Abstract

An architecture for implementing large scale holographic interconnections in photorefractive waveguides is described. Methods for controlling the hologram using unguided light are considered and experimentally demonstrated.

© 1991 Optical Society of America

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References

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  1. See, for example, R. G. Hunsperger, Integrated Optics: Theory and Technology (Springer-Verlag, Berlin, 1985).
  2. V. E. Wood, P. J. Cressman, R. L. Holman, C. M. Verber, “Photorefractive Effects in Waveguides,” in Photorefractive Materials and Their Applications II, P. Gunter, J.-P. Huignard, Eds. (Springer-Verlag, New York, 1989).
    [CrossRef]
  3. T. Jannson, “Information Capacity of Bragg Holograms in Planar Optics,” J. Opt. Soc. Am. 71, 342–347 (1981).
    [CrossRef]
  4. D. Psaltis, D. J. Brady, “A Photorefractive Integrated Optical Vector-matrix Multiplier,” Proc. Soc. Photo-Opt. Instrum. Eng. 835, 153–161 (1987).
  5. See, for example, D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1979).
  6. H. Kogelnik, “Coupled Wave Theory for Thick Hologram Gratings,” Bell Syst. Tech. J. 48, 2909–2947(1969).
  7. A. M. Glass, A. M. Johnson, D. H. Olson, W. Simpson, A. A. Ballman, “Four-wave Mixing in Semi-insulating InP and GaAs Using The Photorefractive Effect,” Appl. Phys. Lett. 44, 948–950 (1984).
    [CrossRef]

1987 (1)

D. Psaltis, D. J. Brady, “A Photorefractive Integrated Optical Vector-matrix Multiplier,” Proc. Soc. Photo-Opt. Instrum. Eng. 835, 153–161 (1987).

1984 (1)

A. M. Glass, A. M. Johnson, D. H. Olson, W. Simpson, A. A. Ballman, “Four-wave Mixing in Semi-insulating InP and GaAs Using The Photorefractive Effect,” Appl. Phys. Lett. 44, 948–950 (1984).
[CrossRef]

1981 (1)

1969 (1)

H. Kogelnik, “Coupled Wave Theory for Thick Hologram Gratings,” Bell Syst. Tech. J. 48, 2909–2947(1969).

Ballman, A. A.

A. M. Glass, A. M. Johnson, D. H. Olson, W. Simpson, A. A. Ballman, “Four-wave Mixing in Semi-insulating InP and GaAs Using The Photorefractive Effect,” Appl. Phys. Lett. 44, 948–950 (1984).
[CrossRef]

Brady, D. J.

D. Psaltis, D. J. Brady, “A Photorefractive Integrated Optical Vector-matrix Multiplier,” Proc. Soc. Photo-Opt. Instrum. Eng. 835, 153–161 (1987).

Cressman, P. J.

V. E. Wood, P. J. Cressman, R. L. Holman, C. M. Verber, “Photorefractive Effects in Waveguides,” in Photorefractive Materials and Their Applications II, P. Gunter, J.-P. Huignard, Eds. (Springer-Verlag, New York, 1989).
[CrossRef]

Glass, A. M.

A. M. Glass, A. M. Johnson, D. H. Olson, W. Simpson, A. A. Ballman, “Four-wave Mixing in Semi-insulating InP and GaAs Using The Photorefractive Effect,” Appl. Phys. Lett. 44, 948–950 (1984).
[CrossRef]

Holman, R. L.

V. E. Wood, P. J. Cressman, R. L. Holman, C. M. Verber, “Photorefractive Effects in Waveguides,” in Photorefractive Materials and Their Applications II, P. Gunter, J.-P. Huignard, Eds. (Springer-Verlag, New York, 1989).
[CrossRef]

Hunsperger, R. G.

See, for example, R. G. Hunsperger, Integrated Optics: Theory and Technology (Springer-Verlag, Berlin, 1985).

Jannson, T.

Johnson, A. M.

A. M. Glass, A. M. Johnson, D. H. Olson, W. Simpson, A. A. Ballman, “Four-wave Mixing in Semi-insulating InP and GaAs Using The Photorefractive Effect,” Appl. Phys. Lett. 44, 948–950 (1984).
[CrossRef]

Kogelnik, H.

H. Kogelnik, “Coupled Wave Theory for Thick Hologram Gratings,” Bell Syst. Tech. J. 48, 2909–2947(1969).

Marcuse, D.

See, for example, D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1979).

Olson, D. H.

A. M. Glass, A. M. Johnson, D. H. Olson, W. Simpson, A. A. Ballman, “Four-wave Mixing in Semi-insulating InP and GaAs Using The Photorefractive Effect,” Appl. Phys. Lett. 44, 948–950 (1984).
[CrossRef]

Psaltis, D.

