Transcript 3-D wave structuring and applications

On Attributes and Limitations of
Linear Optics in Computing
A personal view
Joseph Shamir
Department of Electrical Engineering
Technion, Israel
OSC2009
Outline
1. Motivation
2. Attributes of Optics, a sales man promotion
3. About 3D processing and storage
4. Temporal limitations
5. Conservative and Directed Logic
6. Conclusions
Motivation
•A “salesman” promotion of optical computing:
Attributes of optics:
•High density of information handling, including 3D
capabilities (holography).
•Computing with the speed of light.
•Large (temporal) bandwidth due to high frequency.
•High spatial parallelism and spatial bandwidth.
Why are these statements misleading?
Recording and processing of 3D information
We consider here the recording and processing of
information with 3D capabilities employing optical
architectures in free space and containing bulk
optical components.
The main attribute of light is that it solves the
Maxwell equations in 3D space, at the speed of light.
HOWEVER , the solution is uniquely determined by
a set of boundary conditions distributed over 2D
surfaces. This means that all the information that can
be handled must be distributed over these surfaces.
Is real 3-D Imaging possible?
Hologram
Can view
from here
Can’t view
from here
Can’t view
from here
Propagation by plane wave
spectrum representation
u(x,y,0)
u(x,y,z)
z
0
In the spectral domain:
F u ( x, y, z )  O F u ( x, y,0)
where:
O  exp jkz 1  2  2   2

Back to pace domain:


x
y

u ( x, y, z )  F 1O F u ( x, y,0)
Spatial frequency spectrum
1  2 ( x2   y2 )  2 z2
Define:
For a propagating field:
  0
2
2
z

 (     )   |  |2  1
2
2
x
2
y
2
z
2
Information content of a wavefront ~ L2
Information content of a 3D object ~ L3
3D information storage by space sampling
by importance
Dz
incident wave
input plane
z
Where does technology stand?
• What can we expect in the future?
Technology Competition for Storage
4G
32 G
• Where do we go from here?
Computing with the speed of light?
•
The high velocity of light is efficiently
exploited in long distance optical
communication.
• This does not imply anything related to
computing.
• What are the implications of the finite
velocity of light for massive computational
tasks implemented on bulk architectures?
Time skew in free space.
Out
In
D
θ
R
L
Tpipe  L / c ;
Tskew  ( R  L) c  L L2  D 2  L 
L
c


4 tan 2   1  1
Implications of the time delays
Tpipe  L / c ;
Tskew  ( R  L) c 
L
c


4 tan 2   1  1
For L = 1 cm, Tpipe ~ 30 ps
For D = 1 cm, Tskew ~ 13 ps
For L = 2 cm, Tpipe ~ 60 ps
For D = 1 cm, Tskew ~ 7 ps
The addition of optical components can modify the skew effects
Fourier transform optical system
Tpipe  2 f c ; Tskew  D sin  c  2 f sin  tan  c
Operating the system by short pulses will lead to pulse
broadening by an amount equivalent to the time skew.
Double Fourier transform - Imaging
Filter
Imaging is exact with the skew compensated by the two
successive FT operations.
Inserting a “filter” generates new scattering centers that
may double the skew of a single FT.
Single lens imaging
At a given point, by Fermat’s principle, there is no skew
(pulse broadening) but there is differential delay among
points determined by the quadratic phase factor.
All basic optical systems possess
pipeline delay and most of them have
also a time skew effect. The ultimate
performance of any processing
architecture must be assessed in taking
into account these time effects
Vector-matrix multiplier
Actual implementation involves two 1D FT operations
leading to double the skew of a FT operation leading
to significant reduction in processing speed.
Matrix-matrix multiplier
One possible implementation
The skew limitation here is the sum of two
free-space propagations
“Attributes of optics” revisited:
•High density of information handling, including 3D capabilities
(holography).
•Not necessarily. Hard competition with other storage media.
•Computing with the speed of light.
•Speed of light is finite, leading to pipeline delays and skew.
•Large (temporal) bandwidth due to high frequency.
•While for long-distance communication light has an
unquestionable advantage over any other means of communication,
this is not the case for conventional computing scenarios where
propagation and diffraction effects play an important role.
•High spatial parallelism and spatial bandwidth.
•Not compatible with high temporal bandwidth due to skew
Where we go from here?
To make optics viable in computing new
paradigms must be investigated. Most
available computing paradigms are based
on the characteristics of electrons and they
cannot be effectively translated into
optical procedures.
One promising paradigm is Directed
Logic, based on reversibility.
The Fredkin gate
C
A
C’
A’
C = C’
If C = 1, A’ = B,
B’ = A
B
B’
If C = 0, A’ = A,
B’ = B
The control input, C, determines the gate’s operation on the
signals, A and B. The gate is reversible in a sense that the
control is transmitted and, therefore, the inputs can be
reconstructed form the outputs.
In a reversible gate there is not dissipation of information. As a
consequence, ideally there is also no loss of energy making such
processes faster and more efficient.
Controlled waveguide coupler
implementation of a Fredkin gate and array
Directed Logic
Directed logic is based on an array of Fredkin gates where the
input signals are the control signals. These controls direct a
single input signal toward the output in such a way that any
logic function is implemented. Usually there are two outputs,
the logic function result and its complement.
In the following demonstrative examples each block represents
a Fredkin gate. Each input signal addresses one or several gate
controls and one optical channel is directed to the output
representing the result of the logic function.
Directed logic implementation
of a XOR gate
Input bits
OR/NOR Gate
(A OR B) AND C
Conclusions
•The main drive for optical computing was the correlator,
which exploits the high parallelism. At that time this was
competitive with electronics but progress of the latter
deprived the advantage of optics due to its limitations.
•Apart from optical communication optical storage became
probably the biggest hit but in this field too, optics looses
ground in favor of advanced magnetic and flash memory
devices.
•Will novel computing paradigms together with the
advent of plasmonics, metamaterials and quantum
computing change this trend?
Thank you