Abstract

We predict and analyze the formation of photorefractive polymeric solitons, which are supported by both the orientationally enhanced birefringence and the orientationally enhanced electro-optic effects. The formation conditions and characteristics of this new type of optical spatial soliton are discussed.

© 2001 Optical Society of America

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  1. R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13, 479–482 (1964).
    [CrossRef]
  2. P. L. Kelley, “Self-focusing of optical beams,” Phys. Rev. Lett. 15, 1005–1008 (1965).
    [CrossRef]
  3. V. E. Zakharov and A. M. Rubenchik, “Instability of waveguides and solitons in nonlinear media,” Sov. Phys. JETP 38, 494–500 (1974).
  4. M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923–926 (1992).
    [CrossRef] [PubMed]
  5. M. Segev, G. C. Valley, B. Crosignani, P. Diporto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73, 3211–3214 (1994).
    [CrossRef] [PubMed]
  6. D. N. Christodoulides and M. Carvalho, “Bright, dark, and gray spatial soliton states in photorefractive media,” J. Opt. Soc. Am. B 12, 1628–1633 (1995).
    [CrossRef]
  7. M. Segev, M. Shih, and G. C. Valley, “Photorefractive screening solitons of high and low intensity,” J. Opt. Soc. Am. B 13, 706–718 (1996).
    [CrossRef]
  8. G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. C. Bashaw, “Dark and bright photovoltaic spatial solitons,” Phys. Rev. A 50, R4457–R4460 (1994).
    [CrossRef] [PubMed]
  9. M. Taya, M. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, “Observation of dark photovoltaic spatial solitons,” Phys. Rev. A 52, 3095–3100 (1995).
    [CrossRef] [PubMed]
  10. M. Segev, G. C. Valley, M. C. Bashaw, M. Taya, and M. M. Fejer, “Photovoltaic spatial solitons,” J. Opt. Soc. Am. B 14, 1772–1781 (1997).
    [CrossRef]
  11. M. Segev and A. J. Agranat, “Spatial solitons in centrosymmetric photorefractive media,” Opt. Lett. 22, 1299–1301 (1997).
    [CrossRef]
  12. M. Chauvet, S. Hawkins, G. Salamo, M. Segev, D. Bliss, and G. Bryant, “Self-trapping of planar optical beams by use of the photorefractive effect in InP:Fe,” Opt. Lett. 21, 1333–1335 (1996); “Self-trapping of two-dimensional optical beams and light-induced waveguiding in photorefractive InP at telecommunication wavelengths,” Appl. Phys. Lett. 70, 2499–2501 (1997).
    [CrossRef] [PubMed]
  13. M. Segev and G. Stegeman, “Self-trapping of optical beams: spatial solitons,” Phys. Today 51(8), 42–48 (1998), and references therein.
    [CrossRef]
  14. S. Ducharme, J. C. Scott, R. J. Twieg, and W. E. Moerner, “Observation of the photorefractive effect in a polymer,” Phys. Rev. Lett. 66, 1846–1849 (1991).
    [CrossRef] [PubMed]
  15. C. Poga, P. Lundquist, V. Lee, R. Shelby, R. Twieg, and D. Burland, “Polysiloxane-based photorefractive polymers for digital holographic data storage,” Appl. Phys. Lett. 69, 1047–1049 (1996).
    [CrossRef]
  16. P. Günter and J.-P. Huignard, Photorefractive Materials and Their Applications (Springer, Berlin, 1988 and 1989); Vols. 1 and 2.
  17. K. Meerholz, B. L. Volodin, Sandalphon, B. Kippelen, and N. Peyghambarian, “A photorefractive polymer with high optical gain and diffraction efficiency near 100%,” Nature (London) 371, 497–500 (1994); M. Liphardt, A. Goonesekera, B. Jones, S. Ducharme, J. Takacs, and L. Zhang, “High-performance photorefractive polymers,” Science 263, 367–369 (1994).
    [CrossRef] [PubMed]
  18. W. E. Moerner and S. M. Silence, “Polymeric photorefractive materials,” Chem. Rev. 94, 127–155 (1994).
    [CrossRef]
  19. A. Grunnet-Jepsen, C. L. Thompson, R. J. Twieg, and W. E. Moerner, “High performance photorefractive polymer with improved stability,” Appl. Phys. Lett. 70, 1515–1517 (1997).
    [CrossRef]
  20. W. E. Moerner, S. M. Silence, F. Hache, and G. C. Bjorklund, “Orientationally enhanced photorefractive effect in polymers,” J. Opt. Soc. Am. B 11, 320–330 (1994).
    [CrossRef]
  21. M. Shih and F. Sheu, “Photorefractive polymeric optical spatial solitons,” Opt. Lett. 24, 1853–1855 (1999).
    [CrossRef]
  22. J. W. Wu, “Birefringent and electro-optic effects in poled polymer films: steady-state and transient properties,” J. Opt. Soc. Am. B 8, 142–152 (1991).
    [CrossRef]
  23. By J. X. Mack, L. B. Schein, and A. Peled, “Hole mobilities in hydrazone-polycarbonate dispersions,” Phys. Rev. B 39, 7500–7508 (1989), hole mobility μ∝ exp[C(E−1)], where C is an experimentally determined constant.
    [CrossRef]
  24. By Onsager model [P. J. Melz, “Photogeneration in trinitrofluorenone-poly(n-vinylcarbazole),” J. Chem. Phys. 57, 1694–1699 (1972)], quantum efficiency φ∝Em, for the static dc field E between 10 and 100 V/μm, where m is a material parameter ranging from less than 1.0 to greater than 3.0.
    [CrossRef]
  25. Both approximations were justified physically619 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 the soliton width of no less than 5 μm.
  26. 〈cosm θ〉=∫0π cosm θ exp(−U/ kBTa)sin θ dθ/∫0πexp(−U /kB Ta)×sinθ dθ, where U=−μD⋅E0−p⋅E0/2 is the dipole interaction energy, kB is the Boltzmann constant, and Ta is the ambient temperature. We can safely neglect the induced dipole energy, p⋅E0/2, since for typical photorefractive polymers22 with the orientational enhancement photorefractive effect, μD≅10 D and Δα0=5×10−23 cm3, under the dc field E<100 V/μm, the induced dipole energy is less than 1/60 of the total energy U. Thus U≅−μD⋅E0=−μDE cos θ.
  27. A. Galvan-Gonzalez, M. Canva, G. Stegeman, R. Twieg, K.-P. Chan, T. Kowalczyk, X. Zhang, and H. Lackritz, “Systematic behavior of electro-optic chromophore photostability,” Opt. Lett. 25, 332–334 (2000).
    [CrossRef]
  28. C. Moylan, R. Wortmann, R. Twieg, and I. McComb, “Improved characterization of chromophores for photorefractive applications,” J. Opt. Soc. Am. B 15, 929–932 (1998).
    [CrossRef]
  29. C. Chen and S. Chi, “Subwavelength spatial solitons of TE mode,” Opt. Commun. 157, 170–172 (1998).
    [CrossRef]
  30. J. A. Herlocker, K. B. Ferrio, E. Hendrickx, B. D. Guenther, S. Mery, B. Kippelen, and N. Peyghambarian, “Direct observation of orientation limit in a fast photorefractive polymer composite,” Appl. Phys. Lett. 74, 2253–2255 (1999).
    [CrossRef]
  31. D. Wright, M. A. Diaz-Garcia, J. D. Casperson, M. DeClue, W. E. Moerner, and R. J. Twieg, “High-speed photorefractive polymer composites,” Appl. Phys. Lett. 73, 1490–1492 (1998).
    [CrossRef]
  32. K. S. West, D. P. West, M. D. Rahn, J. D. Shakos, F. A. Wade, K. Khand, and T. A. King, “Photorefractive polymer composite trapping properties and a link with chromophore structure,” J. Appl. Phys. 84, 5893–5899 (1998).
    [CrossRef]
  33. K. D. Singer, J. E. Sohn, and S. J. Lalama, “Second harmonic generation in poled polymer films,” Appl. Phys. Lett. 49, 248–250 (1986).
    [CrossRef]

