Abstract

A planar periodic nonlinear structure composed of alternating waveguiding (WG) and antiwaveguiding (AWG) sections is considered. Detailed simulations demonstrate that fairly long stable propagation of a beam in this structure is achieved when the lengths of the AWG and WG sections are equal, i.e., both ∼25 wavelengths. Another interesting result is that the stable-propagation length is much larger in both a uniform AWG and in the alternate structure if the input has a Gaussian transverse profile rather than a specially prepared shape that corresponds to the eigenmode of the (anti)waveguide. It is demonstrated that an efficient all-optical switching scheme, controlled by a weak hot spot, which is created by a laser beam shone normally to the structure and focused off axis near the end of any AWG section, can readily be realized in the alternate waveguide.

© 2002 Optical Society of America

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References

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  1. N. N. Akhmediev, “Novel class of nonlinear surface waves: Asymmetric modes in a symmetric layered structure,” Sov. Phys. JETP 56, 299–303 (1982) [ Zh. Eksp. Teor. Fiz. 83, 545–553 (1982)].
  2. N. N. Akhmediev, “The problem of stability and excitation of nonlinear surface waves,” in Nonlinear Surface Electromagnetic Phenomena, H.-E. Ponath and G. I. Stegeman, eds., Vol. 29 of Modern Problems in Condensed Matter Sciences (North Holland, Amsterdam, 1991), p. 289.
    [CrossRef]
  3. B. V. Gisin and A. A. Hardy, “Stationary solutions of plane nonlinear optical antiwaveguides,” Opt. Quantum Electron. 27, 565–575 (1995).
    [CrossRef]
  4. B. V. Gisin, A. Kaplan, and B. A. Malomed, “Spontaneous symmetry breaking and switching in a planar nonlinear antiwaveguide,” Phys. Rev. E 61, 2804–2809 (2000).
    [CrossRef]
  5. B. V. Gisin, A. Kaplan, and B. A. Malomed, “All-optical switching in an antiwaveguiding structure,” Opt. Quantum Electron. 33, 201–208 (2001).
    [CrossRef]
  6. B. A. Malomed, Z. H. Wang, P. L. Chu, and G. D. Peng, “Multichannel switchable system for spatial solitons,” J. Opt. Soc. Am. B 16, 1197–1203 (1999).
    [CrossRef]
  7. R. C. Alferness, “Titanium-diffused lithium niobate waveguide devices,” in Guided-Wave Optoelectronics, T. Tamir, ed. (Springer-Verlag, New York, 1988), pp. 145–210.
  8. N. J. Smith, W. Forysiak, and N. J. Doran, “Reduced Gordon–Haus jitter due to enhanced power solitons in strongly dispersion-managed systems,” Electron. Lett. 32, 2085–2086 (1996).
    [CrossRef]
  9. I. Gabitov and S. K. Turitsyn, “Averaged pulse dynamics in a cascaded transmission system with passive dispersion compensation,” Opt. Lett. 21, 327–329 (1996).
    [CrossRef]
  10. J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, “Stable soliton-like propagation in dispersion managed systems with net anomalous, zero and normal dispersion,” Electron. Lett. 33, 1726–1727 (1997).
    [CrossRef]
  11. B. A. Malomed and A. Berntson, “Propagation of an optical pulse in a fiber link with random dispersion management,” J. Opt. Soc. Am. B 18, 1243–1251 (2001).
    [CrossRef]
  12. F. Kh. Abdullaev and B. B. Baizakov, “Disintegration of a soliton in a dispersion-managed optical communication line with random parameters,” Opt. Lett. 25, 93–95 (2000).
    [CrossRef]
  13. L. Torner, “Walkoff-compensated dispersion-mapped quadratic solitons,” IEEE Photonics Technol. Lett. 11, 1268–1270 (1999).
    [CrossRef]
  14. R. Driben and B. A. Malomed, “Split-step solitons in long fiber links,” Opt. Commun. 185, 439–456 (2000).
    [CrossRef]
  15. R. Driben and B. A. Malomed, “Suppression of crosstalk between solitons in a multi-channel split-step system,” Opt. Commun. (to be published).
  16. L. Bergé, V. K. Mezentsev, J. Juul Rasmussen, P. L. Christiansen, and Yu B. Gaididei, “Self-guiding light in layered nonlinear media,” Opt. Lett. 25, 1037–1039 (2000).
    [CrossRef]
  17. I. Towers and B. A. Malomed, “Stable (2+1)-dimensional solitons in a layered medium with sign-alternating Kerr nonlinearity,” J. Opt. Soc. Am. B 19, 537–543 (2002).
    [CrossRef]
  18. S. N. Vlasov, V. A. Petrishchev, and V. I. Talanov, “Theory of periodic self-focusing of light beams,” Appl. Opt. 9, 1486–1488 (1970).
    [CrossRef] [PubMed]
  19. Y. S. Kivshar and B. A. Malomed, “Dynamics of solitons in nearly integrable systems,” Rev. Mod. Phys. 61, 763–915 (1989).
    [CrossRef]

