Abstract

Based on the theory of information optics and binary optics a new method of achieving a perfect shuffle transform is reported by using a microblazed grating array. The field distribution at the output plane and the equations of period of the microblazed grating array are obtained. According to these equations, the technical design and fabricated parameters are accomplished and proposed. It is shown that the theoretical analysis accords well with the practical application in a sequence of fabrications and testing experiments. The conclusions of the theoretical analysis and the experiment are important and will significantly guide the realization of optical switching and optical interconnection by using micro-optical diffractive elements. It is proved that the micro-optical elements will play an important role in the field of optical networks and optical computing.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. S. Stone, "Parallel processing with the perfect shuffle," IEEE Trans. Comput. C-20, 153-161 (1971).
    [CrossRef]
  2. D. S. Parker, Jr., "Notes on shuffle/exchange type switching networks," IEEE Trans. Comput. C-29, 213-222 (1980).
    [CrossRef]
  3. A. W. Lohmann, "What classical optics can do for the digital optical computer," Appl. Opt. 25, 1543-1549 (1986).
    [CrossRef] [PubMed]
  4. A. W. Lohmann, W. Stork, and G. Stucke, "Optical perfect shuffle," Appl. Opt. 25, 1530-1531 (1986).
    [CrossRef] [PubMed]
  5. K. H. Brenner and A. Huang, "Optical implementation of the perfect shuffle interconnection," Appl. Opt. 27, 135-137 (1988).
    [CrossRef] [PubMed]
  6. G. E. Lohman and A. W. Lohmann, "Optical interconnection network utilizing diffraction grating," Opt. Eng. 27, 893-900 (1988).
  7. S. Bain, K. Xu, and J. Hong, "Optical perfect shuffle using Wollaston prisms," Appl. Opt. 30, 173-174 (1991).
    [CrossRef]
  8. G. Eichmann and Y. Li, "Compact optical generalized perfect shuffle," Appl. Opt. 26, 1167-1169 (1987).
    [CrossRef]
  9. C. W. Stirk, R. A. Athale, and M. W. Haney, "Folded perfect shuffle optical processor," Appl. Opt. 27, 202-203 (1988).
    [CrossRef] [PubMed]
  10. Y.-L. Sheng, "Light effective 2-D optical perfect shuffle using Fresnel mirrors," Appl. Opt. 28, 3290-3292 (1989).
    [CrossRef] [PubMed]

1991

1989

1988

1987

1986

1980

D. S. Parker, Jr., "Notes on shuffle/exchange type switching networks," IEEE Trans. Comput. C-29, 213-222 (1980).
[CrossRef]

1971

H. S. Stone, "Parallel processing with the perfect shuffle," IEEE Trans. Comput. C-20, 153-161 (1971).
[CrossRef]

Athale, R. A.

Bain, S.

Brenner, K. H.

Eichmann, G.

Haney, M. W.

Hong, J.

Huang, A.

Li, Y.

Lohman, G. E.

G. E. Lohman and A. W. Lohmann, "Optical interconnection network utilizing diffraction grating," Opt. Eng. 27, 893-900 (1988).

Lohmann, A. W.

Parker, D. S.

D. S. Parker, Jr., "Notes on shuffle/exchange type switching networks," IEEE Trans. Comput. C-29, 213-222 (1980).
[CrossRef]

Sheng, Y.-L.

Stirk, C. W.

Stone, H. S.

H. S. Stone, "Parallel processing with the perfect shuffle," IEEE Trans. Comput. C-20, 153-161 (1971).
[CrossRef]

Stork, W.

Stucke, G.

Xu, K.

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 (8)

Fig. 1
Fig. 1

Blazed grating with binary phase structure.

Fig. 2
Fig. 2

Eight-channel microblazed grating array performing PS transform.

Fig. 3
Fig. 3

Eight-channel microblazed grating array.

Fig. 4
Fig. 4

Experimental setup for performing PS transformation.

Fig. 5
Fig. 5

Schematic for PS transform using a microblazed grating array.

Fig. 6
Fig. 6

Transparent film of input signal.

Fig. 7
Fig. 7

Experimental result of PS transform using a microblazed grating array.

Fig. 8
Fig. 8

Structure of the runner.

Tables (1)

Tables Icon

Table 1 Analysis of Each Channel's Diffractive Efficiency and Cross Talk a

Equations (21)

