Abstract

Simulating the positions of output beams under the assumption that a liquid-crystal display acts as a binary phase modulator reveals that the number of the outputs increases almost linearly with the square root of the number of pixels assigned to an input. This result is confirmed by experiments, and it is estimated that 1016 outputs can be obtained when the number of pixels is 700 × 700. Holographic switches with liquid-crystal displays are therefore suitable for large-scale switches.

© 1995 Optical Society of America

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References

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  1. R. Nagase, A. Himeno, K. Kato, M. Okuno, “Silica-based 8 × 8 optical-matrix switch module with hybrid integrated driving circuits,” in Digest of European Conference on Optical Communication (Convention of National Societies of Electrical Engineers of Western Europe, Montreux, Switzerland, 1993), Vol. 2, pp. 17–20.
  2. J. P. Herriau, A. Delboulbe, J. P. Huignard, G. Roosen, G. Pauliat, “Optical beam steering for fiber array using dynamic holography,” in Digest of European Conference on Optical Communication (Convention of National Societies of Electrical Engineers of Western Europe, Venice, 1985), Vol. 1, pp. 419–422.
  3. D. O. Harris, “Multichannel acousto-optic crossbar switch,” Appl. Opt. 30, 4245–4256 (1991).
    [CrossRef] [PubMed]
  4. P. Gunter, “Holography, coherent light amplification and optical phase conjugation with photorefractive materials,” Phys. Rep. 93, 200–299 (1982).
    [CrossRef]
  5. 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]
  6. H. Yamazaki, M. Yamaguchi, “4 × 4 free-space optical switching using real-time binary phase-only holograms generated by a liquid-crystal display,” Opt. Lett. 16, 1415–1417 (1991).
    [CrossRef] [PubMed]

1992 (1)

1991 (2)

1982 (1)

P. Gunter, “Holography, coherent light amplification and optical phase conjugation with photorefractive materials,” Phys. Rep. 93, 200–299 (1982).
[CrossRef]

Delboulbe, A.

J. P. Herriau, A. Delboulbe, J. P. Huignard, G. Roosen, G. Pauliat, “Optical beam steering for fiber array using dynamic holography,” in Digest of European Conference on Optical Communication (Convention of National Societies of Electrical Engineers of Western Europe, Venice, 1985), Vol. 1, pp. 419–422.

Gunter, P.

P. Gunter, “Holography, coherent light amplification and optical phase conjugation with photorefractive materials,” Phys. Rep. 93, 200–299 (1982).
[CrossRef]

Harris, D. O.

Herriau, J. P.

J. P. Herriau, A. Delboulbe, J. P. Huignard, G. Roosen, G. Pauliat, “Optical beam steering for fiber array using dynamic holography,” in Digest of European Conference on Optical Communication (Convention of National Societies of Electrical Engineers of Western Europe, Venice, 1985), Vol. 1, pp. 419–422.

Himeno, A.

R. Nagase, A. Himeno, K. Kato, M. Okuno, “Silica-based 8 × 8 optical-matrix switch module with hybrid integrated driving circuits,” in Digest of European Conference on Optical Communication (Convention of National Societies of Electrical Engineers of Western Europe, Montreux, Switzerland, 1993), Vol. 2, pp. 17–20.

Huignard, J. P.

J. P. Herriau, A. Delboulbe, J. P. Huignard, G. Roosen, G. Pauliat, “Optical beam steering for fiber array using dynamic holography,” in Digest of European Conference on Optical Communication (Convention of National Societies of Electrical Engineers of Western Europe, Venice, 1985), Vol. 1, pp. 419–422.

Kato, K.

R. Nagase, A. Himeno, K. Kato, M. Okuno, “Silica-based 8 × 8 optical-matrix switch module with hybrid integrated driving circuits,” in Digest of European Conference on Optical Communication (Convention of National Societies of Electrical Engineers of Western Europe, Montreux, Switzerland, 1993), Vol. 2, pp. 17–20.

Nagase, R.

