Fundamentals of Brillouin-Light-Scattering (Fabry-Perot Interferometer)

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Fundamentals of Brillouin-Light-Scattering
(Fabry-Perot Interferometer)

• Andrii Chumak
• Advisers Helmut Schultheiß, Alexander A.
  Serga
• Fachbereich Physik und Forschungsschwerpunkt
  MINAS, Technische Universität Kaiserslautern,
  67663 Kaiserslautern, Germany

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Inelastic light scattering

• Brillouin light scattering occurs when light in a
  medium (such as water or a crystal) interacts
  with time dependent density variations and
  changes its energy (frequency) and path. The
  density variations may be due to acoustic modes,
  such as phonons, magnetic modes, such as magnons,
  or temperature gradients.
• The phenomenon of inelastic scattering of light
  due to acoustic phonons was first described by
  Leon Brillouin (1889-1969) in 1922 and 4 years
  later in 1926 independently by Leonid Mandelstam.
  In order to credit Mandelstam it is also denoted
  as Brillouin-Mandelstam scattering (BMS). Other
  commonly used names are Brillouin light
  scattering (BLS) and Brillouin-Mandelstam light
  scattering (BMLS).

Raman scattering or the Raman effect is the
inelastic scattering of a photon. The difference
in energy between the incident photon and the
Raman scattered photon is equal to the energy of
a vibration of the scattering molecule.
Discovered By Dr. C.V. Raman in liquids and
by Grigory Landsberg and Leonid Mandelstam in
crystals.
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Relationship between Brillouin and Raman
scattering
The inelastic scattering process of Brillouin
light scattering is in principle the same as
Raman scattering (BLS denominates the scattering
of acoustic phonons, while Raman scattering
refers to the scattering from molecule vibrations
and optic phonons). Brillouin scattering is
technically limited to the detection of
quasiparticles with frequencies below about
500 GHz, while with Raman scattering much higher
frequencies in the THz range can be measured.
The Brillouin shift is commonly small (??/? ?
10-5-10-6) and is commonly measured by the use of
a Brillouin spectrometer based on a Fabry-Pérot
interferometer, while Raman scattering labels a
setup employing a grating spectrometer.
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Brillouin light scattering (BLS)
BLS is inelastic scattering process in which a
phonon or magnon is either created (Stokes
process) or annihilated (anti-Stokes process).
Stokes
anti-Stokes
a b a
a b a
Quantum conception
?0 ?m ?sc
?0 ?m ?sc
Energy conservation law
?sc ?0 - ?m
?sc ?0 ?m
Frequency of scatt. light
The energy of the scattered light is slightly
changed, that is decreased for a Stokes process
and increased for an anti-Stokes process
(Brillouin shift).
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Fabry-Pérot interferometer (etalon)
The varying transmission function of an etalon is
caused by interference between the multiple
reflections of light between the two reflecting
surfaces (constructive or destructive
interference occurs).                  
The phase difference
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Transmittance and reflectivity
The transmittance function of the etalon is given
by
The maximum reflectivity is given by
Maximum transmission (Te 1) occurs when 2nl
cos? m ?, m 1, 2, 3
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Main Fabry-Pérot interferometer parameters
The free spectral range (FSR)
The finesse
Maximum transmission (Te 1) occurs when 2nl
cos? m ?, m 1, 2, 3
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Finesse vs reflectivity
Finesse as a function of reflectivity. Very high
finesse factors require highly reflective
mirrors.
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Multi-pass tandem Fabry-Pérot interferometer
Multi pass of the light increases contrast of the
interferometer.
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View of the light pass
The etalons are installed with different angles
corresponding to the direction of movement
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Schematic view of the operation
Such construction gives a possibility to suppress
neighboring resonances
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Fabry-Pérot interferometer photo
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Reflection mode
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BLS setup