Abstract

We predict the formation of optical spatial solitons in photorefractive polymers. The orientational enhancement from the doped chromophores and the dependency of the quantum efficiency of generating mobile holes on the electric field make the polymeric solitons behave differently from other photorefractive solitons.

© 1999 Optical Society of America

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  1. M. Segev, B. Crosignani, A. Yariv, and B. Fischer, Phys. Rev. Lett. 68, 923 (1992).
    [CrossRef] [PubMed]
  2. M. Segev and G. Stegeman, Phys. Today 51(8), 42 (1998), and references therein.
    [CrossRef]
  3. M. Segev, G. C. Valley, B. Crosignani, P. Diporto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994); M. Segev, M. Shih, and G. C. Valley, J. Opt. Soc. Am. B 13, 706 (1996).
    [CrossRef] [PubMed]
  4. D. N. Christodoulides and M. Carvalho, J. Opt. Soc. Am. B 12, 1628 (1995).
    [CrossRef]
  5. M.-F. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, Electron. Lett. 31, 826 (1995).
    [CrossRef]
  6. S. Ducharme, J. C. Scott, R. J. Twieg, and W. E. Moerner, Phy. Rev. Lett. 66, 1846 (1991).
    [CrossRef]
  7. K. Meerholz, B. Volodin, Sandalphon, B. Kippelen, and N. Peyghambarian, Nature 371, 497 (1994); M. Liphardt, A. Goonesekera, B. Jones, S. Ducharme, J. Takacs, and L. Zhang, Science 263, 367 (1994); A. Grunnet-Jepsen, C. Thompson, and W. Moerner, Science 277, 549 (1997).
    [CrossRef] [PubMed]
  8. C. Poga, P. Lundquist, V. Lee, R. Shelby, R. Twieg, and D. Burland, Appl. Phys. Lett. 69, 1047 (1996).
    [CrossRef]
  9. W. E. Moerner and S. M. Silence, Chem. Rev. 94, 127 (1994).
    [CrossRef]
  10. W. Moerner, S. Silence, F. Hache, and G. Bjorklund, J. Opt. Soc. Am. B 11, 320 (1994).
    [CrossRef]
  11. C. Moylan, R. Wortmann, R. Twieg, and I. McComb, J. Opt. Soc. Am. B 15, 929 (1998).
    [CrossRef]
  12. S. Schloter, U. Hofmann, P. Strohriegl, H. Schmidt, and D. Haarer, J. Opt. Soc. Am. B 15, 2473 (1998).
    [CrossRef]
  13. W. Krolikowski, N. Akhmediev, and B. Luther-Davies, Opt. Lett. 21, 782 (1996).
    [CrossRef]
  14. J. S. Schildkraut and A. V. Buettner, J. Appl. Phys. 72, 1888 (1992).
    [CrossRef]
  15. P. J. Melz, J. Chem. Phys. 57, 1694 (1972).
  16. J. X. Mack, L. B. Schein, and A. Peled, Phys. Rev. B 39, 7500 (1989).
    [CrossRef]
  17. A. Grunnet-Jepsen, C. L. Thompson, R. J. Twieg, and W. E. Moerner, Appl. Phys. Lett. 70, 1515 (1997).
    [CrossRef]
  18. Both approximations were justified physically4,17 in terms of the inequality Ed?E?Eq, where Eq and Ed are the limiting space-charge field and the diffusion field, respectively, evaluated at a soliton width of not less than 5 µm.
  19. J. W. Wu, J. Opt. Soc. Am. B 8, 142 (1991).
    [CrossRef]
  20. For a typical example from Ref. 19, with ?D?10 D, ??0=5×10-23 cm3, and E=100 V/µm, the induced dipole contributes only one sixtieth of the total dipole energy.
  21. M. Segev and A. J. Agranat, Opt. Lett. 22, 1299 (1997).
    [CrossRef]

1998 (3)

1997 (2)

