Abstract

We demonstrate numerically that the power transfer from one polarization component of a (1+1)D vector spatial soliton to the other in a birefringent nonlinear medium can be controlled via the electro-optic Kerr effect by varying the externally applied electric field. We show how several all-optical operations involving fundamental vector solitons can be electronically controlled. We also discover that the split-up of the higher-order vector solitons due to the two-photon absorption (TPA) can be suppressed by adjusting the external electric field. The soliton trapping along the slow optical axis is realized by a planar waveguide, filled with a silicon-nanocrystal material. The external electric field is applied along the fast optical axis of the waveguide.

© 2008 Optical Society of America

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  1. G. I. Stegeman and E. M. Wright, "All-optical waveguide switching," Opt. Quantum Electron. 22, 95-122 (1990).
    [CrossRef]
  2. K. J. Blow, N. J. Doran, and D. Wood, "Polarization instabilities for solitons in birefringent fibers," Opt. Lett. 12, 202-204 (1987).
    [CrossRef] [PubMed]
  3. M. Delque, D. Fanjoux, and T. Sylvestre, "Polarization dynamics of the fundamental vector soliton of isotropic Kerr media," Phys. Rev. E 75, 016611 (2007).
    [CrossRef]
  4. U. Hempelmann, "Polarization coupling and transverse interaction of spatial optical solitons in a slab waveguide," J. Opt. Soc. Am. B 12, 77-86 (1995).
    [CrossRef]
  5. For an up-to-date review see, Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic Press, Boston, 2003), Chapter 9.
  6. J. S. Aitchison, J. U. Kang, and G. I. Stegeman, "Signal gain due to a polarization coupling in an AlGaAs channel waveguide," Appl. Phys. Lett. 67, 2456-2458 (1995).
    [CrossRef]
  7. L. Thylen, "Integrated optics in LiNbO3: Recent Developments in Devices for Telecommunications," J. Lightwave Technol. 6, 847-861 (1988).
    [CrossRef]
  8. G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, and C. T. Seaton, "Third Order Nonlinear Integrated Optics," J. Lightwave Technol. 6, 953-970 (1988).
    [CrossRef]
  9. R. W. Boyd, Nonlinear Optics 2nd Edition (Academic Press, Amsterdam, 2003).
  10. M. Cada, M. Qasymeh, and J. Pistora, "Electrically and optically controlled cross-polarized wave conversion," Opt. Express 16, 3083-3100 (2008).
    [CrossRef] [PubMed]
  11. G. P. Agrawal, Nonlinear Fiber Optics 4th Edition (Academic Press, San Diego, 2007).
  12. Q. Lin, O. J. Painter, and G. P. Agrawal, "Nonlinear optical phenomena in silicon waveguides: modeling and applications," Opt. Express 15, 16604-16644 (2007).
    [CrossRef] [PubMed]
  13. J. M. Jarem and P. P. Banerjee, Computational methods for electromagnetic and optical systems (Marcel Dekker Inc., New York, 2000).
  14. The Photonics Research Lab, University of Maryland, "SSPROP-Split-Step Fourier Propagation Software," http://www.photonics.umd.edu/software/ssprop/index.html.
  15. G. V. Prakash, M. Cazzanelli, Z. Gaburro, L. Pavesi, F. Iacona, G. Franzo, and F. Priolo, "Nonlinear optical properties of silicon nanocrystals grown by plasma-enhanced chemical vapor deposition," J. Appl. Phys. 91, 4607-4610 (2002).
    [CrossRef]
  16. F. Riboli, D. Navarro-Urrios, A. Chiasera, N. Daldosso, L. Pavesi, C. J. Oton, J. Heitmann, L. X. Yi, R. Scholz, and M. Zacharias, "Birefringence in optical waveguides made by silicon nanocrystal superlattices," Appl. Phys. Lett. 85, 1268-1270 (2004).
    [CrossRef]
  17. S. M. Anthony, "Optical properties of nanostructured silicon-rich silicon dioxide," Thesis (Ph. D.)-Massachusetts Institute of Technology, Dept. of Materials Science and Engineering, (2006), Chapter 4.
  18. J. S. Aitchison, A. M. Weiner, Y. Silberberg, D. E. Leaird, M. K. Oliver, J. L. Jackel, and P. W. E. Smith, "Experimental observation of spatial soliton interactions," Opt. Lett. 16, 15-17 (1991).
    [CrossRef] [PubMed]
  19. V. V. Afanasjev, J. S. Aitchison, and Y. S. Kivshar, "Splitting of high-order spatial solitons under the action of two-photon absorption," Opt. Commun. 116, 331-338 (1995).
    [CrossRef]
  20. V. Boucher, R. Barille, and G. Rivoire, "Polarization-switching control in a nonlinear liquid planar waveguide," J. Opt. Soc. Am. B 20, 1666-1674 (2003).
    [CrossRef]