2000

1999

M. Shih and F. Sheu, “Photorefractive polymeric optical spatial solitons,” Opt. Lett. 24, 1853–1855 (1999).
[CrossRef]

J. A. Herlocker, K. B. Ferrio, E. Hendrickx, B. D. Guenther, S. Mery, B. Kippelen, and N. Peyghambarian, “Direct observation of orientation limit in a fast photorefractive polymer composite,” Appl. Phys. Lett. 74, 2253–2255 (1999).
[CrossRef]

1998

D. Wright, M. A. Diaz-Garcia, J. D. Casperson, M. DeClue, W. E. Moerner, and R. J. Twieg, “High-speed photorefractive polymer composites,” Appl. Phys. Lett. 73, 1490–1492 (1998).
[CrossRef]

K. S. West, D. P. West, M. D. Rahn, J. D. Shakos, F. A. Wade, K. Khand, and T. A. King, “Photorefractive polymer composite trapping properties and a link with chromophore structure,” J. Appl. Phys. 84, 5893–5899 (1998).
[CrossRef]

C. Moylan, R. Wortmann, R. Twieg, and I. McComb, “Improved characterization of chromophores for photorefractive applications,” J. Opt. Soc. Am. B 15, 929–932 (1998).
[CrossRef]

C. Chen and S. Chi, “Subwavelength spatial solitons of TE mode,” Opt. Commun. 157, 170–172 (1998).
[CrossRef]

M. Segev and G. Stegeman, “Self-trapping of optical beams: spatial solitons,” Phys. Today 51(8), 42–48 (1998), and references therein.
[CrossRef]

1997

1996

C. Poga, P. Lundquist, V. Lee, R. Shelby, R. Twieg, and D. Burland, “Polysiloxane-based photorefractive polymers for digital holographic data storage,” Appl. Phys. Lett. 69, 1047–1049 (1996).
[CrossRef]

M. Segev, M. Shih, and G. C. Valley, “Photorefractive screening solitons of high and low intensity,” J. Opt. Soc. Am. B 13, 706–718 (1996).
[CrossRef]

1995

D. N. Christodoulides and M. Carvalho, “Bright, dark, and gray spatial soliton states in photorefractive media,” J. Opt. Soc. Am. B 12, 1628–1633 (1995).
[CrossRef]

M. Taya, M. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, “Observation of dark photovoltaic spatial solitons,” Phys. Rev. A 52, 3095–3100 (1995).
[CrossRef] [PubMed]

1994

M. Segev, G. C. Valley, B. Crosignani, P. Diporto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73, 3211–3214 (1994).
[CrossRef] [PubMed]

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. C. Bashaw, “Dark and bright photovoltaic spatial solitons,” Phys. Rev. A 50, R4457–R4460 (1994).
[CrossRef] [PubMed]

W. E. Moerner and S. M. Silence, “Polymeric photorefractive materials,” Chem. Rev. 94, 127–155 (1994).
[CrossRef]

W. E. Moerner, S. M. Silence, F. Hache, and G. C. Bjorklund, “Orientationally enhanced photorefractive effect in polymers,” J. Opt. Soc. Am. B 11, 320–330 (1994).
[CrossRef]

1992

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923–926 (1992).
[CrossRef] [PubMed]

1991

S. Ducharme, J. C. Scott, R. J. Twieg, and W. E. Moerner, “Observation of the photorefractive effect in a polymer,” Phys. Rev. Lett. 66, 1846–1849 (1991).
[CrossRef] [PubMed]

J. W. Wu, “Birefringent and electro-optic effects in poled polymer films: steady-state and transient properties,” J. Opt. Soc. Am. B 8, 142–152 (1991).
[CrossRef]

1989

By J. X. Mack, L. B. Schein, and A. Peled, “Hole mobilities in hydrazone-polycarbonate dispersions,” Phys. Rev. B 39, 7500–7508 (1989), hole mobility μ∝ exp[C(E−1)], where C is an experimentally determined constant.
[CrossRef]

1986

K. D. Singer, J. E. Sohn, and S. J. Lalama, “Second harmonic generation in poled polymer films,” Appl. Phys. Lett. 49, 248–250 (1986).
[CrossRef]

1974

V. E. Zakharov and A. M. Rubenchik, “Instability of waveguides and solitons in nonlinear media,” Sov. Phys. JETP 38, 494–500 (1974).

1972

By Onsager model [P. J. Melz, “Photogeneration in trinitrofluorenone-poly(n-vinylcarbazole),” J. Chem. Phys. 57, 1694–1699 (1972)], quantum efficiency φ∝Em, for the static dc field E between 10 and 100 V/μm, where m is a material parameter ranging from less than 1.0 to greater than 3.0.
[CrossRef]

1965

P. L. Kelley, “Self-focusing of optical beams,” Phys. Rev. Lett. 15, 1005–1008 (1965).
[CrossRef]

1964

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13, 479–482 (1964).
[CrossRef]

Agranat, A. J.

Bashaw, M.

M. Taya, M. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, “Observation of dark photovoltaic spatial solitons,” Phys. Rev. A 52, 3095–3100 (1995).
[CrossRef] [PubMed]

Bashaw, M. C.

M. Segev, G. C. Valley, M. C. Bashaw, M. Taya, and M. M. Fejer, “Photovoltaic spatial solitons,” J. Opt. Soc. Am. B 14, 1772–1781 (1997).
[CrossRef]

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. C. Bashaw, “Dark and bright photovoltaic spatial solitons,” Phys. Rev. A 50, R4457–R4460 (1994).
[CrossRef] [PubMed]

Bjorklund, G. C.

Burland, D.

C. Poga, P. Lundquist, V. Lee, R. Shelby, R. Twieg, and D. Burland, “Polysiloxane-based photorefractive polymers for digital holographic data storage,” Appl. Phys. Lett. 69, 1047–1049 (1996).
[CrossRef]

Canva, M.

Carvalho, M.

Casperson, J. D.

D. Wright, M. A. Diaz-Garcia, J. D. Casperson, M. DeClue, W. E. Moerner, and R. J. Twieg, “High-speed photorefractive polymer composites,” Appl. Phys. Lett. 73, 1490–1492 (1998).
[CrossRef]

Chan, K.-P.

Chen, C.

C. Chen and S. Chi, “Subwavelength spatial solitons of TE mode,” Opt. Commun. 157, 170–172 (1998).
[CrossRef]

Chi, S.

C. Chen and S. Chi, “Subwavelength spatial solitons of TE mode,” Opt. Commun. 157, 170–172 (1998).
[CrossRef]

Chiao, R. Y.

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13, 479–482 (1964).
[CrossRef]

Christodoulides, D. N.

Crosignani, B.

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. C. Bashaw, “Dark and bright photovoltaic spatial solitons,” Phys. Rev. A 50, R4457–R4460 (1994).
[CrossRef] [PubMed]

M. Segev, G. C. Valley, B. Crosignani, P. Diporto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73, 3211–3214 (1994).
[CrossRef] [PubMed]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923–926 (1992).
[CrossRef] [PubMed]

DeClue, M.

D. Wright, M. A. Diaz-Garcia, J. D. Casperson, M. DeClue, W. E. Moerner, and R. J. Twieg, “High-speed photorefractive polymer composites,” Appl. Phys. Lett. 73, 1490–1492 (1998).
[CrossRef]

Diaz-Garcia, M. A.

D. Wright, M. A. Diaz-Garcia, J. D. Casperson, M. DeClue, W. E. Moerner, and R. J. Twieg, “High-speed photorefractive polymer composites,” Appl. Phys. Lett. 73, 1490–1492 (1998).
[CrossRef]

Diporto, P.

M. Segev, G. C. Valley, B. Crosignani, P. Diporto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73, 3211–3214 (1994).
[CrossRef] [PubMed]

Ducharme, S.

S. Ducharme, J. C. Scott, R. J. Twieg, and W. E. Moerner, “Observation of the photorefractive effect in a polymer,” Phys. Rev. Lett. 66, 1846–1849 (1991).
[CrossRef] [PubMed]

Fejer, M. M.

