OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 1 — Jan. 13, 2014
  • pp: 295–304

Computing matrix inversion with optical networks

Kan Wu, Cesare Soci, Perry Ping Shum, and Nikolay I. Zheludev  »View Author Affiliations


Optics Express, Vol. 22, Issue 1, pp. 295-304 (2014)
http://dx.doi.org/10.1364/OE.22.000295


View Full Text Article

Enhanced HTML    Acrobat PDF (892 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

With this paper we bring about a discussion on the computing potential of complex optical networks and provide experimental demonstration that an optical fiber network can be used as an analog processor to calculate matrix inversion. A 3x3 matrix is inverted as a proof-of-concept demonstration using a fiber network containing three nodes and operating at telecomm wavelength. For an NxN matrix, the overall solving time (including setting time of the matrix elements and calculation time of inversion) scales as O(N2), whereas matrix inversion by most advanced computer algorithms requires ~O(N2.37) computational time. For well-conditioned matrices, the error of the inversion performed optically is found to be around 3%, limited by the accuracy of measurement equipment.

© 2014 Optical Society of America

OCIS Codes
(060.2310) Fiber optics and optical communications : Fiber optics
(200.0200) Optics in computing : Optics in computing
(200.4960) Optics in computing : Parallel processing

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: October 3, 2013
Revised Manuscript: November 15, 2013
Manuscript Accepted: November 20, 2013
Published: January 2, 2014

Citation
Kan Wu, Cesare Soci, Perry Ping Shum, and Nikolay I. Zheludev, "Computing matrix inversion with optical networks," Opt. Express 22, 295-304 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-1-295


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. H. J. Caulfield, S. Dolev, “Why future supercomputing requires optics,” Nat. Photonics 4(5), 261–263 (2010). [CrossRef]
  2. S. Dolev, H. Fitoussi, “Masking traveling beams: Optical solutions for Np-complete problems, trading space for time,” Theor. Comput. Sci. 411(6), 837–853 (2010). [CrossRef]
  3. M. Oltean and O. Muntean, “Solving Np-complete problems with delayed signals: An overview of current research directions,” in Optical Supercomputing, S. Dolev, T. Haist, and M. Oltean, eds. (Springer, 2008), pp. 115–127.
  4. K. Wu, J. García de Abajo, C. Soci, P. P. Shum, N. I. Zheludev, “Fiber non-Turing all-optical computer for solving complex decision problems,” in Conference on Lasers and Electro-Optics / Europe (CLEO/Europe), (Munich, Germany, 2013), pp. CI-5.2.
  5. J. L. O’Brien, “Optical quantum computing,” Science 318(5856), 1567–1570 (2007). [CrossRef] [PubMed]
  6. M. A. Broome, A. Fedrizzi, S. Rahimi-Keshari, J. Dove, S. Aaronson, T. C. Ralph, A. G. White, “Photonic Boson sampling in a tunable circuit,” Science 339(6121), 794–798 (2013). [CrossRef] [PubMed]
  7. J. B. Spring, B. J. Metcalf, P. C. Humphreys, W. S. Kolthammer, X.-M. Jin, M. Barbieri, A. Datta, N. Thomas-Peter, N. K. Langford, D. Kundys, J. C. Gates, B. J. Smith, P. G. R. Smith, I. A. Walmsley, “Boson sampling on a photonic chip,” Science 339(6121), 798–801 (2013). [CrossRef] [PubMed]
  8. D. Woods, T. J. Naughton, “Optical computing: photonic neural networks,” Nat. Phys. 8(4), 257–259 (2012). [CrossRef]
  9. L. Appeltant, M. C. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, I. Fischer, “Information processing using a single dynamical node as complex system,” Nat Commun. 2, 468 (2011). [CrossRef] [PubMed]
  10. Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, S. Massar, “Optoelectronic reservoir computing,” Sci. Rep. 2, 287 (2012).
  11. D. Petrov, Y. Shkuratov, G. Videen, “Optimized matrix inversion technique for the T-matrix method,” Opt. Lett. 32(9), 1168–1170 (2007). [CrossRef] [PubMed]
  12. O. Arteaga, A. Canillas, “Analytic inversion of the Mueller-Jones polarization matrices for homogeneous media,” Opt. Lett. 35(4), 559–561 (2010). [CrossRef] [PubMed]
  13. V. V. Williams, “Multiplying matrices faster than Coppersmith-Winograd,” in 44th Symposium on Theory of Computing (ACM, 2012), 887–898.
  14. A. J. Stothers, On the Complexity of Matrix Multiplication (University of Edinburgh, 2010).
  15. H. Rajbenbach, Y. Fainman, S. H. Lee, “Optical implementation of an iterative algorithm formatrix inversion,” Appl. Opt. 26(6), 1024–1031 (1987). [CrossRef] [PubMed]
  16. D. Casasent, J. S. Smokelin, “New algorithm for analog optical matrix inversion,” Appl. Opt. 30(23), 3281–3287 (1991). [CrossRef] [PubMed]
  17. Q. Cao, J. W. Goodman, “Coherent optical techniques for diagonalization and inversion of circulant matrices and circulant approximations to Toeplitz matrices,” Appl. Opt. 23(6), 803–811 (1984). [CrossRef] [PubMed]
  18. E. Barnard, D. Casasent, “Optical neural net for matrix inversion,” Appl. Opt. 28(13), 2499–2504 (1989). [CrossRef] [PubMed]
  19. R. Paschotta, “Noise of mode-locked lasers (part I): Numerical model,” Appl. Phys. B 79(2), 153–162 (2004). [CrossRef]
  20. Z. L. Sámson, P. Horak, K. F. MacDonald, N. I. Zheludev, “Femtosecond surface plasmon pulse propagation,” Opt. Lett. 36(2), 250–252 (2011). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Figures

Fig. 1 Fig. 2 Fig. 3
 
Fig. 4 Fig. 5
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited