Abstract

A treatment of a channel waveguide with a nonlinear, Kerr-type substrate is presented. A modified effective-index method was used to calculate mode indices and electric field distributions for the nonlinear waves.

© 1987 Optical Society of America

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References

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  1. G. I. Stegeman, C. T. Seaton, W. M. Kethenington, in Nonlinear Optics: Materials and Devices, C. Flytzanis, J. L. Oudar, eds. (Springer-Verlag, Berlin, 1986).
  2. H. M. Gibbs, P. Mandel, N. Peyghambarian, S. D. Smith, eds., Optical Bistability III (Springer-Verlag, Berlin, 1986).
    [CrossRef]
  3. H. Haus, N. A. Whitaker, M. C. Gabriel, in Integrated Optical Circuit Engineering II, S. Sriram, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 578, 122 (1985).
  4. R. Hoffe, J. Chrostowski, Opt. Commun. 57, 34 (1986).
    [CrossRef]
  5. D. F. Clark, I. Andonovic, B. Culshaw, Opt. Lett. 11, 540 (1986).
    [CrossRef] [PubMed]
  6. P. Li, Kam Wa, P. N. Robson, J. P. R. David, G. Hill, P. Mistry, M. A. Pate, J. S. Roberts, Electron. Lett. 22, 1129 (1986).
    [CrossRef]
  7. G. B. Hocker, W. K. Burns, Appl. Opt. 16, 113 (1977).
    [CrossRef] [PubMed]
  8. S. Patela, H. Jerominek, C. Delisle, R. Tremblay, in Optical Chaos, J. Chrostowski, N. Abraham, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 667, 115 (1986);J. Appl. Phys. 60, 1591 (1986).
  9. R. K. Varishney, M. A. Nehme, R. Srivastava, R. V. Ramaswamy, Appl. Opt. 21, 3899 (1986).
    [CrossRef]
  10. D. J. Robbins, Opt. Commun. 47, 309 (1983).
    [CrossRef]

1986 (5)

R. Hoffe, J. Chrostowski, Opt. Commun. 57, 34 (1986).
[CrossRef]

D. F. Clark, I. Andonovic, B. Culshaw, Opt. Lett. 11, 540 (1986).
[CrossRef] [PubMed]

P. Li, Kam Wa, P. N. Robson, J. P. R. David, G. Hill, P. Mistry, M. A. Pate, J. S. Roberts, Electron. Lett. 22, 1129 (1986).
[CrossRef]

S. Patela, H. Jerominek, C. Delisle, R. Tremblay, in Optical Chaos, J. Chrostowski, N. Abraham, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 667, 115 (1986);J. Appl. Phys. 60, 1591 (1986).

R. K. Varishney, M. A. Nehme, R. Srivastava, R. V. Ramaswamy, Appl. Opt. 21, 3899 (1986).
[CrossRef]

1985 (1)

H. Haus, N. A. Whitaker, M. C. Gabriel, in Integrated Optical Circuit Engineering II, S. Sriram, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 578, 122 (1985).

1983 (1)

D. J. Robbins, Opt. Commun. 47, 309 (1983).
[CrossRef]

1977 (1)

Andonovic, I.

Burns, W. K.

Chrostowski, J.

R. Hoffe, J. Chrostowski, Opt. Commun. 57, 34 (1986).
[CrossRef]

Clark, D. F.

Culshaw, B.

David, J. P. R.

P. Li, Kam Wa, P. N. Robson, J. P. R. David, G. Hill, P. Mistry, M. A. Pate, J. S. Roberts, Electron. Lett. 22, 1129 (1986).
[CrossRef]

Delisle, C.

S. Patela, H. Jerominek, C. Delisle, R. Tremblay, in Optical Chaos, J. Chrostowski, N. Abraham, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 667, 115 (1986);J. Appl. Phys. 60, 1591 (1986).

Gabriel, M. C.

H. Haus, N. A. Whitaker, M. C. Gabriel, in Integrated Optical Circuit Engineering II, S. Sriram, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 578, 122 (1985).

Haus, H.

H. Haus, N. A. Whitaker, M. C. Gabriel, in Integrated Optical Circuit Engineering II, S. Sriram, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 578, 122 (1985).

Hill, G.

P. Li, Kam Wa, P. N. Robson, J. P. R. David, G. Hill, P. Mistry, M. A. Pate, J. S. Roberts, Electron. Lett. 22, 1129 (1986).
[CrossRef]

Hocker, G. B.

