Abstract

We investigate soliton self-steering owing to the power-dependent walk-off in undoped nematic liquid crystals. The theoretical analysis, carried out in three dimensions and then reduced to an effective two-dimensional model retaining the nonlocal features, clarifies the trade-off between self-focusing and self-steering, as mediated by the initial orientation of the optic axis. Experimental results obtained in planar cells are in excellent agreement with the predictions, even when employing the two-dimensional model and in the presence of linear losses.

© 2010 Optical Society of America

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    [CrossRef] [PubMed]
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  47. A. Alberucci, A. Piccardi, M. Peccianti, M. Kaczmarek, and G. Assanto, “Propagation of spatial optical solitons in a dielectric with adjustable nonlinearity,” Phys. Rev. A 82, 023806 (2010).
    [CrossRef]
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    [CrossRef] [PubMed]
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2010 (6)

A. Alberucci, A. Piccardi, M. Peccianti, M. Kaczmarek, and G. Assanto, “Propagation of spatial optical solitons in a dielectric with adjustable nonlinearity,” Phys. Rev. A 82, 023806 (2010).
[CrossRef]

A. Piccardi, A. Alberucci, U. Bortolozzo, S. Residori, and G. Assanto, “Soliton gating and switching in liquid crystal light valve,” Appl. Phys. Lett. 96, 071104 (2010).
[CrossRef]

A. Piccardi, A. Alberucci, U. Bortolozzo, S. Residori, and G. Assanto, “Readdressable interconnects with spatial soliton waveguides in liquid crystal light valves,” IEEE Photon. Technol. Lett. 22, 694–696 (2010).
[CrossRef]

A. Piccardi, A. Alberucci, and G. Assanto, “Soliton self-deflection via power-dependent walk-off,” Appl. Phys. Lett. 96, 061105 (2010).
[CrossRef]

A. Alberucci, A. Piccardi, U. Bortolozzo, S. Residori, and G. Assanto, “Nematicon all-optical control in liquid crystal light valves,” Opt. Lett. 35, 390–392 (2010).
[CrossRef] [PubMed]

Y. V. Izdebskaya, V. G. Shvedov, A. S. Desyatnikov, W. Z. Krolikowski, M. Belic, G. Assanto, and Y. S. Kivshar, “Counterpropagating nematicons in bias-free liquid crystals,” Opt. Express 18, 3258–3263 (2010).
[CrossRef] [PubMed]

2009 (1)

G. F. Calvo, J. Belmonte-Beitia, and V. M. Perez-Garcia, “Exact bright and dark spatial soliton solutions in saturable nonlinear media,” Chaos, Solitons Fractals 41, 1791–1798 (2009).
[CrossRef]

2008 (2)

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, “Escaping solitons from a trapping potential,” Phys. Rev. Lett. 101, 153902 (2008).
[CrossRef] [PubMed]

M. Bache, O. Bang, W. Krolikowski, J. Moses, and F. W. Wise, Opt. Express 16, 3273–3287 (2008).
[CrossRef] [PubMed]

2007 (3)

2006 (3)

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, “Tunable refraction and reflection of self-confined light beams,” Nat. Phys. 2, 737–742 (2006).
[CrossRef]

C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, “Long-range interactions between optical solitons,” Nat. Phys. 2, 769–774 (2006).
[CrossRef]

A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, “Observation of attraction between dark solitons,” Phys. Rev. Lett. 96, 043901 (2006).
[CrossRef] [PubMed]

2005 (2)

P. D. Rasmussen, O. Bang, and W. Królikowski, “Theory of nonlocal soliton interaction in nematic liquid crystals,” Phys. Rev. E 72, 066611 (2005).
[CrossRef]

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of vortex-ring solitons,” Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef] [PubMed]

2004 (4)

M. Peccianti, C. Conti, G. Assanto, A. DeLuca, and C. Umeton, “Routing of anisotropic spatial solitons and modulational instability in nematic liquid crystals,” Nature 432, 733–737 (2004).
[CrossRef] [PubMed]

W. Królikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, “Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media,” J. Opt. B: Quantum Semiclassical Opt. 6, S288–S294 (2004).
[CrossRef]

C. Conti, M. Peccianti, and G. Assanto, “Observation of optical spatial solitons in a highly nonlocal medium,” Phys. Rev. Lett. 92, 113902 (2004).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Tunable soliton self-bending in optical lattices with nonlocal nonlinearity,” Phys. Rev. Lett. 93, 153903 (2004).
[CrossRef] [PubMed]

2003 (5)

M. Peccianti, C. Conti, and G. Assanto, “Observation of optical modulational instability in a non-local medium,” Phys. Rev. E 68, 025602(R) (2003).
[CrossRef]

N. I. Nikolov, D. Neshev, O. Bang, and W. Z. Królikowski, “Quadratic solitons as nonlocal solitons,” Phys. Rev. E 68, 036614 (2003).
[CrossRef]

G. Assanto, M. Peccianti, and C. Conti, “Nematicons: Optical spatial solitons in nematic liquid crystals,” Opt. Photonics News 14, 44–48 (2003).
[CrossRef]