2002 (1)

2001 (2)

B. A. Malomed and A. Berntson, “Propagation of an optical pulse in a fiber link with random dispersion management,” J. Opt. Soc. Am. B 18, 1243–1251 (2001).
[CrossRef]

B. V. Gisin, A. Kaplan, and B. A. Malomed, “All-optical switching in an antiwaveguiding structure,” Opt. Quantum Electron. 33, 201–208 (2001).
[CrossRef]

2000 (4)

B. V. Gisin, A. Kaplan, and B. A. Malomed, “Spontaneous symmetry breaking and switching in a planar nonlinear antiwaveguide,” Phys. Rev. E 61, 2804–2809 (2000).
[CrossRef]

R. Driben and B. A. Malomed, “Split-step solitons in long fiber links,” Opt. Commun. 185, 439–456 (2000).
[CrossRef]

L. Bergé, V. K. Mezentsev, J. Juul Rasmussen, P. L. Christiansen, and Yu B. Gaididei, “Self-guiding light in layered nonlinear media,” Opt. Lett. 25, 1037–1039 (2000).
[CrossRef]

F. Kh. Abdullaev and B. B. Baizakov, “Disintegration of a soliton in a dispersion-managed optical communication line with random parameters,” Opt. Lett. 25, 93–95 (2000).
[CrossRef]

1999 (2)

B. A. Malomed, Z. H. Wang, P. L. Chu, and G. D. Peng, “Multichannel switchable system for spatial solitons,” J. Opt. Soc. Am. B 16, 1197–1203 (1999).
[CrossRef]

L. Torner, “Walkoff-compensated dispersion-mapped quadratic solitons,” IEEE Photonics Technol. Lett. 11, 1268–1270 (1999).
[CrossRef]

1997 (1)

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, “Stable soliton-like propagation in dispersion managed systems with net anomalous, zero and normal dispersion,” Electron. Lett. 33, 1726–1727 (1997).
[CrossRef]

1996 (2)

N. J. Smith, W. Forysiak, and N. J. Doran, “Reduced Gordon–Haus jitter due to enhanced power solitons in strongly dispersion-managed systems,” Electron. Lett. 32, 2085–2086 (1996).
[CrossRef]

I. Gabitov and S. K. Turitsyn, “Averaged pulse dynamics in a cascaded transmission system with passive dispersion compensation,” Opt. Lett. 21, 327–329 (1996).
[CrossRef]

1995 (1)

B. V. Gisin and A. A. Hardy, “Stationary solutions of plane nonlinear optical antiwaveguides,” Opt. Quantum Electron. 27, 565–575 (1995).
[CrossRef]

1989 (1)

Y. S. Kivshar and B. A. Malomed, “Dynamics of solitons in nearly integrable systems,” Rev. Mod. Phys. 61, 763–915 (1989).
[CrossRef]

1970 (1)

Abdullaev, F. Kh.