M. Segev, G. C. Valley, M. C. Bashaw, M. Taya, and M. M. Fejer, “Photovoltaic spatial solitons,” J. Opt. Soc. Am. B 14, 1772–1781 (1997).
[CrossRef]

M. Taya, M. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, “Observation of dark photovoltaic spatial solitons,” Phys. Rev. A 52, 3095–3100 (1995).
[CrossRef] [PubMed]

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. C. Bashaw, “Dark and bright photovoltaic spatial solitons,” Phys. Rev. A 50, R4457–R4460 (1994).
[CrossRef] [PubMed]

Ferrio, K. B.

J. A. Herlocker, K. B. Ferrio, E. Hendrickx, B. D. Guenther, S. Mery, B. Kippelen, and N. Peyghambarian, “Direct observation of orientation limit in a fast photorefractive polymer composite,” Appl. Phys. Lett. 74, 2253–2255 (1999).
[CrossRef]

Fischer, B.

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923–926 (1992).
[CrossRef] [PubMed]

Galvan-Gonzalez, A.

Garmire, E.

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13, 479–482 (1964).
[CrossRef]

Grunnet-Jepsen, A.

A. Grunnet-Jepsen, C. L. Thompson, R. J. Twieg, and W. E. Moerner, “High performance photorefractive polymer with improved stability,” Appl. Phys. Lett. 70, 1515–1517 (1997).
[CrossRef]

Guenther, B. D.

J. A. Herlocker, K. B. Ferrio, E. Hendrickx, B. D. Guenther, S. Mery, B. Kippelen, and N. Peyghambarian, “Direct observation of orientation limit in a fast photorefractive polymer composite,” Appl. Phys. Lett. 74, 2253–2255 (1999).
[CrossRef]

Hache, F.

Hendrickx, E.

J. A. Herlocker, K. B. Ferrio, E. Hendrickx, B. D. Guenther, S. Mery, B. Kippelen, and N. Peyghambarian, “Direct observation of orientation limit in a fast photorefractive polymer composite,” Appl. Phys. Lett. 74, 2253–2255 (1999).
[CrossRef]

Herlocker, J. A.

J. A. Herlocker, K. B. Ferrio, E. Hendrickx, B. D. Guenther, S. Mery, B. Kippelen, and N. Peyghambarian, “Direct observation of orientation limit in a fast photorefractive polymer composite,” Appl. Phys. Lett. 74, 2253–2255 (1999).
[CrossRef]

Kelley, P. L.

P. L. Kelley, “Self-focusing of optical beams,” Phys. Rev. Lett. 15, 1005–1008 (1965).
[CrossRef]

Khand, K.

K. S. West, D. P. West, M. D. Rahn, J. D. Shakos, F. A. Wade, K. Khand, and T. A. King, “Photorefractive polymer composite trapping properties and a link with chromophore structure,” J. Appl. Phys. 84, 5893–5899 (1998).
[CrossRef]

King, T. A.

K. S. West, D. P. West, M. D. Rahn, J. D. Shakos, F. A. Wade, K. Khand, and T. A. King, “Photorefractive polymer composite trapping properties and a link with chromophore structure,” J. Appl. Phys. 84, 5893–5899 (1998).
[CrossRef]

Kippelen, B.

J. A. Herlocker, K. B. Ferrio, E. Hendrickx, B. D. Guenther, S. Mery, B. Kippelen, and N. Peyghambarian, “Direct observation of orientation limit in a fast photorefractive polymer composite,” Appl. Phys. Lett. 74, 2253–2255 (1999).
[CrossRef]

Kowalczyk, T.

Lackritz, H.

Lalama, S. J.

K. D. Singer, J. E. Sohn, and S. J. Lalama, “Second harmonic generation in poled polymer films,” Appl. Phys. Lett. 49, 248–250 (1986).
[CrossRef]

Lee, V.

C. Poga, P. Lundquist, V. Lee, R. Shelby, R. Twieg, and D. Burland, “Polysiloxane-based photorefractive polymers for digital holographic data storage,” Appl. Phys. Lett. 69, 1047–1049 (1996).
[CrossRef]

Lundquist, P.

C. Poga, P. Lundquist, V. Lee, R. Shelby, R. Twieg, and D. Burland, “Polysiloxane-based photorefractive polymers for digital holographic data storage,” Appl. Phys. Lett. 69, 1047–1049 (1996).
[CrossRef]

Mack, J. X.

By J. X. Mack, L. B. Schein, and A. Peled, “Hole mobilities in hydrazone-polycarbonate dispersions,” Phys. Rev. B 39, 7500–7508 (1989), hole mobility μ∝ exp[C(E−1)], where C is an experimentally determined constant.
[CrossRef]

McComb, I.

Melz, P. J.

By Onsager model [P. J. Melz, “Photogeneration in trinitrofluorenone-poly(n-vinylcarbazole),” J. Chem. Phys. 57, 1694–1699 (1972)], quantum efficiency φ∝Em, for the static dc field E between 10 and 100 V/μm, where m is a material parameter ranging from less than 1.0 to greater than 3.0.
[CrossRef]

Mery, S.

J. A. Herlocker, K. B. Ferrio, E. Hendrickx, B. D. Guenther, S. Mery, B. Kippelen, and N. Peyghambarian, “Direct observation of orientation limit in a fast photorefractive polymer composite,” Appl. Phys. Lett. 74, 2253–2255 (1999).
[CrossRef]

Moerner, W. E.