C. Conti, M. Peccianti, and G. Assanto, “Route to nonlocality and observation of accessible solitons,” Phys. Rev. Lett. 91, 073901 (2003).
[CrossRef] [PubMed]

W. Krolikowski, B. Luther-Davies, and C. Denz, “Photorefractive solitons,” IEEE J. Quantum Electron. 39, 3–12 (2003).
[CrossRef]

2002 (3)

2001 (2)

S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and L. Bergé, “Self-guided propagation of ultrashort ir laser pulses in fused silica,” Phys. Rev. Lett. 87, 213902 (2001).
[CrossRef] [PubMed]

H. S. Eisenberg, R. Morandotti, Y. Silberberg, S. Bar-Ad, D. Ross, and J. S. Aitchison, “Kerr spatiotemporal self-focusing in a planar glass waveguide,” Phys. Rev. Lett. 87, 043902 (2001).
[CrossRef] [PubMed]

2000 (2)

L. Bergé and A. Couairon, “Nonlinear propagation of self-guided ultra-short pulses in ionized gases,” Phys. Plasmas 7, 210–230 (2000).
[CrossRef]

M. Peccianti, G. Assanto, A. DeLuca, C. Umeton, and I. C. Khoo, “Electrically assisted self-confinement and waveguiding in planar nematic liquid crystal cells,” Appl. Phys. Lett. 77, 7–9 (2000).
[CrossRef]

1999 (1)

G. I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: universality and diversity,” Science 286, 1518–1523 (1999).
[CrossRef] [PubMed]

1997 (2)

1996 (4)

M. F. Shih, P. Leach, M. Segev, M. H. Garrett, G. Salamo, and G. C. Valley, “Two-dimensional steady-state photorefractive screening solitons,” Opt. Lett. 21, 324–326 (1996).
[CrossRef] [PubMed]

H. A. Haus and W. S. Wong, “Solitons in optical communications,” Rev. Mod. Phys. 68, 423–444 (1996).
[CrossRef]

L. Torner, D. Mazilu, and D. Mihalache, “Walking solitons in quadratic nonlinear media,” Phys. Rev. Lett. 77, 2455–2458 (1996).
[CrossRef] [PubMed]

W. E. Torruellas, G. Assanto, B. L. Lawrence, R. A. Fuerst, and G. I. Stegeman, “All-optical switching by spatial walkoff compensation and solitary-wave locking,” Appl. Phys. Lett. 68, 1449–1451 (1996).
[CrossRef]

1995 (3)

D. W. McLaughlin, D. J. Muraki, M. J. Shelley, and X. Wang, “A paraxial model for optical self-focusing in a nematic liquid crystal,” Physica D 88, 55–81 (1995).
[CrossRef]

A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. Mourou, “Self-channeling of high-peak-power femtosecond laser pulses in air,” Opt. Lett. 20, 73–75 (1995).
[CrossRef] [PubMed]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[CrossRef] [PubMed]

1993 (2)

D. Suter and T. Blasberg, “Stabilization of transverse solitary waves by a nonlocal response of the nonlinear medium,” Phys. Rev. A 48, 4583–4587 (1993).
[CrossRef] [PubMed]

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993).
[CrossRef] [PubMed]

1974 (1)

J. E. Bjorkholm and A. A. Ashkin, “cw self-focusing and self-trapping of light in sodium vapor,” Phys. Rev. Lett. 32, 129–132 (1974).
[CrossRef]

1973 (1)

G. K. L. Wong and Y. R. Shen, “Optical-field-induced ordering in the isotropic phase of a nematic liquid crystal,” Phys. Rev. Lett. 30, 895–897 (1973).
[CrossRef]

1968 (1)

F. W. Dabby and J. R. Whinnery, “Thermal self-focusing of laser beams in lead glasses,” Appl. Phys. Lett. 13, 284–286 (1968).
[CrossRef]

Aitchison, J. S.

H. S. Eisenberg, R. Morandotti, Y. Silberberg, S. Bar-Ad, D. Ross, and J. S. Aitchison, “Kerr spatiotemporal self-focusing in a planar glass waveguide,” Phys. Rev. Lett. 87, 043902 (2001).
[CrossRef] [PubMed]

Alberucci, A.

A. Alberucci, A. Piccardi, M. Peccianti, M. Kaczmarek, and G. Assanto, “Propagation of spatial optical solitons in a dielectric with adjustable nonlinearity,” Phys. Rev. A 82, 023806 (2010).
[CrossRef]

A. Piccardi, A. Alberucci, and G. Assanto, “Soliton self-deflection via power-dependent walk-off,” Appl. Phys. Lett. 96, 061105 (2010).
[CrossRef]

A. Piccardi, A. Alberucci, U. Bortolozzo, S. Residori, and G. Assanto, “Soliton gating and switching in liquid crystal light valve,” Appl. Phys. Lett. 96, 071104 (2010).
[CrossRef]

A. Alberucci, A. Piccardi, U. Bortolozzo, S. Residori, and G. Assanto, “Nematicon all-optical control in liquid crystal light valves,” Opt. Lett. 35, 390–392 (2010).
[CrossRef] [PubMed]

