Abstract

Spontaneous symmetry breaking (SSB) occurs when noise triggers an initially symmetric system to evolve toward one of its nonsymmetric states. Topological and optical SSB involve material reconfiguration/transition and light propagation/distribution in time or space, respectively. In anisotropic optical media, light beam propagation and distribution of the optic axis can be linked, thereby connecting topological and optical SSB. Using nonlinear soft matter, namely uniaxial liquid crystals, we report on simultaneous topological and optical SSB, showing that spatial solitons enhance the noise-driven transition of the medium from a symmetric to an asymmetric configuration, while acquiring a power-dependent transverse velocity in either of two specular directions with respect to the initial wavevector. Solitons enhance SSB by further distorting the optic axis distribution through nonlinear reorientation, resulting in power-tunable walk-off as well as hysteresis in beam refraction versus angle of incidence.

© 2015 Optical Society of America

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References

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2015 (3)

B. A. Malomed, “Nonlinear optics: Symmetry breaking in laser cavities,”Nat. Photonics 9, 287–289 (2015).
[Crossref]

P. Hamel, S. Haddadi, F. Raineri, P. Monnier, G. Beaudoin, I. Sagnes, A. Levenson, and A. M. Yacomotti, “Spontaneous mirror-symmetry breaking in coupled photonic-crystal nanolasers,” Nat. Photonics 9, 311–315 (2015).
[Crossref]

M. Nikkhou, M. Skarabot, S. Copar, M. Ravnik, S. Zumer, and I. Musevic, “Light-controlled topological charge in a nematic liquid crystal,” Nat. Phys. 11, 183–187 (2015).
[Crossref]

2014 (4)

A. Piccardi, A. Alberucci, N. Kravets, O. Buchnev, and G. Assanto, “Power-controlled transition from standard to negative refraction in reorientational soft matter,” Nat. Commun. 5, 5533–5541 (2014).
[Crossref]

N. Kravets, A. Piccardi, A. Alberucci, O. Buchnev, M. Kaczmarek, and G. Assanto, “Bistability with optical beams propagating in a reorientational medium,” Phys. Rev. Lett. 113, 023901 (2014).
[Crossref]

M. Liu, D. A. Powell, I. A. Shadrivov, M. Lapine, and Y. S. Kivshar, “Spontaneous chiral symmetry breaking in metamaterials,” Nat. Commun. 5, 4441 (2014).

Y. Xu and S. Coen, “Experimental observation of the spontaneous breaking of the time-reversal symmetry in a synchronously pumped passive Kerr resonator,” Opt. Lett. 39, 3492–3495 (2014).
[Crossref]

2013 (3)

R. Barboza, U. Bortolozzo, G. Assanto, E. Vidal-Henriquez, M. G. Clerc, and S. Residori, “Harnessing optical vortices in soft matter lattices,” Phys. Rev. Lett. 111, 093902 (2013).
[Crossref]

D. A. Smirnova, A. V. Gorbach, I. V. Iorsh, I. V. Shadrivov, and Y. S. Kivshar, “Nonlinear switching with a graphene coupler,” Phys. Rev. B 88, 045443 (2013).
[Crossref]

C. M. de Sterke, I. V. Kabakova, I. Uddin, J. Jeyaratnam, and B. A. Malomed, “Spontaneous symmetry breaking in a double-defect nonlinear grating,” Phys. Rev. A 88, 033825 (2013).
[Crossref]

2012 (2)

X. Shi, B. A. Malomed, F. Ye, and X. Chen, “Symmetric and asymmetric solitons in a nonlocal nonlinear coupler,” Phys. Rev. A 85, 053839 (2012).
[Crossref]

M. Peccianti and G. Assanto, “Nematicons,” Phys. Rep. 516, 147–208 (2012).
[Crossref]

2011 (3)

A. Alberucci and G. Assanto, “Nonparaxial solitary waves in anisotropic dielectrics,” Phys. Rev. A 83, 033822 (2011).
[Crossref]

C. P. Jisha, Y. Lin, T.-D. Lee, and R.-K. Lee, “Crescent waves in optical cavities,” Phys. Rev. Lett. 107, 183902 (2011).
[Crossref]

J. Beeckman, A. Madani, P. J. M. Vanbrabant, P. Henneaux, S.-P. Gorza, and M. Haelterman, “Switching and intrinsic position bistability of soliton beams in chiral nematic liquid crystals,” Phys. Rev. A 83, 033832 (2011).