Hoffe, R.

R. Hoffe, J. Chrostowski, Opt. Commun. 57, 34 (1986).
[CrossRef]

Jerominek, H.

S. Patela, H. Jerominek, C. Delisle, R. Tremblay, in Optical Chaos, J. Chrostowski, N. Abraham, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 667, 115 (1986);J. Appl. Phys. 60, 1591 (1986).

Kethenington, W. M.

G. I. Stegeman, C. T. Seaton, W. M. Kethenington, in Nonlinear Optics: Materials and Devices, C. Flytzanis, J. L. Oudar, eds. (Springer-Verlag, Berlin, 1986).

Li, P.

P. Li, Kam Wa, P. N. Robson, J. P. R. David, G. Hill, P. Mistry, M. A. Pate, J. S. Roberts, Electron. Lett. 22, 1129 (1986).
[CrossRef]

Mistry, P.

P. Li, Kam Wa, P. N. Robson, J. P. R. David, G. Hill, P. Mistry, M. A. Pate, J. S. Roberts, Electron. Lett. 22, 1129 (1986).
[CrossRef]

Nehme, M. A.

R. K. Varishney, M. A. Nehme, R. Srivastava, R. V. Ramaswamy, Appl. Opt. 21, 3899 (1986).
[CrossRef]

Pate, M. A.

P. Li, Kam Wa, P. N. Robson, J. P. R. David, G. Hill, P. Mistry, M. A. Pate, J. S. Roberts, Electron. Lett. 22, 1129 (1986).
[CrossRef]

Patela, S.

S. Patela, H. Jerominek, C. Delisle, R. Tremblay, in Optical Chaos, J. Chrostowski, N. Abraham, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 667, 115 (1986);J. Appl. Phys. 60, 1591 (1986).

Ramaswamy, R. V.

R. K. Varishney, M. A. Nehme, R. Srivastava, R. V. Ramaswamy, Appl. Opt. 21, 3899 (1986).
[CrossRef]

Robbins, D. J.

D. J. Robbins, Opt. Commun. 47, 309 (1983).
[CrossRef]

Roberts, J. S.

P. Li, Kam Wa, P. N. Robson, J. P. R. David, G. Hill, P. Mistry, M. A. Pate, J. S. Roberts, Electron. Lett. 22, 1129 (1986).
[CrossRef]

Robson, P. N.

P. Li, Kam Wa, P. N. Robson, J. P. R. David, G. Hill, P. Mistry, M. A. Pate, J. S. Roberts, Electron. Lett. 22, 1129 (1986).
[CrossRef]

Seaton, C. T.

G. I. Stegeman, C. T. Seaton, W. M. Kethenington, in Nonlinear Optics: Materials and Devices, C. Flytzanis, J. L. Oudar, eds. (Springer-Verlag, Berlin, 1986).

Srivastava, R.

R. K. Varishney, M. A. Nehme, R. Srivastava, R. V. Ramaswamy, Appl. Opt. 21, 3899 (1986).
[CrossRef]

Stegeman, G. I.

G. I. Stegeman, C. T. Seaton, W. M. Kethenington, in Nonlinear Optics: Materials and Devices, C. Flytzanis, J. L. Oudar, eds. (Springer-Verlag, Berlin, 1986).

Tremblay, R.

S. Patela, H. Jerominek, C. Delisle, R. Tremblay, in Optical Chaos, J. Chrostowski, N. Abraham, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 667, 115 (1986);J. Appl. Phys. 60, 1591 (1986).

Varishney, R. K.

R. K. Varishney, M. A. Nehme, R. Srivastava, R. V. Ramaswamy, Appl. Opt. 21, 3899 (1986).
[CrossRef]

Wa, Kam

P. Li, Kam Wa, P. N. Robson, J. P. R. David, G. Hill, P. Mistry, M. A. Pate, J. S. Roberts, Electron. Lett. 22, 1129 (1986).
[CrossRef]

Whitaker, N. A.

H. Haus, N. A. Whitaker, M. C. Gabriel, in Integrated Optical Circuit Engineering II, S. Sriram, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 578, 122 (1985).

