```Optical Information Processing
The Processing Power of Light
By
Jake Clive
Ph 464/564
Applied Optics
2/17/2005
What is Optical Information Processing?
It is the use of light to process information.
Why use light anyways?
1) Information travels at the speed of light. Limitations are only due to the slow
speed of the Spatial Light Modulators.
2) Parallel processing if arrays are used.
3) Immune to outside Electro-magnetic interference and crosstalk between
waveguides and fiberoptic cables.
4) No short circuiting problems.
Light by itself does not carry any information unless it is modulated by some
means.
Frequency, Polarization, Amplitude or the direct current of a semiconductor laser
itself can be modulated, so that it may represent some form of information.
Once modulated, light can then be used for performing arithmetic operations for
analog or digital information processing.
I. Fourier Transform Property of a Lens. (FOURIER OPTICS)
In a nutshell, the FT provides information on the frequency content of the
signal.
Coherent Laser Light illuminates the transparency at different path lengths.
Each path diffracts through the lens at a different OPL causing phase shifts
related to each path.
All these paths from each element of the transparency add up at the back
focal plane, thereby forming a diffraction pattern which is the Fourier
Transform (FT) of the input transparency. The back focal plane is hence
known as the Fourier Plane of the lens.
When the FT pattern goes through the second lens, it performs another FT
and that is the restored image. Hence, FT of the FT is called the Convolution
and the second lens is called the Convolver.
This is a completely reversible operation so if the FT of the signal is
completely known, the signal is also completely determined.
A sinusoidal pattern appears, this indicates that points along the axis
represent spatial frequency components in an image.
How is it parallel processing?
The input transparency is 2-Dimensional. Hence all illuminated elements of
the transparency form an image on the focal plane simultaneously.
Real Images are Analog in nature. By using Fourier Optics we
can perform arithmetic functions:
Multiplication- The output image is nothing but multiplication of
all individual paths that make up the image.
Addition- If a hologram is used as the input transparency, then
sum and product terms are present in the equation of a
hologram. These are the signal and reference signals used to
form a Hologram. Hence these addition and multiplication
functions can be performed.
Division- An inverted or reciprocal of the input image is used in
the second focal plane. This performs a division of the input
image.
Subtraction- When an image is formed due to constructive
(addition) and destructive (subtraction) interference produced
due to different path lengths and related phase shifts.
What does Fourier Optics accomplish?
We can perform Convolution, Cross-correlation, Autocorrelation
and Matched Filtering which are all properties of a Fourier
Transform.
Cross-correlation is a useful technique for determining the
similarity between two objects. In effect, what cross-correlation
does is compare an object point by point with an input pattern.
Fig. Fourier Transform and Correlation Property in Pattern Recognition
Light Deflectors used for processing of Vectors Matrix Multiplication.
Fig. An Optical Recognition System
The Main Element of Digital Optical Information Processing.
‘0’
The Transistor – It is basically an ON-OFF switch. Which gives a value of ‘1’ or
for ON or OFF.
Figure 7 NPN Transistor-Conducting
The language of computers - ‘0’ or ‘1’ are two binary digits used in digital
computers and digital arithmetic.
By using Boolean Logic Algebra, we can form any Logic gate for the purpose
of performing mathematical operations.
SPATIAL LIGHT MODULATORS and OPTICAL SWITCHES
Property used for the modulation of light.
Birefringence – It is the property of a solid crystal or liquid exhibiting two
indices of refraction in the presence of an electric or acoustic field.
Due to the change in the refraction index, the speed of light changes in
the solid or liquid. Hence the light beam either passes or does not pass
depending on index of refraction.
Birefringence is also called double
refraction because when the light
enters the crystal, it is refracted into
two different directions.
Many crystalline materials exhibit
birefringence naturally, without
application of any voltage. The
birefringence is present all the time.
Examples of such crystals are quartz
and calcite.
Birefringence can also be induced by the following means:
1) Electro-Optic (Electric current),
2) Acousto-Optic (Ultrasound),
Electro-Optic Modulator
There are also a number of crystals that are not birefringent naturally but
in which application of a voltage induces birefringence. This is called the
Electro-Optic effect in the crystal.
Fig 2. Schematic diagram of the operation of a modulator based on the electrooptic effect. In this configuration, the voltage is applied parallel to the direction of
light propagation.
One uses transparent electrodes or electrodes with central apertures. When the voltage is
applied parallel to the direction of light propagation This is called a longitudinal electro-optic
modulator.
In another form, metal electrodes are used on the sides of the crystal (which has a square
cross section) and the voltage is perpendicular to the light propagation. This is called a
transverse electro-optic modulator.
Fig 2. Transverse Electro-Optic Modulator.