2010 (2)

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]

2009 (1)

I. C. Khoo, “Nonlinear optics of liquid crystalline materials,” Phys. Rep. 471, 221–267 (2009).
[Crossref]

2008 (2)

J. J. Baumberg, A. V. Kavokin, S. Christopoulos, A. J. D. Grundy, R. Butté, G. Christmann, D. D. Solnyshkov, G. Malpuech, G. Baldassarri Höger von Högersthal, E. Feltin, J.-F. Carlin, and N. Grandjean, “Spontaneous polarization buildup in a room-temperature polariton laser,” Phys. Rev. Lett. 101, 136409 (2008).
[Crossref]

K. Gallo, A. Pasquazi, S. Stivala, and G. Assanto, “Parametric solitons in two-dimensional lattices of purely nonlinear origin,” Phys. Rev. Lett. 100, 053901 (2008).
[Crossref]

2007 (1)

M. Matuszewski, B. A. Malomed, and M. Trippenbach, “Spontaneous symmetry breaking of solitons trapped in a double-channel potential,” Phys. Rev. A 75, 063621 (2007).
[Crossref]

2005 (1)

P. Kevrekidis, Z. Chen, B. Malomed, D. Frantzeskakis, and M. Weinstein, “Spontaneous symmetry breaking in photonic lattices: theory and experiment,” Phys. Lett. A 340, 275–280 (2005).
[Crossref]

2003 (2)

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

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[Crossref]

2002 (1)

C. Cambournac, T. Sylvestre, H. Maillotte, B. Vanderlinden, P. Kockaert, P. Emplit, and M. Haelterman, “Symmetry-breaking instability of multimode vector solitons,” Phys. Rev. Lett. 89, 083901 (2002).
[Crossref]

2000 (1)

M. Peccianti, G. Assanto, A. D. Luca, 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. Blake, T. Mullin, and S. J. Tavener, “The Freedericksz transition as a bifurcation problem,” Dynam. Stab. Syst. 14, 299–331 (1999).
[Crossref]

1997 (1)

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

1995 (1)

D. Engin, S. Orlov, M. Segev, G. C. Valley, and A. Yariv, “Order-disorder phase transition and critical slowing down in photorefractive self-oscillators,” Phys. Rev. Lett. 74, 1743–1746 (1995).

1994 (1)

1993 (2)

N. Akhmediev and A. Ankiewicz, “Novel soliton states and bifurcation phenomena in nonlinear fiber couplers,” Phys. Rev. Lett. 70, 2395–2398 (1993).
[Crossref]

E. Braun, L. P. Faucheux, and A. Libchaber, “Strong self-focusing in nematic liquid crystals,” Phys. Rev. A 48, 611–622 (1993).
[Crossref]

1991 (2)

I. Chuang, R. Durrer, N. Turok, and B. Yurke, “Cosmology in the laboratory: defect dynamics in liquid crystals,” Science 251, 1336–1342 (1991).
[Crossref]

A. W. Snyder, D. J. Mitchell, L. Poladian, D. R. Rowland, and Y. Chen, “Physics of nonlinear fiber couplers,” J. Opt. Soc. Am. B 8, 2102–2118 (1991).
[Crossref]

1988 (1)

G. Derfel, “Field effects in nematic liquid crystals in terms of catastrophe theory,” Liq. Cryst. 3, 1411–1424 (1988).
[Crossref]

1984 (1)

T. Yabuzaki, T. Okamoto, M. Kitano, and T. Ogawa, “Optical bistability with symmetry breaking,” Phys. Rev. A 29, 1964–1972 (1984).
[Crossref]

1983 (1)