Appl. Opt. (2)

G. B. Hocker, W. K. Burns, Appl. Opt. 16, 113 (1977).
[CrossRef] [PubMed]

R. K. Varishney, M. A. Nehme, R. Srivastava, R. V. Ramaswamy, Appl. Opt. 21, 3899 (1986).
[CrossRef]

Electron. Lett. (1)

P. Li, Kam Wa, P. N. Robson, J. P. R. David, G. Hill, P. Mistry, M. A. Pate, J. S. Roberts, Electron. Lett. 22, 1129 (1986).
[CrossRef]

Opt. Commun. (2)

R. Hoffe, J. Chrostowski, Opt. Commun. 57, 34 (1986).
[CrossRef]

D. J. Robbins, Opt. Commun. 47, 309 (1983).
[CrossRef]

Opt. Lett. (1)

Proc. Soc. Photo-Opt. Instrum. Eng. (2)

H. Haus, N. A. Whitaker, M. C. Gabriel, in Integrated Optical Circuit Engineering II, S. Sriram, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 578, 122 (1985).

S. Patela, H. Jerominek, C. Delisle, R. Tremblay, in Optical Chaos, J. Chrostowski, N. Abraham, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 667, 115 (1986);J. Appl. Phys. 60, 1591 (1986).

Other (2)

G. I. Stegeman, C. T. Seaton, W. M. Kethenington, in Nonlinear Optics: Materials and Devices, C. Flytzanis, J. L. Oudar, eds. (Springer-Verlag, Berlin, 1986).

H. M. Gibbs, P. Mandel, N. Peyghambarian, S. D. Smith, eds., Optical Bistability III (Springer-Verlag, Berlin, 1986).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

The nonlinear rib waveguide configuration.

Fig. 2
Fig. 2

The nonlinear modal-index profile along the rib structure for the following parameters: w = 3 μm, t = 1 μm, t1 = 0.1 μm, λ = 0.85 μm, nc = 1.0, nf = 3.645, ns = 3.625, n2s = 1.38 × 10−6 cm2/W. Total power in the mode, P = 0.14 mW. The broken line corresponds to the linear effective-index profile.

Fig. 3
Fig. 3

The modal-index changes with power for different substrate indices. The parameters of the rib waveguide are the same as in Fig. 2.

Fig. 4
Fig. 4

The electric field distribution in the nonlinear rib structure for P = 0.14 mW. The maximum is shifted by 0.1 μm toward the substrate compared to the linear case. The modal-index change corresponds to the power P = 0.019 mW/μm in the nonlinear slab waveguide with the same parameters.

Equations (12)

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{ / y 2 + / y 2 + k 0 2 [ n 2 ( x , y ) α | E | 2 N 2 ] } × E ( x , y ) = 0
E ( x , y ) = ψ ( x ) { cos [ f ( x ) d ϕ ( x ) ] exp [ δ ( x ) ( y d ) ] / cos ϕ ( x ) y d cos [ f ( x ) y ϕ ( x ) ] / cos ϕ ( x ) d y 0 { cosh ( s ( x ) k 0 y ) q ( ψ ) sinh [ s ( x ) k 0 y ] } 1 y 0 ,
n ( x , y ) = n f , n c , n s
α = 0 c n s 2 n 2 s ,
f ( x ) = k 0 [ n f 2 N 2 ( x ) ] 1 / 2 , δ ( x ) = k 0 [ N eff 2 ( x ) n c 2 ] 1 / 2 ;
q ( ψ ) = [ 1 α ψ 2 ( x ) / 2 s 2 ( x ) ] 1 / 2 , s ( x ) = [ N eff 2 ( x ) n s 2 ] 1 / 2 .
f ( x ) d arctan [ δ ( x ) f ( x ) ] arctan [ q ( ψ ) s ( x ) k 0 f ( x ) ] m π = 0 ,
{ d 2 / d x 2 + k 0 2 [ N eff 2 ( x ) N 2 ] } ψ ( x ) = 0 ,
ψ ( 1 ) ( x ) = E ( 0 , 0 ) { cos [ F ( ω / 2 ) ] exp [ D ( | x | ) ] for | x | ω / 2 cos [ F ( x ) ] for | x | ω / 2
D ( | x | ) = k 0 w / 2 | x | [ N 2 N eff ( 1 ) 2 ( x ) ] 1 / 2 d x ,
F ( x ) = k 0 0 x [ N eff ( 1 ) 2 ( x ) N 2 ] 1 / 2 d x .
P = ½ N 0 c E 2 ( x , y ) d x d y .

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