A. Piccardi, A. Alberucci, U. Bortolozzo, S. Residori, and G. Assanto, “Readdressable interconnects with spatial soliton waveguides in liquid crystal light valves,” IEEE Photon. Technol. Lett. 22, 694–696 (2010).
[CrossRef]

A. Alberucci, M. Peccianti, and G. Assanto, “Nonlinear bouncing of nonlocal spatial solitons at the boundaries,” Opt. Lett. 32, 2795–2797 (2007).
[CrossRef] [PubMed]

A. Alberucci and G. Assanto, “Propagation of optical spatial solitons in finite-size media: interplay between nonlocality and boundary conditions,” J. Opt. Soc. Am. B 24, 2314–2320 (2007).
[CrossRef]

Alfassi, B.

Ashkin, A. A.

J. E. Bjorkholm and A. A. Ashkin, “cw self-focusing and self-trapping of light in sodium vapor,” Phys. Rev. Lett. 32, 129–132 (1974).
[CrossRef]

Assanto, G.

A. Piccardi, A. Alberucci, U. Bortolozzo, S. Residori, and G. Assanto, “Readdressable interconnects with spatial soliton waveguides in liquid crystal light valves,” IEEE Photon. Technol. Lett. 22, 694–696 (2010).
[CrossRef]

A. Alberucci, A. Piccardi, U. Bortolozzo, S. Residori, and G. Assanto, “Nematicon all-optical control in liquid crystal light valves,” Opt. Lett. 35, 390–392 (2010).
[CrossRef] [PubMed]

A. Piccardi, A. Alberucci, U. Bortolozzo, S. Residori, and G. Assanto, “Soliton gating and switching in liquid crystal light valve,” Appl. Phys. Lett. 96, 071104 (2010).
[CrossRef]

A. Piccardi, A. Alberucci, and G. Assanto, “Soliton self-deflection via power-dependent walk-off,” Appl. Phys. Lett. 96, 061105 (2010).
[CrossRef]

A. Alberucci, A. Piccardi, M. Peccianti, M. Kaczmarek, and G. Assanto, “Propagation of spatial optical solitons in a dielectric with adjustable nonlinearity,” Phys. Rev. A 82, 023806 (2010).
[CrossRef]

Y. V. Izdebskaya, V. G. Shvedov, A. S. Desyatnikov, W. Z. Krolikowski, M. Belic, G. Assanto, and Y. S. Kivshar, “Counterpropagating nematicons in bias-free liquid crystals,” Opt. Express 18, 3258–3263 (2010).
[CrossRef] [PubMed]

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, “Escaping solitons from a trapping potential,” Phys. Rev. Lett. 101, 153902 (2008).
[CrossRef] [PubMed]

A. Alberucci, M. Peccianti, and G. Assanto, “Nonlinear bouncing of nonlocal spatial solitons at the boundaries,” Opt. Lett. 32, 2795–2797 (2007).
[CrossRef] [PubMed]

A. Alberucci and G. Assanto, “Propagation of optical spatial solitons in finite-size media: interplay between nonlocality and boundary conditions,” J. Opt. Soc. Am. B 24, 2314–2320 (2007).
[CrossRef]

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, “Tunable refraction and reflection of self-confined light beams,” Nat. Phys. 2, 737–742 (2006).
[CrossRef]

M. Peccianti, C. Conti, G. Assanto, A. DeLuca, and C. Umeton, “Routing of anisotropic spatial solitons and modulational instability in nematic liquid crystals,” Nature 432, 733–737 (2004).
[CrossRef] [PubMed]

C. Conti, M. Peccianti, and G. Assanto, “Observation of optical spatial solitons in a highly nonlocal medium,” Phys. Rev. Lett. 92, 113902 (2004).
[CrossRef] [PubMed]

M. Peccianti, C. Conti, and G. Assanto, “Observation of optical modulational instability in a non-local medium,” Phys. Rev. E 68, 025602(R) (2003).
[CrossRef]

G. Assanto, M. Peccianti, and C. Conti, “Nematicons: Optical spatial solitons in nematic liquid crystals,” Opt. Photonics News 14, 44–48 (2003).
[CrossRef]

C. Conti, M. Peccianti, and G. Assanto, “Route to nonlocality and observation of accessible solitons,” Phys. Rev. Lett. 91, 073901 (2003).
[CrossRef] [PubMed]

G. Assanto and G. Stegeman, “Simple physics of quadratic spatial solitons,” Opt. Express 10, 388–396 (2002).
[PubMed]

M. Peccianti, K. Brzadkiewicz, and G. Assanto, “Nonlocal spatial soliton interactions in nematic liquid crystals,” Opt. Lett. 27, 1460–1462 (2002).
[CrossRef]

M. Peccianti, G. Assanto, A. DeLuca, C. Umeton, and I. C. Khoo, “Electrically assisted self-confinement and waveguiding in planar nematic liquid crystal cells,” Appl. Phys. Lett. 77, 7–9 (2000).
[CrossRef]