D. Psaltis, D. J. Brady, “A Photorefractive Integrated Optical Vector-matrix Multiplier,” Proc. Soc. Photo-Opt. Instrum. Eng. 835, 153–161 (1987).

Simpson, W.

A. M. Glass, A. M. Johnson, D. H. Olson, W. Simpson, A. A. Ballman, “Four-wave Mixing in Semi-insulating InP and GaAs Using The Photorefractive Effect,” Appl. Phys. Lett. 44, 948–950 (1984).
[CrossRef]

Verber, C. M.

V. E. Wood, P. J. Cressman, R. L. Holman, C. M. Verber, “Photorefractive Effects in Waveguides,” in Photorefractive Materials and Their Applications II, P. Gunter, J.-P. Huignard, Eds. (Springer-Verlag, New York, 1989).
[CrossRef]

Wood, V. E.

V. E. Wood, P. J. Cressman, R. L. Holman, C. M. Verber, “Photorefractive Effects in Waveguides,” in Photorefractive Materials and Their Applications II, P. Gunter, J.-P. Huignard, Eds. (Springer-Verlag, New York, 1989).
[CrossRef]

Appl. Phys. Lett. (1)

A. M. Glass, A. M. Johnson, D. H. Olson, W. Simpson, A. A. Ballman, “Four-wave Mixing in Semi-insulating InP and GaAs Using The Photorefractive Effect,” Appl. Phys. Lett. 44, 948–950 (1984).
[CrossRef]

Bell Syst. Tech. J. (1)

H. Kogelnik, “Coupled Wave Theory for Thick Hologram Gratings,” Bell Syst. Tech. J. 48, 2909–2947(1969).

J. Opt. Soc. Am. (1)

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

D. Psaltis, D. J. Brady, “A Photorefractive Integrated Optical Vector-matrix Multiplier,” Proc. Soc. Photo-Opt. Instrum. Eng. 835, 153–161 (1987).

Other (3)

See, for example, D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1979).

See, for example, R. G. Hunsperger, Integrated Optics: Theory and Technology (Springer-Verlag, Berlin, 1985).

V. E. Wood, P. J. Cressman, R. L. Holman, C. M. Verber, “Photorefractive Effects in Waveguides,” in Photorefractive Materials and Their Applications II, P. Gunter, J.-P. Huignard, Eds. (Springer-Verlag, New York, 1989).
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Architecture for a holographic integrated optical vector–matrix multiplier.

Fig. 2
Fig. 2

Optical wave vectors of the coupled guided beams on the wave normal curve in the guided plane. Connecting grating wave vectors are shown as dashed lines.

Fig. 3
Fig. 3

Wave normal surface showing a grating wave vector and its associated degeneracy cone.

Fig. 4
Fig. 4

Projection of the wave normal surface onto the guided plane.

Fig. 5
Fig. 5

(a) Projection in the guided plane of the normal surface and a pair of unguided wave vectors. The grating wave vector and its degeneracy lines are also shown. A set of grating wave vectors in the guided plane and their associated degeneracy lines. The set shown interconnects three guided input beams with three guided output beams. (c) Grating wave vectors of (b) displaced along the degeneracy lines.

Fig. 6
Fig. 6

Projection in the guided plane of the end points of a set of unguided recording beams. The lines in the figure correspond to the grating wave vectors of Fig. 5. The grating wave vectors have been shifted off their degeneracy lines to allow recording with a single reference.

Fig. 7
Fig. 7

Architecture for controlling gratings in the guided plane using a single reference and an SLM.

Fig. 8
Fig. 8

Grating wave vectors recorded in the guided plane as a function of γ, the angle of rotation of the control grating. The gratings recorded in the plane due to the zeroth, first, and second orders of the control grating are shown.

Fig. 9
Fig. 9

Diffracted He–Ne signals at the output of a TI:LiNbO3 waveguide. The diffracting hologram was recorded using unguided Ar+ control beams consisting of a single reference and the diffracted orders of a Ronchi ruling.

Fig. 10
Fig. 10

Architecture for monolithic integration of active devices and photorefractive waveguides in GaAs.