2008 (1)

2007 (2)

Q. Lin, O. J. Painter, and G. P. Agrawal, "Nonlinear optical phenomena in silicon waveguides: modeling and applications," Opt. Express 15, 16604-16644 (2007).
[CrossRef] [PubMed]

M. Delque, D. Fanjoux, and T. Sylvestre, "Polarization dynamics of the fundamental vector soliton of isotropic Kerr media," Phys. Rev. E 75, 016611 (2007).
[CrossRef]

2004 (1)

F. Riboli, D. Navarro-Urrios, A. Chiasera, N. Daldosso, L. Pavesi, C. J. Oton, J. Heitmann, L. X. Yi, R. Scholz, and M. Zacharias, "Birefringence in optical waveguides made by silicon nanocrystal superlattices," Appl. Phys. Lett. 85, 1268-1270 (2004).
[CrossRef]

2003 (1)

2002 (1)

G. V. Prakash, M. Cazzanelli, Z. Gaburro, L. Pavesi, F. Iacona, G. Franzo, and F. Priolo, "Nonlinear optical properties of silicon nanocrystals grown by plasma-enhanced chemical vapor deposition," J. Appl. Phys. 91, 4607-4610 (2002).
[CrossRef]

1995 (3)

U. Hempelmann, "Polarization coupling and transverse interaction of spatial optical solitons in a slab waveguide," J. Opt. Soc. Am. B 12, 77-86 (1995).
[CrossRef]

J. S. Aitchison, J. U. Kang, and G. I. Stegeman, "Signal gain due to a polarization coupling in an AlGaAs channel waveguide," Appl. Phys. Lett. 67, 2456-2458 (1995).
[CrossRef]

V. V. Afanasjev, J. S. Aitchison, and Y. S. Kivshar, "Splitting of high-order spatial solitons under the action of two-photon absorption," Opt. Commun. 116, 331-338 (1995).
[CrossRef]

1991 (1)

1990 (1)

G. I. Stegeman and E. M. Wright, "All-optical waveguide switching," Opt. Quantum Electron. 22, 95-122 (1990).
[CrossRef]

1988 (2)

L. Thylen, "Integrated optics in LiNbO3: Recent Developments in Devices for Telecommunications," J. Lightwave Technol. 6, 847-861 (1988).
[CrossRef]

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, and C. T. Seaton, "Third Order Nonlinear Integrated Optics," J. Lightwave Technol. 6, 953-970 (1988).
[CrossRef]

1987 (1)

Afanasjev, V. V.

V. V. Afanasjev, J. S. Aitchison, and Y. S. Kivshar, "Splitting of high-order spatial solitons under the action of two-photon absorption," Opt. Commun. 116, 331-338 (1995).
[CrossRef]

Agrawal, G. P.

Aitchison, J. S.

J. S. Aitchison, J. U. Kang, and G. I. Stegeman, "Signal gain due to a polarization coupling in an AlGaAs channel waveguide," Appl. Phys. Lett. 67, 2456-2458 (1995).
[CrossRef]

V. V. Afanasjev, J. S. Aitchison, and Y. S. Kivshar, "Splitting of high-order spatial solitons under the action of two-photon absorption," Opt. Commun. 116, 331-338 (1995).
[CrossRef]

J. S. Aitchison, A. M. Weiner, Y. Silberberg, D. E. Leaird, M. K. Oliver, J. L. Jackel, and P. W. E. Smith, "Experimental observation of spatial soliton interactions," Opt. Lett. 16, 15-17 (1991).
[CrossRef] [PubMed]

Barille, R.

Blow, K. J.

Boucher, V.

Cada, M.

Cazzanelli, M.

G. V. Prakash, M. Cazzanelli, Z. Gaburro, L. Pavesi, F. Iacona, G. Franzo, and F. Priolo, "Nonlinear optical properties of silicon nanocrystals grown by plasma-enhanced chemical vapor deposition," J. Appl. Phys. 91, 4607-4610 (2002).
[CrossRef]

Chiasera, A.

F. Riboli, D. Navarro-Urrios, A. Chiasera, N. Daldosso, L. Pavesi, C. J. Oton, J. Heitmann, L. X. Yi, R. Scholz, and M. Zacharias, "Birefringence in optical waveguides made by silicon nanocrystal superlattices," Appl. Phys. Lett. 85, 1268-1270 (2004).
[CrossRef]

Daldosso, N.

