Abstract

Self-focusing effects in periodic leaky-wave coupled (antiguided) and evanescent-wave coupled array structures are analyzed for what is to our knowledge the first time. The results obtained can be explained in terms of spatial gap solitons. For infinite-extent arrays of antiguides it is found that (for interelement-spacing values), below the in-phase-mode resonance, self-focusing occurs with increasing light intensity even when the medium is intrinsically self-defocusing (i.e., negative nonlinearity). If the medium has positive nonlinearity the analysis shows that antiguided arrays possess either self-focusing or self-defocusing properties depending on the parameters of the structure, whereas evanescent-wave in-phase coupled arrays always have self-focusing properties.

© 1993 Optical Society of America

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  1. U. Langbein, F. Lederer, T. Peschel, U. Trutschel, D. Mihalache, Phys. Rep. 194, 325 (1990).
    [CrossRef]
  2. P. M. Lambkin, K. A. Shore, IEEE J. Quantum Electron. 27, 824 (1991).
    [CrossRef]
  3. R. F. Nabiev, A. I. Onishchenko, IEEE J. Quantum Electron. 28, 2024 (1992).
    [CrossRef]
  4. C. A. Zmudzinski, D. Botez, L. J. Mawst, Appl. Phys. Lett. 60, 1049 (1992).
    [CrossRef]
  5. N. N. Akhmediev, R. F. Nabiev, Yu. M. Popov, Solid State Commun. 66, 981 (1988).
    [CrossRef]
  6. J. E. Sipe, H. G. Winful, Opt. Lett. 13, 132 (1988).
    [CrossRef] [PubMed]
  7. A. A. Kolokolov, Zh. Prikl. Mekh. Tech. Fiz. 3, 153 (1973).
  8. R. F. Nabiev, P. Yeh, D. Botez, Appl. Phys. Lett. 62, 916 (1993).
    [CrossRef]
  9. G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, A. E. Kaplan, Phys. Rev. Lett. 66, 1583 (1991).
    [CrossRef] [PubMed]
  10. J. S. Aitchinson, K. Al-Hemyari, C. N. Ironside, R. S. Grant, W. Sibbett, Electron. Lett. 28, 1879 (1992).
    [CrossRef]
  11. K.-L. Chen, S. Wang, Appl. Phys. Lett. 47, 555 (1985).
    [CrossRef]

1993

R. F. Nabiev, P. Yeh, D. Botez, Appl. Phys. Lett. 62, 916 (1993).
[CrossRef]

1992

R. F. Nabiev, A. I. Onishchenko, IEEE J. Quantum Electron. 28, 2024 (1992).
[CrossRef]

C. A. Zmudzinski, D. Botez, L. J. Mawst, Appl. Phys. Lett. 60, 1049 (1992).
[CrossRef]

J. S. Aitchinson, K. Al-Hemyari, C. N. Ironside, R. S. Grant, W. Sibbett, Electron. Lett. 28, 1879 (1992).
[CrossRef]

1991

G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, A. E. Kaplan, Phys. Rev. Lett. 66, 1583 (1991).
[CrossRef] [PubMed]

P. M. Lambkin, K. A. Shore, IEEE J. Quantum Electron. 27, 824 (1991).
[CrossRef]

1990

U. Langbein, F. Lederer, T. Peschel, U. Trutschel, D. Mihalache, Phys. Rep. 194, 325 (1990).
[CrossRef]

1988

N. N. Akhmediev, R. F. Nabiev, Yu. M. Popov, Solid State Commun. 66, 981 (1988).
[CrossRef]

J. E. Sipe, H. G. Winful, Opt. Lett. 13, 132 (1988).
[CrossRef] [PubMed]

1985

K.-L. Chen, S. Wang, Appl. Phys. Lett. 47, 555 (1985).
[CrossRef]

1973

A. A. Kolokolov, Zh. Prikl. Mekh. Tech. Fiz. 3, 153 (1973).

Aitchinson, J. S.

J. S. Aitchinson, K. Al-Hemyari, C. N. Ironside, R. S. Grant, W. Sibbett, Electron. Lett. 28, 1879 (1992).
[CrossRef]

Akhmediev, N. N.

N. N. Akhmediev, R. F. Nabiev, Yu. M. Popov, Solid State Commun. 66, 981 (1988).
[CrossRef]

Al-Hemyari, K.