M. Segev and A. J. Agranat, Opt. Lett. 22, 1299 (1997).
[CrossRef]

A. Grunnet-Jepsen, C. L. Thompson, R. J. Twieg, and W. E. Moerner, Appl. Phys. Lett. 70, 1515 (1997).
[CrossRef]

1996 (2)

W. Krolikowski, N. Akhmediev, and B. Luther-Davies, Opt. Lett. 21, 782 (1996).
[CrossRef]

C. Poga, P. Lundquist, V. Lee, R. Shelby, R. Twieg, and D. Burland, Appl. Phys. Lett. 69, 1047 (1996).
[CrossRef]

1995 (2)

M.-F. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, Electron. Lett. 31, 826 (1995).
[CrossRef]

D. N. Christodoulides and M. Carvalho, J. Opt. Soc. Am. B 12, 1628 (1995).
[CrossRef]

1994 (4)

W. Moerner, S. Silence, F. Hache, and G. Bjorklund, J. Opt. Soc. Am. B 11, 320 (1994).
[CrossRef]

W. E. Moerner and S. M. Silence, Chem. Rev. 94, 127 (1994).
[CrossRef]

M. Segev, G. C. Valley, B. Crosignani, P. Diporto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994); M. Segev, M. Shih, and G. C. Valley, J. Opt. Soc. Am. B 13, 706 (1996).
[CrossRef] [PubMed]

K. Meerholz, B. Volodin, Sandalphon, B. Kippelen, and N. Peyghambarian, Nature 371, 497 (1994); M. Liphardt, A. Goonesekera, B. Jones, S. Ducharme, J. Takacs, and L. Zhang, Science 263, 367 (1994); A. Grunnet-Jepsen, C. Thompson, and W. Moerner, Science 277, 549 (1997).
[CrossRef] [PubMed]

1992 (2)

J. S. Schildkraut and A. V. Buettner, J. Appl. Phys. 72, 1888 (1992).
[CrossRef]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, Phys. Rev. Lett. 68, 923 (1992).
[CrossRef] [PubMed]

1991 (2)

S. Ducharme, J. C. Scott, R. J. Twieg, and W. E. Moerner, Phy. Rev. Lett. 66, 1846 (1991).
[CrossRef]

J. W. Wu, J. Opt. Soc. Am. B 8, 142 (1991).
[CrossRef]

1989 (1)

J. X. Mack, L. B. Schein, and A. Peled, Phys. Rev. B 39, 7500 (1989).
[CrossRef]

1972 (1)

P. J. Melz, J. Chem. Phys. 57, 1694 (1972).

Agranat, A. J.

Akhmediev, N.

Bjorklund, G.

Buettner, A. V.

J. S. Schildkraut and A. V. Buettner, J. Appl. Phys. 72, 1888 (1992).
[CrossRef]

Burland, D.

C. Poga, P. Lundquist, V. Lee, R. Shelby, R. Twieg, and D. Burland, Appl. Phys. Lett. 69, 1047 (1996).
[CrossRef]

Carvalho, M.

Christodoulides, D. N.

Crosignani, B.

M.-F. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, Electron. Lett. 31, 826 (1995).
[CrossRef]

M. Segev, G. C. Valley, B. Crosignani, P. Diporto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994); M. Segev, M. Shih, and G. C. Valley, J. Opt. Soc. Am. B 13, 706 (1996).
[CrossRef] [PubMed]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, Phys. Rev. Lett. 68, 923 (1992).
[CrossRef] [PubMed]

DiPorto, P.

M.-F. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, Electron. Lett. 31, 826 (1995).
[CrossRef]

M. Segev, G. C. Valley, B. Crosignani, P. Diporto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994); M. Segev, M. Shih, and G. C. Valley, J. Opt. Soc. Am. B 13, 706 (1996).
[CrossRef] [PubMed]

Ducharme, S.

S. Ducharme, J. C. Scott, R. J. Twieg, and W. E. Moerner, Phy. Rev. Lett. 66, 1846 (1991).
[CrossRef]

Fischer, B.

