Abstract

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

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    [CrossRef]
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2011 (1)

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]

2010 (1)

T. A. Strasser and J. L. Wagener, “Wavelength-selective switches for ROADM applications,” IEEE J. Sel. Top. Quantum Electron. 16, 1150 (2010).
[CrossRef]

2009 (1)

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]

2008 (2)

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]

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]

2006 (2)

2005 (1)

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]

2003 (1)

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]

2002 (1)

2001 (1)

2000 (1)

1999 (1)

1998 (1)

1996 (3)

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]

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]

L. M. Bernardo, “ABCD matrix formalism of fractional Fourier optics,” Opt. Eng. 35, 732–740 (1996).
[CrossRef]

1995 (1)

1994 (1)

1993 (1)

1972 (1)

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).

1970 (1)

Alper Kutay, M.

H. M. Ozaktas, Z. Zalevsky, and M. Alper Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, 2000).

Arikan, O.

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]

Bernado, L. M.

Bernardo, L. M.

L. M. Bernardo, “ABCD matrix formalism of fractional Fourier optics,” Opt. Eng. 35, 732–740 (1996).
[CrossRef]

Blanchard, P. M.

Bonas, I. G.

Bozdagi, G.

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]

Campos, J.

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]

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

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).

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).

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

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]

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).

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).

Collins, S. A.

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

Crossland, W.

Crossland, W. A.

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]

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]

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, 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).

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).

Croucher, J.

Dong, B. Z.

Dorsch, R. G.

Faulkner, G.

Franklin, R.

Frisken, S.

S. Frisken, “Advances in liquid crystal on silicon wavelength selective switching,” in Proceedings of OFC/NFOEC 2007, pp. 1–3 (2007).

Georgiou, A.

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]

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]

Gerchberg, R. W.

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).

Gil Leyva, D.

Greenaway, A. H.

Gu, B. Y.

Hällstig, E.

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]

Handerek, V. A.

Hård, S.

Henderson, C.

Henshall, G.

Holmes, M. J.

Iemmi, C.

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]

Jeriorska-Chapman, A. M.

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).

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

Johansson, M.

Komarcevic, M.

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]

Kutay, M. A.

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]

Lin, R. S.

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).

Lingdron, M.

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]

Liu, J. S.

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).

Lizana, A.

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]

Lohmann, A. W.

Manolis, I.

Manolis, I. G.

Márquez, A.

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]

Mears, R. J.

Mendlovic, D.

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

Moore, J. R.

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).

Moreno, I.

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]

O’Brien, D.

Ozaktas, H. M.

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]

H. M. Ozaktas and D. Mendlovic, “Fractional Fourier optics,” J. Opt. Soc. Am. A 12, 743–750 (1995).
[CrossRef]

H. M. Ozaktas, Z. Zalevsky, and M. Alper Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, 2000).

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

Pivnenko, M.

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).

Redmond, M.

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).

Redmond, M. M.

Robertson, B.

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]

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]

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, 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).

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).

Saxton, W. O.

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).

Sjövist, L.

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]

Soares, O. D.

Stace, C.

Strasser, T. A.

T. A. Strasser and J. L. Wagener, “Wavelength-selective switches for ROADM applications,” IEEE J. Sel. Top. Quantum Electron. 16, 1150 (2010).
[CrossRef]

Tan, K. L.

Testorf, M.

Wagener, J. L.

T. A. Strasser and J. L. Wagener, “Wavelength-selective switches for ROADM applications,” IEEE J. Sel. Top. Quantum Electron. 16, 1150 (2010).
[CrossRef]

Warr, S. T.

White, H. J.

Wilkinson, T.

Wilkinson, T. D.

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]

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, G. Z.

Yang, H.

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).

Yariv, A.

A. Yariv, Optical Electronics, 3rd ed. (Holt-Saunders International Ed., 1985).

Yzuel, M. J.

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]

Zalevsky, Z.

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]

H. M. Ozaktas, Z. Zalevsky, and M. Alper Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, 2000).

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, Y.

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

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).

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).