D. Wright, M. A. Diaz-Garcia, J. D. Casperson, M. DeClue, W. E. Moerner, and R. J. Twieg, “High-speed photorefractive polymer composites,” Appl. Phys. Lett. 73, 1490–1492 (1998).
[CrossRef]

A. Grunnet-Jepsen, C. L. Thompson, R. J. Twieg, and W. E. Moerner, “High performance photorefractive polymer with improved stability,” Appl. Phys. Lett. 70, 1515–1517 (1997).
[CrossRef]

W. E. Moerner, S. M. Silence, F. Hache, and G. C. Bjorklund, “Orientationally enhanced photorefractive effect in polymers,” J. Opt. Soc. Am. B 11, 320–330 (1994).
[CrossRef]

W. E. Moerner and S. M. Silence, “Polymeric photorefractive materials,” Chem. Rev. 94, 127–155 (1994).
[CrossRef]

S. Ducharme, J. C. Scott, R. J. Twieg, and W. E. Moerner, “Observation of the photorefractive effect in a polymer,” Phys. Rev. Lett. 66, 1846–1849 (1991).
[CrossRef] [PubMed]

Moylan, C.

Peled, A.

By J. X. Mack, L. B. Schein, and A. Peled, “Hole mobilities in hydrazone-polycarbonate dispersions,” Phys. Rev. B 39, 7500–7508 (1989), hole mobility μ∝ exp[C(E−1)], where C is an experimentally determined constant.
[CrossRef]

Peyghambarian, N.

J. A. Herlocker, K. B. Ferrio, E. Hendrickx, B. D. Guenther, S. Mery, B. Kippelen, and N. Peyghambarian, “Direct observation of orientation limit in a fast photorefractive polymer composite,” Appl. Phys. Lett. 74, 2253–2255 (1999).
[CrossRef]

Poga, C.

C. Poga, P. Lundquist, V. Lee, R. Shelby, R. Twieg, and D. Burland, “Polysiloxane-based photorefractive polymers for digital holographic data storage,” Appl. Phys. Lett. 69, 1047–1049 (1996).
[CrossRef]

Rahn, M. D.

K. S. West, D. P. West, M. D. Rahn, J. D. Shakos, F. A. Wade, K. Khand, and T. A. King, “Photorefractive polymer composite trapping properties and a link with chromophore structure,” J. Appl. Phys. 84, 5893–5899 (1998).
[CrossRef]

Rubenchik, A. M.

V. E. Zakharov and A. M. Rubenchik, “Instability of waveguides and solitons in nonlinear media,” Sov. Phys. JETP 38, 494–500 (1974).

Schein, L. B.

By J. X. Mack, L. B. Schein, and A. Peled, “Hole mobilities in hydrazone-polycarbonate dispersions,” Phys. Rev. B 39, 7500–7508 (1989), hole mobility μ∝ exp[C(E−1)], where C is an experimentally determined constant.
[CrossRef]

Scott, J. C.

S. Ducharme, J. C. Scott, R. J. Twieg, and W. E. Moerner, “Observation of the photorefractive effect in a polymer,” Phys. Rev. Lett. 66, 1846–1849 (1991).
[CrossRef] [PubMed]

Segev, M.

M. Segev and G. Stegeman, “Self-trapping of optical beams: spatial solitons,” Phys. Today 51(8), 42–48 (1998), and references therein.
[CrossRef]

M. Segev and A. J. Agranat, “Spatial solitons in centrosymmetric photorefractive media,” Opt. Lett. 22, 1299–1301 (1997).
[CrossRef]

M. Segev, G. C. Valley, M. C. Bashaw, M. Taya, and M. M. Fejer, “Photovoltaic spatial solitons,” J. Opt. Soc. Am. B 14, 1772–1781 (1997).
[CrossRef]

M. Segev, M. Shih, and G. C. Valley, “Photorefractive screening solitons of high and low intensity,” J. Opt. Soc. Am. B 13, 706–718 (1996).
[CrossRef]

M. Taya, M. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, “Observation of dark photovoltaic spatial solitons,” Phys. Rev. A 52, 3095–3100 (1995).
[CrossRef] [PubMed]

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. C. Bashaw, “Dark and bright photovoltaic spatial solitons,” Phys. Rev. A 50, R4457–R4460 (1994).
[CrossRef] [PubMed]

M. Segev, G. C. Valley, B. Crosignani, P. Diporto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73, 3211–3214 (1994).
[CrossRef] [PubMed]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923–926 (1992).
[CrossRef] [PubMed]

Shakos, J. D.

K. S. West, D. P. West, M. D. Rahn, J. D. Shakos, F. A. Wade, K. Khand, and T. A. King, “Photorefractive polymer composite trapping properties and a link with chromophore structure,” J. Appl. Phys. 84, 5893–5899 (1998).
[CrossRef]

Shelby, R.

C. Poga, P. Lundquist, V. Lee, R. Shelby, R. Twieg, and D. Burland, “Polysiloxane-based photorefractive polymers for digital holographic data storage,” Appl. Phys. Lett. 69, 1047–1049 (1996).
[CrossRef]

Sheu, F.

Shih, M.

Silence, S. M.

Singer, K. D.

K. D. Singer, J. E. Sohn, and S. J. Lalama, “Second harmonic generation in poled polymer films,” Appl. Phys. Lett. 49, 248–250 (1986).
[CrossRef]

Sohn, J. E.

K. D. Singer, J. E. Sohn, and S. J. Lalama, “Second harmonic generation in poled polymer films,” Appl. Phys. Lett. 49, 248–250 (1986).
[CrossRef]

Stegeman, G.

