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TWO-PHOTON ABSORPTION IN SEMICONDUCTORS
Fabien BOITIER, Antoine GODARD, Emmanuel
ROSENCHER Claude FABRE
ONERA Palaiseau Laboratoire Kastler Brossel Paris
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Measuring intensity correlations Hanbury-Brown
Twiss experiment
Photon Bunching effect
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Understanding Photon bunching
- simple explanation in terms of fluctuating
waves - more difficult to understand in terms of
photons as particles
1 for shot noise, even present when the intensity
is constant, 1 due to extreme fluctuations of the
mean intensity in chaotic light
Fanos explanation in terms of constructive
interference between undistinguishable paths
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Full quantum treatment given by Glauber
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g(2)lt1 no classical explanation possible
g(2)gt1 classical explanation possible
but full quantum explanation still possible
and interesting
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Detectors response time limits observation of
narrow features in time or broad in frequency
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How to study broadband sources with ultra-short
correlation times ?
Use fast nonlinear effects
I. Abram et al 1986, Silberberg et al
Use Hong Ou Mandel interferometer
parametric fluorescence
Lame semi-réfléchissante
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Another possibility two-photon absorption in
semi-conductors
transient state
- Broadband - No phase matching
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Two photon characterization of a GaAs phototube
N2 f(P)
b f(l)
Two photon absorption coefficient b 10 cm/GW
_at_1.55 µm

• Quadratic response between 0.1 and 100 µW

Low efficiency not yet a two-photon counter
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Photocount histograms and detection operator
What is the two-photon counter observable ?
classical approach
for perfect quantum efficiency
acceptable for photon numbers lt3
limited efficiency accounted by attenuator in
front
exact quantum theory of two photon counter
remains to be done
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Two-photon absorption Intensity correlation
apparatus
Asph. Lens
Time delay
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Interferometric recorded signal
Intensity correlation function obtained by low
pass filtering
Source cw ASE _at_ 1.55µm , 4dBm Detector
Hamamatsu PMT GaAs
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TPA measurement of g(2)(?) (1) laser, amplified
spontaneous emission, blackbody
Boitier et al., Nature phys. 5, 267(2009)

• Summary table of the main properties

g(2)(0) ?c (fs) ?0 (nm) ?? (nm)
Laser 1.01 0.03 ? 1560 small
ASE 1.97 0.05 534 1530 6
Blackbody 1.8 0.1 37 1130 155
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TPA measurement of g(2)(?) (2) high gain
parametric fluorescence
with N. Dubreuil, P. Delaye
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Whole pulse two photon interferogram
CW source ?
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Second order correlation function g(2)(?)
without dispersion compensation
with dispersion compensation
far from degeneracy
near degeneracy
Evidence of an extrabunching effect

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Photon correlations in parametric
fluorescence(1) full quantum calculation
quantum state produced by parametric fluorescence
of gain G
quantum calculation of g(2)(0)
(in the experiment Ggt106)
nothing prevents g(2)(0) to be very large in weak
sources with large noise ( value of 28 observed
on squeezed vacuum (Ping Koy Lam)
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Photon correlations in parametric
fluorescence(2) fluctuating field approach
- The signal and idler fields are classical
fields taken as a sum of wavepackets with
random phases fs and fi. -the classical
equations of parametric mixing imply
fs fifpump
vacuum fluctuations are needed to trigger the
spontaneous parametric fluorescence
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Photon correlations in parametric
fluorescence(3) corpuscular approach
three kinds of photon coincidences
- accidental
- pairs due to the twin photon source
- linked to the chaotic distribution of pairs
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in a dispersive medium

• Ideal case without dispersion

• Increase of chromatic dispersion

dispersion compensation needed !
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CONCLUSION
TPA efficient technique to measure g(2)(t) down
to femtosecond range
not yet a two-photon counter efficiency can be
improved
no measurement so far in the full quantum regime
g(2)(t) lt1 in ideal tool for high flux isolated
photon sources
classical and/or quantum effects ? -many
competing physical pictures - even
classical pictures have some quantum flavour
- quantum approach often provides more
physical insight and simple
calculations than semi-classical ones