G. Leo, G. Assanto, and W. E. Torruellas, “Intensity-controlled interactions between vectorial spatial solitary waves in quadratic nonlinear media,” Opt. Lett. 22, 7–9 (1997).
[CrossRef] [PubMed]

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W. Królikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, “Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media,” J. Opt. B: Quantum Semiclassical Opt. 6, S288–S294 (2004).
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A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, “Observation of attraction between dark solitons,” Phys. Rev. Lett. 96, 043901 (2006).
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A. Alberucci, A. Piccardi, M. Peccianti, M. Kaczmarek, and G. Assanto, “Propagation of spatial optical solitons in a dielectric with adjustable nonlinearity,” Phys. Rev. A 82, 023806 (2010).
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A. Alberucci, M. Peccianti, and G. Assanto, “Nonlinear bouncing of nonlocal spatial solitons at the boundaries,” Opt. Lett. 32, 2795–2797 (2007).
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M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, “Tunable refraction and reflection of self-confined light beams,” Nat. Phys. 2, 737–742 (2006).
[CrossRef]

M. Peccianti, C. Conti, G. Assanto, A. DeLuca, and C. Umeton, “Routing of anisotropic spatial solitons and modulational instability in nematic liquid crystals,” Nature 432, 733–737 (2004).
[CrossRef] [PubMed]

C. Conti, M. Peccianti, and G. Assanto, “Observation of optical spatial solitons in a highly nonlocal medium,” Phys. Rev. Lett. 92, 113902 (2004).
[CrossRef] [PubMed]

M. Peccianti, C. Conti, and G. Assanto, “Observation of optical modulational instability in a non-local medium,” Phys. Rev. E 68, 025602(R) (2003).
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G. Assanto, M. Peccianti, and C. Conti, “Nematicons: Optical spatial solitons in nematic liquid crystals,” Opt. Photonics News 14, 44–48 (2003).
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C. Conti, M. Peccianti, and G. Assanto, “Route to nonlocality and observation of accessible solitons,” Phys. Rev. Lett. 91, 073901 (2003).
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M. Peccianti, K. Brzadkiewicz, and G. Assanto, “Nonlocal spatial soliton interactions in nematic liquid crystals,” Opt. Lett. 27, 1460–1462 (2002).
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M. Peccianti, G. Assanto, A. DeLuca, C. Umeton, and I. C. Khoo, “Electrically assisted self-confinement and waveguiding in planar nematic liquid crystal cells,” Appl. Phys. Lett. 77, 7–9 (2000).
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G. F. Calvo, J. Belmonte-Beitia, and V. M. Perez-Garcia, “Exact bright and dark spatial soliton solutions in saturable nonlinear media,” Chaos, Solitons Fractals 41, 1791–1798 (2009).
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A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, “Observation of attraction between dark solitons,” Phys. Rev. Lett. 96, 043901 (2006).
[CrossRef] [PubMed]

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A. Alberucci, A. Piccardi, U. Bortolozzo, S. Residori, and G. Assanto, “Nematicon all-optical control in liquid crystal light valves,” Opt. Lett. 35, 390–392 (2010).
[CrossRef] [PubMed]

A. Piccardi, A. Alberucci, U. Bortolozzo, S. Residori, and G. Assanto, “Readdressable interconnects with spatial soliton waveguides in liquid crystal light valves,” IEEE Photon. Technol. Lett. 22, 694–696 (2010).
[CrossRef]

A. Piccardi, A. Alberucci, and G. Assanto, “Soliton self-deflection via power-dependent walk-off,” Appl. Phys. Lett. 96, 061105 (2010).
[CrossRef]

A. Piccardi, A. Alberucci, U. Bortolozzo, S. Residori, and G. Assanto, “Soliton gating and switching in liquid crystal light valve,” Appl. Phys. Lett. 96, 071104 (2010).
[CrossRef]

A. Alberucci, A. Piccardi, M. Peccianti, M. Kaczmarek, and G. Assanto, “Propagation of spatial optical solitons in a dielectric with adjustable nonlinearity,” Phys. Rev. A 82, 023806 (2010).
[CrossRef]

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S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and L. Bergé, “Self-guided propagation of ultrashort ir laser pulses in fused silica,” Phys. Rev. Lett. 87, 213902 (2001).
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W. Królikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, “Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media,” J. Opt. B: Quantum Semiclassical Opt. 6, S288–S294 (2004).
[CrossRef]

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, “Collapse arrest and soliton stabilization in nonlocal nonlinear media,” Phys. Rev. E 66, 046619 (2002).
[CrossRef]

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P. D. Rasmussen, O. Bang, and W. Królikowski, “Theory of nonlocal soliton interaction in nematic liquid crystals,” Phys. Rev. E 72, 066611 (2005).
[CrossRef]

Residori, S.