Taya, M.

M. Segev, G. C. Valley, M. C. Bashaw, M. Taya, and M. M. Fejer, “Photovoltaic spatial solitons,” J. Opt. Soc. Am. B 14, 1772–1781 (1997).
[CrossRef]

M. Taya, M. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, “Observation of dark photovoltaic spatial solitons,” Phys. Rev. A 52, 3095–3100 (1995).
[CrossRef] [PubMed]

Thompson, C. L.

A. Grunnet-Jepsen, C. L. Thompson, R. J. Twieg, and W. E. Moerner, “High performance photorefractive polymer with improved stability,” Appl. Phys. Lett. 70, 1515–1517 (1997).
[CrossRef]

Townes, C. H.

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13, 479–482 (1964).
[CrossRef]

Twieg, R.

Twieg, R. J.

D. Wright, M. A. Diaz-Garcia, J. D. Casperson, M. DeClue, W. E. Moerner, and R. J. Twieg, “High-speed photorefractive polymer composites,” Appl. Phys. Lett. 73, 1490–1492 (1998).
[CrossRef]

A. Grunnet-Jepsen, C. L. Thompson, R. J. Twieg, and W. E. Moerner, “High performance photorefractive polymer with improved stability,” Appl. Phys. Lett. 70, 1515–1517 (1997).
[CrossRef]

S. Ducharme, J. C. Scott, R. J. Twieg, and W. E. Moerner, “Observation of the photorefractive effect in a polymer,” Phys. Rev. Lett. 66, 1846–1849 (1991).
[CrossRef] [PubMed]

Valley, G. C.

M. Segev, G. C. Valley, M. C. Bashaw, M. Taya, and M. M. Fejer, “Photovoltaic spatial solitons,” J. Opt. Soc. Am. B 14, 1772–1781 (1997).
[CrossRef]

M. Segev, M. Shih, and G. C. Valley, “Photorefractive screening solitons of high and low intensity,” J. Opt. Soc. Am. B 13, 706–718 (1996).
[CrossRef]

M. Taya, M. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, “Observation of dark photovoltaic spatial solitons,” Phys. Rev. A 52, 3095–3100 (1995).
[CrossRef] [PubMed]

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. C. Bashaw, “Dark and bright photovoltaic spatial solitons,” Phys. Rev. A 50, R4457–R4460 (1994).
[CrossRef] [PubMed]

M. Segev, G. C. Valley, B. Crosignani, P. Diporto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73, 3211–3214 (1994).
[CrossRef] [PubMed]

Wade, F. A.

K. S. West, D. P. West, M. D. Rahn, J. D. Shakos, F. A. Wade, K. Khand, and T. A. King, “Photorefractive polymer composite trapping properties and a link with chromophore structure,” J. Appl. Phys. 84, 5893–5899 (1998).
[CrossRef]

West, D. P.

K. S. West, D. P. West, M. D. Rahn, J. D. Shakos, F. A. Wade, K. Khand, and T. A. King, “Photorefractive polymer composite trapping properties and a link with chromophore structure,” J. Appl. Phys. 84, 5893–5899 (1998).
[CrossRef]

West, K. S.

K. S. West, D. P. West, M. D. Rahn, J. D. Shakos, F. A. Wade, K. Khand, and T. A. King, “Photorefractive polymer composite trapping properties and a link with chromophore structure,” J. Appl. Phys. 84, 5893–5899 (1998).
[CrossRef]

Wortmann, R.

Wright, D.

D. Wright, M. A. Diaz-Garcia, J. D. Casperson, M. DeClue, W. E. Moerner, and R. J. Twieg, “High-speed photorefractive polymer composites,” Appl. Phys. Lett. 73, 1490–1492 (1998).
[CrossRef]

Wu, J. W.

Yariv, A.

M. Segev, G. C. Valley, B. Crosignani, P. Diporto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73, 3211–3214 (1994).
[CrossRef] [PubMed]

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. C. Bashaw, “Dark and bright photovoltaic spatial solitons,” Phys. Rev. A 50, R4457–R4460 (1994).
[CrossRef] [PubMed]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923–926 (1992).
[CrossRef] [PubMed]

Zakharov, V. E.

V. E. Zakharov and A. M. Rubenchik, “Instability of waveguides and solitons in nonlinear media,” Sov. Phys. JETP 38, 494–500 (1974).

Zhang, X.

Appl. Phys. Lett.

C. Poga, P. Lundquist, V. Lee, R. Shelby, R. Twieg, and D. Burland, “Polysiloxane-based photorefractive polymers for digital holographic data storage,” Appl. Phys. Lett. 69, 1047–1049 (1996).
[CrossRef]

A. Grunnet-Jepsen, C. L. Thompson, R. J. Twieg, and W. E. Moerner, “High performance photorefractive polymer with improved stability,” Appl. Phys. Lett. 70, 1515–1517 (1997).
[CrossRef]

J. A. Herlocker, K. B. Ferrio, E. Hendrickx, B. D. Guenther, S. Mery, B. Kippelen, and N. Peyghambarian, “Direct observation of orientation limit in a fast photorefractive polymer composite,” Appl. Phys. Lett. 74, 2253–2255 (1999).
[CrossRef]

D. Wright, M. A. Diaz-Garcia, J. D. Casperson, M. DeClue, W. E. Moerner, and R. J. Twieg, “High-speed photorefractive polymer composites,” Appl. Phys. Lett. 73, 1490–1492 (1998).
[CrossRef]

K. D. Singer, J. E. Sohn, and S. J. Lalama, “Second harmonic generation in poled polymer films,” Appl. Phys. Lett. 49, 248–250 (1986).
[CrossRef]

Chem. Rev.