Application in Optical Information Processing - Right circular
polarized can be used for ‘0’ and left circular polarized can be
used for ‘1’.
Or if it is a Liquid Crystal, then polarization will allow some light to
pass when current is on and stop the light from passing when the
current is off.
When the beams emerge from the crystal, the polarization of the combined single beam d
depends on the accumulated phase difference. If the phase difference is one-half
wavelength, the polarization is rotated by 90º from its original direction. This is done by
using the Polarizer.
This by itself does not change the intensity of the beam.
But, with the analyzer, the transmission of the entire system varies, according to
T = T0 sin2(p D nL/l ) --------------------------------------------- Equation 1
where
T is the transmission,
T0 the intrinsic transmission of the assembly, taking into account all the losses,
D n the birefringence (that is, the difference in refractive index for the two polarizations),
L the length of the crystal,
l the wavelength of the light.
The birefringence is an increasing function of the applied voltage, so that the transmission
of the device will be an oscillatory function of applied voltage. The maximum transmission
occurs when
D n = l /2L -------------------------------------------------------Equation 2
This occurs at a voltage called the half-wave voltage, denoted V1/2. The half-wave voltage
depends on the nature of the electro-optic material.
The half-wave voltage for a particular material increases with the wavelength. Thus, in the
infrared the required voltage is higher than in the visible. This factor can limit the application of
electro-optic modulators in the infrared.
Fig. 3
Transmission of an electro-optic device as a function of applied voltage. V1/2 denotes the
half-wave voltage.
Acousto-Optic Modulators
The Elasto-optic properties of the medium respond to the
acoustic wave so as to produce a periodic variation of the index
of refraction. A light beam incident on this disturbance is
partially deflected in much the same way that light is deflected
by a diffraction grating.
The operation is shown in Figure 6. The alternate compressions
and rarefactions associated with the sound wave form a grating
that diffracts the incident light beam. No light is deflected unless
the acoustic wave is present.
Fig. 6 Diagram showing the principles of operation of an acousto-optic light-beam modulator
or deflector.
The transmission T of an acousto-optic modulator is
T = T0 sin2(p (M2PL/2H)0.5/l cos Q )-------------------------- Equation 4
where
P ----------is the acoustic power supplied to the medium,
l ------------is the wavelength,
L------------ is the length of the medium (length of the region in which the light wave
interacts with the acoustic wave),
H------------------- is the width of the medium (width across which the sound wave travels),
T0 ------------------- inherent transmission is a function of reflective and absorptive losses in
the device.
The quantity M2 is a figure of merit or diffraction efficiency, a material parameter that
indicates the suitability of a particular material for this application. It is defined by
M2 = n6p2/r v3 --------------------------------------------------- Equation 5
Where
p is the photoelastic constant of the material,
r is its density, and v is the velocity of sound in the material.
The Bragg angle Q is defined as the angle the beam makes
with the reflecting waves. It is given by:
sin Q = l/2nL...................................................................... Equation
where n is the index of refraction of the material, l is the optical
wavelength and L is the acoustic wavelength.
Hence AO modulates the intensities as well as deflects the
beam.
The diffracted output signal has intensities dependent upon the
index of refraction and the frequency of light.
Its application in Optical Information Processing – Different
intensities e.g dark or light can be used to represent a ‘0’ or ‘1’.
Light deflection properties are used in array arithmetic e.g
Vector Matrix Multiplication as seen before.
Light Deflectors used for processing of Vectors Matrix Multiplication.
Advantages of Acousto-optic switches
Using an acoustic wave containing M frequencies, the incoming beam
can be routed simultaneously over M directions, and the Acousto-optic
switch can be used to route information carried by one or more optical
beams to one or more outputs.
Disadvantages of Acousto-optic switches
Limited switching time due to the time it takes for the acousto-optic signal
to propagate across the length of the device … remember the speed of
sound is much less than that of light!
(1)
A+B=B+A
Commutative law for addition
(2)
A + (B + C) = (A + B) + C
Associative law of addition
(3)
A+0=A
0 is the zero matrix
(4)
A + (-A) = 0
-A = (-aij)
(5)
A(BC) = (AB)C
Associative law for multiplication
(6)
ImA = A;
AIn = A
(if A is m × n) the identity matrix behaves as a unit
(7)
A(B + C) = AB + AC
(A + B)C = AC + BC
Distributive law
(8)
(a + b)C = aC + bC
a, b scalars
(9)
a(B + C) = aB + aC
(10)
a(BC) = (aB)C = B(aC)
Optical Digital Information
Processing
Elements
A B Q
OR Gate
A B Q
0 0 0
0 0 0
AND Gate
0 1 0
1 0 0
1 1 1
NOR Gate
0 1 1
1 0 1
1 1 1
NAND Gate
A B Q
A B Q
0 0 1
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 0
Fig : Circuit of a Full Adder
Fabry-Perot Etalon Optical Transistors using Nonlinear Crystals
We can implement a full adder using a single Etalon by controlling the
intensity of the input signals and using the transmission and reflection
signals of the Etalon. A nonlinear material such as Lithium niobate
(LiNbO3) is used in the Etalon cavity.