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

k = { 2 k 2 k + 1 N if   0 2 k < N / 2 if   N / 2 k N ,
rect ( x 0 T ) k = 0 L 1 rect ( x 0 k T / L T / L ) exp ( j 2 π L k ) ,
t s ( x 0 ) = m δ ( x 0 m T ) { rect ( x 0 T ) k = 0 L - 1 rect ( x 0 k T / L T / L ) × exp ( j 2 π L k ) } ,
U ( x , y ) = 1 j λ z  exp ( j k z ) exp [ j k 2 z ( x 2 + y 2 ) ] × U 0 ( x 0 , y 0 ) exp [ j k 2 z ( x 0 2 + y 0 2 ) ] × exp [ j 2 π λ z ( x 0 x + y 0 y ) ] d x 0 d y 0 ,
t s ( x ) = 1 j λ z  exp ( j k z ) exp ( j k 2 z x 2 ) t s ( x 0 ) exp ( j k 2 z x 0 2 ) × exp ( j 2 π λ z x 0 x ) d x 0 = 1 j λ z  exp ( j k z ) exp ( j k 2 z x 2 ) F { t s ( x 0 ) exp ( j k 2 z x 0 2 ) } ,
F { t s ( x 0 ) exp ( j k 2 z x 0 2 ) } = F { t s ( x 0 ) } F { exp ( j k 2 z x 0 2 ) } ,
F { t s ( x 0 ) } = m δ ( f m T ) exp ( j 2 π f T L ) × ( 1 L ) sin ( π f T / L ) π f T / L × k = 0 L 1 exp [ j 2 π k T L ( 1 T f ) ] ,
F { exp ( j k 2 z x 0 2 ) } = - exp ( j π λ z x 0 2 ) × exp ( - j 2 π f x 0 ) d x 0 = λ z exp ( j π 4 ) exp ( - j π z λ f 2 ) ,
F { t s ( x 0 ) exp ( j k 2 z x 0 2 ) } = λ z L  exp ( j π 4 ) exp ( - j 2 π f T L ) × exp [ - j π ( L 1 ) T L ( f 1 T ) ] × sin ( π f T L ) π f T L sin [ π T ( f 1 T ) ] sin [ π T 1 L ( f 1 T ) ] × m exp [ j π λ z ( f m T ) 2 ] .
t s ( x ) = 1 j λ z  exp ( j k z ) exp ( j k 2 z x 2 ) λ z L  exp ( j π 4 ) × exp ( - j 2 π x λ z T L ) exp [ - j π ( L 1 ) T L ( x λ z 1 T ) ] × sin ( π x λ z T L ) π x λ z T L sin [ π T ( x λ z 1 T ) ] sin [ π T 1 L ( x λ z 1 T ) ] × m exp [ j π λ z ( x λ z m T ) 2 ] .
U s ( x 0 ) = n = 0 2 δ ( x 0 n D ) rect ( x 0 D / 2 D ) ,
t s ( x ) = 1 j λ z exp ( j k z ) exp ( j k 2 z x 2 ) × F { U s ( x 0 ) t s ( x 0 ) exp ( j k 2 z x 2 ) } ,
F { U s ( x 0 ) t s ( x 0 ) exp ( j k 2 z x 2 ) } = F { U s ( x 0 ) } F { t s ( x 0 ) exp ( j k 2 z x 2 ) } ,
F { U s ( x 0 ) } = n δ ( f n D ) sin   c ( D f ) exp ( - j 2 π f D 2 ) .
F { U s ( x 0 ) t s ( x 0 ) exp ( j k 2 z x 2 ) } = λ z L  exp ( j π 4 ) sin   c ( D f ) exp ( j 2 π f D 2 ) n exp [ - j 2 π ( f n D ) T L ] exp [ - j π ( L 1 ) T L ( f n D 1 T ) ] × sin [ π ( f - n D ) T L ] π ( f - n D ) T L sin [ π T ( f n D 1 T ) ] sin [ π T 1 L ( f n D 1 T ) ] m exp [ - j π λ z ( f n D m T ) 2 ] .
t s ( x ) = 1 j λ z  exp ( j k z ) exp ( j k 2 z x 2 ) λ z L  exp ( j π 4 ) sin   c ( D x λ z ) × exp ( j 2 π x λ z D 2 ) n { exp [ - j 2 π ( x λ z n D ) T L ] × exp [ - j π ( L 1 ) T L ( x λ z n D 1 T ) ] × sin [ π ( x λ z - n D ) T L ] π ( x λ z - n D ) T L sin [ π T ( x λ z n D 1 T ) ] sin [ π T 1 L ( x λ z n D 1 T ) ] × m exp [ - j π λ z ( x λ z n D m T ) 2 ] } .
I ( x ) = 1 L λ z  sin   c 2 ( D x λ z ) | n { exp [ - j 2 π ( x λ z n D ) T L ] × exp [ - j π ( L 1 ) T L ( x λ z n D 1 T ) ] × sin [ π ( x λ z - n D ) T L ] π ( x λ z - n D ) T L sin [ π T ( x λ z n D 1 T ) ] sin [ π T 1 L ( x λ z n D 1 T ) ] × m exp [ - j π λ z ( x λ z n D m T ) 2 ] } | 2 .
x λ z = n D + 1 T .
λ z T = 3 D T 4 = λ z 3 D ;
( 1 D + 1 T ) λ z = 2 D Σ , T 3 = λ z D 2 D 2 λ z ;
( 2 D + 1 T ) λ z = D Σ , T 2 = λ z D D 2 2 λ z .

Metrics