W. E. Moerner and S. M. Silence, “Polymeric photorefractive materials,” Chem. Rev. 94, 127–155 (1994).
[CrossRef]

J. Appl. Phys.

K. S. West, D. P. West, M. D. Rahn, J. D. Shakos, F. A. Wade, K. Khand, and T. A. King, “Photorefractive polymer composite trapping properties and a link with chromophore structure,” J. Appl. Phys. 84, 5893–5899 (1998).
[CrossRef]

J. Chem. Phys.

By Onsager model [P. J. Melz, “Photogeneration in trinitrofluorenone-poly(n-vinylcarbazole),” J. Chem. Phys. 57, 1694–1699 (1972)], quantum efficiency φ∝Em, for the static dc field E between 10 and 100 V/μm, where m is a material parameter ranging from less than 1.0 to greater than 3.0.
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

C. Chen and S. Chi, “Subwavelength spatial solitons of TE mode,” Opt. Commun. 157, 170–172 (1998).
[CrossRef]

Opt. Lett.

Phys. Rev. A

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. C. Bashaw, “Dark and bright photovoltaic spatial solitons,” Phys. Rev. A 50, R4457–R4460 (1994).
[CrossRef] [PubMed]

M. Taya, M. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, “Observation of dark photovoltaic spatial solitons,” Phys. Rev. A 52, 3095–3100 (1995).
[CrossRef] [PubMed]

Phys. Rev. B

By J. X. Mack, L. B. Schein, and A. Peled, “Hole mobilities in hydrazone-polycarbonate dispersions,” Phys. Rev. B 39, 7500–7508 (1989), hole mobility μ∝ exp[C(E−1)], where C is an experimentally determined constant.
[CrossRef]

Phys. Rev. Lett.

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13, 479–482 (1964).
[CrossRef]

P. L. Kelley, “Self-focusing of optical beams,” Phys. Rev. Lett. 15, 1005–1008 (1965).
[CrossRef]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923–926 (1992).
[CrossRef] [PubMed]

M. Segev, G. C. Valley, B. Crosignani, P. Diporto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73, 3211–3214 (1994).
[CrossRef] [PubMed]

S. Ducharme, J. C. Scott, R. J. Twieg, and W. E. Moerner, “Observation of the photorefractive effect in a polymer,” Phys. Rev. Lett. 66, 1846–1849 (1991).
[CrossRef] [PubMed]

Phys. Today

M. Segev and G. Stegeman, “Self-trapping of optical beams: spatial solitons,” Phys. Today 51(8), 42–48 (1998), and references therein.
[CrossRef]

Sov. Phys. JETP

V. E. Zakharov and A. M. Rubenchik, “Instability of waveguides and solitons in nonlinear media,” Sov. Phys. JETP 38, 494–500 (1974).

Other

M. Chauvet, S. Hawkins, G. Salamo, M. Segev, D. Bliss, and G. Bryant, “Self-trapping of planar optical beams by use of the photorefractive effect in InP:Fe,” Opt. Lett. 21, 1333–1335 (1996); “Self-trapping of two-dimensional optical beams and light-induced waveguiding in photorefractive InP at telecommunication wavelengths,” Appl. Phys. Lett. 70, 2499–2501 (1997).
[CrossRef] [PubMed]

P. Günter and J.-P. Huignard, Photorefractive Materials and Their Applications (Springer, Berlin, 1988 and 1989); Vols. 1 and 2.

K. Meerholz, B. L. Volodin, Sandalphon, B. Kippelen, and N. Peyghambarian, “A photorefractive polymer with high optical gain and diffraction efficiency near 100%,” Nature (London) 371, 497–500 (1994); M. Liphardt, A. Goonesekera, B. Jones, S. Ducharme, J. Takacs, and L. Zhang, “High-performance photorefractive polymers,” Science 263, 367–369 (1994).
[CrossRef] [PubMed]

Both approximations were justified physically619 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 the soliton width of no less than 5 μm.

〈cosm θ〉=∫0π cosm θ exp(−U/ kBTa)sin θ dθ/∫0πexp(−U /kB Ta)×sinθ dθ, where U=−μD⋅E0−p⋅E0/2 is the dipole interaction energy, kB is the Boltzmann constant, and Ta is the ambient temperature. We can safely neglect the induced dipole energy, p⋅E0/2, since for typical photorefractive polymers22 with the orientational enhancement photorefractive effect, μD≅10 D and Δα0=5×10−23 cm3, under the dc field E<100 V/μm, the induced dipole energy is less than 1/60 of the total energy U. Thus U≅−μD⋅E0=−μDE cos θ.

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Figures (7)

Fig. 1
Fig. 1

Formation of bright photorefractive polymeric optical spatial solitons: (a) arrangement; (b) intensity distribution; (c) electric field distribution; (d) the alignment of the chromophores, where the degrees of the alignment are exaggerated and should be more random in a real situation; (e) the index-change profile for Cx,y>0; (f) the index-change profile for Cx,y<0.

Fig. 2
Fig. 2

Formation of dark photorefractive polymeric optical spatial solitons: (a) arrangement; (b) intensity distribution; (c) electric field distribution; (d) the alignment of the chromophores; (e) the index-change profile for Cx,y>0; (f) the index-change profile for Cx,y<0.