A. Piccardi, A. Alberucci, U. Bortolozzo, S. Residori, and G. Assanto, “Soliton gating and switching in liquid crystal light valve,” Appl. Phys. Lett. 96, 071104 (2010).
[CrossRef]

A. Piccardi, A. Alberucci, U. Bortolozzo, S. Residori, and G. Assanto, “Readdressable interconnects with spatial soliton waveguides in liquid crystal light valves,” IEEE Photon. Technol. Lett. 22, 694–696 (2010).
[CrossRef]

A. Alberucci, A. Piccardi, U. Bortolozzo, S. Residori, and G. Assanto, “Nematicon all-optical control in liquid crystal light valves,” Opt. Lett. 35, 390–392 (2010).
[CrossRef] [PubMed]

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H. S. Eisenberg, R. Morandotti, Y. Silberberg, S. Bar-Ad, D. Ross, and J. S. Aitchison, “Kerr spatiotemporal self-focusing in a planar glass waveguide,” Phys. Rev. Lett. 87, 043902 (2001).
[CrossRef] [PubMed]

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B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, “Boundary force effects exerted on solitons in highly nonlocal nonlinear media,” Opt. Lett. 32, 154–156 (2007).
[CrossRef]

C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, “Long-range interactions between optical solitons,” Nat. Phys. 2, 769–774 (2006).
[CrossRef]

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of vortex-ring solitons,” Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef] [PubMed]

Salamo, G.

Salamo, G. J.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993).
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B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, “Boundary force effects exerted on solitons in highly nonlocal nonlinear media,” Opt. Lett. 32, 154–156 (2007).
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C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, “Long-range interactions between optical solitons,” Nat. Phys. 2, 769–774 (2006).
[CrossRef]

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of vortex-ring solitons,” Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef] [PubMed]

G. I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: universality and diversity,” Science 286, 1518–1523 (1999).
[CrossRef] [PubMed]

M. F. Shih, P. Leach, M. Segev, M. H. Garrett, G. Salamo, and G. C. Valley, “Two-dimensional steady-state photorefractive screening solitons,” Opt. Lett. 21, 324–326 (1996).
[CrossRef] [PubMed]

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993).
[CrossRef] [PubMed]

Sharp, E. J.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993).
[CrossRef] [PubMed]

Shelley, M. J.

D. W. McLaughlin, D. J. Muraki, M. J. Shelley, and X. Wang, “A paraxial model for optical self-focusing in a nematic liquid crystal,” Physica D 88, 55–81 (1995).
[CrossRef]

Shen, Y. R.

G. K. L. Wong and Y. R. Shen, “Optical-field-induced ordering in the isotropic phase of a nematic liquid crystal,” Phys. Rev. Lett. 30, 895–897 (1973).
[CrossRef]

Shih, M. F.

Shultz, J. L.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993).
[CrossRef] [PubMed]

Shvedov, V. G.

Silberberg, Y.

H. S. Eisenberg, R. Morandotti, Y. Silberberg, S. Bar-Ad, D. Ross, and J. S. Aitchison, “Kerr spatiotemporal self-focusing in a planar glass waveguide,” Phys. Rev. Lett. 87, 043902 (2001).
[CrossRef] [PubMed]

Snyder, A. W.

A. W. Snyder and D. J. Mitchell, “Accessible solitons,” Science 276, 1538–1541 (1997).
[CrossRef]

Squier, J.

Stegeman, G.

Stegeman, G. I.

G. I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: universality and diversity,” Science 286, 1518–1523 (1999).
[CrossRef] [PubMed]

W. E. Torruellas, G. Assanto, B. L. Lawrence, R. A. Fuerst, and G. I. Stegeman, “All-optical switching by spatial walkoff compensation and solitary-wave locking,” Appl. Phys. Lett. 68, 1449–1451 (1996).
[CrossRef]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[CrossRef] [PubMed]

Sudrie, L.

S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and L. Bergé, “Self-guided propagation of ultrashort ir laser pulses in fused silica,” Phys. Rev. Lett. 87, 213902 (2001).
[CrossRef] [PubMed]

Suter, D.

D. Suter and T. Blasberg, “Stabilization of transverse solitary waves by a nonlocal response of the nonlinear medium,” Phys. Rev. A 48, 4583–4587 (1993).
[CrossRef] [PubMed]

Torner, L.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Tunable soliton self-bending in optical lattices with nonlocal nonlinearity,” Phys. Rev. Lett. 93, 153903 (2004).
[CrossRef] [PubMed]

L. Torner, D. Mazilu, and D. Mihalache, “Walking solitons in quadratic nonlinear media,” Phys. Rev. Lett. 77, 2455–2458 (1996).
[CrossRef] [PubMed]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[CrossRef] [PubMed]

Torruellas, W. E.

G. Leo, G. Assanto, and W. E. Torruellas, “Intensity-controlled interactions between vectorial spatial solitary waves in quadratic nonlinear media,” Opt. Lett. 22, 7–9 (1997).
[CrossRef] [PubMed]

W. E. Torruellas, G. Assanto, B. L. Lawrence, R. A. Fuerst, and G. I. Stegeman, “All-optical switching by spatial walkoff compensation and solitary-wave locking,” Appl. Phys. Lett. 68, 1449–1451 (1996).
[CrossRef]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[CrossRef] [PubMed]

Tzortzakis, S.

S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and L. Bergé, “Self-guided propagation of ultrashort ir laser pulses in fused silica,” Phys. Rev. Lett. 87, 213902 (2001).
[CrossRef] [PubMed]

Umeton, C.