H. L. Ong, “Optically induced Freedericksz transition and bistability in a nematic liquid crystal,” Phys. Rev. A 28, 2393–2407 (1983).
[Crossref]

1981 (1)

S. D. Durbin, S. M. Arakelian, and Y. R. Shen, “Optical-field-induced birefringence and Freedericksz transition in a nematic liquid crystal,” Phys. Rev. Lett. 47, 1411–1414 (1981).
[Crossref]

1972 (2)

P. E. Cladis and M. Kleman, “Non-singular disclinations,” J. Phys. 33, 591–598 (1972).
[Crossref]

C. Williams, P. Pierański, and P. E. Cladis, “Nonsingular s = + 1 screw disclination lines in nematics,” Phys. Rev. Lett. 29, 90–92 (1972).
[Crossref]

1961 (1)

J. Goldstone, “Field theories with superconductor solutions,” Il Nuovo Cimento 19, 154–164 (1961).
[Crossref]

Akhmediev, N.

N. Akhmediev and A. Ankiewicz, “Novel soliton states and bifurcation phenomena in nonlinear fiber couplers,” Phys. Rev. Lett. 70, 2395–2398 (1993).
[Crossref]

Alberucci, A.

N. Kravets, A. Piccardi, A. Alberucci, O. Buchnev, M. Kaczmarek, and G. Assanto, “Bistability with optical beams propagating in a reorientational medium,” Phys. Rev. Lett. 113, 023901 (2014).
[Crossref]

A. Piccardi, A. Alberucci, N. Kravets, O. Buchnev, and G. Assanto, “Power-controlled transition from standard to negative refraction in reorientational soft matter,” Nat. Commun. 5, 5533–5541 (2014).
[Crossref]

A. Alberucci and G. Assanto, “Nonparaxial solitary waves in anisotropic dielectrics,” Phys. Rev. A 83, 033822 (2011).
[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]

Ankiewicz, A.

N. Akhmediev and A. Ankiewicz, “Novel soliton states and bifurcation phenomena in nonlinear fiber couplers,” Phys. Rev. Lett. 70, 2395–2398 (1993).
[Crossref]

Arakelian, S. M.

S. D. Durbin, S. M. Arakelian, and Y. R. Shen, “Optical-field-induced birefringence and Freedericksz transition in a nematic liquid crystal,” Phys. Rev. Lett. 47, 1411–1414 (1981).
[Crossref]

Assanto, G.

N. Kravets, A. Piccardi, A. Alberucci, O. Buchnev, M. Kaczmarek, and G. Assanto, “Bistability with optical beams propagating in a reorientational medium,” Phys. Rev. Lett. 113, 023901 (2014).
[Crossref]

A. Piccardi, A. Alberucci, N. Kravets, O. Buchnev, and G. Assanto, “Power-controlled transition from standard to negative refraction in reorientational soft matter,” Nat. Commun. 5, 5533–5541 (2014).
[Crossref]

R. Barboza, U. Bortolozzo, G. Assanto, E. Vidal-Henriquez, M. G. Clerc, and S. Residori, “Harnessing optical vortices in soft matter lattices,” Phys. Rev. Lett. 111, 093902 (2013).
[Crossref]

M. Peccianti and G. Assanto, “Nematicons,” Phys. Rep. 516, 147–208 (2012).
[Crossref]

A. Alberucci and G. Assanto, “Nonparaxial solitary waves in anisotropic dielectrics,” Phys. Rev. A 83, 033822 (2011).
[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]

K. Gallo, A. Pasquazi, S. Stivala, and G. Assanto, “Parametric solitons in two-dimensional lattices of purely nonlinear origin,” Phys. Rev. Lett. 100, 053901 (2008).
[Crossref]

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

M. Peccianti, G. Assanto, A. D. Luca, 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]

Baldassarri Höger von Högersthal, G.

J. J. Baumberg, A. V. Kavokin, S. Christopoulos, A. J. D. Grundy, R. Butté, G. Christmann, D. D. Solnyshkov, G. Malpuech, G. Baldassarri Höger von Högersthal, E. Feltin, J.-F. Carlin, and N. Grandjean, “Spontaneous polarization buildup in a room-temperature polariton laser,” Phys. Rev. Lett. 101, 136409 (2008).
[Crossref]

Barboza, R.