R. Nagase, A. Himeno, K. Kato, M. Okuno, “Silica-based 8 × 8 optical-matrix switch module with hybrid integrated driving circuits,” in Digest of European Conference on Optical Communication (Convention of National Societies of Electrical Engineers of Western Europe, Montreux, Switzerland, 1993), Vol. 2, pp. 17–20.

Okuno, M.

R. Nagase, A. Himeno, K. Kato, M. Okuno, “Silica-based 8 × 8 optical-matrix switch module with hybrid integrated driving circuits,” in Digest of European Conference on Optical Communication (Convention of National Societies of Electrical Engineers of Western Europe, Montreux, Switzerland, 1993), Vol. 2, pp. 17–20.

Pauliat, G.

J. P. Herriau, A. Delboulbe, J. P. Huignard, G. Roosen, G. Pauliat, “Optical beam steering for fiber array using dynamic holography,” in Digest of European Conference on Optical Communication (Convention of National Societies of Electrical Engineers of Western Europe, Venice, 1985), Vol. 1, pp. 419–422.

Roosen, G.

J. P. Herriau, A. Delboulbe, J. P. Huignard, G. Roosen, G. Pauliat, “Optical beam steering for fiber array using dynamic holography,” in Digest of European Conference on Optical Communication (Convention of National Societies of Electrical Engineers of Western Europe, Venice, 1985), Vol. 1, pp. 419–422.

Yamaguchi, M.

Yamazaki, H.

Appl. Opt. (1)

Opt. Lett. (2)

Phys. Rep. (1)

P. Gunter, “Holography, coherent light amplification and optical phase conjugation with photorefractive materials,” Phys. Rep. 93, 200–299 (1982).
[CrossRef]

Other (2)

R. Nagase, A. Himeno, K. Kato, M. Okuno, “Silica-based 8 × 8 optical-matrix switch module with hybrid integrated driving circuits,” in Digest of European Conference on Optical Communication (Convention of National Societies of Electrical Engineers of Western Europe, Montreux, Switzerland, 1993), Vol. 2, pp. 17–20.

J. P. Herriau, A. Delboulbe, J. P. Huignard, G. Roosen, G. Pauliat, “Optical beam steering for fiber array using dynamic holography,” in Digest of European Conference on Optical Communication (Convention of National Societies of Electrical Engineers of Western Europe, Venice, 1985), Vol. 1, pp. 419–422.

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Figures (11)

Fig. 1
Fig. 1

Holographic switch with an LCD: (a) schematic diagram, (b) determination of an output position by the angle that the signal beams are diffracted by the holograms.

Fig. 2
Fig. 2

Active-matrix LCD: (a) structure, (b) simplified model used for calculation.

Fig. 3
Fig. 3

Phase hologram written on the LCD.

Fig. 4
Fig. 4

Arrangement of the output beams when the value of b is constant.

Fig. 5
Fig. 5

Relationship between the number of outputs and the square root Q of the number of pixels assigned to an input.

Fig. 6
Fig. 6

Experimental results of sequential switching of the output light spot to each of 72 positions.

Fig. 7
Fig. 7

Loss distribution of the 1 × 72 holographic switch.

Fig. 8
Fig. 8

Definition of the width of the output light determined by the hologram.

Fig. 9
Fig. 9

Fourier transform of the hologram pattern approximated by use of Eq. (6).

Fig. 10
Fig. 10

Result of calculating how the output peak moves as the value of a changes from −1 to 1 when b = 2 and Q = 80: (a) results calculated by use of Eq. (5), that is, without the approximation int(am) = am; (b) results calculated by use of Eq. (6), that is, with the approximation.

Fig. 11
Fig. 11

Intensity distribution on the parallelogram ABCD in Fig. 9 calculated for a = 0.6, b = 3, and Q = 80: (a) without the approximation int(am) = am, (b) with the approximation.