F. Riboli, D. Navarro-Urrios, A. Chiasera, N. Daldosso, L. Pavesi, C. J. Oton, J. Heitmann, L. X. Yi, R. Scholz, and M. Zacharias, "Birefringence in optical waveguides made by silicon nanocrystal superlattices," Appl. Phys. Lett. 85, 1268-1270 (2004).
[CrossRef]

Delque, M.

M. Delque, D. Fanjoux, and T. Sylvestre, "Polarization dynamics of the fundamental vector soliton of isotropic Kerr media," Phys. Rev. E 75, 016611 (2007).
[CrossRef]

Doran, N. J.

Fanjoux, D.

M. Delque, D. Fanjoux, and T. Sylvestre, "Polarization dynamics of the fundamental vector soliton of isotropic Kerr media," Phys. Rev. E 75, 016611 (2007).
[CrossRef]

Finlayson, N.

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, and C. T. Seaton, "Third Order Nonlinear Integrated Optics," J. Lightwave Technol. 6, 953-970 (1988).
[CrossRef]

Gaburro, Z.

G. V. Prakash, M. Cazzanelli, Z. Gaburro, L. Pavesi, F. Iacona, G. Franzo, and F. Priolo, "Nonlinear optical properties of silicon nanocrystals grown by plasma-enhanced chemical vapor deposition," J. Appl. Phys. 91, 4607-4610 (2002).
[CrossRef]

Heitmann, J.

F. Riboli, D. Navarro-Urrios, A. Chiasera, N. Daldosso, L. Pavesi, C. J. Oton, J. Heitmann, L. X. Yi, R. Scholz, and M. Zacharias, "Birefringence in optical waveguides made by silicon nanocrystal superlattices," Appl. Phys. Lett. 85, 1268-1270 (2004).
[CrossRef]

Hempelmann, U.

Iacona, F.

G. V. Prakash, M. Cazzanelli, Z. Gaburro, L. Pavesi, F. Iacona, G. Franzo, and F. Priolo, "Nonlinear optical properties of silicon nanocrystals grown by plasma-enhanced chemical vapor deposition," J. Appl. Phys. 91, 4607-4610 (2002).
[CrossRef]

Jackel, J. L.

Kang, J. U.

J. S. Aitchison, J. U. Kang, and G. I. Stegeman, "Signal gain due to a polarization coupling in an AlGaAs channel waveguide," Appl. Phys. Lett. 67, 2456-2458 (1995).
[CrossRef]

Kivshar, Y. S.

V. V. Afanasjev, J. S. Aitchison, and Y. S. Kivshar, "Splitting of high-order spatial solitons under the action of two-photon absorption," Opt. Commun. 116, 331-338 (1995).
[CrossRef]

Leaird, D. E.

Lin, Q.

Navarro-Urrios, D.

F. Riboli, D. Navarro-Urrios, A. Chiasera, N. Daldosso, L. Pavesi, C. J. Oton, J. Heitmann, L. X. Yi, R. Scholz, and M. Zacharias, "Birefringence in optical waveguides made by silicon nanocrystal superlattices," Appl. Phys. Lett. 85, 1268-1270 (2004).
[CrossRef]

Oliver, M. K.

Oton, C. J.

F. Riboli, D. Navarro-Urrios, A. Chiasera, N. Daldosso, L. Pavesi, C. J. Oton, J. Heitmann, L. X. Yi, R. Scholz, and M. Zacharias, "Birefringence in optical waveguides made by silicon nanocrystal superlattices," Appl. Phys. Lett. 85, 1268-1270 (2004).
[CrossRef]

Painter, O. J.

Pavesi, L.

F. Riboli, D. Navarro-Urrios, A. Chiasera, N. Daldosso, L. Pavesi, C. J. Oton, J. Heitmann, L. X. Yi, R. Scholz, and M. Zacharias, "Birefringence in optical waveguides made by silicon nanocrystal superlattices," Appl. Phys. Lett. 85, 1268-1270 (2004).
[CrossRef]

G. V. Prakash, M. Cazzanelli, Z. Gaburro, L. Pavesi, F. Iacona, G. Franzo, and F. Priolo, "Nonlinear optical properties of silicon nanocrystals grown by plasma-enhanced chemical vapor deposition," J. Appl. Phys. 91, 4607-4610 (2002).
[CrossRef]

Pistora, J.

Prakash, G. V.

G. V. Prakash, M. Cazzanelli, Z. Gaburro, L. Pavesi, F. Iacona, G. Franzo, and F. Priolo, "Nonlinear optical properties of silicon nanocrystals grown by plasma-enhanced chemical vapor deposition," J. Appl. Phys. 91, 4607-4610 (2002).
[CrossRef]

Qasymeh, M.