M. Peccianti, C. Conti, G. Assanto, A. DeLuca, and C. Umeton, “Routing of anisotropic spatial solitons and modulational instability in nematic liquid crystals,” Nature 432, 733–737 (2004).
[CrossRef] [PubMed]

M. Peccianti, G. Assanto, A. DeLuca, C. Umeton, and I. C. Khoo, “Electrically assisted self-confinement and waveguiding in planar nematic liquid crystal cells,” Appl. Phys. Lett. 77, 7–9 (2000).
[CrossRef]

Valley, G. C.

VanStryland, E. W.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[CrossRef] [PubMed]

Vysloukh, V. A.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Tunable soliton self-bending in optical lattices with nonlocal nonlinearity,” Phys. Rev. Lett. 93, 153903 (2004).
[CrossRef] [PubMed]

Wang, X.

D. W. McLaughlin, D. J. Muraki, M. J. Shelley, and X. Wang, “A paraxial model for optical self-focusing in a nematic liquid crystal,” Physica D 88, 55–81 (1995).
[CrossRef]

Wang, Z.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[CrossRef] [PubMed]

Whinnery, J. R.

F. W. Dabby and J. R. Whinnery, “Thermal self-focusing of laser beams in lead glasses,” Appl. Phys. Lett. 13, 284–286 (1968).
[CrossRef]

Wise, F. W.

Wong, G. K. L.

G. K. L. Wong and Y. R. Shen, “Optical-field-induced ordering in the isotropic phase of a nematic liquid crystal,” Phys. Rev. Lett. 30, 895–897 (1973).
[CrossRef]

Wong, W. S.

H. A. Haus and W. S. Wong, “Solitons in optical communications,” Rev. Mod. Phys. 68, 423–444 (1996).
[CrossRef]

Wyller, J.

W. Królikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, “Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media,” J. Opt. B: Quantum Semiclassical Opt. 6, S288–S294 (2004).
[CrossRef]

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, “Collapse arrest and soliton stabilization in nonlocal nonlinear media,” Phys. Rev. E 66, 046619 (2002).
[CrossRef]

Yariv, A.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993).
[CrossRef] [PubMed]

Appl. Phys. Lett. (5)

F. W. Dabby and J. R. Whinnery, “Thermal self-focusing of laser beams in lead glasses,” Appl. Phys. Lett. 13, 284–286 (1968).
[CrossRef]

M. Peccianti, G. Assanto, A. DeLuca, C. Umeton, and I. C. Khoo, “Electrically assisted self-confinement and waveguiding in planar nematic liquid crystal cells,” Appl. Phys. Lett. 77, 7–9 (2000).
[CrossRef]

A. Piccardi, A. Alberucci, U. Bortolozzo, S. Residori, and G. Assanto, “Soliton gating and switching in liquid crystal light valve,” Appl. Phys. Lett. 96, 071104 (2010).
[CrossRef]

W. E. Torruellas, G. Assanto, B. L. Lawrence, R. A. Fuerst, and G. I. Stegeman, “All-optical switching by spatial walkoff compensation and solitary-wave locking,” Appl. Phys. Lett. 68, 1449–1451 (1996).
[CrossRef]

A. Piccardi, A. Alberucci, and G. Assanto, “Soliton self-deflection via power-dependent walk-off,” Appl. Phys. Lett. 96, 061105 (2010).
[CrossRef]

Chaos, Solitons Fractals (1)

G. F. Calvo, J. Belmonte-Beitia, and V. M. Perez-Garcia, “Exact bright and dark spatial soliton solutions in saturable nonlinear media,” Chaos, Solitons Fractals 41, 1791–1798 (2009).
[CrossRef]

IEEE J. Quantum Electron. (1)

W. Krolikowski, B. Luther-Davies, and C. Denz, “Photorefractive solitons,” IEEE J. Quantum Electron. 39, 3–12 (2003).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

A. Piccardi, A. Alberucci, U. Bortolozzo, S. Residori, and G. Assanto, “Readdressable interconnects with spatial soliton waveguides in liquid crystal light valves,” IEEE Photon. Technol. Lett. 22, 694–696 (2010).
[CrossRef]

J. Opt. B: Quantum Semiclassical Opt. (1)

W. Królikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, “Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media,” J. Opt. B: Quantum Semiclassical Opt. 6, S288–S294 (2004).
[CrossRef]

J. Opt. Soc. Am. B (1)

Nat. Phys. (2)

C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, “Long-range interactions between optical solitons,” Nat. Phys. 2, 769–774 (2006).
[CrossRef]

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, “Tunable refraction and reflection of self-confined light beams,” Nat. Phys. 2, 737–742 (2006).
[CrossRef]

Nature (1)

M. Peccianti, C. Conti, G. Assanto, A. DeLuca, and C. Umeton, “Routing of anisotropic spatial solitons and modulational instability in nematic liquid crystals,” Nature 432, 733–737 (2004).
[CrossRef] [PubMed]

Opt. Express (3)

Opt. Lett. (7)

Opt. Photonics News (1)