Baizakov, B. B.

Bergé, L.

Berntson, A.

Christiansen, P. L.

Chu, P. L.

Doran, N. J.

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, “Stable soliton-like propagation in dispersion managed systems with net anomalous, zero and normal dispersion,” Electron. Lett. 33, 1726–1727 (1997).
[CrossRef]

N. J. Smith, W. Forysiak, and N. J. Doran, “Reduced Gordon–Haus jitter due to enhanced power solitons in strongly dispersion-managed systems,” Electron. Lett. 32, 2085–2086 (1996).
[CrossRef]

Driben, R.

R. Driben and B. A. Malomed, “Split-step solitons in long fiber links,” Opt. Commun. 185, 439–456 (2000).
[CrossRef]

Forysiak, W.

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, “Stable soliton-like propagation in dispersion managed systems with net anomalous, zero and normal dispersion,” Electron. Lett. 33, 1726–1727 (1997).
[CrossRef]

N. J. Smith, W. Forysiak, and N. J. Doran, “Reduced Gordon–Haus jitter due to enhanced power solitons in strongly dispersion-managed systems,” Electron. Lett. 32, 2085–2086 (1996).
[CrossRef]

Gabitov, I.

Gaididei, Yu B.

Gisin, B. V.

B. V. Gisin, A. Kaplan, and B. A. Malomed, “All-optical switching in an antiwaveguiding structure,” Opt. Quantum Electron. 33, 201–208 (2001).
[CrossRef]

B. V. Gisin, A. Kaplan, and B. A. Malomed, “Spontaneous symmetry breaking and switching in a planar nonlinear antiwaveguide,” Phys. Rev. E 61, 2804–2809 (2000).
[CrossRef]

B. V. Gisin and A. A. Hardy, “Stationary solutions of plane nonlinear optical antiwaveguides,” Opt. Quantum Electron. 27, 565–575 (1995).
[CrossRef]

Hardy, A. A.

B. V. Gisin and A. A. Hardy, “Stationary solutions of plane nonlinear optical antiwaveguides,” Opt. Quantum Electron. 27, 565–575 (1995).
[CrossRef]

Juul Rasmussen, J.

Kaplan, A.

B. V. Gisin, A. Kaplan, and B. A. Malomed, “All-optical switching in an antiwaveguiding structure,” Opt. Quantum Electron. 33, 201–208 (2001).
[CrossRef]

B. V. Gisin, A. Kaplan, and B. A. Malomed, “Spontaneous symmetry breaking and switching in a planar nonlinear antiwaveguide,” Phys. Rev. E 61, 2804–2809 (2000).
[CrossRef]

Kivshar, Y. S.

Y. S. Kivshar and B. A. Malomed, “Dynamics of solitons in nearly integrable systems,” Rev. Mod. Phys. 61, 763–915 (1989).
[CrossRef]

Knox, F. M.

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, “Stable soliton-like propagation in dispersion managed systems with net anomalous, zero and normal dispersion,” Electron. Lett. 33, 1726–1727 (1997).
[CrossRef]

Malomed, B. A.

I. Towers and B. A. Malomed, “Stable (2+1)-dimensional solitons in a layered medium with sign-alternating Kerr nonlinearity,” J. Opt. Soc. Am. B 19, 537–543 (2002).
[CrossRef]

B. A. Malomed and A. Berntson, “Propagation of an optical pulse in a fiber link with random dispersion management,” J. Opt. Soc. Am. B 18, 1243–1251 (2001).
[CrossRef]

B. V. Gisin, A. Kaplan, and B. A. Malomed, “All-optical switching in an antiwaveguiding structure,” Opt. Quantum Electron. 33, 201–208 (2001).
[CrossRef]

R. Driben and B. A. Malomed, “Split-step solitons in long fiber links,” Opt. Commun. 185, 439–456 (2000).
[CrossRef]

B. V. Gisin, A. Kaplan, and B. A. Malomed, “Spontaneous symmetry breaking and switching in a planar nonlinear antiwaveguide,” Phys. Rev. E 61, 2804–2809 (2000).
[CrossRef]

B. A. Malomed, Z. H. Wang, P. L. Chu, and G. D. Peng, “Multichannel switchable system for spatial solitons,” J. Opt. Soc. Am. B 16, 1197–1203 (1999).
[CrossRef]

Y. S. Kivshar and B. A. Malomed, “Dynamics of solitons in nearly integrable systems,” Rev. Mod. Phys. 61, 763–915 (1989).
[CrossRef]

Mezentsev, V. K.

