Abstract

A new technique for coding and decoding of optical signals through the use of polarization is described. In this technique the concept of coding is translated to polarization. In other words, coding is done in such a way that each code represents a unique polarization. This is done by implementing a binary pattern on a spatial light modulator in such a way that the reflected light has the required polarization. Decoding is done by the detection of the received beam’s polarization. By linking the concept of coding to polarization we can use each of these concepts in measuring the other one, attaining some gains. In this paper the construction of a simple point-to-point communication where coding and decoding is done through polarization will be discussed.

© 2008 Optical Society of America

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References

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  1. “Optical multiple access networks,” IEEE Network 3, 31-39(1989).
  2. “Lightwave systems and components,” IEEE Commun. Mag. 27, 20-26 (1989).
  3. J. A. Salehi, A. M. Weiner, and J. P. Heritage, “Coherent ultrashort light pulse code-division multiple access communication systems,” J. Lightwave Technol. 8, 478-491 (1990).
    [CrossRef]
  4. P. R. Prucnal, M. A. Santoro, and T. R. Fan, “Spread spectrum fiber optic local area network using optical processing,” J. Lightwave Technol. 4, 547-554 (1986).
    [CrossRef]
  5. J. A. Salehi and E. G. Paek, “Holographic CDMA,” IEEE Trans. Commun. 43, 2434-2438 (1995).
    [CrossRef]
  6. K. Takasago, M. Takekawa, A. Shirakawa, and F. Kannari, “Spatial phase code-division multiple-access system with multiplexed Fourier holography switching for reconfigurable optical interconnection,” Appl. Opt. 39, 2278-2286 (2000).
    [CrossRef]
  7. K. Kitayama, M. Nakamura, Y. Igasaki, and K. Kaneda, “Image fiber-optic two-dimensional parallel links based upon optical space-CDMA: experiment,” J. Lightwave Technol. 15, 202-212 (1997).
    [CrossRef]
  8. A. A. Hassan, J. Hershey, and N. A. Riza, “Spatial optical CDMA,” IEEE J. Select. Areas Commun. 13, 609-613 (1995).
    [CrossRef]
  9. M. Abtahi, J. A. Salehi, and B. Cabon, “Holographic CDMA: a possible application of holography in infrared wireless communication systems,” Proc. SPIE 4149, 196-204 (2000).
    [CrossRef]
  10. M. A. A. Neil, T. Wilson, and R. Juskaitis, “A wavefront generation for complex pupil function synthesis and point spread function engineering,” J. Microsc. 197, 197-219 (2000).
    [CrossRef]
  11. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).
  12. W. H. Lee, “Computer generated holograms: techniques and applications,”in Progress in Optics (North-Holland, 1978), Vol. 16, pp. 21-231.
    [CrossRef]
  13. F. Massoumian, R. Juskaitis, M. A. A. Neil, and T. Wilson, “Quantitative polarized light microscopy,” J. Microsc. 209, 13-22 (2003).
    [CrossRef] [PubMed]
  14. R. C. Jones, “New calculus for the treatment of optical systems,” J. Opt. Soc. Am. 31, 488-493 (1941).
    [CrossRef]
  15. F. Zernike, “How I discovered phase contrast,” Science 121, 345-349 (1955).
    [CrossRef] [PubMed]
  16. The authors are preparing a paper entitled “Spread-space CDMA through polarization using a spatial light modulator,” to be submitted to Appl. Opt.
    [PubMed]

2003

F. Massoumian, R. Juskaitis, M. A. A. Neil, and T. Wilson, “Quantitative polarized light microscopy,” J. Microsc. 209, 13-22 (2003).
[CrossRef] [PubMed]

2000

M. Abtahi, J. A. Salehi, and B. Cabon, “Holographic CDMA: a possible application of holography in infrared wireless communication systems,” Proc. SPIE 4149, 196-204 (2000).
[CrossRef]

M. A. A. Neil, T. Wilson, and R. Juskaitis, “A wavefront generation for complex pupil function synthesis and point spread function engineering,” J. Microsc. 197, 197-219 (2000).
[CrossRef]

K. Takasago, M. Takekawa, A. Shirakawa, and F. Kannari, “Spatial phase code-division multiple-access system with multiplexed Fourier holography switching for reconfigurable optical interconnection,” Appl. Opt. 39, 2278-2286 (2000).
[CrossRef]

1997

K. Kitayama, M. Nakamura, Y. Igasaki, and K. Kaneda, “Image fiber-optic two-dimensional parallel links based upon optical space-CDMA: experiment,” J. Lightwave Technol. 15, 202-212 (1997).
[CrossRef]

1995

A. A. Hassan, J. Hershey, and N. A. Riza, “Spatial optical CDMA,” IEEE J. Select. Areas Commun. 13, 609-613 (1995).
[CrossRef]

