Abstract

A holographic switch with a ferroelectric liquid-crystal spatial light modulator is proposed for large switching systems such as those used in subscriber networks. Preliminary experiments have achieved a one-input, 48-output switch. The relationship between the power of the control-light source and the number of outputs is calculated; the results agree well with the experiment. The calculation suggests that 10384-output switching can be obtained with a 25-mW control-light source. It should therefore be possible to control a large-scale switch with low-power control-light sources.

© 1995 Optical Society of America

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References

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  1. H. Yamazaki, M. Yamaguchi, “Experiments on a multichannel holographic optical switch with the use of a liquid-crystal display,” Opt. Lett. 17, 1228–1230 (1992).
    [CrossRef] [PubMed]
  2. E. Marom, N. Konforti, “Dynamic optical interconnections,” Opt. Lett. 12, 539–541 (1987).
    [CrossRef] [PubMed]
  3. D. C. O'Brien, R. J. Mears, T. D. Wilkinson, W. A. Crossland, “Dynamic holographic interconnects that use ferroelectric liquid-crystal spatial light modulators,” Appl. Opt. 33, 2795–2803 (1994).
    [CrossRef]
  4. S. Fukushima, T. Kurokawa, M. Ohno, “Real-time hologram construction and reconstruction using a high-resolution spatial light modulator,” Appl. Phys. Lett. 58, 787–789 (1991).
    [CrossRef]
  5. H. Dammann, K. Gortler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3,312–315 (1971).
    [CrossRef]
  6. S. Fukushima, T. Kurokawa, “Diffraction characteristics of ferroelectric liquid crystal grating,” Jpn. J. Appl. Phys. 33, 5747–5754 (1994).
    [CrossRef]

1994

S. Fukushima, T. Kurokawa, “Diffraction characteristics of ferroelectric liquid crystal grating,” Jpn. J. Appl. Phys. 33, 5747–5754 (1994).
[CrossRef]

D. C. O'Brien, R. J. Mears, T. D. Wilkinson, W. A. Crossland, “Dynamic holographic interconnects that use ferroelectric liquid-crystal spatial light modulators,” Appl. Opt. 33, 2795–2803 (1994).
[CrossRef]

1992

1991

S. Fukushima, T. Kurokawa, M. Ohno, “Real-time hologram construction and reconstruction using a high-resolution spatial light modulator,” Appl. Phys. Lett. 58, 787–789 (1991).
[CrossRef]

1987

1971

H. Dammann, K. Gortler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3,312–315 (1971).
[CrossRef]

Crossland, W. A.

Dammann, H.

H. Dammann, K. Gortler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3,312–315 (1971).
[CrossRef]

Fukushima, S.

S. Fukushima, T. Kurokawa, “Diffraction characteristics of ferroelectric liquid crystal grating,” Jpn. J. Appl. Phys. 33, 5747–5754 (1994).
[CrossRef]

S. Fukushima, T. Kurokawa, M. Ohno, “Real-time hologram construction and reconstruction using a high-resolution spatial light modulator,” Appl. Phys. Lett. 58, 787–789 (1991).
[CrossRef]

Gortler, K.

H. Dammann, K. Gortler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3,312–315 (1971).
[CrossRef]

Konforti, N.

Kurokawa, T.

S. Fukushima, T. Kurokawa, “Diffraction characteristics of ferroelectric liquid crystal grating,” Jpn. J. Appl. Phys. 33, 5747–5754 (1994).
[CrossRef]

S. Fukushima, T. Kurokawa, M. Ohno, “Real-time hologram construction and reconstruction using a high-resolution spatial light modulator,” Appl. Phys. Lett. 58, 787–789 (1991).
[CrossRef]

Marom, E.

Mears, R. J.

O'Brien, D. C.

Ohno, M.

S. Fukushima, T. Kurokawa, M. Ohno, “Real-time hologram construction and reconstruction using a high-resolution spatial light modulator,” Appl. Phys. Lett. 58, 787–789 (1991).
[CrossRef]

Wilkinson, T. D.

Yamaguchi, M.

Yamazaki, H.

Appl. Opt.

Appl. Phys. Lett.

S. Fukushima, T. Kurokawa, M. Ohno, “Real-time hologram construction and reconstruction using a high-resolution spatial light modulator,” Appl. Phys. Lett. 58, 787–789 (1991).
[CrossRef]

Jpn. J. Appl. Phys.

S. Fukushima, T. Kurokawa, “Diffraction characteristics of ferroelectric liquid crystal grating,” Jpn. J. Appl. Phys. 33, 5747–5754 (1994).
[CrossRef]

Opt. Commun.