Nijhof, J. H. B.

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, “Stable soliton-like propagation in dispersion managed systems with net anomalous, zero and normal dispersion,” Electron. Lett. 33, 1726–1727 (1997).
[CrossRef]

Peng, G. D.

Petrishchev, V. A.

Smith, N. J.

N. J. Smith, W. Forysiak, and N. J. Doran, “Reduced Gordon–Haus jitter due to enhanced power solitons in strongly dispersion-managed systems,” Electron. Lett. 32, 2085–2086 (1996).
[CrossRef]

Talanov, V. I.

Torner, L.

L. Torner, “Walkoff-compensated dispersion-mapped quadratic solitons,” IEEE Photonics Technol. Lett. 11, 1268–1270 (1999).
[CrossRef]

Towers, I.

Turitsyn, S. K.

Vlasov, S. N.

Wang, Z. H.

Appl. Opt. (1)

Electron. Lett. (2)

N. J. Smith, W. Forysiak, and N. J. Doran, “Reduced Gordon–Haus jitter due to enhanced power solitons in strongly dispersion-managed systems,” Electron. Lett. 32, 2085–2086 (1996).
[CrossRef]

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, “Stable soliton-like propagation in dispersion managed systems with net anomalous, zero and normal dispersion,” Electron. Lett. 33, 1726–1727 (1997).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

L. Torner, “Walkoff-compensated dispersion-mapped quadratic solitons,” IEEE Photonics Technol. Lett. 11, 1268–1270 (1999).
[CrossRef]

J. Opt. Soc. Am. B (3)

Opt. Commun. (1)

R. Driben and B. A. Malomed, “Split-step solitons in long fiber links,” Opt. Commun. 185, 439–456 (2000).
[CrossRef]

Opt. Lett. (3)

Opt. Quantum Electron. (2)

B. V. Gisin, A. Kaplan, and B. A. Malomed, “All-optical switching in an antiwaveguiding structure,” Opt. Quantum Electron. 33, 201–208 (2001).
[CrossRef]

B. V. Gisin and A. A. Hardy, “Stationary solutions of plane nonlinear optical antiwaveguides,” Opt. Quantum Electron. 27, 565–575 (1995).
[CrossRef]

Phys. Rev. E (1)

B. V. Gisin, A. Kaplan, and B. A. Malomed, “Spontaneous symmetry breaking and switching in a planar nonlinear antiwaveguide,” Phys. Rev. E 61, 2804–2809 (2000).
[CrossRef]

Rev. Mod. Phys. (1)

Y. S. Kivshar and B. A. Malomed, “Dynamics of solitons in nearly integrable systems,” Rev. Mod. Phys. 61, 763–915 (1989).
[CrossRef]

Other (4)

R. C. Alferness, “Titanium-diffused lithium niobate waveguide devices,” in Guided-Wave Optoelectronics, T. Tamir, ed. (Springer-Verlag, New York, 1988), pp. 145–210.

N. N. Akhmediev, “Novel class of nonlinear surface waves: Asymmetric modes in a symmetric layered structure,” Sov. Phys. JETP 56, 299–303 (1982) [ Zh. Eksp. Teor. Fiz. 83, 545–553 (1982)].

N. N. Akhmediev, “The problem of stability and excitation of nonlinear surface waves,” in Nonlinear Surface Electromagnetic Phenomena, H.-E. Ponath and G. I. Stegeman, eds., Vol. 29 of Modern Problems in Condensed Matter Sciences (North Holland, Amsterdam, 1991), p. 289.
[CrossRef]

R. Driben and B. A. Malomed, “Suppression of crosstalk between solitons in a multi-channel split-step system,” Opt. Commun. (to be published).