G. Assanto, M. Peccianti, and C. Conti, “Nematicons: Optical spatial solitons in nematic liquid crystals,” Opt. Photonics News 14, 44–48 (2003).
[CrossRef]

Phys. Plasmas (1)

L. Bergé and A. Couairon, “Nonlinear propagation of self-guided ultra-short pulses in ionized gases,” Phys. Plasmas 7, 210–230 (2000).
[CrossRef]

Phys. Rev. A (2)

D. Suter and T. Blasberg, “Stabilization of transverse solitary waves by a nonlocal response of the nonlinear medium,” Phys. Rev. A 48, 4583–4587 (1993).
[CrossRef] [PubMed]

A. Alberucci, A. Piccardi, M. Peccianti, M. Kaczmarek, and G. Assanto, “Propagation of spatial optical solitons in a dielectric with adjustable nonlinearity,” Phys. Rev. A 82, 023806 (2010).
[CrossRef]

Phys. Rev. E (4)

M. Peccianti, C. Conti, and G. Assanto, “Observation of optical modulational instability in a non-local medium,” Phys. Rev. E 68, 025602(R) (2003).
[CrossRef]

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, “Collapse arrest and soliton stabilization in nonlocal nonlinear media,” Phys. Rev. E 66, 046619 (2002).
[CrossRef]

N. I. Nikolov, D. Neshev, O. Bang, and W. Z. Królikowski, “Quadratic solitons as nonlocal solitons,” Phys. Rev. E 68, 036614 (2003).
[CrossRef]

P. D. Rasmussen, O. Bang, and W. Królikowski, “Theory of nonlocal soliton interaction in nematic liquid crystals,” Phys. Rev. E 72, 066611 (2005).
[CrossRef]

Phys. Rev. Lett. (13)

A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, “Observation of attraction between dark solitons,” Phys. Rev. Lett. 96, 043901 (2006).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Tunable soliton self-bending in optical lattices with nonlocal nonlinearity,” Phys. Rev. Lett. 93, 153903 (2004).
[CrossRef] [PubMed]

C. Conti, M. Peccianti, and G. Assanto, “Route to nonlocality and observation of accessible solitons,” Phys. Rev. Lett. 91, 073901 (2003).
[CrossRef] [PubMed]

C. Conti, M. Peccianti, and G. Assanto, “Observation of optical spatial solitons in a highly nonlocal medium,” Phys. Rev. Lett. 92, 113902 (2004).
[CrossRef] [PubMed]

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, “Escaping solitons from a trapping potential,” Phys. Rev. Lett. 101, 153902 (2008).
[CrossRef] [PubMed]

L. Torner, D. Mazilu, and D. Mihalache, “Walking solitons in quadratic nonlinear media,” Phys. Rev. Lett. 77, 2455–2458 (1996).
[CrossRef] [PubMed]

H. S. Eisenberg, R. Morandotti, Y. Silberberg, S. Bar-Ad, D. Ross, and J. S. Aitchison, “Kerr spatiotemporal self-focusing in a planar glass waveguide,” Phys. Rev. Lett. 87, 043902 (2001).
[CrossRef] [PubMed]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[CrossRef] [PubMed]

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993).
[CrossRef] [PubMed]

J. E. Bjorkholm and A. A. Ashkin, “cw self-focusing and self-trapping of light in sodium vapor,” Phys. Rev. Lett. 32, 129–132 (1974).
[CrossRef]

S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and L. Bergé, “Self-guided propagation of ultrashort ir laser pulses in fused silica,” Phys. Rev. Lett. 87, 213902 (2001).
[CrossRef] [PubMed]

G. K. L. Wong and Y. R. Shen, “Optical-field-induced ordering in the isotropic phase of a nematic liquid crystal,” Phys. Rev. Lett. 30, 895–897 (1973).
[CrossRef]

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of vortex-ring solitons,” Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef] [PubMed]

Physica D (1)

D. W. McLaughlin, D. J. Muraki, M. J. Shelley, and X. Wang, “A paraxial model for optical self-focusing in a nematic liquid crystal,” Physica D 88, 55–81 (1995).
[CrossRef]

Rev. Mod. Phys. (1)

H. A. Haus and W. S. Wong, “Solitons in optical communications,” Rev. Mod. Phys. 68, 423–444 (1996).
[CrossRef]

Science (2)

G. I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: universality and diversity,” Science 286, 1518–1523 (1999).
[CrossRef] [PubMed]

A. W. Snyder and D. J. Mitchell, “Accessible solitons,” Science 276, 1538–1541 (1997).
[CrossRef]

Other (3)

P. G. DeGennes and J. Prost, The Physics of Liquid Crystals (Oxford Science, 1993).

R.W.Boyd, S.G.Lukishova, and Y.R.Shen, eds., Self-Focusing: Past and Present (Springer, 2009).
[CrossRef]

C. Conti and G. Assanto, “Solitons: Bright spatial solitons,” in Encyclopedia of Modern Optics (Elsevier, 2004), Vol. 5, pp. 43–55.

