Abstract

A technique of cross talk mitigation developed for liquid crystal on silicon spatial light modulator based optical interconnects and fiber switches is demonstrated. By purposefully introducing an appropriate aberration into the system, it is possible to reduce the worst-case cross talk by over 10dB compared to conventional Fourier-transform-based designs. Tests at a wavelength of 674nm validate this approach, and show that there is no noticeable reduction in diffraction efficiency. A 27% spot increase in beam diameter is observed, which is predicted to reduce at longer datacom and telecom wavelengths.

© 2012 Optical Society of America

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  1. M. C. Wu, O. Solgaard, and J. E. Ford, “Optical MEMS for lightwave communication,” J. Lightwave Technol. 24, 4433–4454 (2006).
    [CrossRef]
  2. D. T. Neilson, R. Frahm, P. Kolodner, C. A. Bolle, R. Ryf, J. Kim, A. R. Papazian, C. J. Nuzman, A. Gasparyan, N. R. Basavanhally, V. A. Aksyuk, and J. V. Gates, “256×256 port optical cross-connect subsystem,” J. Lightwave Technol. 22, 1499–1509 (2004).
    [CrossRef]
  3. 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]
  4. C. Uche, B. Fracasso, W. A. Crossland, J. L. de Bougrenet de la Tocnaye, and T. D. Wilkinson, “Development of large capacity and low-crosstalk holographic switches using LCOS spatial light modulators,” Ferroelectrics 278, 219–226 (2002).
    [CrossRef]
  5. E. Hallstig, L. Sjoqvist, and M. Lindgren, “Intensity variations using a quantized spatial light modulator for non-mechanical beam steering,” Opt. Eng. 42, 613–619 (2003).
    [CrossRef]
  6. 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]
  7. 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, 4904–4911 (2002).
    [CrossRef]
  8. 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]
  9. A. G. 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]
  10. J. E. Stockley, D. Subacius, and S. A. Serati, “The influence of the interpixel region in liquid crystal diffraction gratings,” Proc. SPIE 3635, 127–136 (1999).
  11. M. A. A. Neil, M. J. Booth, and T. Wilson, “New modal wavefront sensor: a theoretical analysis,” J. Opt. Soc. Am. A 17, 1098–1107 (2000).
    [CrossRef]
  12. D. G. Leyva, B. Robertson, T. D. Wilkinson, and C. J. Henderson, “Aberration correction in an adaptive free-space optical interconnect with an error diffusion algorithm,” Appl. Opt. 45, 3782–3792 (2006).
    [CrossRef]
  13. P. M. Blanchard and A. H. Greenaway, “Simultaneous multiplane imaging with a distorted diffraction grating,” Appl. Opt. 38, 6692–6699 (1999).
    [CrossRef]
  14. D. Marcuse, “Loss analysis of single-mode fiber splices,” Bell Syst. Tech. J. 56, 703–718 (1977).
  15. D. G. Leyva, B. Robertson, C. J. Henderson, T. D. Wilkinson, A. C. O’Brien, and G. Faulkner, “Cross-talk analysis in a telecentric adaptive free-space optical relay based on a spatial light modulator,” Appl. Opt. 45, 63–75 (2006).
    [CrossRef]
  16. E. Noponen, J. Turunen, and A. Vasara, “Electromagnetic theory and design of diffractive-lens arrays,” J. Opt. Soc. Am. A 10, 434–443 (1993).
    [CrossRef]
  17. M. J. Yzuel, J. Campos, A. Márquez, J. C. Escalera, J. A. Davis, C. Iemmi, and S. Ledesma, “Inherent apodization of lenses encoded on liquid-crystal spatial light modulators,” Appl. Opt. 39, 6034–6039 (2000).
    [CrossRef]
  18. Zemax, Radiant ZEMAX LLC.
  19. B. Robertson, Z. Zhang, H. Yang, M. M. Redmond, N. Collings, J. Liu, R. Lin, A. M. Jeziorska-Chapman, J. R. Moore, W. A. Crossland, and D. P. Chu are preparing a manuscript to be called, “Application of the fractional fast Fourier transform to the design of LCOS based optical interconnects and fiber switches,” to be submitted to Applied Optics (2011).
  20. H. M. Ozaktas, The Fractional Fourier Transform: with Applications in Optics and Signal Processing (Wiley, 2001).
  21. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1965), Chap. 7.
  22. 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. Displ. Technol. 7, 120–126 (2011).
    [CrossRef]
  23. R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

