CHAPTER 6-2---ACOUSTIC-OPTICS
Chapter 6
ACOUSTO-OPTICS
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CHAPTER 6-2---ACOUSTIC-OPTICS
Acousto-optic effect
• The refractive index of an optical medium is altered
by the presence of sound
• An acoustic wave creates a perturbation of the
refractive index in the form of a wave
Sound
Medium
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CHAPTER 6-2---ACOUSTIC-OPTICS
x
x
Rarefaction
Compression
L
L
Refractive index
Variation of the refractive index accompanying a harmonic sound
wave. The pattern has a period L, the wavelength of sound, and
travels with the velocity of sound
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CHAPTER 6-2---ACOUSTIC-OPTICS
Bragg Diffraction
Bragg
diffraction
Bragg reflection
Bragg scattering
Diffracted
light
Incident
light


L
Sound
Transmitted
light
Bragg reflector
Bragg deflector
Bragg cell
Only reflect light with incidence angle :
sin  
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Bragg condition
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CHAPTER 6-2---ACOUSTIC-OPTICS
1 Interaction of light and sound
• Bragg Diffraction
The strain in a medium
s( x, t )  S0 cos(t  qx)
S0: the amplitude
= 2f
q = 2/L wavenumber
The acoustic intensity (W/m2):
Is 
1 3 2
 vs S0
2
: the mass density
Vs: acoustic plane wave velocity
refractive index perturbation:
p: photoelastic constant n( x, t )  
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pn s( x, t )
2
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CHAPTER 6-2---ACOUSTIC-OPTICS
n( x, t )  n  n0 cos(t  qx)
1 3
n0  pn S0
2
refractive index to acoustic intensity
1
n0  ( MI s )1/ 2
2
p 2 n6
M
 vs3
merit for the strength of the acousto-optic effect
For light
n( x, t )  n  n0 cos(qx   )
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CHAPTER 6-2---ACOUSTIC-OPTICS
x

L/2

0
L
-L/2
Lsin
r
L/2
L/ 2
From Fresnel equations:
e
Lsin
j 2 kx sin 
dr
dx
dx
1
r 
n
2
2n sin 
 cos 2
r 
n
2
2n sin 
(TE)
(TM)
In most acousto-optic devices  is very small cos 2  1
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CHAPTER 6-2---ACOUSTIC-OPTICS
dr dr dn
1


[qn0 sin(qx   )]  r 'sin(qx   )
2
dx dn dx 2n sin 
r'
q
n0
2
2n sin 
L/2
L/2
1
1
j
j (2 k sin   q ) x
 j
r  jr ' e  e
dx  jr ' e  e j (2 k sin  q ) x dx
L/ 2
L/ 2
2
2
Max: 2k sin = q
Max: 2k sin =- q
upshifted
downshifted
Amplitude reflectance upshifted
1
L jt
r  jr ' L sin c[(q  2k sin  ) ]e
2
2
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CHAPTER 6-2---ACOUSTIC-OPTICS
Upshifted Bragg Diffraction
1
L jt
r  jr ' L sin c[(q  2k sin  ) ]e
2
2
q = 2 k sin
r max
B = sin -1(q/2k): Bragg angle.
sin  B 

2L
kr  k  q
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Kr


q
K
2
L
2
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CHAPTER 6-2---ACOUSTIC-OPTICS
Tolerance in the Bragg Condition
 -  B = /2L
Doppler Shift r    
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CHAPTER 6-2---ACOUSTIC-OPTICS
Reflectance in the Bragg Condition
2
2
R  r  r ' L2 / 4
2 L 2 2
R 2(
) n0
0 sin 
2
L 2
R 2(
) MI s
20 sin 
R  2 2 n 2
L2 L2

4
0
MI s
R is proportional to the intensity of the acoustic wave Is
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CHAPTER 6-2---ACOUSTIC-OPTICS
For large Is:
Re  sin
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R
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CHAPTER 6-2---ACOUSTIC-OPTICS
Downshifted Bragg Diffraction
1
r   jr ' Le  jt
2
K
s    


-q
KS
2
L
2
ks  k  q

Quantum Interpretation
Photons hk
Phonons hq
Fundamentals of Photonics
ћk r  ћk  ћq
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CHAPTER 6-2---ACOUSTIC-OPTICS
Raman-Nath Diffraction
Diffraction of an Optical Plane Wave from a Thin Acoustic Beam
sin
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2



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L
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CHAPTER 6-2---ACOUSTIC-OPTICS
Ds

q
Kr

Incident light


K
q
The higher-order diffracted waves generated at angles  2,  3,…
Kr=kiq
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CHAPTER 6-2---ACOUSTIC-OPTICS
2 ACOUSTO-OPTIC DEVICES
• Modulators
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CHAPTER 6-2---ACOUSTIC-OPTICS
Modulation Bandwidth
the maximum frequency at which the madulator can efficiently modulate
The waveform of an amplitude-modulated acoustic signal and its spectrum.
bandwidth B
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CHAPTER 6-2---ACOUSTIC-OPTICS
For plane waves:
  sin 1

2L
 sin 1
f


f
2vs 2vs
Only one frequency component of sound matching Bragg condition
B=0
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CHAPTER 6-2---ACOUSTIC-OPTICS
The incident light: width D , angular divergence  = /D
(2 / s ) B 
 
 B
2 / 
s
B  vs
or
 vs

 D
1
D
B  ,T 
T
vs
T is the transit time of sound across the waist of the light beam.
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CHAPTER 6-2---ACOUSTIC-OPTICS
Scanners
2 

vs
f
changing the sound frequency f
Scan Angle
 

vs
B
Incident angle change by using phased array of acoustic transducers
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CHAPTER 6-2---ACOUSTIC-OPTICS
Number of Resolvable Spots
( / vs ) B D
N

 B

/D
vs

or : N  TB
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CHAPTER 6-2---ACOUSTIC-OPTICS
The Acousto-Optic Scanner as a Spectrum Analyzer
The acousto-optic cell serves as an acoustic spectrum analyzer
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CHAPTER 6-2---ACOUSTIC-OPTICS
Interconnections
routes one beam to any
of N directions.
one beam is connected to any
pair of many possible directions
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CHAPTER 6-2---ACOUSTIC-OPTICS
Routing each of two light
beams to a set of specified
directions. The acoustic
wave is generated by a
frequency-shift-keyed
electric signal.
The spatial light
modulator modulates N
optical beams. The
acoustic wave is driven
by an amplitudemodulated electric
signal.
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CHAPTER 6-2---ACOUSTIC-OPTICS
An arbitrary-interconnection switch routes each of L incoming light
beams for the random access of M points.
Interconnection Capacity
ML  N
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CHAPTER 6-2---ACOUSTIC-OPTICS
Frequency Shifters
Optical isolators
frequency-upshifted Bragg-diffracted light can be blocked by a filter
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