Riboli, F.

F. Riboli, D. Navarro-Urrios, A. Chiasera, N. Daldosso, L. Pavesi, C. J. Oton, J. Heitmann, L. X. Yi, R. Scholz, and M. Zacharias, "Birefringence in optical waveguides made by silicon nanocrystal superlattices," Appl. Phys. Lett. 85, 1268-1270 (2004).
[CrossRef]

Rivoire, G.

Scholz, R.

F. Riboli, D. Navarro-Urrios, A. Chiasera, N. Daldosso, L. Pavesi, C. J. Oton, J. Heitmann, L. X. Yi, R. Scholz, and M. Zacharias, "Birefringence in optical waveguides made by silicon nanocrystal superlattices," Appl. Phys. Lett. 85, 1268-1270 (2004).
[CrossRef]

Seaton, C. T.

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, and C. T. Seaton, "Third Order Nonlinear Integrated Optics," J. Lightwave Technol. 6, 953-970 (1988).
[CrossRef]

Silberberg, Y.

Smith, P. W. E.

Stegeman, G. I.

J. S. Aitchison, J. U. Kang, and G. I. Stegeman, "Signal gain due to a polarization coupling in an AlGaAs channel waveguide," Appl. Phys. Lett. 67, 2456-2458 (1995).
[CrossRef]

G. I. Stegeman and E. M. Wright, "All-optical waveguide switching," Opt. Quantum Electron. 22, 95-122 (1990).
[CrossRef]

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, and C. T. Seaton, "Third Order Nonlinear Integrated Optics," J. Lightwave Technol. 6, 953-970 (1988).
[CrossRef]

Sylvestre, T.

M. Delque, D. Fanjoux, and T. Sylvestre, "Polarization dynamics of the fundamental vector soliton of isotropic Kerr media," Phys. Rev. E 75, 016611 (2007).
[CrossRef]

Thylen, L.

L. Thylen, "Integrated optics in LiNbO3: Recent Developments in Devices for Telecommunications," J. Lightwave Technol. 6, 847-861 (1988).
[CrossRef]

Weiner, A. M.

Wood, D.

Wright, E. M.

G. I. Stegeman and E. M. Wright, "All-optical waveguide switching," Opt. Quantum Electron. 22, 95-122 (1990).
[CrossRef]

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, and C. T. Seaton, "Third Order Nonlinear Integrated Optics," J. Lightwave Technol. 6, 953-970 (1988).
[CrossRef]

Yi, L. X.

F. Riboli, D. Navarro-Urrios, A. Chiasera, N. Daldosso, L. Pavesi, C. J. Oton, J. Heitmann, L. X. Yi, R. Scholz, and M. Zacharias, "Birefringence in optical waveguides made by silicon nanocrystal superlattices," Appl. Phys. Lett. 85, 1268-1270 (2004).
[CrossRef]

Zacharias, M.

F. Riboli, D. Navarro-Urrios, A. Chiasera, N. Daldosso, L. Pavesi, C. J. Oton, J. Heitmann, L. X. Yi, R. Scholz, and M. Zacharias, "Birefringence in optical waveguides made by silicon nanocrystal superlattices," Appl. Phys. Lett. 85, 1268-1270 (2004).
[CrossRef]

Zanoni, R.

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, and C. T. Seaton, "Third Order Nonlinear Integrated Optics," J. Lightwave Technol. 6, 953-970 (1988).
[CrossRef]

Appl. Phys. Lett. (2)

J. S. Aitchison, J. U. Kang, and G. I. Stegeman, "Signal gain due to a polarization coupling in an AlGaAs channel waveguide," Appl. Phys. Lett. 67, 2456-2458 (1995).
[CrossRef]

F. Riboli, D. Navarro-Urrios, A. Chiasera, N. Daldosso, L. Pavesi, C. J. Oton, J. Heitmann, L. X. Yi, R. Scholz, and M. Zacharias, "Birefringence in optical waveguides made by silicon nanocrystal superlattices," Appl. Phys. Lett. 85, 1268-1270 (2004).
[CrossRef]

J. Appl. Phys. (1)

G. V. Prakash, M. Cazzanelli, Z. Gaburro, L. Pavesi, F. Iacona, G. Franzo, and F. Priolo, "Nonlinear optical properties of silicon nanocrystals grown by plasma-enhanced chemical vapor deposition," J. Appl. Phys. 91, 4607-4610 (2002).
[CrossRef]

