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Waves and beam optics, Waves in dielectric media, Waveguides and coupled waveguides, Fourier optics and holography, Optical resonators, Laser amplifiers and lasers, Semiconductor lasers and Nonlinear optics are major topic for Quantum Electronics course. This lecture is includes: Stimulated Brillouin Scattering, Acoustic Waves, Electromagnetic Waves, Electromagnetic Wave Equation, Nonlinear Polarization
Typology: Study notes
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Interaction of light wave with acoustic waves
A light wave interacting with an acoustic wave through the refractive index (dielectric
constant) moving grating set up by the acoustics.
k 1 (^) k 2
Moving strain grating
k 2
k 1
k s
ks
k 1 k 2
The acoustic waves set up a displacement u in the media. The strain is the time derivative of
the displacement with position.
The Electromagnetic wave equation
i i PNL i t
E rt t
E ( r , t ) ( ,) 2 ( )
2
2
2 2
For Brillouin scattering, the nonlinear polarization source is cause by the changes in dielectric
constant by the traveling acoustic waves. The acoustic waves are in turn driven by the beat
waves of the electric field of light.
Acoutic waves driven by electromagnetic waves
The change in the dielectric constant caused by
the strain x
u
is
x
u
where is a constant quantifying the changes in
dielectric constant..
The changes in electrostatic energy density is
given by 2 2
x
u
the enegy density changes. The electrostrictive
pressure associated with the energy change is the work divided by the strain.
2 2
Thus the force applied to a unit volume is the gradient of pressure or
x
2
The equation of motion for acoustic waves driven by a force is given by
2 2
2
2
2
x x
u T t
u
t
u
Where T and are the elastic constant and mass density.
The speed of acoustic waves is vs =
How to understand equation (4)
Two electric fields and acoustic field are in the form of plane waves:
U(x 1 )
x
x
u Strain
U(x 2 )
i
NL i r
urt P E Ert
From (11) and using slow-varying envelope for the electric field along the propagation
direction of a plane wave
NL i
j t k r P t
e cc j dr
dE r k 2
2 ( )
1
1 1 1
1 1 ( )
(^)
Combining (12) and (13) and by choosing terms that satisfies conservation of momentum and
energy:
i
j t k r s s
j t kr j t k r s s u e r
E e t
e j dr
dE r k
(^)
(^) ( ) * ( 2 2
2 ( )
1
1 1 1
1 1 2 2
4
( ) (13)
This equation govens the generation of E 1 by the interation of E 2 with acoustic wave u.
2
2 1
1
1 1 s
s s dr
du E jku
j
dr
dE k
(14)
For acoustic wave whose amplitude do not change quickly, the derivative with respect to rs
can be neglected,
2 1
2 1
1
1 4
E ku dr k
dE s