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, Phys. Rev. Lett. 68, 923 (1992).
[CrossRef] [PubMed]

Grunnet-Jepsen, A.

A. Grunnet-Jepsen, C. L. Thompson, R. J. Twieg, and W. E. Moerner, Appl. Phys. Lett. 70, 1515 (1997).
[CrossRef]

Haarer, D.

Hache, F.

Hofmann, U.

Kippelen, B.

K. Meerholz, B. Volodin, Sandalphon, B. Kippelen, and N. Peyghambarian, Nature 371, 497 (1994); M. Liphardt, A. Goonesekera, B. Jones, S. Ducharme, J. Takacs, and L. Zhang, Science 263, 367 (1994); A. Grunnet-Jepsen, C. Thompson, and W. Moerner, Science 277, 549 (1997).
[CrossRef] [PubMed]

Krolikowski, W.

Lee, V.

C. Poga, P. Lundquist, V. Lee, R. Shelby, R. Twieg, and D. Burland, Appl. Phys. Lett. 69, 1047 (1996).
[CrossRef]

Lundquist, P.

C. Poga, P. Lundquist, V. Lee, R. Shelby, R. Twieg, and D. Burland, Appl. Phys. Lett. 69, 1047 (1996).
[CrossRef]

Luther-Davies, B.

Mack, J. X.

J. X. Mack, L. B. Schein, and A. Peled, Phys. Rev. B 39, 7500 (1989).
[CrossRef]

McComb, I.

Meerholz, K.

K. Meerholz, B. Volodin, Sandalphon, B. Kippelen, and N. Peyghambarian, Nature 371, 497 (1994); M. Liphardt, A. Goonesekera, B. Jones, S. Ducharme, J. Takacs, and L. Zhang, Science 263, 367 (1994); A. Grunnet-Jepsen, C. Thompson, and W. Moerner, Science 277, 549 (1997).
[CrossRef] [PubMed]

Melz, P. J.

P. J. Melz, J. Chem. Phys. 57, 1694 (1972).

Moerner, W.

Moerner, W. E.

A. Grunnet-Jepsen, C. L. Thompson, R. J. Twieg, and W. E. Moerner, Appl. Phys. Lett. 70, 1515 (1997).
[CrossRef]

W. E. Moerner and S. M. Silence, Chem. Rev. 94, 127 (1994).
[CrossRef]

S. Ducharme, J. C. Scott, R. J. Twieg, and W. E. Moerner, Phy. Rev. Lett. 66, 1846 (1991).
[CrossRef]

Moylan, C.

Peled, A.

J. X. Mack, L. B. Schein, and A. Peled, Phys. Rev. B 39, 7500 (1989).
[CrossRef]

Peyghambarian, N.

K. Meerholz, B. Volodin, Sandalphon, B. Kippelen, and N. Peyghambarian, Nature 371, 497 (1994); M. Liphardt, A. Goonesekera, B. Jones, S. Ducharme, J. Takacs, and L. Zhang, Science 263, 367 (1994); A. Grunnet-Jepsen, C. Thompson, and W. Moerner, Science 277, 549 (1997).
[CrossRef] [PubMed]

Poga, C.

C. Poga, P. Lundquist, V. Lee, R. Shelby, R. Twieg, and D. Burland, Appl. Phys. Lett. 69, 1047 (1996).
[CrossRef]

Salamo, G.

M.-F. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, Electron. Lett. 31, 826 (1995).
[CrossRef]

Sandalphon,

K. Meerholz, B. Volodin, Sandalphon, B. Kippelen, and N. Peyghambarian, Nature 371, 497 (1994); M. Liphardt, A. Goonesekera, B. Jones, S. Ducharme, J. Takacs, and L. Zhang, Science 263, 367 (1994); A. Grunnet-Jepsen, C. Thompson, and W. Moerner, Science 277, 549 (1997).
[CrossRef] [PubMed]

Schein, L. B.

