OSA's Digital Library

Applied Optics

Applied Optics


  • Editor: James C. Wyant
  • Vol. 45, Iss. 20 — Jul. 10, 2006
  • pp: 4864–4872

Implementation of discrete unitary transformations by multimode waveguide holograms

Shuo-Yen Tseng, Younggu Kim, Christopher J. K. Richardson, and Julius Goldhar  »View Author Affiliations

Applied Optics, Vol. 45, Issue 20, pp. 4864-4872 (2006)

View Full Text Article

Enhanced HTML    Acrobat PDF (1822 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Integration of holograms into multimode waveguides allows the implementation of arbitrary unitary mode transformations and unitary matrix–vector multiplication. Theoretical analysis is used to justify a design approach to implement specific functions in these devices. Based on this approach, a compact mode-order converter, a Hadamard transformer, and a spatial pattern generator–correlator are proposed and analyzed. Beam propagation simulations are used to verify the theoretical calculations and to address bandwidth, scalability, and fabrication criteria. Optical pattern generators were successfully fabricated using standard photolithographic techniques to demonstrate the feasibility of the devices.

© 2006 Optical Society of America

OCIS Codes
(070.4550) Fourier optics and signal processing : Correlators
(070.6020) Fourier optics and signal processing : Continuous optical signal processing
(090.1760) Holography : Computer holography
(090.7330) Holography : Volume gratings
(130.3120) Integrated optics : Integrated optics devices
(200.4860) Optics in computing : Optical vector-matrix systems

Original Manuscript: July 12, 2005
Manuscript Accepted: January 6, 2006

Shuo-Yen Tseng, Younggu Kim, Christopher J. K. Richardson, and Julius Goldhar, "Implementation of discrete unitary transformations by multimode waveguide holograms," Appl. Opt. 45, 4864-4872 (2006)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).
  2. B. G. Boone, Signal Processing Using Optics (Oxford, 1998).
  3. T. Jannson, "Information capacity of Bragg holograms in planar optics," J. Opt. Soc. Am. 71, 342-347 (1981). [CrossRef]
  4. M. E. Marhic, "Discrete Fourier transforms by single-mode star networks," Opt. Lett. 12, 63-65 (1987). [CrossRef] [PubMed]
  5. A. E. Siegman, "Fiber Fourier optics," Opt. Lett. 26, 1215-1217 (2001). [CrossRef]
  6. A. R. Gupta, K. Tsutsumi, and J. Nakayama, "Synthesis of Hadamard transformers by use of multimode interference optical waveguides," Appl. Opt. 15, 2730-2738 (2003). [CrossRef]
  7. M. Reck and A. Zeilinger, "Experimental realization of any discrete unitary operator," Phys. Rev. Lett. 73, 58-61 (1994). [CrossRef] [PubMed]
  8. D. J. Brady and D. Psaltis, "Holographic interconnections in photorefractive waveguides," Appl. Opt. 30, 2324-2333 (1991). [CrossRef] [PubMed]
  9. A. Yariv, "Coupled-mode theory for guided-wave optics," IEEE J. Quantum Electron. 9, 919-933 (1973). [CrossRef]
  10. L. B. Soldano and E. C. M. Pennings, "Optical multimode interference devices based on self-imaging: principles and applications," J. Lightwave Technol. 13, 615-627 (1995). [CrossRef]
  11. S.-Y. Tseng, Y. Kim, C. Richardson, and J. Goldhar, "Optical processor using waveguide holograms in multimode interference (MMI) couplers," in Conference on Lasers and Electrooptics on CD-ROM (Optical Society of America, 2005), paper JTuC70.
  12. J. M. Heaton and R. M. Jenkins, "General matrix theory of self-imaging in multimode interference (MMI) couplers," IEEE Photon. Technol. Lett. 11, 212-214 (1999). [CrossRef]
  13. G. R. Hadley, "Wide-angle beam propagation using Pade approximant operators," Opt. Lett 17, 1426-1428 (1992). [CrossRef] [PubMed]
  14. B.-T. Lee and S.-Y. Shin, "Mode-order converter in a multimode waveguide," Opt. Lett. 28, 1660-1662 (2003). [CrossRef] [PubMed]
  15. O. Moriwaki, T. Kitoh, T. Sakamoto, and A. Okada, "Novel PLC-based optical correlator for multiple phase-modulated labels," IEEE Photon. Technol. Lett. 17, 489-491 (2005). [CrossRef]
  16. A. Yariv, Optical Electronics in Modern Communications (Oxford, 1997).
  17. T. Erdogan, "Cladding-mode resonances in short- and long-period fiber grating filters," J. Opt. Soc. Am. A 14, 1760-1773 (1997). [CrossRef]
  18. P. A. Besse, M. Bachmann, H. Nelchior, L. B. Soldano, and M. K. Smit, "Optical bandwidth and fabrication tolerances of multimode interference couplers," J. Lightwave Technol. 12, 1004-1009 (1994). [CrossRef]

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.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited