OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 51, Iss. 12 — Apr. 20, 2012
  • pp: 2212–2222

Application of the fractional Fourier transform to the design of LCOS based optical interconnects and fiber switches

Brian Robertson, Zichen Zhang, Haining Yang, Maura M. Redmond, Neil Collings, Jinsong Liu, Ruisheng Lin, Anna M. Jeziorska-Chapman, John R. Moore, William A. Crossland, and D. P. Chu  »View Author Affiliations

Applied Optics, Vol. 51, Issue 12, pp. 2212-2222 (2012)

View Full Text Article

Enhanced HTML    Acrobat PDF (1429 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



It is shown that reflective liquid crystal on silicon (LCOS) spatial light modulator (SLM) based interconnects or fiber switches that use defocus to reduce crosstalk can be evaluated and optimized using a fractional Fourier transform if certain optical symmetry conditions are met. Theoretically the maximum allowable linear hologram phase error compared to a Fourier switch is increased by a factor of six before the target crosstalk for telecom applications of 40dB is exceeded. A Gerchberg–Saxton algorithm incorporating a fractional Fourier transform modified for use with a reflective LCOS SLM is used to optimize multi-casting holograms in a prototype telecom switch. Experiments are in close agreement to predicted performance.

© 2012 Optical Society of America

OCIS Codes
(090.0090) Holography : Holography
(070.2575) Fourier optics and signal processing : Fractional Fourier transforms
(060.6718) Fiber optics and optical communications : Switching, circuit
(070.6120) Fourier optics and signal processing : Spatial light modulators

ToC Category:
Fourier Optics and Signal Processing

Original Manuscript: December 13, 2011
Revised Manuscript: February 3, 2012
Manuscript Accepted: February 6, 2012
Published: April 20, 2012