J. A. Salehi and E. G. Paek, “Holographic CDMA,” IEEE Trans. Commun. 43, 2434-2438 (1995).
[CrossRef]

1990

J. A. Salehi, A. M. Weiner, and J. P. Heritage, “Coherent ultrashort light pulse code-division multiple access communication systems,” J. Lightwave Technol. 8, 478-491 (1990).
[CrossRef]

1986

P. R. Prucnal, M. A. Santoro, and T. R. Fan, “Spread spectrum fiber optic local area network using optical processing,” J. Lightwave Technol. 4, 547-554 (1986).
[CrossRef]

1955

F. Zernike, “How I discovered phase contrast,” Science 121, 345-349 (1955).
[CrossRef] [PubMed]

1941

Abtahi, M.

M. Abtahi, J. A. Salehi, and B. Cabon, “Holographic CDMA: a possible application of holography in infrared wireless communication systems,” Proc. SPIE 4149, 196-204 (2000).
[CrossRef]

Cabon, B.

M. Abtahi, J. A. Salehi, and B. Cabon, “Holographic CDMA: a possible application of holography in infrared wireless communication systems,” Proc. SPIE 4149, 196-204 (2000).
[CrossRef]

Fan, T. R.

P. R. Prucnal, M. A. Santoro, and T. R. Fan, “Spread spectrum fiber optic local area network using optical processing,” J. Lightwave Technol. 4, 547-554 (1986).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

Hassan, A. A.

A. A. Hassan, J. Hershey, and N. A. Riza, “Spatial optical CDMA,” IEEE J. Select. Areas Commun. 13, 609-613 (1995).
[CrossRef]

Heritage, J. P.

J. A. Salehi, A. M. Weiner, and J. P. Heritage, “Coherent ultrashort light pulse code-division multiple access communication systems,” J. Lightwave Technol. 8, 478-491 (1990).
[CrossRef]

Hershey, J.

A. A. Hassan, J. Hershey, and N. A. Riza, “Spatial optical CDMA,” IEEE J. Select. Areas Commun. 13, 609-613 (1995).
[CrossRef]

Igasaki, Y.

K. Kitayama, M. Nakamura, Y. Igasaki, and K. Kaneda, “Image fiber-optic two-dimensional parallel links based upon optical space-CDMA: experiment,” J. Lightwave Technol. 15, 202-212 (1997).
[CrossRef]

Jones, R. C.

Juskaitis, R.

F. Massoumian, R. Juskaitis, M. A. A. Neil, and T. Wilson, “Quantitative polarized light microscopy,” J. Microsc. 209, 13-22 (2003).
[CrossRef] [PubMed]

M. A. A. Neil, T. Wilson, and R. Juskaitis, “A wavefront generation for complex pupil function synthesis and point spread function engineering,” J. Microsc. 197, 197-219 (2000).
[CrossRef]

Kaneda, K.

K. Kitayama, M. Nakamura, Y. Igasaki, and K. Kaneda, “Image fiber-optic two-dimensional parallel links based upon optical space-CDMA: experiment,” J. Lightwave Technol. 15, 202-212 (1997).
[CrossRef]

Kannari, F.

Kitayama, K.

K. Kitayama, M. Nakamura, Y. Igasaki, and K. Kaneda, “Image fiber-optic two-dimensional parallel links based upon optical space-CDMA: experiment,” J. Lightwave Technol. 15, 202-212 (1997).
[CrossRef]

Lee, W. H.

W. H. Lee, “Computer generated holograms: techniques and applications,”in Progress in Optics (North-Holland, 1978), Vol. 16, pp. 21-231.
[CrossRef]

Massoumian, F.

F. Massoumian, R. Juskaitis, M. A. A. Neil, and T. Wilson, “Quantitative polarized light microscopy,” J. Microsc. 209, 13-22 (2003).
[CrossRef] [PubMed]

Nakamura, M.

K. Kitayama, M. Nakamura, Y. Igasaki, and K. Kaneda, “Image fiber-optic two-dimensional parallel links based upon optical space-CDMA: experiment,” J. Lightwave Technol. 15, 202-212 (1997).
[CrossRef]

Neil, M. A. A.

F. Massoumian, R. Juskaitis, M. A. A. Neil, and T. Wilson, “Quantitative polarized light microscopy,” J. Microsc. 209, 13-22 (2003).
[CrossRef] [PubMed]

M. A. A. Neil, T. Wilson, and R. Juskaitis, “A wavefront generation for complex pupil function synthesis and point spread function engineering,” J. Microsc. 197, 197-219 (2000).
[CrossRef]

Paek, E. G.

J. A. Salehi and E. G. Paek, “Holographic CDMA,” IEEE Trans. Commun. 43, 2434-2438 (1995).
[CrossRef]

Prucnal, P. R.