Much faster than a Silicon transistor with switching times 10 power –15
seconds.
The Etalon can be used as an ON-OFF switch.
Hence the laser intensity of the output pulses can be modified by this onoff switch and can represent a ‘0’ or ‘1’.
Hence, to implement a logic function you simply apply optical signals of
an appropriate intensity to the input of the device.
For an Optical Etalon Transistor
Define the input signals A and B to be equal or greater than
the switching threshold intensity (set to I the maximum output
intensity, I, corresponding to a logic ‘1’), then
For an OR Gate - if either A or B are high, the output will be
high (I).
For an AND Gate - if both A or B are high, the output will be
high (I).
Fig :
Resonant and nonresonant Fabry-Perot arrangements.
The condition for producing a maximum in transmission is given by
Nl =
for example, is the optical path length between A and B in
Figure 3. With the aid of some trigonometric relationships, the condition becomes:
Nl = 2nd cos q
l = The wavelength of the radiation in vacuum (or air).
d = The separation of the reflecting surfaces.
n = The index of refraction of the material between the reflecting surfaces.
q = The angle of incidence, as shown in Figure
N = An integer.
The spacing D l between maxima of transmission is:
Dl=
,
Flip Flops
The flip-flop I O (0,1) utilizes two logic gates in order to
implement a 1-bit storage device or memory.
Optical bistable devices can be used to produce singleelement storage devices or RAM or ROM (Memory).
One of the more interesting things that you can do with
Boolean gates is to create memory with them. If you arrange
the gates correctly, they will remember an input value. This
simple concept is the basis of RAM (random access memory)
in computers, and also makes it possible to create a wide
variety of other useful circuits.
Memory relies on a concept called feedback. That is, the
output of a gate is fed back into the input. The simplest
possible feedback circuit using two inverters is shown below:
If you follow the feedback path, you can see that if Q happens to
be 1, it will always be 1. If it happens to be 0, it will always be 0.
Since it's nice to be able to control the circuits we create, this one
doesn't have much use -- but it does let you see how feedback
works.
It turns out that in "real" circuits, you can actually use this sort of
simple inverter feedback approach.
A more useful feedback circuit using two NAND gates is shown
below:
A bistable optical device is simply a device that has two states
in output power for all input power levels: a ‘1’ state for high
input power levels and a ‘0’ state for small input power levels.
Bistable optical devices require nonlinear optical elements with
feedback applied.
IV. Nonlinear Optics in Optical Information Processing
Nonlinear materials belong to a group of noncentrosymmetric crystals. This means that the internal
motion of electrons in an oscillating electric field is not
symmetric.
The material should furthermore exhibit a large index of
refraction since there is, as a rule, a strong dependence of
nonlinear optical properties on the refractive index.
Imaging through distortion: If the image information has been distorted
by the transmitting medium (glass, air, water) on the way to the PCM,
then these aberrations will be corrected when the reflected signal
retraces its original path through the medium.
From three beams, a fourth beam is formed. Hence a three
input AND logic gate can be formed using Four Wave mixing.
Due to self focusing nature of phase conjugation
property of NLO, a very stable Fabry-Perot Etalon
resonator can be formed, since there are no diffraction
losses in the cavity.
Its oscillations can remain self sustained without using
an external probe beam.
These oscillations are called Parametric Oscillations.
The resonator is not dependent upon the size L of the
cavity or the radius of curvature R of the mirror.
Optical Bistable Systems
• Definition of a Bistable System
– A bistable system has an output that can take
only one of 2 distinct values (called states), no
matter what input is applied.
•As the input is increased beyond the
threshold value n1 it switches to a high
level.
Output
•If the input level is then decreased below
the threshold value n2, it switches to a low
level.
n1
n2
Input
•Between n1 and n2 two states are
possible; the state assumed depends on the
history of the input.
•Bistable devices are used
as switches, logic gates
and memory elements.
•An electronic bistable
flip-flop circuit is made by
connecting the output of
each of 2 transistors to the
input of the other.
Principle of Optical Bistability
• Two requirements needed for bistability:
– non linearity
– feed-back
• Both of these are possible in in optics.
Ii
T(Io)
Io
• The transmittance, T, is defined as: T 
Io
Ii
• Suppose that the output intensity dependent
transmittance, T(Io) is given by the non-monotonic
function below.
Ii 
Io
T (Io )
Bistable System
Switching axes
• P lies between points 1 and 2.
