photon laser, the atoms of an excited
laser medium, when hit by two photons by
stimulated-emission, each give off a resulting
four photons.
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Two-photon laser microscope
Spinal cord neuron
http//www.meduniwien.ac.at/typo3/?id2142
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Simple rate-equation model for two-photon lasers
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Simple rate-equation model for two-photon lasers
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Population inversion refers to a state of the
system in which more atoms are available to
amplify the field by stimulated emission than to
attenuate it by absorption 2.
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?N0 is the inversion in the absence of the pump
process. During the pump process we optically
pump photons into the laser medium by way of a
flashlamp to excite the atoms in the laser medium
into a higher energy state
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The mean cavity photon number q, is the number of
photons within the laser cavity.
qinj the photons we initially inject into the
system to initiate Lasing
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Finding our steady state solutions
We begin by analyzing the simpler case of the
system prior to photon injection, setting qinj
0.
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Determining our threshold values, i.e.
Bifurcation and
By setting our discriminant to zero, we get
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Finding stability
As we can see finding the stability is hardly
simple as our models title might suggest
Always stable
Stable for a good cavity Unstable for a bad
cavity
Always unstable
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Behavior of the system
--- __ -.-
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Lets turn on the laser!
We now let qinj ? 0, and find our new steady
state solutions.
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Finding our steady state solutions
Since contains no qint, again we get
However our q solution will now be in the form of
a general cubic
Not so simple to find here either.
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Finding our steady state solutions









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Behavior of the system

--- __ -.-
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So what does this all look like?
Java Applet
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References
Concannon, Hope M., Gauthier, Daniel J., Simple
rate-equation model for two-photon lasers, 1994,
Optics Letters, Vol. 19, No. 7 V.Makarov, A.
Anisimov, S.Sauge, Can Eve control PerkinElmer
actively-quenched single-photon detector?, 2008,
Department of Electronics and Telecommunications,
Norwegian University of Science and Technology,
Trondheim Norway makarov_at_vad1.com Milonni,
Peter W., Lasers, 1988, John Wiley Sons,
Inc. Cubic function, webreference,
http//en.wikipedia.org/wiki/Cubic_equation
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Any Questions?
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