Creation of Colloidal Periodic Structure

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Chapter 12. Interaction of Light and Sound
12.0 Introduction Acousto-Optic(AO) effect
Effect of change in the index of refraction
of medium (crystal) by an Acoustic wave
Acoustic wave ? Photoelastic effect ? Change in
refractive index
Reference A. Ghatak, K. Thyagarajam, Optical
Electronics, Cambridge Univ. Press A. Yariv, P.
Yeh, Optical Waves in Crystals, John Wiley
Sons
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Photoelastic effect
Mechanical strain ? Index of refraction
Index ellipsoid for Principal axes
Strain tensor elements, S
Normal strain
Shear strain
where, u, v, w displacements along the x, y, z
axes
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Change in index of refraction due to the
mechanical strain
where, Pij Elasto-Optic (Strain Optic)
Coefficient (6x6 matrix) ? Table 9.1 / 9.2
The equation of the index ellipsoid in the
presence of a strain field
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Example) Sound wave propagating along the z
direction in water
Sound wave
Elasto-Optic Coefficient for the water
(isotropic, Table 9.1)
The new index ellipsoid
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Example) y-polarized Shear wave propagating along
the z direction in Ge
Sound wave
Elasto-Optic Coefficient for the Ge (cubic, Table
9.1)
The new index ellipsoid
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Acousto-Optic effect
Bragg diffraction Raman-Nath diffraction
Vector Representation
light wave
acoustic wave
Spread angle of Acoustic wave
Raman-Nath diffraction acoustic wave vector
has an angular distribution
Bragg diffraction acoustic wave vector is
well defined
Diffraction angle of Light
Dimensionless parameter
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Example) Water, n1.33, W6MHz (vs1,500 m/s),
l632.8 nm
Raman-Nath diffraction Multiple order
diffraction
Bragg diffraction Single order diffraction
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Raman-Nath diffraction
Moving periodic refractive index grating
Consider L is small enough so that the medium
behave as a thin phase grating,
where, f1(2p/l)n0L, f1(2p/l)Dn0L
The transmitted field on the plane xL
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amplitude reduction
Frequency
Wave vector
Propagation in xgtL
1 order -1 order
Diffraction angles
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m-th order diffractive wave Frequency
Diffraction angle

The restriction on length of medium is severe
at higher frequency ? Diffraction efficiency
reduction
First order diffraction maximum
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Bragg diffraction
In this regime, we can no longer consider the
refractive index perturbation to act as a
thin phase grating. We should consider the
propagation equation of light
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Let,
And, slow varying approximation
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(No Transcript)
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(1) Small Bragg angle diffraction
Bragg condition
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These equations have a solution for when
only , The solutions for aa, a-a are
independent each other, so let aa
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Diffraction efficiency, h
0-th and 1-st diffraction powers
i)
ii) Maximum transfer
Diffration efficiency
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Acoustic intensity
(Text p. 483)
Figure of Merit
Diffraction efficiency
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Acoustic intensity for maximum efficiency
Diffraction figure of merit of the material
relative to water
Acoustic power for maximum efficiency (LH
cross-section, maximum impedance matching case)
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(2) Large Bragg angle diffraction
x-dependent term ?
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These equations have a solution for when
only , The two solutions are
independent each other, so let 1) bbK
(Co-directional coupling)
Solutions
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Diffraction efficiency, h
0-th and 1-st diffraction powers
Diffraction efficiency
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2) b-b-K (Counter-directional coupling)
Solutions
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Application DBR reflector
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Surface Acousto-Optics
Diffraction effect through a thin film surface
or wave guide High intensity localized on the
interface ? enhancing the diffraction efficiency
1967, Ippen et al. (first experimental
demonstration in a quartz)
Surface undulation profile by the acoustic wave
Wave vectors of reflected and transmitted light
waves
Electric field on the surface
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1) Reflection wave
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Diffraction angle
the amplitude of reflected wave
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Diffraction efficiency of l-th order
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2) Transmitted wave
Similarly,
Diffraction efficiency of l-th order