R. Barboza, U. Bortolozzo, G. Assanto, E. Vidal-Henriquez, M. G. Clerc, and S. Residori, “Harnessing optical vortices in soft matter lattices,” Phys. Rev. Lett. 111, 093902 (2013).
[Crossref]

Baumberg, J. J.

J. J. Baumberg, A. V. Kavokin, S. Christopoulos, A. J. D. Grundy, R. Butté, G. Christmann, D. D. Solnyshkov, G. Malpuech, G. Baldassarri Höger von Högersthal, E. Feltin, J.-F. Carlin, and N. Grandjean, “Spontaneous polarization buildup in a room-temperature polariton laser,” Phys. Rev. Lett. 101, 136409 (2008).
[Crossref]

Beaudoin, G.

P. Hamel, S. Haddadi, F. Raineri, P. Monnier, G. Beaudoin, I. Sagnes, A. Levenson, and A. M. Yacomotti, “Spontaneous mirror-symmetry breaking in coupled photonic-crystal nanolasers,” Nat. Photonics 9, 311–315 (2015).
[Crossref]

Beeckman, J.

J. Beeckman, A. Madani, P. J. M. Vanbrabant, P. Henneaux, S.-P. Gorza, and M. Haelterman, “Switching and intrinsic position bistability of soliton beams in chiral nematic liquid crystals,” Phys. Rev. A 83, 033832 (2011).

Bjorklund, G.

Blake, G. I.

G. I. Blake, T. Mullin, and S. J. Tavener, “The Freedericksz transition as a bifurcation problem,” Dynam. Stab. Syst. 14, 299–331 (1999).
[Crossref]

Bortolozzo, U.

R. Barboza, U. Bortolozzo, G. Assanto, E. Vidal-Henriquez, M. G. Clerc, and S. Residori, “Harnessing optical vortices in soft matter lattices,” Phys. Rev. Lett. 111, 093902 (2013).
[Crossref]

Bosshard, C.

Braun, E.

E. Braun, L. P. Faucheux, and A. Libchaber, “Strong self-focusing in nematic liquid crystals,” Phys. Rev. A 48, 611–622 (1993).
[Crossref]

Buchnev, O.

A. Piccardi, A. Alberucci, N. Kravets, O. Buchnev, and G. Assanto, “Power-controlled transition from standard to negative refraction in reorientational soft matter,” Nat. Commun. 5, 5533–5541 (2014).
[Crossref]

N. Kravets, A. Piccardi, A. Alberucci, O. Buchnev, M. Kaczmarek, and G. Assanto, “Bistability with optical beams propagating in a reorientational medium,” Phys. Rev. Lett. 113, 023901 (2014).
[Crossref]

Butté, R.

J. J. Baumberg, A. V. Kavokin, S. Christopoulos, A. J. D. Grundy, R. Butté, G. Christmann, D. D. Solnyshkov, G. Malpuech, G. Baldassarri Höger von Högersthal, E. Feltin, J.-F. Carlin, and N. Grandjean, “Spontaneous polarization buildup in a room-temperature polariton laser,” Phys. Rev. Lett. 101, 136409 (2008).
[Crossref]

Cambournac, C.

C. Cambournac, T. Sylvestre, H. Maillotte, B. Vanderlinden, P. Kockaert, P. Emplit, and M. Haelterman, “Symmetry-breaking instability of multimode vector solitons,” Phys. Rev. Lett. 89, 083901 (2002).
[Crossref]

Carlin, J.-F.

J. J. Baumberg, A. V. Kavokin, S. Christopoulos, A. J. D. Grundy, R. Butté, G. Christmann, D. D. Solnyshkov, G. Malpuech, G. Baldassarri Höger von Högersthal, E. Feltin, J.-F. Carlin, and N. Grandjean, “Spontaneous polarization buildup in a room-temperature polariton laser,” Phys. Rev. Lett. 101, 136409 (2008).
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X. Shi, B. A. Malomed, F. Ye, and X. Chen, “Symmetric and asymmetric solitons in a nonlocal nonlinear coupler,” Phys. Rev. A 85, 053839 (2012).
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Chen, Y.