• In this region, a small increase
in Io leads to a sharp increase in
T(Io).
• This in turn leads to a further
increase in Io and so the process
repeats until state 2 is reached.
• This means that the
intermediate path is bypassed
and the system jumps directly
to the upper state.
• The opposite is true when Io is
decreased.
Bistable Optical Devices
•
Bistable systems are possible when setups such as the
Fabry Perot etalon or ring cavity are used in
combination with a non-linear medium.
• The Fabry Perot etalon and ring cavity supply the
feed back mechanism.
• Two types of non-linear optical elements can be used:
– Dispersive elements: the refractive index, n, is a
function of the optical intensity.
– Absorptive non-linear elements: the absorption
coefficient, a, is a function of the optical intensity.
Dispersive Element
•
A 3rd order non-linear medium with P   E
an optical intensity dependent refractive index:
(3)
3
n  n1  n 2 I
eqn 6 (Kerr effect)
T
T
EI, II
e(0)
non-linear
ET, IT
l
100 %
100 %
Absorptive Element
• A saturable absorber has an absorption coefficient
which is a non-linear function of I:
a 
ao
1 I / Is
eqn 9
where I s is the saturation intensity
• The cavity is setup for resonance.
• At small intensities, the absorption due to the
element is high and the output is low.
• As the intensity is increase beyond Is, the
absorption rapidly decreases and the output goes
to high.
Ring Cavity Transmission
Function
Let e n  1 ( 0 ) 
T E I  Re
al
e
jKL
e n (0)
where e n  1 is the electric field after the n  1 th path around the cavity,
L is the round trip length, a is the complex absorption
coefficien t
and R  1 - T the mirror ref lectance.
T
EI, II
e(0)
T
non-linear
ET, IT
l
100 %
100 %
 At steady state the electric field inside the cavity
must be constant so that e n  1 ( 0 )  e n ( 0 )  e 0
 e0 
T E 1  Re
a l
e
iKL
e0
reara nging this gives : e 0 

T EI
(1  Re
 a l  iKL
)
The output field is given by the mirror transmitta nce
times the internal electric field at a distance l .
ET 

eqn 1
T e (l ) 
combining
T e oe
(  a  iK ) l
this with eqn 1 gives the
amplitude transmissi on function :
ET
EI

Te
e
iK ( l  L )
a l  iKL
R
eqn 2
Absorptive Bistability
• A saturable absorber, at resonance has an absorption
coefficient which is a non-linear function of I:
a 
ao
1 I / Is
eqn 5
where I s is the saturation intensity
• Earlier the transmission function for the ring cavity was
iK ( l  L )
derived as:
ET
Te
EI

e
a l  iKL
R
eqn 2
• Ignoring the phase term in the numerator and assuming
that al<<1 so that e-al~1-al, gives: E T
1

EI
1  al / T
substituti ng in eqn 5 and using I 
IT
T

a ol / T 
E I  E T 1 

1

I
/
I
T
T
s


• This equation is only bistable for for aol/T8
Non-Linear Optic materials
Lithium niobate (LiNbO3)
It’s transparent from 400 nm to 5 mm, and its nonlinear coefficient is about ten-times
larger than that of KDP.
This means that lithium niobate is two orders of magnitude more efficient than KDP,
and SHG efficiencies close to 100 percent are possible. It’s one of the few nonlinear
materials available in large sizes in commercial quantities.
Since it has a very large birefringence in the visible and near-infrared region, it
allows phase-matching of the fundamental and harmonic waves. Phase-matching
usually is accomplished by heating the crystal to the phase-matching temperature for
the particular laser being used.
Disadvantage of Lithium Niobate:
One problem with lithium niobate is that it has a very low damage threshold. In some
samples, this damage disappears by itself soon after the laser beam is turned off. But
in other samples the characteristic "tracks" can remain for days. Fortunately, the
damage can be reversed by heating the crystal to about 200°C. This is one reason
for using temperature-controlled phase-matching.
Barium sodium niobate (BaNaNb5O15)
This nonlinear material is similar to lithium niobate. But it doesn’t suffer as
much from optical damage when its temperature is maintained above
room temperature. Barium sodium niobate has a nonlinear coefficient
that’s about three times larger than lithium niobate.
BaNaNb5O15 is optically transparent from 370 nm to about 5 mm. Some
samples don’t have a good optical quality due to a marked brown
discoloration. Phase-matching for the second harmonic generation of 1.06
mm radiation from an Nd:YAG laser occurs around 100°C. The exact
temperature depends on the stoichiometric composition.
Applications
This material has been used for very efficient generation of the second
harmonic of 1.06 nm radiation and in the building of parametric oscillators.
END OF PRESENTATION
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