On Attributes and Limitations of Linear Optics in

On Attributes and Limitations of Linear Optics in Computing A personal view Joseph Shamir Department of Electrical Engineering Technion, Israel OSC 2009

Outline 1. Motivation 2. Attributes of Optics, a sales man promotion 3. About 3 D 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 3 D 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 3 D information We consider here the recording and processing of information with 3 D 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 3 D space, at the speed of light. HOWEVER , the solution is uniquely determined by a set of boundary conditions distributed over 2 D 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

Propagation by plane wave spectrum representation u(x, y, 0) 0 In the spectral domain: where: Back to pace domain: u(x, y, z) z

Spatial frequency spectrum Define: For a propagating field: Information content of a wavefront ~ L 2 Information content of a 3 D object ~ L 3

3 D 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 4 G 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.

Implications of the time delays 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 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 1 D 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 3 D 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