Abstract

We present the theory of operation of a ring-channel waveguide coupled to two line channels in which the ring has an optical-power-dependent refractive index. The bistability of the device is analyzed in terms of the geometry of the ring, the nonlinear properties of the ring or the cladding, the coupling coefficients, and the optical losses. A numerical example demonstrates that when InSb is used at a wavelength of 5 μm, switching can take place with a power level of 1.5 μW.

© 1981 Optical Society of America

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References

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  1. R. Bonifacio, L. A. Lugiato, Opt. Commun. 19, 172 (1976).
    [CrossRef]
  2. R. Bonifacio, L. A. Lugiato, Lett. Nuovo Cimento 21, 517 (1978).
    [CrossRef]
  3. R. Bonifacio, M. Gronchi, L. A. Lugiato, Nuovo Cimento 53B, 311 (1979).
  4. G. P. Agrawal, Appl. Phys. Lett. 38, 505 (1981).
    [CrossRef]
  5. D. A. B. Miller, S. D. Smith, C. T. Seaton, IEEE J. Quantum Electron. QE-17, 312 (1980).
  6. J. Haavisto, G. A. Pajer, Opt. Lett. 5, 510 (1980).
    [CrossRef] [PubMed]
  7. E. A. J. Marcatili, Bell Syst. Tech. J. 48, 2071 (1969).
  8. D. Marcuse, Theory of Dielectric Waveguides (Academic, New York, 1974).
  9. H. M. Gibbs, S. L. McCall, T. N. C. Venkatesan, Appl. Phys. Lett. 36, 1135 (1976).
    [CrossRef]

1981 (1)

G. P. Agrawal, Appl. Phys. Lett. 38, 505 (1981).
[CrossRef]

1980 (2)

D. A. B. Miller, S. D. Smith, C. T. Seaton, IEEE J. Quantum Electron. QE-17, 312 (1980).

J. Haavisto, G. A. Pajer, Opt. Lett. 5, 510 (1980).
[CrossRef] [PubMed]

1979 (1)

R. Bonifacio, M. Gronchi, L. A. Lugiato, Nuovo Cimento 53B, 311 (1979).

1978 (1)

R. Bonifacio, L. A. Lugiato, Lett. Nuovo Cimento 21, 517 (1978).
[CrossRef]

1976 (2)

R. Bonifacio, L. A. Lugiato, Opt. Commun. 19, 172 (1976).
[CrossRef]

H. M. Gibbs, S. L. McCall, T. N. C. Venkatesan, Appl. Phys. Lett. 36, 1135 (1976).
[CrossRef]

1969 (1)

E. A. J. Marcatili, Bell Syst. Tech. J. 48, 2071 (1969).

Agrawal, G. P.

G. P. Agrawal, Appl. Phys. Lett. 38, 505 (1981).
[CrossRef]

Bonifacio, R.

R. Bonifacio, M. Gronchi, L. A. Lugiato, Nuovo Cimento 53B, 311 (1979).

R. Bonifacio, L. A. Lugiato, Lett. Nuovo Cimento 21, 517 (1978).
[CrossRef]

R. Bonifacio, L. A. Lugiato, Opt. Commun. 19, 172 (1976).
[CrossRef]

Gibbs, H. M.

H. M. Gibbs, S. L. McCall, T. N. C. Venkatesan, Appl. Phys. Lett. 36, 1135 (1976).
[CrossRef]

Gronchi, M.

R. Bonifacio, M. Gronchi, L. A. Lugiato, Nuovo Cimento 53B, 311 (1979).

Haavisto, J.

Lugiato, L. A.

R. Bonifacio, M. Gronchi, L. A. Lugiato, Nuovo Cimento 53B, 311 (1979).

R. Bonifacio, L. A. Lugiato, Lett. Nuovo Cimento 21, 517 (1978).
[CrossRef]

R. Bonifacio, L. A. Lugiato, Opt. Commun. 19, 172 (1976).
[CrossRef]

Marcatili, E. A. J.

E. A. J. Marcatili, Bell Syst. Tech. J. 48, 2071 (1969).

Marcuse, D.

D. Marcuse, Theory of Dielectric Waveguides (Academic, New York, 1974).

McCall, S. L.

H. M. Gibbs, S. L. McCall, T. N. C. Venkatesan, Appl. Phys. Lett. 36, 1135 (1976).
[CrossRef]

Miller, D. A. B.

D. A. B. Miller, S. D. Smith, C. T. Seaton, IEEE J. Quantum Electron. QE-17, 312 (1980).

Pajer, G. A.

Seaton, C. T.

D. A. B. Miller, S. D. Smith, C. T. Seaton, IEEE J. Quantum Electron. QE-17, 312 (1980).

Smith, S. D.

D. A. B. Miller, S. D. Smith, C. T. Seaton, IEEE J. Quantum Electron. QE-17, 312 (1980).

Venkatesan, T. N. C.

H. M. Gibbs, S. L. McCall, T. N. C. Venkatesan, Appl. Phys. Lett. 36, 1135 (1976).
[CrossRef]

Appl. Phys. Lett. (2)

G. P. Agrawal, Appl. Phys. Lett. 38, 505 (1981).
[CrossRef]

H. M. Gibbs, S. L. McCall, T. N. C. Venkatesan, Appl. Phys. Lett. 36, 1135 (1976).
[CrossRef]

Bell Syst. Tech. J. (1)

E. A. J. Marcatili, Bell Syst. Tech. J. 48, 2071 (1969).

IEEE J. Quantum Electron. (1)

D. A. B. Miller, S. D. Smith, C. T. Seaton, IEEE J. Quantum Electron. QE-17, 312 (1980).

Lett. Nuovo Cimento (1)

R. Bonifacio, L. A. Lugiato, Lett. Nuovo Cimento 21, 517 (1978).
[CrossRef]

Nuovo Cimento (1)

R. Bonifacio, M. Gronchi, L. A. Lugiato, Nuovo Cimento 53B, 311 (1979).

Opt. Commun. (1)

R. Bonifacio, L. A. Lugiato, Opt. Commun. 19, 172 (1976).
[CrossRef]

Opt. Lett. (1)

Other (1)

D. Marcuse, Theory of Dielectric Waveguides (Academic, New York, 1974).

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Figures (2)

Fig. 1
Fig. 1

Geometry of the ring-channel waveguide that is coupled to two line channels.

Fig. 2
Fig. 2

Characteristics of the nonlinear ring-channel waveguide for δ = π/4 and δ = π/2.

Equations (11)

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X = A Y [ 1 + B sin 2 ( δ + C ) ] .
A = ( 1 R ) 2 κ 4 exp ( α d ) ,
B = 4 R / ( 1 R ) 2 ,
C = K d Δ β / 2 .
Δ β = c 0 2 P n ( x , y ) n 2 , E | E E * | 2 d x d y .
E ( x , y , z ) = E 0 f ( x , y , z ) ,
H ( x , y , z ) = E 0 g ( x , y , z ) .
Δ β = β c 2 0 2 P n ( x , y ) n 2 , I | f | 4 d x d y / [ ( f × g ) ê z d x d y ] 2 ,
P ring = Y κ 2 exp ( α d ) .
Δ β = n 2 , I P / area ,
C = η K d n 2 , I exp ( α d ) / ( 2 λ 2 κ 2 ) .

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