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Figures (9)

Fig. 1
Fig. 1

(a) Beam diffraction in the linear regime. (b) Soliton formation without changes in walk-off. (c) Soliton self-steering with (high) input power. (d) Side view of a typical planar cell.

Fig. 2
Fig. 2

Plots of c N L (left) and c δ (right) versus θ 0 . We considered an optical anisotropy n 2 n 2 = 0.2 .

Fig. 3
Fig. 3

Soliton features versus rest angle θ 0 and power P in the highly nonlocal limit. First row: maximum reorientation angle (left) and corresponding walk-off (right). Second row: soliton waist (left) and effective refractive index (right). Here the NLC cell thickness is L = 100 μ m , and the wavelength λ is 1064 nm.

Fig. 4
Fig. 4

Director distribution θ 0 + ψ u (left) and corresponding soliton profile | u | 2 (right) versus y for P = 0.1 (solid red line) 0.5 (dashed-dotted blue line), and 10 (dashed black line) mW. Thickness and wavelength are same as in Fig. 3.

Fig. 5
Fig. 5

From left to right: plots of soliton waist, maximum reorientation angle, and walk-off versus P and θ 0 . Thickness and wavelength are same as in Fig. 3.

Fig. 6
Fig. 6

Photographs of beam evolution for several initial angles θ 0 and power. P MAX indicates the maximum power before instabilities kicked in. P MAX = [ 60 , 30 , 10 , 10 , 10 , 30 ]   mW for θ 0 = [ 80 ° , 70 ° , 50 ° , 40 ° , 30 ° , 20 ° ] , respectively.

Fig. 7
Fig. 7

Acquired beam trajectories and their dependence on θ 0 and P 0 . (a)–(f) correspond to θ 0 = 80 ° , 70°, 50°, 40°, 30°, and 20°, respectively. Blue, green, and red lines correspond to P 0 = 1 , 5 , 10   mW , from top to bottom in (a)-(b), in the reverse order otherwise. The cyan line (where present) corresponds to the maximum usable excitation, P 0 = 60   mW for θ 0 = 80 ° (bottom line) and P 0 = 30   mW for θ 0 = 70 ° (bottom line) and 20° (top line), respectively.

Fig. 8
Fig. 8

Numerically computed soliton trajectory in the plane y z for various θ 0 ’s and P 0 0   mW (blue line), P 0 = 1   mW (green line), P 0 = 3   mW (red line), and P 0 = 5   mW (cyan line) versus θ 0 . Power increases from bottom to top lines for the cases of θ 0 = 20 ° and θ 0 = 30 ° ; it decreases in the other cases. The parameters are consistent with the experimental values.

Fig. 9
Fig. 9

Nonlinear soliton deviation Δ y sol versus θ 0 , evaluated in z out = 500 μ m for P 0 = 2   mW (circles), 5 mW (squares), and 10 mW (triangles). Dots are experimental data, and solid lines (corresponding theoretical powers as labeled in the graph) derive from the effective 2D model. The horizontal error bars stem from the experimental uncertainties in walk-off.

Equations (12)

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2 i k 0 n e ( b ) ( A z + tan   δ ( b ) A y ) + D y 2 A y 2 + 2 A x 2 + k 0 2 Δ n e 2 A = 0 ,
2 θ + γ | E t | 2 sin [ 2 ( θ δ b ) ] = 0 ,
2 i k 0 n e ( b ) ( Φ z + tan   δ ( b ) Φ y ) + D y 2 Φ y 2 + k 0 2 Δ n e 2 Φ = 0 ,
2 ψ y 2 + 2 ψ z 2 ( π L ) 2 ψ + γ   sin [ 2 ( ψ + θ 0 δ ( b ) ) ] I y z = 0 ,
2 n N L n e ( b ) k 0 2 u = D y 2 u y 2 + k 0 2 Δ n e 2 u ,
( 1 + tan 2 δ ( b ) ) 2 ψ u y 2 + ( π L ) 2 ψ u + γ α 0   sin [ 2 ( ψ u + θ 0 δ ( b ) ) ] | u | 2 = 0.
w s 2 ( P ) = D y λ 2 ( 1 + tan 2 δ ( b ) ) 8 π Z 0 γ   sin [ 2 ( θ 0 + ψ 0 δ ( b ) ) ] ( d n e / d θ ) θ 0 + ψ 0 1 P ,
n N L ( P ) = D y n e ( b ) w s 2 k 0 2 ,
c N L ( θ 0 ) = 8 π Z 0 γ   sin [ 2 ( θ 0 δ 0 ) ] D y ( 1 + tan 2 δ 0 ) d n e ( θ 0 ) d θ 0 ,
c δ ( θ 0 ) = sin [ 2 ( θ 0 δ 0 ) ] 1 + tan 2 δ 0 d δ 0 d θ 0 .
Δ ρ = α 0 γ G ( y ξ ) sin [ 2 ( θ 0 + ρ 0 δ ( b ) ) ] Δ φ d ξ .
ψ u ( y , P ) 2 Z 0 n e ( b ) cos 2 δ ( b ) γ G ( y ) 0 P sin { 2 [ θ 0 + ψ u ( y = 0 , P ) δ ( b ) ] } d P .

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