J. X. Mack, L. B. Schein, and A. Peled, Phys. Rev. B 39, 7500 (1989).
[CrossRef]

Schildkraut, J. S.

J. S. Schildkraut and A. V. Buettner, J. Appl. Phys. 72, 1888 (1992).
[CrossRef]

Schloter, S.

Schmidt, H.

Scott, J. C.

S. Ducharme, J. C. Scott, R. J. Twieg, and W. E. Moerner, Phy. Rev. Lett. 66, 1846 (1991).
[CrossRef]

Segev, M.

M. Segev and G. Stegeman, Phys. Today 51(8), 42 (1998), and references therein.
[CrossRef]

M. Segev and A. J. Agranat, Opt. Lett. 22, 1299 (1997).
[CrossRef]

M.-F. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, Electron. Lett. 31, 826 (1995).
[CrossRef]

M. Segev, G. C. Valley, B. Crosignani, P. Diporto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994); M. Segev, M. Shih, and G. C. Valley, J. Opt. Soc. Am. B 13, 706 (1996).
[CrossRef] [PubMed]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, Phys. Rev. Lett. 68, 923 (1992).
[CrossRef] [PubMed]

Shelby, R.

C. Poga, P. Lundquist, V. Lee, R. Shelby, R. Twieg, and D. Burland, Appl. Phys. Lett. 69, 1047 (1996).
[CrossRef]

Shih, M.-F.

M.-F. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, Electron. Lett. 31, 826 (1995).
[CrossRef]

Silence, S.

Silence, S. M.

W. E. Moerner and S. M. Silence, Chem. Rev. 94, 127 (1994).
[CrossRef]

Stegeman, G.

M. Segev and G. Stegeman, Phys. Today 51(8), 42 (1998), and references therein.
[CrossRef]

Strohriegl, P.

Thompson, C. L.

A. Grunnet-Jepsen, C. L. Thompson, R. J. Twieg, and W. E. Moerner, Appl. Phys. Lett. 70, 1515 (1997).
[CrossRef]

Twieg, R.

C. Moylan, R. Wortmann, R. Twieg, and I. McComb, J. Opt. Soc. Am. B 15, 929 (1998).
[CrossRef]

C. Poga, P. Lundquist, V. Lee, R. Shelby, R. Twieg, and D. Burland, Appl. Phys. Lett. 69, 1047 (1996).
[CrossRef]

Twieg, R. J.

A. Grunnet-Jepsen, C. L. Thompson, R. J. Twieg, and W. E. Moerner, Appl. Phys. Lett. 70, 1515 (1997).
[CrossRef]

S. Ducharme, J. C. Scott, R. J. Twieg, and W. E. Moerner, Phy. Rev. Lett. 66, 1846 (1991).
[CrossRef]

Valley, G. C.

M.-F. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, Electron. Lett. 31, 826 (1995).
[CrossRef]

M. Segev, G. C. Valley, B. Crosignani, P. Diporto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994); M. Segev, M. Shih, and G. C. Valley, J. Opt. Soc. Am. B 13, 706 (1996).
[CrossRef] [PubMed]

Volodin, B.

K. Meerholz, B. Volodin, Sandalphon, B. Kippelen, and N. Peyghambarian, Nature 371, 497 (1994); M. Liphardt, A. Goonesekera, B. Jones, S. Ducharme, J. Takacs, and L. Zhang, Science 263, 367 (1994); A. Grunnet-Jepsen, C. Thompson, and W. Moerner, Science 277, 549 (1997).
[CrossRef] [PubMed]

Wortmann, R.

Wu, J. W.

Yariv, A.

M. Segev, G. C. Valley, B. Crosignani, P. Diporto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994); M. Segev, M. Shih, and G. C. Valley, J. Opt. Soc. Am. B 13, 706 (1996).
[CrossRef] [PubMed]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, Phys. Rev. Lett. 68, 923 (1992).
[CrossRef] [PubMed]

Appl. Phys. Lett. (2)

C. Poga, P. Lundquist, V. Lee, R. Shelby, R. Twieg, and D. Burland, Appl. Phys. Lett. 69, 1047 (1996).
[CrossRef]

A. Grunnet-Jepsen, C. L. Thompson, R. J. Twieg, and W. E. Moerner, Appl. Phys. Lett. 70, 1515 (1997).
[CrossRef]

Chem. Rev. (1)

W. E. Moerner and S. M. Silence, Chem. Rev. 94, 127 (1994).
[CrossRef]

Electron. Lett. (1)

M.-F. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, Electron. Lett. 31, 826 (1995).
[CrossRef]

J. Appl. Phys. (1)

J. S. Schildkraut and A. V. Buettner, J. Appl. Phys. 72, 1888 (1992).
[CrossRef]

J. Chem. Phys. (1)

P. J. Melz, J. Chem. Phys. 57, 1694 (1972).

J. Opt. Soc. Am. B (5)

Nature (1)

K. Meerholz, B. Volodin, Sandalphon, B. Kippelen, and N. Peyghambarian, Nature 371, 497 (1994); M. Liphardt, A. Goonesekera, B. Jones, S. Ducharme, J. Takacs, and L. Zhang, Science 263, 367 (1994); A. Grunnet-Jepsen, C. Thompson, and W. Moerner, Science 277, 549 (1997).
[CrossRef] [PubMed]

Opt. Lett. (2)

Phy. Rev. Lett. (1)

S. Ducharme, J. C. Scott, R. J. Twieg, and W. E. Moerner, Phy. Rev. Lett. 66, 1846 (1991).
[CrossRef]

Phys. Rev. B (1)

J. X. Mack, L. B. Schein, and A. Peled, Phys. Rev. B 39, 7500 (1989).
[CrossRef]

Phys. Rev. Lett. (2)

M. Segev, G. C. Valley, B. Crosignani, P. Diporto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994); M. Segev, M. Shih, and G. C. Valley, J. Opt. Soc. Am. B 13, 706 (1996).
[CrossRef] [PubMed]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, Phys. Rev. Lett. 68, 923 (1992).
[CrossRef] [PubMed]

Phys. Today (1)

M. Segev and G. Stegeman, Phys. Today 51(8), 42 (1998), and references therein.
[CrossRef]

Other (2)

Both approximations were justified physically4,17 in terms of the inequality Ed?E?Eq, where Eq and Ed are the limiting space-charge field and the diffusion field, respectively, evaluated at a soliton width of not less than 5 µm.

For a typical example from Ref. 19, with ?D?10 D, ??0=5×10-23 cm3, and E=100 V/µm, the induced dipole contributes only one sixtieth of the total dipole energy.

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Figures (3)

Fig. 1
Fig. 1

Arrangement for observing (a) bright and (g) dark polymeric solitons. Formation of (b–f) bright and (h–l) dark polymeric solitons. (d), and (j) Alignment of the chromophores. The degrees of the alignment are exaggerated and should be more random in a real situation.

Fig. 2
Fig. 2

Angle distribution cos2 θ-1/3. The inset shows that cos2 θ-1/3 (solid curve) can be approximated by 0.043µDE/kBTa2 (dashed curve) for μDE/kBTa<0.8.

Fig. 3
Fig. 3

Normalized soliton widths of (a) bright solitons as function of u0 and (b) dark solitons as function of γ for several m values.

Equations (10)

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

J=eμρE-eDρx=const. or Jx=0,
N-t=sϕN-N-I+Ib-eμ0rρN-=0,
T+t=eμ0rρT-T+-rT+=0,
Ex=e0rρ-N-+T+,
2x2+2z2Eopt+k0n2Eopt=0.
Em+1=E0m+1I0+Ib/I+Ib,
iφz+12kφxx+k022kΔn2φ=0,
iφz+12kφxx+k022kCx,yE2φ=0,
iφζ+φξξ+βγ+1φ2+12/m+1φ=0,
d2µdξ2=Γ±γ+1u2+12/m+1u,

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