H. Dammann, K. Gortler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3,312–315 (1971).
[CrossRef]

Opt. Lett.

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Figures (7)

Fig. 1
Fig. 1

Optical setup of the control system in a holographic switch with a FLC-SLM.

Fig. 2
Fig. 2

Schematic diagram of the proposed switch.

Fig. 3
Fig. 3

Determination of the output position when M is 7: (a) The positions where the plus first-order light can appear. The gray points show the plus first-order positions when one of the open shutters is in the bottom-right corner and the other is one of the other shutters. The white points show the plus first-order positions when the fixed shutter is in the bottom-left, the upper-left, or the upper-right corner. (b) The plus first-order light positions after the positions are eliminated where the minus first-order light is superimposed. (c) An example of higher-order positions (white points) when an output position (black point) is determined. (d) The plus first-order light positions (the output positions) after the positions are eliminated where higher-order light is superimposed, the number of which is 48.

Fig. 4
Fig. 4

Relationship between M and the number of outputs.

Fig. 5
Fig. 5

Experimental results for the relationship between the control-light power and the diffraction efficiency of the output light for the 1 × 48 switch. The power required for switching is calculated by use of Eq. (23).

Fig. 6
Fig. 6

Experimental results of sequentially switching the output light spot to each of 48 positions.

Fig. 7
Fig. 7

Relationship between the power of the control-light source and the number of outputs.

Equations (26)

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H ( u , v ) = h ( x , y ) exp [ j 2 π ( x u + y v ) ] d x d y , u = X λ f , v = Y λ f ,
g c ( x , y ) = A exp ( x 2 + y 2 r c 2 ) ,
d g ( x , y ) = h ( x , y ) comb ( x 2 d ) comb ( y 2 d ) ,
comb ( x ) = n = δ ( x n ) .
S 1 ( x , y ) = g c ( x , y ) h ( x , y ) comb ( x 2 d ) comb ( y 2 d ) .
S 2 ( u , v ) = G c ( u , v ) H ( u , v ) 4 d 2 comb ( 2 d u ) comb ( 2 d v ) = G c ( u , v ) H ( u , v ) m = n = × δ ( u m 2 d , v n 2 d ) ,
G c ( u , v ) = A π r c 2 exp [ π 2 r c 2 ( u 2 + v 2 ) ] .
S 2 ( u , v ) = G c ( u , v ) H 0 m = N N n = N N × δ ( u m 2 d , v n 2 d ) ,
S 3 ( u , v ) = G c ( u , v ) H 0 [ δ ( u m 1 2 d , v n 1 2 d ) + δ ( u m 2 2 d , v n 2 2 d ) ] ,
S 4 ( x , y ) = H 0 A exp ( x 2 + y 2 r c 2 ) × { exp [ j π d ( m 1 x + n 1 y ) ] + exp [ j π d ( m 2 x + n 2 y ) ] } .
I 4 ( X , Y ) = S 4 S 4 * = 2 H 0 2 A 2 exp [ 2 ( x 2 + y 2 ) r c 2 ] × { 1 + cos [ π d ( Δ m x + Δ n y ) ] } ,
Δ m = m 1 m 2 ,
Δ n = n 1 n 2 .
I 4 ( s , t ) = 2 H 0 2 A 2 exp [ 2 ( s 2 + t 2 ) r c 2 ] × { 1 + cos [ π d ( Δ m 2 + Δ n 2 ) 1 / 2 S ] } .
g s ( s , t ) = B exp ( s 2 + t 2 r s 2 ) ,
s 2 + t 2 r s 2 .
I 4 ( 0 , r s ) = T h ,
4 H 0 2 A 2 exp ( 2 r s 2 r c 2 ) = T h .
g SLM ( x , y ) = H 0 A exp [ x 2 + y 2 r c 2 j π d ( m 1 x + n 1 y ) ] .
P SLM = g SLM g SLM * d x d y = H 0 2 A 2 π r c 2 2 .
α P c = M 2 P SLM ,
M = 2 N + 1 .
P c = T h M 2 π r c 2 8 α exp ( 2 r s 2 r c 2 ) ,
M = odd [ ( 8 α P c T h π r c 2 ) 1 / 2 exp ( r s 2 r c 2 ) ] .
d P c d r c = T h M 2 π 4 α exp ( 2 r s 2 r c 2 ) ( r c 2 r s 2 r c ) .
r c = 2 r s .

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