Tables (1)

Tables Icon

Table 1 Available Values of b for Various Values of the Square Root Q of the Number of Pixels Assigned to an Input

Equations (30)

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n 1 = int ( a m ) + 2 l b + i ,
n 2 = int ( a m ) + ( 2 l + 1 ) b + i ,
h ( x , y ) = m = m 0 m 0 l = l 0 l 0 i = 0 b 1 rect ( x 2 d m 2 c d ) × rect ( y 2 d n 1 2 c d ) exp ( j θ ) + m = m 0 m 0 l = l 0 l 0 i = 0 b 1 rect ( x 2 d m 2 c d ) × rect ( y 2 d n 2 2 c d ) exp [ j ( θ + π ) ] ,
H ( u , υ ) = h ( x , y ) exp [ j ( x u + y υ ) ] d x d y , u = ( 2 π / λ f ) X , υ = ( 2 π / λ f ) Y ,
H ( u , υ ) = 2 sin ( c d u ) u 2 sin ( c d υ ) υ sin ( b d υ ) sin ( d υ ) sin [ 2 b d ( 2 l 0 + 1 ) υ ] sin ( 2 b d υ ) × 2 cos ( b d υ + π / 2 ) exp { j [ ( 2 b 1 ) d υ + θ + π / 2 ] } × m = m 0 m 0 exp { j 2 d [ m u + int ( a m ) υ ] } .
H ( u , υ ) = 2 sin ( c d u ) u 2 sin ( c d υ ) υ sin ( b d υ ) sin ( d υ ) sin [ 2 b d ( 2 l 0 + 1 ) υ ] sin ( 2 b d υ ) × 2 cos ( b d υ + π / 2 ) exp { j [ ( 2 b 1 ) d υ + θ + π / 2 ] } × sin [ d ( 2 m 0 + 1 ) ( u + a υ ) ] sin [ d ( u + a υ ) ] .
( u , υ ) = [ π k 1 d a π ( 2 k 2 1 ) 2 b d , π ( 2 k 2 1 ) 2 b d ] ,
( u , υ ) = ( a π / 2 b d , π / 2 b d ) .
L = π / b d .
D 0 = 8 / d Q .
D 1 = π ( 2 l 0 + 1 ) d l 0 ( 2 m 0 + 1 ) .
Q < 2 m 0 + 1 ,
Q < 2 b ( 2 l 0 + 1 ) .
m 0 = int [ ( Q + 1 ) / 2 ] ,
l 0 = int ( Q / 4 b + 1 / 2 ) .
N t = 2 int ( π Q / 8 b ) , D 0 D 1 ,
N t = 2 int [ l 0 ( 2 m 0 + 1 ) b ( 2 l 0 + 1 ) ] , D 0 < D 1 .
D 1 = π ( 2 l 0 + 1 ) d l 0 ( 2 m 0 + 1 ) .
h ( x , y ) = m = m 0 m 0 n = 2 b l 0 2 b ( l 0 + 1 ) 1 rect ( x 2 d m 2 c d ) × rect ( y 2 d n 2 c d ) exp ( j θ ) .
H ( u , υ ) = 2 sin ( c d u ) u 2 sin ( c d υ ) υ sin [ d ( 2 m 0 + 1 ) u ] sin ( d u ) × sin [ 2 b d ( 2 l 0 + 1 ) υ ] sin ( d υ ) exp { j [ ( 2 b 1 ) d υ + θ ] } .
L u = 2 π d ( 2 m 0 + 1 ) ,
L υ = 2 π 2 b d ( 2 l 0 + 1 ) .
S υ = 2 π 2 b d ( 2 l 0 + 1 ) .
υ b s 1 > D 0 ,
2 b s int ( π Q / 16 ) .
| υ b s k 2 υ b 1 | > D 0 .
| ( 2 k 2 1 ) / b s 1 / b | > 16 / π Q ,
υ b s k 2 υ 2 1 > D 0 .
1 k 2 int ( 8 b s / π Q + b s / 4 + 1 / 2 ) + 1 .
π / 4 d D 0 / 2 u π / 4 d + D 0 / 2 , π / 4 d D 0 / 2 υ π / 4 d + D 0 / 2 .

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