J. S. Aitchinson, K. Al-Hemyari, C. N. Ironside, R. S. Grant, W. Sibbett, Electron. Lett. 28, 1879 (1992).
[CrossRef]

Andersen, D. R.

G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, A. E. Kaplan, Phys. Rev. Lett. 66, 1583 (1991).
[CrossRef] [PubMed]

Botez, D.

R. F. Nabiev, P. Yeh, D. Botez, Appl. Phys. Lett. 62, 916 (1993).
[CrossRef]

C. A. Zmudzinski, D. Botez, L. J. Mawst, Appl. Phys. Lett. 60, 1049 (1992).
[CrossRef]

Chen, K.-L.

K.-L. Chen, S. Wang, Appl. Phys. Lett. 47, 555 (1985).
[CrossRef]

Grant, R. S.

J. S. Aitchinson, K. Al-Hemyari, C. N. Ironside, R. S. Grant, W. Sibbett, Electron. Lett. 28, 1879 (1992).
[CrossRef]

Ironside, C. N.

J. S. Aitchinson, K. Al-Hemyari, C. N. Ironside, R. S. Grant, W. Sibbett, Electron. Lett. 28, 1879 (1992).
[CrossRef]

Kaplan, A. E.

G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, A. E. Kaplan, Phys. Rev. Lett. 66, 1583 (1991).
[CrossRef] [PubMed]

Kolokolov, A. A.

A. A. Kolokolov, Zh. Prikl. Mekh. Tech. Fiz. 3, 153 (1973).

Lambkin, P. M.

P. M. Lambkin, K. A. Shore, IEEE J. Quantum Electron. 27, 824 (1991).
[CrossRef]

Langbein, U.

U. Langbein, F. Lederer, T. Peschel, U. Trutschel, D. Mihalache, Phys. Rep. 194, 325 (1990).
[CrossRef]

Lederer, F.

U. Langbein, F. Lederer, T. Peschel, U. Trutschel, D. Mihalache, Phys. Rep. 194, 325 (1990).
[CrossRef]

Mawst, L. J.

C. A. Zmudzinski, D. Botez, L. J. Mawst, Appl. Phys. Lett. 60, 1049 (1992).
[CrossRef]

Mihalache, D.

U. Langbein, F. Lederer, T. Peschel, U. Trutschel, D. Mihalache, Phys. Rep. 194, 325 (1990).
[CrossRef]

Nabiev, R. F.

R. F. Nabiev, P. Yeh, D. Botez, Appl. Phys. Lett. 62, 916 (1993).
[CrossRef]

R. F. Nabiev, A. I. Onishchenko, IEEE J. Quantum Electron. 28, 2024 (1992).
[CrossRef]

N. N. Akhmediev, R. F. Nabiev, Yu. M. Popov, Solid State Commun. 66, 981 (1988).
[CrossRef]

Onishchenko, A. I.

R. F. Nabiev, A. I. Onishchenko, IEEE J. Quantum Electron. 28, 2024 (1992).
[CrossRef]

Peschel, T.

U. Langbein, F. Lederer, T. Peschel, U. Trutschel, D. Mihalache, Phys. Rep. 194, 325 (1990).
[CrossRef]

Popov, Yu. M.

N. N. Akhmediev, R. F. Nabiev, Yu. M. Popov, Solid State Commun. 66, 981 (1988).
[CrossRef]

Regan, J. J.

G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, A. E. Kaplan, Phys. Rev. Lett. 66, 1583 (1991).
[CrossRef] [PubMed]

Shore, K. A.

P. M. Lambkin, K. A. Shore, IEEE J. Quantum Electron. 27, 824 (1991).
[CrossRef]

Sibbett, W.

J. S. Aitchinson, K. Al-Hemyari, C. N. Ironside, R. S. Grant, W. Sibbett, Electron. Lett. 28, 1879 (1992).
[CrossRef]

Sipe, J. E.

Swartzlander, G. A.

G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, A. E. Kaplan, Phys. Rev. Lett. 66, 1583 (1991).
[CrossRef] [PubMed]

Trutschel, U.

U. Langbein, F. Lederer, T. Peschel, U. Trutschel, D. Mihalache, Phys. Rep. 194, 325 (1990).
[CrossRef]

Wang, S.

K.-L. Chen, S. Wang, Appl. Phys. Lett. 47, 555 (1985).
[CrossRef]

Winful, H. G.