2011

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. Displ. Technol. 7, 120–126 (2011).
[CrossRef]

2009

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]

2006

2005

A. G. 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]

2004

2003

E. Hallstig, L. Sjoqvist, and M. Lindgren, “Intensity variations using a quantized spatial light modulator for non-mechanical beam steering,” Opt. Eng. 42, 613–619 (2003).
[CrossRef]

2002

C. Uche, B. Fracasso, W. A. Crossland, J. L. de Bougrenet de la Tocnaye, and T. D. Wilkinson, “Development of large capacity and low-crosstalk holographic switches using LCOS spatial light modulators,” Ferroelectrics 278, 219–226 (2002).
[CrossRef]

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, 4904–4911 (2002).
[CrossRef]

2001

2000

1999

P. M. Blanchard and A. H. Greenaway, “Simultaneous multiplane imaging with a distorted diffraction grating,” Appl. Opt. 38, 6692–6699 (1999).
[CrossRef]

J. E. Stockley, D. Subacius, and S. A. Serati, “The influence of the interpixel region in liquid crystal diffraction gratings,” Proc. SPIE 3635, 127–136 (1999).

1993

1977

D. Marcuse, “Loss analysis of single-mode fiber splices,” Bell Syst. Tech. J. 56, 703–718 (1977).

1972

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Abramowitz, M.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1965), Chap. 7.

Aksyuk, V. A.

Basavanhally, N. R.

Blanchard, P. M.

Bolle, C. A.

Bonas, I. G.

Booth, M. J.

Campos, J.

Chu, D. P.

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. Displ. Technol. 7, 120–126 (2011).
[CrossRef]

B. Robertson, Z. Zhang, H. Yang, M. M. Redmond, N. Collings, J. Liu, R. Lin, A. M. Jeziorska-Chapman, J. R. Moore, W. A. Crossland, and D. P. Chu are preparing a manuscript to be called, “Application of the fractional fast Fourier transform to the design of LCOS based optical interconnects and fiber switches,” to be submitted to Applied Optics (2011).

Chu, H. H.

Collings, N.

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. Displ. Technol. 7, 120–126 (2011).
[CrossRef]

B. Robertson, Z. Zhang, H. Yang, M. M. Redmond, N. Collings, J. Liu, R. Lin, A. M. Jeziorska-Chapman, J. R. Moore, W. A. Crossland, and D. P. Chu are preparing a manuscript to be called, “Application of the fractional fast Fourier transform to the design of LCOS based optical interconnects and fiber switches,” to be submitted to Applied Optics (2011).

Crossland, A. A.

Crossland, B.

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. Displ. Technol. 7, 120–126 (2011).
[CrossRef]

Crossland, W.

Crossland, W. A.

A. G. 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]

C. Uche, B. Fracasso, W. A. Crossland, J. L. de Bougrenet de la Tocnaye, and T. D. Wilkinson, “Development of large capacity and low-crosstalk holographic switches using LCOS spatial light modulators,” Ferroelectrics 278, 219–226 (2002).
[CrossRef]

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]

B. Robertson, Z. Zhang, H. Yang, M. M. Redmond, N. Collings, J. Liu, R. Lin, A. M. Jeziorska-Chapman, J. R. Moore, W. A. Crossland, and D. P. Chu are preparing a manuscript to be called, “Application of the fractional fast Fourier transform to the design of LCOS based optical interconnects and fiber switches,” to be submitted to Applied Optics (2011).

Croucher, J.

Davis, J. A.

de Bougrenet de la Tocnaye, J. L.

C. Uche, B. Fracasso, W. A. Crossland, J. L. de Bougrenet de la Tocnaye, and T. D. Wilkinson, “Development of large capacity and low-crosstalk holographic switches using LCOS spatial light modulators,” Ferroelectrics 278, 219–226 (2002).
[CrossRef]

Escalera, J. C.

Faulkner, G.

Ford, J. E.

Fracasso, B.

C. Uche, B. Fracasso, W. A. Crossland, J. L. de Bougrenet de la Tocnaye, and T. D. Wilkinson, “Development of large capacity and low-crosstalk holographic switches using LCOS spatial light modulators,” Ferroelectrics 278, 219–226 (2002).
[CrossRef]

Frahm, R.

Franklin, R.

Gasparyan, A.

Gates, J. V.

