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Stimulated Brillouin Scattering - Quantum Electronics - Lecture Notes, Study notes of Quantum Physics

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

2012/2013

Uploaded on 08/21/2013

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Stimulated Brillouin Scattering
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.
k2
k1
21 kk
ks
Moving strain
grating
k2
k1
ks
ks
k1k2
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
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pf4

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Stimulated Brillouin Scattering

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 2

k 1

k 1 (^)  k 2

ks

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

E

x

u

 . When the field is varying,

the enegy density changes. The electrostrictive

pressure associated with the energy change is the work divided by the strain.

2 2

p   E (2)

Thus the force applied to a unit volume is the gradient of pressure or

x

E

F

2

The equation of motion for acoustic waves driven by a force is given by

2 2

2

2

2

E

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 =

T

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.

For  s  2   1 , Eq (13) can be simplified as

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