Abstract

A checkerboard phase plate is proposed to be used together with computer generated holograms to eliminate the zero order by working as a convolution function that shifts the zero order away from the center of a reconstructed pattern. By performing a preshift in the desired hologram pattern, it is possible to obtain a reconstructed pattern that is free of zero order. Simulation results have shown that the technique is tolerant of fabrication errors in the hologram. The technique is also shown to effectively reduce the zero order intensity by two orders in the presence of phase depth errors in the checkerboard. Experimental results using a spatial light modulator support the results shown in the simulation.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |

  1. H. H. Refai, J. J. Sluss, H. H. Refai, and M. Atiquzzaman, "Comparative study of the performance of analog fiber optic links versus free-space optical links," Opt. Eng. 45, 025003 (2006).
    [CrossRef]
  2. D. W. K. Wong, G. C. K. Chen, and J. P. Yao, "Optimization of spot pattern in indoor diffuse optical wireless local area networks," Opt. Express 13, 3000-3014 (2005).
    [CrossRef] [PubMed]
  3. S. Jivkova and M. Kavehrad, "Receiver designs and channel characterization for multi-spot high-bit-rate wireless infrared communications," IEEE Trans. Commun. 49, 2145-2153 (2001).
    [CrossRef]
  4. A. G. Al-Ghamdi and J. M. H. Elmirghani, "Multiple spot diffusing geometries for indoor optical wireless communication systems," Int. J. Commun. Syst. 16, 909-922 (2003).
    [CrossRef]
  5. J. P. Yao, G. C. K. Chen, and T. K. Lim, "Holographic diffuser for diffuse infrared wireless home networking," Opt. Eng. 42, 317-324 (2003).
    [CrossRef]
  6. D. C. O'Shea, "Reduction of the zero-order intensity in binary Dammann gratings," Appl. Opt. 34, 6533-6537 (1995).
    [CrossRef] [PubMed]
  7. P. L. Eardley, D. R. Wisely, D. Wood, and P. McKee, "Holograms for optical wireless LANs," IEE Proc. Optoelectron. 143, 365-369 (1996).
    [CrossRef]
  8. V. R. Daria, P. J. Rodrigo, and J. Gluckstad, "Programmable complex field coupling to high-order guided modes of micro-structured fibres," Opt. Commun. 232, 229-237 (2004).
    [CrossRef]
  9. J. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).
  10. M. P. Dames, R. J. Dowling, P. McKee, and D. Wood, "Efficient optical elements to generate intensity weighted spot arrays: design and fabrication," Appl. Opt. 30, 2685-2691 (1991).
    [CrossRef] [PubMed]
  11. E. H. Anderson, D. Ha, and J. A. Liddle, "Sub-pixel alignment for direct-write electron beam lithography," Microelectron. Eng. 73-74, 74-79 (2004).
    [CrossRef]

2006 (1)

H. H. Refai, J. J. Sluss, H. H. Refai, and M. Atiquzzaman, "Comparative study of the performance of analog fiber optic links versus free-space optical links," Opt. Eng. 45, 025003 (2006).
[CrossRef]

2005 (1)

2004 (2)

V. R. Daria, P. J. Rodrigo, and J. Gluckstad, "Programmable complex field coupling to high-order guided modes of micro-structured fibres," Opt. Commun. 232, 229-237 (2004).
[CrossRef]

E. H. Anderson, D. Ha, and J. A. Liddle, "Sub-pixel alignment for direct-write electron beam lithography," Microelectron. Eng. 73-74, 74-79 (2004).
[CrossRef]

2003 (2)

A. G. Al-Ghamdi and J. M. H. Elmirghani, "Multiple spot diffusing geometries for indoor optical wireless communication systems," Int. J. Commun. Syst. 16, 909-922 (2003).
[CrossRef]

J. P. Yao, G. C. K. Chen, and T. K. Lim, "Holographic diffuser for diffuse infrared wireless home networking," Opt. Eng. 42, 317-324 (2003).
[CrossRef]

2001 (1)

S. Jivkova and M. Kavehrad, "Receiver designs and channel characterization for multi-spot high-bit-rate wireless infrared communications," IEEE Trans. Commun. 49, 2145-2153 (2001).
[CrossRef]

1996 (1)

P. L. Eardley, D. R. Wisely, D. Wood, and P. McKee, "Holograms for optical wireless LANs," IEE Proc. Optoelectron. 143, 365-369 (1996).
[CrossRef]

1995 (1)

1991 (1)

Appl. Opt. (2)

IEE Proc. Optoelectron. (1)

P. L. Eardley, D. R. Wisely, D. Wood, and P. McKee, "Holograms for optical wireless LANs," IEE Proc. Optoelectron. 143, 365-369 (1996).
[CrossRef]

IEEE Trans. Commun. (1)

S. Jivkova and M. Kavehrad, "Receiver designs and channel characterization for multi-spot high-bit-rate wireless infrared communications," IEEE Trans. Commun. 49, 2145-2153 (2001).
[CrossRef]

Int. J. Commun. Syst. (1)

A. G. Al-Ghamdi and J. M. H. Elmirghani, "Multiple spot diffusing geometries for indoor optical wireless communication systems," Int. J. Commun. Syst. 16, 909-922 (2003).
[CrossRef]

Microelectron. Eng. (1)