Georgiou, A. G.

A. G. 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]

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Greenaway, A. H.

Hallstig, E.

E. Hallstig, L. Sjoqvist, and M. Lindgren, “Intensity variations using a quantized spatial light modulator for non-mechanical beam steering,” Opt. Eng. 42, 613–619 (2003).
[CrossRef]

Handerek, V. A.

Hård, S.

Henderson, C. J.

Henshall, G.

Holmes, M. J.

Iemmi, C.

Jeziorska-Chapman, A. M.

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. Displ. Technol. 7, 120–126 (2011).
[CrossRef]

B. Robertson, Z. Zhang, H. Yang, M. M. Redmond, N. Collings, J. Liu, R. Lin, A. M. Jeziorska-Chapman, J. R. Moore, W. A. Crossland, and D. P. Chu are preparing a manuscript to be called, “Application of the fractional fast Fourier transform to the design of LCOS based optical interconnects and fiber switches,” to be submitted to Applied Optics (2011).

Johansson, M.

Kim, J.

Kolodner, P.

Komarcevic, M.

A. G. 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]

Ledesma, S.

Leyva, D. G.

Lin, R.

B. Robertson, Z. Zhang, H. Yang, M. M. Redmond, N. Collings, J. Liu, R. Lin, A. M. Jeziorska-Chapman, J. R. Moore, W. A. Crossland, and D. P. Chu are preparing a manuscript to be called, “Application of the fractional fast Fourier transform to the design of LCOS based optical interconnects and fiber switches,” to be submitted to Applied Optics (2011).

Lindgren, M.

E. Hallstig, L. Sjoqvist, and M. Lindgren, “Intensity variations using a quantized spatial light modulator for non-mechanical beam steering,” Opt. Eng. 42, 613–619 (2003).
[CrossRef]

Liu, J.

B. Robertson, Z. Zhang, H. Yang, M. M. Redmond, N. Collings, J. Liu, R. Lin, A. M. Jeziorska-Chapman, J. R. Moore, W. A. Crossland, and D. P. Chu are preparing a manuscript to be called, “Application of the fractional fast Fourier transform to the design of LCOS based optical interconnects and fiber switches,” to be submitted to Applied Optics (2011).

Manolis, I.

Manolis, I. G.

Marcuse, D.

D. Marcuse, “Loss analysis of single-mode fiber splices,” Bell Syst. Tech. J. 56, 703–718 (1977).

Márquez, A.

Mears, R. J.

Milne, B.

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. Displ. Technol. 7, 120–126 (2011).
[CrossRef]

Moore, J.

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. Displ. Technol. 7, 120–126 (2011).
[CrossRef]

Moore, J. R.

B. Robertson, Z. Zhang, H. Yang, M. M. Redmond, N. Collings, J. Liu, R. Lin, A. M. Jeziorska-Chapman, J. R. Moore, W. A. Crossland, and D. P. Chu are preparing a manuscript to be called, “Application of the fractional fast Fourier transform to the design of LCOS based optical interconnects and fiber switches,” to be submitted to Applied Optics (2011).

Neil, M. A. A.

Neilson, D. T.

Noponen, E.

Nuzman, C. J.

O’Brien, A. C.

Ozaktas, H. M.

H. M. Ozaktas, The Fractional Fourier Transform: with Applications in Optics and Signal Processing (Wiley, 2001).

Papazian, A. R.

Parker, T. R.

Pivenko, M.

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. Displ. Technol. 7, 120–126 (2011).
[CrossRef]

Redmond, M. M.

Robertson, B.

D. G. Leyva, B. Robertson, C. J. Henderson, T. D. Wilkinson, A. C. O’Brien, and G. Faulkner, “Cross-talk analysis in a telecentric adaptive free-space optical relay based on a spatial light modulator,” Appl. Opt. 45, 63–75 (2006).
[CrossRef]

D. G. Leyva, B. Robertson, T. D. Wilkinson, and C. J. Henderson, “Aberration correction in an adaptive free-space optical interconnect with an error diffusion algorithm,” Appl. Opt. 45, 3782–3792 (2006).
[CrossRef]

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, 4904–4911 (2002).
[CrossRef]

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]

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]

B. Robertson, Z. Zhang, H. Yang, M. M. Redmond, N. Collings, J. Liu, R. Lin, A. M. Jeziorska-Chapman, J. R. Moore, W. A. Crossland, and D. P. Chu are preparing a manuscript to be called, “Application of the fractional fast Fourier transform to the design of LCOS based optical interconnects and fiber switches,” to be submitted to Applied Optics (2011).