Chen, Z.

P. Kevrekidis, Z. Chen, B. Malomed, D. Frantzeskakis, and M. Weinstein, “Spontaneous symmetry breaking in photonic lattices: theory and experiment,” Phys. Lett. A 340, 275–280 (2005).
[Crossref]

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J. J. Baumberg, A. V. Kavokin, S. Christopoulos, A. J. D. Grundy, R. Butté, G. Christmann, D. D. Solnyshkov, G. Malpuech, G. Baldassarri Höger von Högersthal, E. Feltin, J.-F. Carlin, and N. Grandjean, “Spontaneous polarization buildup in a room-temperature polariton laser,” Phys. Rev. Lett. 101, 136409 (2008).
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J. J. Baumberg, A. V. Kavokin, S. Christopoulos, A. J. D. Grundy, R. Butté, G. Christmann, D. D. Solnyshkov, G. Malpuech, G. Baldassarri Höger von Högersthal, E. Feltin, J.-F. Carlin, and N. Grandjean, “Spontaneous polarization buildup in a room-temperature polariton laser,” Phys. Rev. Lett. 101, 136409 (2008).
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I. Chuang, R. Durrer, N. Turok, and B. Yurke, “Cosmology in the laboratory: defect dynamics in liquid crystals,” Science 251, 1336–1342 (1991).
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C. Williams, P. Pierański, and P. E. Cladis, “Nonsingular s = + 1 screw disclination lines in nematics,” Phys. Rev. Lett. 29, 90–92 (1972).
[Crossref]

P. E. Cladis and M. Kleman, “Non-singular disclinations,” J. Phys. 33, 591–598 (1972).
[Crossref]

Clerc, M. G.

R. Barboza, U. Bortolozzo, G. Assanto, E. Vidal-Henriquez, M. G. Clerc, and S. Residori, “Harnessing optical vortices in soft matter lattices,” Phys. Rev. Lett. 111, 093902 (2013).
[Crossref]

Coen, S.

Conti, C.

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

Copar, S.

M. Nikkhou, M. Skarabot, S. Copar, M. Ravnik, S. Zumer, and I. Musevic, “Light-controlled topological charge in a nematic liquid crystal,” Nat. Phys. 11, 183–187 (2015).
[Crossref]

de Sterke, C. M.

C. M. de Sterke, I. V. Kabakova, I. Uddin, J. Jeyaratnam, and B. A. Malomed, “Spontaneous symmetry breaking in a double-defect nonlinear grating,” Phys. Rev. A 88, 033825 (2013).
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P. G. DeGennes and J. Prost, The Physics of Liquid Crystals (Oxford, 1993).

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G. Derfel, “Field effects in nematic liquid crystals in terms of catastrophe theory,” Liq. Cryst. 3, 1411–1424 (1988).
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R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
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S. D. Durbin, S. M. Arakelian, and Y. R. Shen, “Optical-field-induced birefringence and Freedericksz transition in a nematic liquid crystal,” Phys. Rev. Lett. 47, 1411–1414 (1981).
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I. Chuang, R. Durrer, N. Turok, and B. Yurke, “Cosmology in the laboratory: defect dynamics in liquid crystals,” Science 251, 1336–1342 (1991).
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C. Cambournac, T. Sylvestre, H. Maillotte, B. Vanderlinden, P. Kockaert, P. Emplit, and M. Haelterman, “Symmetry-breaking instability of multimode vector solitons,” Phys. Rev. Lett. 89, 083901 (2002).
[Crossref]

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D. Engin, S. Orlov, M. Segev, G. C. Valley, and A. Yariv, “Order-disorder phase transition and critical slowing down in photorefractive self-oscillators,” Phys. Rev. Lett. 74, 1743–1746 (1995).