E. H. Anderson, D. Ha, and J. A. Liddle, "Sub-pixel alignment for direct-write electron beam lithography," Microelectron. Eng. 73-74, 74-79 (2004).
[CrossRef]

Opt. Commun. (1)

V. R. Daria, P. J. Rodrigo, and J. Gluckstad, "Programmable complex field coupling to high-order guided modes of micro-structured fibres," Opt. Commun. 232, 229-237 (2004).
[CrossRef]

Opt. Eng. (2)

J. P. Yao, G. C. K. Chen, and T. K. Lim, "Holographic diffuser for diffuse infrared wireless home networking," Opt. Eng. 42, 317-324 (2003).
[CrossRef]

H. H. Refai, J. J. Sluss, H. H. Refai, and M. Atiquzzaman, "Comparative study of the performance of analog fiber optic links versus free-space optical links," Opt. Eng. 45, 025003 (2006).
[CrossRef]

Opt. Express (1)

Other (1)

J. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (13)

Fig. 1
Fig. 1

(Color online) (a) Desired 8 × 8 spot intensity pattern and (b) intensity profile for the desired pattern.

Fig. 2
Fig. 2

Geometric sketch of the PCF.

Fig. 3
Fig. 3

Intensity plot in one dimension of the far-field complex amplitude of the PCF presented in Fig. 2.

Fig. 4
Fig. 4

Implementation of the combined CGH-PCF optical element.

Fig. 5
Fig. 5

(Color online) Intensity plot for the combined PCF-CGH optical element and 2D intensity distribution of the same element.

Fig. 6
Fig. 6

(Color online) Intensity plot for the CGH with an introduced phase depth error; inset shows the corresponding 2D the intensity distribution.

Fig. 7
Fig. 7

(Color online) (a) Intensity plot of the SCGH-PCF optical element, (b) SCGH design, and (c) 2D spatial distribution of the intensity plot shown in (a).

Fig. 8
Fig. 8

(a) Two by two spot array with zero order using CGH and (b) application of the PCF SCGH technique shifts away zero order with no effect on spot distribution.

Fig. 9
Fig. 9

(a) Performance of the CGH and SCGH PCF optical element in the presence of phase level errors. GZO / I s refers to the normalized GZO of a conventional CGH. SZO / I s refers to the normalized shifted zero order intensity. ( GZO / I s ) K refers to the normalized zero order when the SCGH phase levels are varied and the PCF phase levels are set at [ 0 , 0.9 π ] . (b) Shows the change in the shifted zero order ( SZO / I s ) M as alignment errors are introduced between the PCF and the SCGH.

Fig. 10
Fig. 10

Effect of fill-factor imbalance on the zero order for a CGH and SCGH PCF.

Fig. 11
Fig. 11

Experimental setup to reconstruct the diffracted pattern using a phase-only reflective SLM.

Fig. 12
Fig. 12

(a) Diffraction pattern when no phase error is introduced into the system and (b) the SZO when the SCGH PCF is used in the presence of [ 0 , 0.6 π ] phase heights in the SCGH.

Fig. 13
Fig. 13

(a) Diffracted intensity for the SCGH PCF and the CGH as the phase level is varied and (b) zero order intensity levels for the SCGH PCF and the CGH. The minimum zero order has also been included as a reference.

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

U 2 ( x , y ) = e j k z e i ( k / 2 z ) ( x 2 + y 2 ) j λ z U 1 ( ξ , η ) × exp [ j 2 π λ z ( x ξ + y η ) ] d ξ d η ,
H ( ξ , η ) = [ comb ( ξ Δ , η Δ ) p ( ξ , η ) ] [ rect ( ξ Δ , η Δ ) ] .
U 2 ( x , y ) = [ comb ( x Δ , y Δ ) P ( x , y ) ] [ sinc ( x Δ , y Δ ) ] .
k ( ξ , η ) = c ( ξ , η ) comb ( ξ 2 Γ , η 2 Γ ) .
c ( ξ , η ) = rect ( ξ Γ , η Γ ) δ ( ξ Γ 2 , η + Γ 2 ) exp ( j π ) + rect ( ξ Γ , η Γ ) δ ( ξ + Γ 2 , η + Γ 2 ) + rect ( ξ Γ , η Γ ) δ ( ξ Γ 2 , η η 2 ) + rect ( ξ Γ , η Γ ) δ ( ξ + Γ 2 , η Γ 2 ) exp ( j π ) .
C ( x , y ) = sin ( π Γ x ) sin ( π Γ y ) sinc ( x Γ , y Γ ) ,
K ( x , y ) = sin ( π Γ x ) sin ( π Γ y ) sinc ( x Γ , y Γ ) × comb ( x 2 Γ , y 2 Γ ) ,
U 3 ( ξ , η ) = U 3 ( ξ , η ) k ( ξ , η ) = { [ comb ( ξ Δ , η Δ ) k ( ξ , η ) ] rect ( ξ Δ , η Δ ) } × k ( ξ , η ) .
U 4 ( ξ , η ) = { [ comb ( x Δ , y Δ ) P ( x , y ) ] [ sinc ( x Δ , y Δ ) ] } K ( x , y ) = { [ comb ( x Δ , y Δ ) P ( x , y ) ] [ sinc ( x Δ , y Δ ) ] } [ sin ( π Γ x ) sin ( π Γ y ) sinc ( x Γ , y Γ ) × comb ( x 2 Γ , y 2 Γ ) ] .

Metrics