Ryf, R.

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Serati, S. A.

J. E. Stockley, D. Subacius, and S. A. Serati, “The influence of the interpixel region in liquid crystal diffraction gratings,” Proc. SPIE 3635, 127–136 (1999).

Sjoqvist, L.

E. Hallstig, L. Sjoqvist, and M. Lindgren, “Intensity variations using a quantized spatial light modulator for non-mechanical beam steering,” Opt. Eng. 42, 613–619 (2003).
[CrossRef]

Solgaard, O.

Stace, C.

Stegun, I. A.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1965), Chap. 7.

Stockley, J. E.

J. E. Stockley, D. Subacius, and S. A. Serati, “The influence of the interpixel region in liquid crystal diffraction gratings,” Proc. SPIE 3635, 127–136 (1999).

Subacius, D.

J. E. Stockley, D. Subacius, and S. A. Serati, “The influence of the interpixel region in liquid crystal diffraction gratings,” Proc. SPIE 3635, 127–136 (1999).

Tan, K. L.

Turunen, J.

Uche, C.

C. Uche, B. Fracasso, W. A. Crossland, J. L. de Bougrenet de la Tocnaye, and T. D. Wilkinson, “Development of large capacity and low-crosstalk holographic switches using LCOS spatial light modulators,” Ferroelectrics 278, 219–226 (2002).
[CrossRef]

Vasara, A.

Warr, S. T.

White, H. J.

Wilkinson, T.

Wilkinson, T. D.

D. G. Leyva, B. Robertson, T. D. Wilkinson, and C. J. Henderson, “Aberration correction in an adaptive free-space optical interconnect with an error diffusion algorithm,” Appl. Opt. 45, 3782–3792 (2006).
[CrossRef]

D. G. Leyva, B. Robertson, C. J. Henderson, T. D. Wilkinson, A. C. O’Brien, and G. Faulkner, “Cross-talk analysis in a telecentric adaptive free-space optical relay based on a spatial light modulator,” Appl. Opt. 45, 63–75 (2006).
[CrossRef]

A. G. 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]

C. Uche, B. Fracasso, W. A. Crossland, J. L. de Bougrenet de la Tocnaye, and T. D. Wilkinson, “Development of large capacity and low-crosstalk holographic switches using LCOS spatial light modulators,” Ferroelectrics 278, 219–226 (2002).
[CrossRef]

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]

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]

Wilson, T.

Woolley, R. A.

Wu, L. Y.

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]

Wu, M. C.

Xu, L.

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]

Yang, H.

B. Robertson, Z. Zhang, H. Yang, M. M. Redmond, N. Collings, J. Liu, R. Lin, A. M. Jeziorska-Chapman, J. R. Moore, W. A. Crossland, and D. P. Chu are preparing a manuscript to be called, “Application of the fractional fast Fourier transform to the design of LCOS based optical interconnects and fiber switches,” to be submitted to Applied Optics (2011).

Yzuel, M. J.

Zhang, J.

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]

Zhang, Z.

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. Displ. Technol. 7, 120–126 (2011).
[CrossRef]

B. Robertson, Z. Zhang, H. Yang, M. M. Redmond, N. Collings, J. Liu, R. Lin, A. M. Jeziorska-Chapman, J. R. Moore, W. A. Crossland, and D. P. Chu are preparing a manuscript to be called, “Application of the fractional fast Fourier transform to the design of LCOS based optical interconnects and fiber switches,” to be submitted to Applied Optics (2011).

Appl. Opt.

Bell Syst. Tech. J.

D. Marcuse, “Loss analysis of single-mode fiber splices,” Bell Syst. Tech. J. 56, 703–718 (1977).

Ferroelectrics

C. Uche, B. Fracasso, W. A. Crossland, J. L. de Bougrenet de la Tocnaye, and T. D. Wilkinson, “Development of large capacity and low-crosstalk holographic switches using LCOS spatial light modulators,” Ferroelectrics 278, 219–226 (2002).
[CrossRef]

J. Displ. Technol.

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. Displ. Technol. 7, 120–126 (2011).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. A

Mol. Cryst. Liq. Cryst.

A. G. 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]

Opt. Eng.