Yeh, P.

R. F. Nabiev, P. Yeh, D. Botez, Appl. Phys. Lett. 62, 916 (1993).
[CrossRef]

Yin, H.

G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, A. E. Kaplan, Phys. Rev. Lett. 66, 1583 (1991).
[CrossRef] [PubMed]

Zmudzinski, C. A.

C. A. Zmudzinski, D. Botez, L. J. Mawst, Appl. Phys. Lett. 60, 1049 (1992).
[CrossRef]

Appl. Phys. Lett.

C. A. Zmudzinski, D. Botez, L. J. Mawst, Appl. Phys. Lett. 60, 1049 (1992).
[CrossRef]

R. F. Nabiev, P. Yeh, D. Botez, Appl. Phys. Lett. 62, 916 (1993).
[CrossRef]

K.-L. Chen, S. Wang, Appl. Phys. Lett. 47, 555 (1985).
[CrossRef]

Electron. Lett.

J. S. Aitchinson, K. Al-Hemyari, C. N. Ironside, R. S. Grant, W. Sibbett, Electron. Lett. 28, 1879 (1992).
[CrossRef]

IEEE J. Quantum Electron.

P. M. Lambkin, K. A. Shore, IEEE J. Quantum Electron. 27, 824 (1991).
[CrossRef]

R. F. Nabiev, A. I. Onishchenko, IEEE J. Quantum Electron. 28, 2024 (1992).
[CrossRef]

Opt. Lett.

Phys. Rep.

U. Langbein, F. Lederer, T. Peschel, U. Trutschel, D. Mihalache, Phys. Rep. 194, 325 (1990).
[CrossRef]

Phys. Rev. Lett.

G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, A. E. Kaplan, Phys. Rev. Lett. 66, 1583 (1991).
[CrossRef] [PubMed]

Solid State Commun.

N. N. Akhmediev, R. F. Nabiev, Yu. M. Popov, Solid State Commun. 66, 981 (1988).
[CrossRef]

Zh. Prikl. Mekh. Tech. Fiz.

A. A. Kolokolov, Zh. Prikl. Mekh. Tech. Fiz. 3, 153 (1973).

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Figures (5)

Fig. 1
Fig. 1

Dependence of band edges and the differential gain d Im(β)/d Im2) (Ref. 4) of the wave propagating along a periodical structure on the width of guiding region d1. Solid and dotted lines correspond to the top and the bottom of allowed zones of β, respectively. The shaded regions indicate the forbidden band gap for β. Other parameters of the structure are d2 = 3 μm, 2 = 12.25, and Δ = 0.2 (see the inset).

Fig. 2
Fig. 2

Electromagnetic field profile of spatial soliton for propagation constants β = 3.49785 (dotted curve) and β = 3.4996 (solid curve). The energy integrals (see text) are equal to I = 0.1268 and I = 0.5756, respectively. The structure parameters are d1 = d2 = 3 μm, 2 = 12.25, Δ = 0.2, and positive nonlinearity [n2 > 0 in Eq. (1)]. The thin solid line at the bottom shows the profile of the dielectric constant (x).

Fig. 3
Fig. 3

Dependence of energy integral I (solid curves) and its square I2 (dotted curves) on propagation constant β for two periodic structures with positive nonlinearity. The structure parameters are d2 = 3 μm, 2 = 12.25, Δ = 0.2, d1 = 2.8 μm, and 3 μm. The dashed–dotted curve corresponds to a sech-like spatial soliton in a uniform Kerr-like medium.

Fig. 4
Fig. 4

Electromagnetic field profile of spatial soliton for propagation constants β = 3.4967 (dotted curve) and β = 3.4958 (solid curve). The energy integrals I are equal to I – 0.2105 and I = 0.5951, respectively. The structure parameters are d1 = 2.5 μm, d2 = 3 μm, 2 = 12.25, Δ = 0.2, and negative nonlinearity [n2 < 0 in Eq. (1)].

Fig. 5
Fig. 5

Dependence of energy integral I (solid curve) and its square I2 (dotted curve) on propagation constant β for the periodic structures with negative nonlinearity. The structure parameters are d1 = 2.5 μm, d2 = 3 μm, 2 = 12.25, and Δ = 0.2.

Equations (1)

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d 2 A d x 2 A [ β 2 ( x ) ] + sgn ( n 2 ) | A | 2 A = 0 .

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