P. R. Prucnal, M. A. Santoro, and T. R. Fan, “Spread spectrum fiber optic local area network using optical processing,” J. Lightwave Technol. 4, 547-554 (1986).
[CrossRef]

Riza, N. A.

A. A. Hassan, J. Hershey, and N. A. Riza, “Spatial optical CDMA,” IEEE J. Select. Areas Commun. 13, 609-613 (1995).
[CrossRef]

Salehi, J. A.

M. Abtahi, J. A. Salehi, and B. Cabon, “Holographic CDMA: a possible application of holography in infrared wireless communication systems,” Proc. SPIE 4149, 196-204 (2000).
[CrossRef]

J. A. Salehi and E. G. Paek, “Holographic CDMA,” IEEE Trans. Commun. 43, 2434-2438 (1995).
[CrossRef]

J. A. Salehi, A. M. Weiner, and J. P. Heritage, “Coherent ultrashort light pulse code-division multiple access communication systems,” J. Lightwave Technol. 8, 478-491 (1990).
[CrossRef]

Santoro, M. A.

P. R. Prucnal, M. A. Santoro, and T. R. Fan, “Spread spectrum fiber optic local area network using optical processing,” J. Lightwave Technol. 4, 547-554 (1986).
[CrossRef]

Shirakawa, A.

Takasago, K.

Takekawa, M.

Weiner, A. M.

J. A. Salehi, A. M. Weiner, and J. P. Heritage, “Coherent ultrashort light pulse code-division multiple access communication systems,” J. Lightwave Technol. 8, 478-491 (1990).
[CrossRef]

Wilson, T.

F. Massoumian, R. Juskaitis, M. A. A. Neil, and T. Wilson, “Quantitative polarized light microscopy,” J. Microsc. 209, 13-22 (2003).
[CrossRef] [PubMed]

M. A. A. Neil, T. Wilson, and R. Juskaitis, “A wavefront generation for complex pupil function synthesis and point spread function engineering,” J. Microsc. 197, 197-219 (2000).
[CrossRef]

Zernike, F.

F. Zernike, “How I discovered phase contrast,” Science 121, 345-349 (1955).
[CrossRef] [PubMed]

Appl. Opt.

IEEE J. Select. Areas Commun.

A. A. Hassan, J. Hershey, and N. A. Riza, “Spatial optical CDMA,” IEEE J. Select. Areas Commun. 13, 609-613 (1995).
[CrossRef]

IEEE Trans. Commun.

J. A. Salehi and E. G. Paek, “Holographic CDMA,” IEEE Trans. Commun. 43, 2434-2438 (1995).
[CrossRef]

J. Lightwave Technol.

K. Kitayama, M. Nakamura, Y. Igasaki, and K. Kaneda, “Image fiber-optic two-dimensional parallel links based upon optical space-CDMA: experiment,” J. Lightwave Technol. 15, 202-212 (1997).
[CrossRef]

J. A. Salehi, A. M. Weiner, and J. P. Heritage, “Coherent ultrashort light pulse code-division multiple access communication systems,” J. Lightwave Technol. 8, 478-491 (1990).
[CrossRef]

P. R. Prucnal, M. A. Santoro, and T. R. Fan, “Spread spectrum fiber optic local area network using optical processing,” J. Lightwave Technol. 4, 547-554 (1986).
[CrossRef]

J. Microsc.

M. A. A. Neil, T. Wilson, and R. Juskaitis, “A wavefront generation for complex pupil function synthesis and point spread function engineering,” J. Microsc. 197, 197-219 (2000).
[CrossRef]

F. Massoumian, R. Juskaitis, M. A. A. Neil, and T. Wilson, “Quantitative polarized light microscopy,” J. Microsc. 209, 13-22 (2003).
[CrossRef] [PubMed]

J. Opt. Soc. Am.

Proc. SPIE

M. Abtahi, J. A. Salehi, and B. Cabon, “Holographic CDMA: a possible application of holography in infrared wireless communication systems,” Proc. SPIE 4149, 196-204 (2000).
[CrossRef]

Science

F. Zernike, “How I discovered phase contrast,” Science 121, 345-349 (1955).
[CrossRef] [PubMed]

Other

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

W. H. Lee, “Computer generated holograms: techniques and applications,”in Progress in Optics (North-Holland, 1978), Vol. 16, pp. 21-231.
[CrossRef]

“Optical multiple access networks,” IEEE Network 3, 31-39(1989).

“Lightwave systems and components,” IEEE Commun. Mag. 27, 20-26 (1989).

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Figures (7)

Fig. 1
Fig. 1

Polarization ellipse.

Fig. 2
Fig. 2

Schematic diagram of the 4 f system used to generate wavefronts of arbitrary polarization.