E. Hallstig, L. Sjoqvist, and M. Lindgren, “Intensity variations using a quantized spatial light modulator for non-mechanical beam steering,” Opt. Eng. 42, 613–619 (2003).
[CrossRef]

Opt. Laser Technol.

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]

Optik

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Proc. SPIE

J. E. Stockley, D. Subacius, and S. A. Serati, “The influence of the interpixel region in liquid crystal diffraction gratings,” Proc. SPIE 3635, 127–136 (1999).

Other

Zemax, Radiant ZEMAX LLC.

B. Robertson, Z. Zhang, H. Yang, M. M. Redmond, N. Collings, J. Liu, R. Lin, A. M. Jeziorska-Chapman, J. R. Moore, W. A. Crossland, and D. P. Chu are preparing a manuscript to be called, “Application of the fractional fast Fourier transform to the design of LCOS based optical interconnects and fiber switches,” to be submitted to Applied Optics (2011).

H. M. Ozaktas, The Fractional Fourier Transform: with Applications in Optics and Signal Processing (Wiley, 2001).

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1965), Chap. 7.

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Figures (12)

Fig. 1.
Fig. 1.

Experimental outline of wavefront encoding as applied to a 4f optical routing geometry. (a) Perfectly aligned system. (b) Defocused system.

Fig. 2.
Fig. 2.

Defocus for the specified orders as a function of fH(+1). Lens focal length is f=25mm.

Fig. 3.
Fig. 3.

Coupling efficiency plot for the specified orders as a function of fH(+1). Note that the m=1 and m=+3 orders overlap.

Fig. 4.
Fig. 4.

Variation in minimum local period of an on-axis lens as a function of focal length at a wavelength of 1550nm. Pixel size is 15μm, and lens covers 500×500 pixels. Curves plotted for offsets of 0, 1, 2, 3, 4, 5, and 6mm, with period monotonically decreasing with offset.

Fig. 5.
Fig. 5.

Theoretical coupling efficiency as a single-mode fiber is translated along the +1 order focal plane (plane F1 or F2) for diffraction orders m=0, ±1, 2, and 3. Target fiber is 35μm from input axis. Top subplot: configuration for a Fourier-transform-based system. Lower subplot: wavefront-encoded system.

Fig. 6.
Fig. 6.

Replay field at focal plane of +1 order of 500×500 pixel SLM displaying off-axis lens with a 10% phase error to show up higher orders. Intensity profile plotted as 10log10 (Intensity).

Fig. 7.
Fig. 7.

Experimental system for comparing cross talk of blazed grating and wavefront encoding schemes using visible light.

Fig. 8.
Fig. 8.

Phase patterns used on the LCOS device: (a) Blazed grating (covers whole of device); (b) wavefront-encoded pattern (500×500 pixels).

Fig. 9.
Fig. 9.

Intensity images of the replay planes at 674nm: (a) Blazed grating; (b) wavefront encoded. The images were taken at the same laser power and at the same magnification.

Fig. 10.
Fig. 10.

Diffraction efficiency to all target positions for a blazed grating (yellow), and an equivalent wavefront-encoded pattern (blue).

Fig. 11.
Fig. 11.

Measured performances (signal and cross talk). This typical result was taken at location 12, with the SLM cycling through all 12 blazed grating and wavefront-encoded patterns.

Fig. 12.
Fig. 12.

Maximum cross talk at each of the 12 target positions for a standard blazed grating and the wavefront-encoded pattern.

Tables (3)

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Table 1. Parameters for Blazed Grating and Wavefront-Encoded Patterns

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Table 2. Cross Talk Matrix (in Decibels) for Blazed Grating Patternsa

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Table 3. Cross Talk Matrix (in Decibels) for Wavefront-Encoded Hologramsa

Equations (14)

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sin(θm)=mλT.
δm=ftan(θm).
fH(m)=fHm.
d(m)=2s+f2fHm,
fH=f22s.
PC(m,t)=Pmη(d(m),xmxt,ymyt).
δ+1=2sfδH.
ηD=(1PT)dx/2dx/2dy/2dy/2I(x,y)dxdy,
ηD=Ioα2PTπ4[erf[dx2α]erf[dx2α]][erf[dy2α]erf[dy2α]].
δ+1=f4f3f2tan(asin(λT)).
d(m)=f42fH2m,
δ+1=δH2f4+fH2(f4+f42fH2),
fH2=(f2f3)2fH
δH2=f2δHf3.

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