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Figures (4)

Fig. 1
Fig. 1

Schematic of the refractive-index distribution in the AWG–WG alternate structure. In this and subsequent figures, propagation and transverse coordinates z and x are measured in units defined in Eq. (5).

Fig. 2
Fig. 2

Evolution of the beam generated by the Gaussian input in a uniform AWG structure.

Fig. 3
Fig. 3

Stable long-distance propagation of the beam in the periodic structure with the alternating AWG and WG sections. The length of both the AWG and the WG sections is 2 in normalized units.

Fig. 4
Fig. 4

Juxtaposition of switching induced by the hot spot applied on the left or the right sides off axis to different AWG sections in the alternate waveguide. The lengths of the AWG and WG sections are 4 and 2, respectively, in normalized units.

Equations (31)

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=n2(X, Z)+N2|F|2,
δn(z)n(X=0, Z)-n(X=, Z)=δn+>0inWGsegmentsδn-<0inAWGsegments
2iβFZ+2FX2=β2-ω2c2n2(X, Z)F-ω2c2N2|F|2F,
iΨz+2Ψx2=[E+U(x, z)]Ψ-|Ψ|2Ψ,
zZ/(2βX02),xX/X0,
E[β2-(n0ω/c)2]X02
U(x, z)[n02-n2(x, z)](X0ω/c)2,
n(x, z)=n0+δn(z)f(x)f(x)12erf x0+xD+erf x0-xD,
U(x, z)=-A(z)f(x),
A(z)2(2πX0/λ)2n0δn+A+>0inWGsegments-2(2πX0/λ)2n0|δn-|A-<0inAWGsegments.
Ψ(x, z)=exp[iqx+iϕ(z)]Ψ0[x-ξ(z)],
d2ξdz2=-M-1A(z)dUdξ,
M=-+ Ψ02(x)dx4E,
U(ξ)=-+[Ψ0(x-ξ)]2f(x)dx
d2ξdz2=-(U0/M)A(z)ξ-ω2(z)ξ,
ω2(z)=2(2πX0/λ)2(U0/M)n0δn+ω+2inWGsegments-2(2πX0/λ)2(U0/M)n0|δn-|-ω-2inAWGsegments
ξWG(z)=a+cos(ω+z)+b+sin(ω+z),
ξAWG(z)=a-cosh(ω+z)+b-sinh(ω+z),
a-=a+cos(φ+)+b+sin(φ+),
b-=(ω+/ω-)[-a+sin(φ+)+b+cos(φ+)],
a+=a-cosh(φ-)+b-sinh(φ-),
b+=(ω-/ω+)[a-sin(φ-)+b-cos(φ-)],
cos(φ+)cosh(φ-)-(ω+/ω-)sin(φ+)sinh(φ-)sin(φ+)cosh(φ-)+(ω+/ω-)cos(φ+)sinh(φ-)-sin(φ+)cosh(φ-)+(ω-/ω+)cos(φ+)sinh(φ-)cos(φ+)cosh(φ-)+(ω-/ω+)sin(φ+)sinh(φ-)
μ1,2=τ/2±(τ2/4-1)1/2,
τ=2 cos(φ+)cosh(φ-)+ω+2-ω-22ω+ω-sin(φ+)sinh(φ-).
cos(φ+)cosh(φ-)-ω+2-ω-22ω+ω-sin(φ+)sinh(φ-)1.
ω+(L+)min=cos-11[cosh2(φ-)+Ω2 sinh2(φ-)]1/2-tan-1[Ω tanh(φ-)],
cos-1[sech(φ-)]+2πN
ω+L+-cos-1[sech(φ-)]+2π(N+1),
N=0, 1, 2 ,,
Ψ(z=0)=C exp[-(x/σ)2].

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