Fig. 3
Fig. 3

Solid lines indicate the laboratory coordinates axes (x, y, z). Dashed lines indicate the molecular principal axes (1, 2, 3) with the c axis along the 3-axis. The dc bias electric field is applied along the x axis. θ is the angle between the chromophore dipole (3-axis) and the dc poling field (x axis). This system has a macroscopic rotational symmetry along the x axis.

Fig. 4
Fig. 4

Normalized soliton profiles u(ξ)/u0 of bright photorefractive polymeric optical spatial solitons, for several u0 values, and for (a) m=2 and (b) m=3.

Fig. 5
Fig. 5

Normalized soliton widths Δξ of bright photorefractive polymeric optical spatial solitons, as a function of u0, for several m values.

Fig. 6
Fig. 6

Normalized soliton profiles u(ξ)/u of dark photorefractive polymeric optical spatial solitons, for several u values, and for (a) m=2 and (b) m=3.

Fig. 7
Fig. 7

Normalized soliton widths Δξ of dark photorefractive polymeric optical spatial solitons, as a function of u, for several m values.

Equations (40)

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J=eμρE-eD ρx=const.
N-t=sϕ(N-N-)(I+Ib)-eμεrρN-=0,
T+t=eμεrρ(T-T+)-rT+=0,
Ex=4πeεr(ρ-N-+T+),
2x2+2z2Eopt+(k0n)2Eopt=0,
d2u(ξ)dξ2=u(ξ)=[Γ-k02x02Δ(n2)]u(ξ).
Em+1=Em+1(I+Ib)/(I+Ib)=Em+1(I+Ib)/(u2Ib+Ib),
Pω=Nchpω=Nchα(ω)·Eω+Nchβ(-ω;0, ω) : E0Eω+ ,
Px(1),BR=Nchpx(1)=Nchp1(1) cos θ1x+p2(1) cos θ2x+p3(1) cos θ3x=NchαExω cos2 θ1x+αExω cos2 θ2x+αExω cos2 θ3x=Nchα+Δα cos2 θExω,
Px(2),EO=Nchpx(2)=Nchp3(2) cos θ3x=Nchβ333E30E3ω cos θ3x=Nchβ333cos3 θEx0Exω,
ΔPxω=[Px(1),BR+Px(2),EO]Ex0=E-[Px(1),BR+Px(2),EO]Ex0=0=NchΔα(cos2 θE-cos2 θ0)Exω+Nchβ333(cos3 θEE)Exω.
Py(1),BR=Nchα+Δα cos2 θ3yEyω,
Py(2),EO=Nchβ333cos θ3x cos2 θ3yEx0Eyω.
ΔPyω=[Py(1),BR+Py(2),EO]Ex0=E-[Py(1),BR+Py(2),EO]Ex0=0=-NchΔα 12(cos2 θE-cos2 θ0)Eyω+Nchβ333 12[(cos θE-cos3 θE)E]Eyω.
Δ(n2)x=4πNch[Δα(cos2 θE-cos2 θ0)+β333cos3 θEE],
Δ(n2)y=4πNch-12Δα(cos2 θE-cos2 θ0)+12β333(cos θE-cos3 θE)E.
cosm θ=0π cosm θ exp(μDE cos θ/kBTa)sin θdθ/0π exp(μDE cos θ/kBTa)sin θ dθ.
(cos2 θE-cos2 θ0)(2/45)(μDE/kBTa)2,
cos3 θE(μDE/kBTa)/5,
(cos θE-cos3 θE/2)(μDE/kBTa)/15cos3 θE/3.
Δ(n2)x=Δ(n2)xBR+Δ(n2)xEO(CxBR+CxEO)E2CxE2,
Δ(n2)y=Δ(n2)yBR+Δ(n2)yEO(CyBR+CyEO)E2=(-CxBR/2+CxEO/3)E2CyE2,
u(ξ)=Γ-k02x02Cx, yE2u2+1u2(ξ)+12/(m+1)u(ξ),
u(ξ)=Γ±u2+1u2(ξ)+12/(m+1)u(ξ),
u=Γ+1u2+12/(m+1)u.
[u(ξ)]2=Γ[u2(ξ)-u02]+m+1m-1{[u2(ξ)+1](m-1)/(m+1)-[u02+1](m-1)/(m+1)}form1,
[u(ξ)]2=Γ[u2(ξ)-u02]+ln[u2(ξ)+1]-ln(u02+1)form=1.
Γ=m+1m-1[1-(u02+1)(m-1)/(m+1)]/u02 form1,
Γ=-ln(u02+1)/u02 form=1,
u=Γ(u2-u02)+m+1m-1[(u2+1)(m-1)/(m+1)-(u02+1)(m-1)/(m+1)]1/2 form1,
u=[Γ(u2-u02)+ln(u2+1)-ln(u02+1)]1/2
form=1.
u=1-u2+1u2+12/(m+1)u.
u=u2-m+1m-1(u2+1)2/(m+1)×[(u2+1)(m-1)/(m+1)-1]+[u(0)]21/2
form1,
u={u2-(u2+1)ln(u2+1)+[u(0)]2}1/2
form=1.
[u(0)]2=m+1m-1(u2+1)2/(m+1)×[(u2+1)(m-1)/(m+1)-1]-u2
form1,
[u(0)]2=(u2+1)ln(u2+1)-u2 form=1.

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