J. Lightwave Technol. (2)

L. Thylen, "Integrated optics in LiNbO3: Recent Developments in Devices for Telecommunications," J. Lightwave Technol. 6, 847-861 (1988).
[CrossRef]

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, and C. T. Seaton, "Third Order Nonlinear Integrated Optics," J. Lightwave Technol. 6, 953-970 (1988).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Commun. (1)

V. V. Afanasjev, J. S. Aitchison, and Y. S. Kivshar, "Splitting of high-order spatial solitons under the action of two-photon absorption," Opt. Commun. 116, 331-338 (1995).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Opt. Quantum Electron. (1)

G. I. Stegeman and E. M. Wright, "All-optical waveguide switching," Opt. Quantum Electron. 22, 95-122 (1990).
[CrossRef]

Phys. Rev. E (1)

M. Delque, D. Fanjoux, and T. Sylvestre, "Polarization dynamics of the fundamental vector soliton of isotropic Kerr media," Phys. Rev. E 75, 016611 (2007).
[CrossRef]

Other (6)

For an up-to-date review see, Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic Press, Boston, 2003), Chapter 9.

R. W. Boyd, Nonlinear Optics 2nd Edition (Academic Press, Amsterdam, 2003).

S. M. Anthony, "Optical properties of nanostructured silicon-rich silicon dioxide," Thesis (Ph. D.)-Massachusetts Institute of Technology, Dept. of Materials Science and Engineering, (2006), Chapter 4.

J. M. Jarem and P. P. Banerjee, Computational methods for electromagnetic and optical systems (Marcel Dekker Inc., New York, 2000).

The Photonics Research Lab, University of Maryland, "SSPROP-Split-Step Fourier Propagation Software," http://www.photonics.umd.edu/software/ssprop/index.html.

G. P. Agrawal, Nonlinear Fiber Optics 4th Edition (Academic Press, San Diego, 2007).

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Figures (4)

Fig. 1.
Fig. 1.

Slab waveguide geometry (Ref. [4], Fig.1)

Fig. 2.
Fig. 2.

Evolution of the intensity profiles of the fundamental vector soliton, ��=1, for different values of Eext and θ. The dimensionless TPA strength is K=0.0025.

Fig. 3.
Fig. 3.

Evolution of the powers of the fundamental vector soliton components, ��=1, for different values of Eext and θ. The dimensionless TPA strength is K=0.0025.

Fig. 4.
Fig. 4.

Evolution of the intensity profiles of the second-order, ��=2, vector soliton, K=0.0025 (a) in the absence of birefringence,i.e., Δβ=0 (b) with internal birefringence and the external field present.

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

E = 1 2 [ a x 𝓔 x e i ω 0 t + a y ( 𝓔 y e i ω 0 t + E ext ) ] + c . c .
χ ijkl ( 3 ) = 1 3 χ xxxx ( 3 ) ( δ i j δ k l + δ i k δ j l + δ i l δ j k ) .
P NL = ε 0 χ ( 3 ) E E E .
P NL = 1 2 ( a x 𝒫 x + a y 𝒫 y ) e i ω 0 t + c . c . ,
𝒫 x = 3 ε 0 4 χ xxxx ( 3 ) [ ( 𝓔 x 2 + 2 3 𝓔 y 2 ) 𝓔 x + 1 3 ( 𝓔 x * 𝓔 y ) 𝓔 y + 4 3 E ext 2 𝓔 x ] ,
𝒫 y = 3 ε 0 4 χ xxxx ( 3 ) [ ( 𝓔 y 2 + 2 3 𝓔 x 2 ) 𝓔 x + 1 3 ( 𝓔 y * 𝓔 x ) 𝓔 x + 4 E ext 2 𝓔 y ] .
R e { χ xxxx ( 3 ) ( ω 0 , ω 0 , ω 0 , ω 0 ) } R e { χ xxxx ( 3 ) ( ω 0 , ω 0 , 0 , 0 ) } .
2 E 1 ε 0 c 2 2 D t 2 = μ 0 2 P NL t 2 .
𝓗 j ( x , z ) = F ( y ) u j ( x , z ) e i β j z ,
u 1 = u x + i u y 2 e 2 i κ Z ; u 2 = u x i u y 2 e 2 i κ Z .
U j Z + i 2 2 U j X 2 = α ˜ U j + i κ U 3 j + 2 i 3 𝒩 2 ( 1 + i K ) ( U j 2 + 2 U 3 j 2 ) U j .
κ = ( β x β y ) L D 2 4 3 k 0 n 2 L D E ext 2 ,
𝒩 2 = L D L NL = k 0 2 w 0 n L n NL p ,
K = β T P A n L 2 k 0 n 2 .

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