Equations (32)

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Δ n ( r ) = g κ g exp [ j K g · r ) ,
K l m = k ( m ) - k ( l ) .
k ( l ) = k cos ( ϕ - l α ) z ^ - k sin ( ϕ + l α ) y ^ k [ cos ( ϕ ) - l α sin ( ϕ ) ] z ^ - k [ sin ( ϕ ) - l α cos ( ϕ ) ] y ^ ,
k ( m ) = k cos ( ϕ + m α ) z ^ + k sin ϕ + m α ) y ^ k [ cos ( ϕ ) - m α sin ( ϕ ) ] z ^ + k [ sin ( ϕ ) + m α cos ( ϕ ) ] y ^ .
E ( r ) = E ( x ) l Ψ l ( z ) exp [ j k ( l ) · ρ ] e ^ l + ɛ ( x ) m Φ m ( z ) exp [ j k ( m ) · ρ ] e ^ m ,
× × E - n 2 ( r ) k 2 E = 0 ,
l j k z ( l ) exp [ j k ( l ) · ρ ] ψ l ( z ) z + m j k z ( m ) exp [ j k ( m ) · ρ ] Φ m ( z ) z = g n o ( x ) k 2 κ g exp ( j K g · r ) × { l ψ l ( z ) exp [ j k ( l ) · ρ ] + m Φ m ( z ) exp [ j k ( m ) · ρ ] } ,
l j k z ( l ) exp [ j k ( l ) · ρ ] Ψ l ( z ) z + m j k z ( m ) exp [ j k ( m ) · ρ ] Ψ m ( z ) z = K g sin ( k g x d / 2 ) K g x d / 2 n 2 k 2 κ g exp ( j K g · ρ ) × [ l Ψ l ( z ) exp [ j k ( l ) · ρ ] + m Φ m ( z ) exp [ j k ( m ) · ρ ] ] .
exp { j [ k ( r ) - k ( s ) ] · ρ } d ρ = sin [ Δ k r s ( y ) L y / 2 ] Δ k r s ( y ) / 2 sin [ Δ k r s ( z ) L z / 2 ] Δ k r s ( z ) / 2 ,
α > λ 2 π n eff L y cos ϕ ,             λ 2 π n eff L z sin ϕ .
j k z ( m ) L y L z Φ m ( z ) z = g l sin [ Δ K g l m ( y ) L y / 2 ] Δ K g l m ( y ) / 2 × sin [ Δ K g l m ( z ) L z / 2 ] Δ K g l m ( z ) / 2 n 2 k 2 κ g Ψ l ( z ) ,
Δ K g l m ( y ) < π L y ,
Δ K g l m ( z ) < π L z .
j k z ( m ) Φ m ( z ) z = l n 2 k 2 κ l m Ψ l ( z ) ,
Φ = H ¯ ¯ Ψ ,
R 2 = A 2 sin 2 ϕ 2 λ 2 f 2 .
λ r 2 F 2 / δ > A ,
k = k r [ 1 - ( u 2 + v 2 ) 2 k r 2 ] x ^ + u y ^ + v z ^ = { k r [ 1 - ( u 2 + v 2 ) 2 k r 2 ] cos θ + u sin θ } x ^ + { u cos θ - k r [ 1 - ( u 2 + v 2 ) 2 k r 2 ] sin θ } y ^ + u z ^ ,
U ( x , y , z ) = exp [ j k r ( x cos θ - y sin θ ) ] × l m H l m exp [ - j k r ( x cos θ - y sin θ ) ( u l m 2 + v l m 2 ) 2 k r 2 ] × exp { j [ u l m ( y cos θ + x sin θ ) + v l m z ] } .
I ( x , y , z ) = exp ( - j 2 k r y sin θ ) l m H l m × exp [ - j k r ( x cos θ - y sin θ ) ( u l m 2 + v l m 2 ) 2 k r 2 ] × exp { j [ u l m ( y cos θ + x sin θ ) + v l m ] } + c . c
K l m = [ u l m sin θ - cos θ u l m 2 + u l m 2 2 k r ] x ^ - [ 2 k r sin θ - u l m cos θ - sin θ ( u l m 2 + v l m 2 ) 2 k r ] y ^ + v l m z ^
u l m = ( l + m ) α k cos ϕ cos θ , u l m = ( l - m ) α k sin ϕ ;
y = - z tan ϕ cos θ + 2 l α F λ r cos ϕ λ cos θ .
y = z tan ϕ cos θ + 2 m α F λ r cos ϕ λ cos θ .
| [ u l m sin θ - cos θ ( u l m 2 + v l m 2 ) 2 k r ] | < π d .
| ( k r r F sin θ + cos θ k r r 2 2 F 2 ) | < π d .
r < 2 π F k r d .
S < λ r F 2 d δ .
S = A λ r d ;
p ( n ) = k r 1 - n 2 k f 2 k r 2 x + n k f ξ ^ .
U ( x , y , z ) = n H n exp [ j p ( n ) · r ] .
l = n K f α k ( cos γ cos θ cos ϕ + sin γ sin ϕ ) , m = n K f α k ( cos γ cos θ cos ϕ - sin γ sin ϕ ) ,

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