Fig. 3
Fig. 3

Schematic diagram of the 4 f system used to generate wavefronts of arbitrary polarization with two incoming beams.

Fig. 4
Fig. 4

Structure of the transmission part (coding) of coding through polarization.

Fig. 5
Fig. 5

Schematic diagram of the rotating analyzer [13].

Fig. 6
Fig. 6

Schematic diagram of the lock-in detection circuit.

Fig. 7
Fig. 7

Simulation results: (a) Fourier transform of the x component of the electric field, E x , of the received code; (b) spatially filtered Fourier transform of the E x of the code; (c) inverse Fourier transform of the filtered Fourier transform of E x ; (d) Inverse Fourier transform of the filtered Fourier transform of E y .

Equations (29)

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ψ = 1 2 tan 1 ( 2 A B A 2 B 2 cos ( δ ) ) ,
a = [ 1 2 { ( A 2 + B 2 ) + [ A 4 + B 4 + 2 A 2 B 2 cos ( 2 δ ) ] 1 / 2 } ] 1 / 2 ,
b = [ 1 2 { ( A 2 + B 2 ) [ A 4 + B 4 + 2 A 2 B 2 cos ( 2 δ ) ] 1 / 2 } ] 1 / 2 ,
g ( r ) = { 1 for     | f ( r ) | < α ( r ) 1 for     | f ( r ) | > α ( r ) ,
g ( r ) = 4 π { α ( r ) 2 π 4 + sin ( α ( r ) ) cos ( ϕ ( r ) + τ . r ) + 1 2 sin ( 2 α ( r ) ) cos ( 2 [ ϕ ( r ) + τ . r ] ) + } = 2 π { α ( r ) π 2 + sin ( α ( r ) ) { exp [ i ( ϕ ( r ) + τ . r ) ] + exp [ i ( ϕ ( r ) + τ . r ) ] } + 1 2 sin ( 2 α ( r ) ) { exp [ 2 i ( ϕ ( r ) + τ . r ) ] + exp [ 2 i ( ϕ ( r ) + τ . r ) ] } + } .
G ( r 1 ) = 2 π { A ( r 1 ) π 2 δ ( r 1 ) + [ ϕ 1 ( τ + r 1 ) + ϕ 1 * ( τ r 1 ) ] + 1 2 [ ϕ 2 ( 2 τ + r 1 ) + ϕ 2 * ( 2 τ r 1 ) ] + } ,
f ( r ) = sin α ( r ) exp ( j ϕ ( r ) ) .
E = ( f 1 ( r ) f 2 ( r ) ) ,
f ( r ) = f 1 ( r ) exp ( i τ a . r ) + f 2 ( r ) exp ( i τ b . r ) ,
E 0 = ( exp ( i τ . r ) exp ( i τ . r ) ) ,
E 1 = ( F 1 ( r 1 τ a τ ) + F 2 ( r 1 τ b τ ) F 1 ( r 1 τ a + τ ) + F 2 ( r 1 τ b + τ ) ) .
| f 1 ( r ) | = sin α 1 ( r ) ,
| f 2 ( r ) | = sin α 2 ( r ) .
f 1 ( r ) = k 1 x ( k 1 x ) 2 + y 2 exp ( j δ 1 ) ,
f 2 ( r ) = k 2 y x 2 + ( k 2 y ) 2 exp ( j δ 2 ) ,
A = | f 1 ( r 2 ) | = k 1 r 2 x ( k 1 r 2 x ) 2 + r 2 y 2 .
δ = δ 1 δ 2 .
T ( ϕ ) = [ exp ( j ϕ / 2 ) 0 0 exp ( j ϕ / 2 ) ] ,
E = R ( 45 ° ) × T ( ϕ ) × R ( 45 ° ) × E 0 .
E = P × R ( 45 ° ) × T ( ϕ ) × R ( 45 ° ) × Q ( 1 / 4 ) × E 0 .
E = E x cos ω t + E y sin ω t .
I = E E * = A 2 cos 2 ω t + B 2 sin 2 ω t + A B cos ω t sin ω t exp ( j ( δ 1 δ 2 ) ) + A B sin ω t cos ω t exp ( j ( δ 1 δ 2 ) ) = A 2 + B 2 2 + A 2 B 2 2 cos 2 ω t + A B sin 2 ω t cos δ ,
A = 0.35 , B = 0.218 , δ = 0.55.
τ = [ π / 2 , π / 2 ] ,
τ a = [ π / 3 , 0 ] ,
τ b = [ 2 π / 3 , π ] .
f 1 ( r ) = 0.3736 x ( 0.3736 x ) 2 + y 2 exp ( j 0.8 ) ,
f 2 ( r ) = 0.2233 y x 2 + ( 0.2233 y ) 2 exp ( j ( 0.8 0.55 ) ) .
A = 0.346 , B = 0.217 , δ = 0.551 ,

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