Appl. Opt. (6)

IEEE J. Sel. Top. Quantum Electron. (1)

T. A. Strasser and J. L. Wagener, “Wavelength-selective switches for ROADM applications,” IEEE J. Sel. Top. Quantum Electron. 16, 1150 (2010).
[CrossRef]

IEEE Trans. Signal Process. (1)

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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).
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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).
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Figures (13)

Fig. 1.
Fig. 1.

Experimental outline of wavefront encoding as applied to a 2f optical routing geometry. (a) Conventional 2f system where orders are focused along plane Q1. (b) Defocused system where diffraction orders are focused along the plane Q2.

Fig. 2.
Fig. 2.

Relationship between Lohmann type I fractional Fourier-transform optical system and terms used in analysis. The input and output planes are a distance f+s from a lens of focal length f.

Fig. 3.
Fig. 3.

Three lens equivalent model. The single lens arrangement of Fig. 2 can be replaced by the above equivalent optical system.

Fig. 4.
Fig. 4.

Unfolded optical system representing switch of Fig. 1(b). (a) Full switch geometry. (b) Only first lens shown to illustrate the calculation of ρH.

Fig. 5.
Fig. 5.

Simulated replay field at fiber plane with +1 order deflected through 140 µm. SLM displaying off-axis lens with a γ=0.05 phase error to show up higher orders. Figure plotted as 10log10 (Intensity).

Fig. 6.
Fig. 6.

Simulated replay field along y-axis at fiber plane with SLM deflecting +1 order through 140 µm. SLM displaying off-axis lens with a γ=0.05 phase error to show up higher orders. Figure plotted as 10log10 (Intensity).

Fig. 7.
Fig. 7.

Comparison of theoretical blazed grating and wavefront encoded replay fields along the beam displacement axis for a deflection of 35 µm with (a) ideal reconstruction, and (b) a uniform γ=0.05 phase error applied to the phase patterns. Dotted line—blazed grating. Solid line—wavefront encoded system.

Fig. 8.
Fig. 8.

Theoretical maximum crosstalk for equivalent blazed grating and wavefront encoded switch as a function of number of phase levels, N.

Fig. 9.
Fig. 9.

Theoretical dependence of maximum replay field crosstalk for equivalent blazed grating and wavefront encoded switches as a function of uniform phase error, γ.

Fig. 10.
Fig. 10.

Theoretical dependence of maximum fiber crosstalk for equivalent blazed grating and wavefront encoded switches as a function of uniform phase error, γ. Output fiber has a mode field radius of 5.2 μm at 1550 nm.

Fig. 11.
Fig. 11.

Layout of telecom test switch. System consists of an input/output fiber array, a lenslet array, lens L1, mirror M1, and a nematic LCOS SLM.

Fig. 12.
Fig. 12.

Example of a multi-casting hologram designed to deflect light to two output ports and optimized using a modified Gerchberg–Saxton algorithm. The scale to the right shows phase retardation (0 to 2π).

Fig. 13.
Fig. 13.

Normalized intensity distribution at the replay field of multi-casting hologram.

Tables (1)

Tables Icon

Table 1. Multi-Casting Performance—Comparison of Target, Predicted, and Measured Power Levels. a

Equations (18)

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E1(u,v)=KA(x,y,u,v)EH(x,y)dxdy,
KA(x,y,u,v)=Aϕexp[iπ(cot(ϕ)u22csc(ϕ)ux+cot(ϕ)x2)]×Aϕexp[iπ(cot(ϕ)v22csc(ϕ)vy+cot(ϕ)y2)],
ϕ=aπ2,
Aϕ=1icotϕ.
E1(u,v)=EH(x,y)exp(ik2B[A(x2+y2)+D(u2+v2)2(xu+yv)])dxdy.
M=[1z1fz1+z2z1z2f1f1z2f].
cosϕ=1z1f.
M=[cosϕfsin2ϕ1fcosϕ].
M=[fFf1fFfFf121fFfFf1].
fF=fsin2ϕ,
f1=fFcosϕ,
EI(u,v)=FT(Ein(x,y)exp[iα(x,y)]exp[ik(x2+y2)2f1])exp[ik(u2+v2)2f2].
u=nλffNΔ,
ρH=z1ff2s,
z2=ρH+fρH+z1fz1.
fp=ρHfρH+z1f.
fH=(1/2)ρH.
s=f22fH.

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