Convergence properties of a neural optical resonator model for logic operations

Darren M. Simon; Steven C. Gustafson; Gordon R. Little

doi:10.1117/12.18092

1 July 1990 Convergence properties of a neural optical resonator model for logic operations

Darren M. Simon, Steven C. Gustafson, Gordon R. Little

Proceedings Volume 1215, Digital Optical Computing II; (1990) https://doi.org/10.1117/12.18092
Event: OE/LASE '90, 1990, Los Angeles, CA, United States

Abstract

The convergence of a neural network model based on optical resonator designs is examined for Boolean logic operations. Computer simulations are performed to investigate convergence performance and to assess possible optical implementations. The model is a simple and general mathematical formulation obtained using standard methods in which plane wave amplitudes and phases are specified at discrete times separated by the resonator period. The model is trained and tested as an associative memory neural network using an input state vector and a hologram matrix that evolves in time according to a set of coupled nonlinear difference equations. In general, these equations represent a high-order threshold logic, and the hologram matrix is a function of the outer product matrix of the evolving complex-element state vector. Model parameters are explored to provide insight on convergence mechanisms, robustness to input perturbations, and optimization of convergence times for both training and testing. The model is of interest for optical resonator designs that incorporate (1) dynamic holograms for massively parallel interconnection and storage functions and (2) nonlinear components such as phase conjugate mirrors (with thresholding and gain) for decision operations.2 These components are often incorporated into resonator loops to provide feedback and adaptation interactions. The neural

Citation Download Citation

Darren M. Simon, Steven C. Gustafson, and Gordon R. Little "Convergence properties of a neural optical resonator model for logic operations", Proc. SPIE 1215, Digital Optical Computing II, (1 July 1990); https://doi.org/10.1117/12.18092

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available

Members: $17.00

Non-members: $21.00 ADD TO CART

PROCEEDINGS
11 PAGES

DOWNLOAD PAPER SAVE TO MY LIBRARY

GET CITATION

RIGHTS & PERMISSIONS

Get copyright permission Get copyright permission on Copyright Marketplace

KEYWORDS

Logic

Holograms

Statistical modeling

Logic devices

Optical design

Optical resonators

Mathematical modeling

Show All Keywords

Keywords/Phrases

Search In:

Publication Years