Brian Robertson, Zichen Zhang, Haining Yang, Maura M. Redmond, Neil Collings, Jinsong Liu, Ruisheng Lin, Anna M. Jeziorska-Chapman, John R. Moore, William A. Crossland, and D. P. Chu, "Application of the fractional Fourier transform to the design of LCOS based optical interconnects and fiber switches," Appl. Opt. 51, 2212-2222 (2012)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. T. A. Strasser and J. L. Wagener, “Wavelength-selective switches for ROADM applications,” IEEE J. Sel. Top. Quantum Electron. 16, 1150 (2010). [CrossRef]
  2. S. Frisken, “Advances in liquid crystal on silicon wavelength selective switching,” in Proceedings of OFC/NFOEC 2007, pp. 1–3 (2007).
  3. D. Gil Leyva, B. Robertson, C. Henderson, T. Wilkinson, D. O’Brien, and G. Faulkner, “Crosstalk analysis of a free-space optical interconnect based on a spatial light modulator,” Appl. Opt. 45, 63–75 (2006). [CrossRef]
  4. K. L. Tan, S. T. Warr, I. G. Manolis, T. D. Wilkinson, M. M. Redmond, A. A. Crossland, R. J. Mears, and B. Robertson, “Dynamic holography for optical interconnections II. Routing holograms with predictable location and intensity of each diffraction order,” J. Opt. Soc. Am. A 18, 205–215 (2001). [CrossRef]
  5. E. Hällstig, L. Sjövist, and M. Lingdron, “Intensity variations using a quantized spatial light modulator for nonmechanical beam steering,” Opt. Eng. 42, 613 (2003). [CrossRef]
  6. Z. Zhang, H. Yang, B. Robertson, M. Redmond, M. Pivnenko, N. Collings, W. A. Crossland, and D. P. Chu, “Static phase compensation for a phase-only liquid crystal on silicon (LCOS) device,” Appl. Opt. (to be published).
  7. A. Lizana, A. Márquez, I. Moreno, C. Iemmi, J. Campos, and M. J. Yzuel, “Wavelength dependence of polarimetric and phase-shift characterization of a liquid crystal on silicon display,” JEOS RP 3, 08012 (2008). [CrossRef]
  8. L. Xu, J. Zhang, and L. Y. Wu, “Influence of phase delay profile on diffraction efficiency of liquid crystal optical phased array,” Opt. Laser Technol. 41, 509–516 (2009). [CrossRef]
  9. B. Robertson, Z. Zhang, M. M. Redmond, N. Collings, J. S. Liu, R. S. Lin, A. M. Jeriorska-Chapman, J. R. Moore, W. A. Crossland, and D. P. Chu, “The use of wavefront encoding in optical interconnects and fiber switches,” Appl. Opt. (to be published).
  10. H. M. Ozaktas, Z. Zalevsky, and M. Alper Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, 2000).
  11. H. M. Ozaktas and D. Mendlovic, “Fractional Fourier optics,” J. Opt. Soc. Am. A 12, 743–750 (1995). [CrossRef]
  12. A. W. Lohmann, “Image rotation, Wigner rotation, and the fractional Fourier transform,” J. Opt. Soc. Am. A 10, 2181–2186 (1993). [CrossRef]
  13. R. W. Gerchberg and W. O. Saxton, “A practical algorithm for determination of the phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).
  14. Y. Zhang, B. Z. Dong, B. Y. Gu, and G. Z. Yang, “Beam shaping in the fractional Fourier transform domain,” J. Opt. Soc. Am. A 15, 1114–1120 (1998). [CrossRef]
  15. Z. Zalevsky, D. Mendlovic, and R. G. Dorsch, “Gerchberg–Saxton algorithm applied to the fractional Fourier or the Fresnel domain,” Opt. Lett. 21, 842–844 (1996). [CrossRef]
  16. M. Testorf, “Design of diffractive optical elements for the fractional Fourier transform domain: phase-space approach,” Appl. Opt. 45, 76–82 (2006). [CrossRef]
  17. W. A. Crossland, I. G. Manolis, M. M. Redmond, K. L. Tan, T. D. Wilkinson, M. J. Holmes, T. R. Parker, H. H. Chu, J. Croucher, V. A. Handerek, S. T. Warr, B. Robertson, I. G. Bonas, R. Franklin, C. Stace, H. J. White, R. A. Woolley, and G. Henshall, “Holographic optical switching: the ROSES demonstrator,” J. Lightwave Technol. 18, 1845–1854 (2000). [CrossRef]
  18. P. M. Blanchard and A. H. Greenaway, “Simultaneous multiplane imaging with a distorted diffraction grating,” Appl. Opt. 38, 6692–6699 (1999). [CrossRef]
  19. L. M. Bernardo, “ABCD matrix formalism of fractional Fourier optics,” Opt. Eng. 35, 732–740 (1996). [CrossRef]
  20. A. Yariv, Optical Electronics, 3rd ed. (Holt-Saunders International Ed., 1985).
  21. S. A. Collins, “Lens-system diffraction integral written in terms of matrix optics,” J. Opt. Soc. Am. 60, 1168–1177 (1970). [CrossRef]
  22. H. M. Ozaktas, O. Arikan, M. A. Kutay, and G. Bozdagi, “Digital computation of the fractional Fourier transform,” IEEE Trans. Signal Process. 44, 2141–2150 (1996). [CrossRef]
  23. L. M. Bernado and O. D. Soares, “Fractional Fourier transforms and imaging,” J. Opt. Soc. Am. A 11, 2622–2626 (1994). [CrossRef]
  24. M. Johansson, S. Hård, B. Robertson, I. Manolis, T. Wilkinson, and W. Crossland, “Adaptive beam steering implemented in a ferroelectric liquid crystal spatial-light-modulator free-space, fiber-optic switch,” Appl. Opt. 41 (23), 4904–4911 (2002). [CrossRef]
  25. Z. Zhang, A. M. Jeziorska-Chapman, N. Collings, M. Pivenko, J. Moore, B. Crossland, D. P. Chu, and B. Milne, “High quality assembly of phase-only liquid crystal on silicon (LCOS) devices,” J. Disp. Technol. 7, 120–126 (2011). [CrossRef]
  26. A. Georgiou, M. Komarcevic, T. D. Wilkinson, and W. A. Crossland, “Hologram optimisation using liquid crystal modelling,” Mol. Cryst. Liq. Cryst. 434, 183–198 (2005). [CrossRef]
  27. A. Georgiou, T. D. Wilkinson, N. Collings, and W. A. Crossland, “An algorithm for computing spot-generating holograms,” J. Opt. A: Pure Appl. Opt. 10015306 (2008). [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

OSA is a member of CrossRef.

CrossCheck Deposited