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E. Braun, L. P. Faucheux, and A. Libchaber, “Strong self-focusing in nematic liquid crystals,” Phys. Rev. A 48, 611–622 (1993).
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J. J. Baumberg, A. V. Kavokin, S. Christopoulos, A. J. D. Grundy, R. Butté, G. Christmann, D. D. Solnyshkov, G. Malpuech, G. Baldassarri Höger von Högersthal, E. Feltin, J.-F. Carlin, and N. Grandjean, “Spontaneous polarization buildup in a room-temperature polariton laser,” Phys. Rev. Lett. 101, 136409 (2008).
[Crossref]

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P. Kevrekidis, Z. Chen, B. Malomed, D. Frantzeskakis, and M. Weinstein, “Spontaneous symmetry breaking in photonic lattices: theory and experiment,” Phys. Lett. A 340, 275–280 (2005).
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K. Gallo, A. Pasquazi, S. Stivala, and G. Assanto, “Parametric solitons in two-dimensional lattices of purely nonlinear origin,” Phys. Rev. Lett. 100, 053901 (2008).
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D. A. Smirnova, A. V. Gorbach, I. V. Iorsh, I. V. Shadrivov, and Y. S. Kivshar, “Nonlinear switching with a graphene coupler,” Phys. Rev. B 88, 045443 (2013).
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J. Beeckman, A. Madani, P. J. M. Vanbrabant, P. Henneaux, S.-P. Gorza, and M. Haelterman, “Switching and intrinsic position bistability of soliton beams in chiral nematic liquid crystals,” Phys. Rev. A 83, 033832 (2011).

Grandjean, N.

J. J. Baumberg, A. V. Kavokin, S. Christopoulos, A. J. D. Grundy, R. Butté, G. Christmann, D. D. Solnyshkov, G. Malpuech, G. Baldassarri Höger von Högersthal, E. Feltin, J.-F. Carlin, and N. Grandjean, “Spontaneous polarization buildup in a room-temperature polariton laser,” Phys. Rev. Lett. 101, 136409 (2008).
[Crossref]

Grundy, A. J. D.

J. J. Baumberg, A. V. Kavokin, S. Christopoulos, A. J. D. Grundy, R. Butté, G. Christmann, D. D. Solnyshkov, G. Malpuech, G. Baldassarri Höger von Högersthal, E. Feltin, J.-F. Carlin, and N. Grandjean, “Spontaneous polarization buildup in a room-temperature polariton laser,” Phys. Rev. Lett. 101, 136409 (2008).
[Crossref]

Haddadi, S.

P. Hamel, S. Haddadi, F. Raineri, P. Monnier, G. Beaudoin, I. Sagnes, A. Levenson, and A. M. Yacomotti, “Spontaneous mirror-symmetry breaking in coupled photonic-crystal nanolasers,” Nat. Photonics 9, 311–315 (2015).
[Crossref]

Haelterman, M.

J. Beeckman, A. Madani, P. J. M. Vanbrabant, P. Henneaux, S.-P. Gorza, and M. Haelterman, “Switching and intrinsic position bistability of soliton beams in chiral nematic liquid crystals,” Phys. Rev. A 83, 033832 (2011).

C. Cambournac, T. Sylvestre, H. Maillotte, B. Vanderlinden, P. Kockaert, P. Emplit, and M. Haelterman, “Symmetry-breaking instability of multimode vector solitons,” Phys. Rev. Lett. 89, 083901 (2002).
[Crossref]

Hamel, P.

P. Hamel, S. Haddadi, F. Raineri, P. Monnier, G. Beaudoin, I. Sagnes, A. Levenson, and A. M. Yacomotti, “Spontaneous mirror-symmetry breaking in coupled photonic-crystal nanolasers,” Nat. Photonics 9, 311–315 (2015).
[Crossref]

Henneaux, P.

J. Beeckman, A. Madani, P. J. M. Vanbrabant, P. Henneaux, S.-P. Gorza, and M. Haelterman, “Switching and intrinsic position bistability of soliton beams in chiral nematic liquid crystals,” Phys. Rev. A 83, 033832 (2011).

Iorsh, I. V.

D. A. Smirnova, A. V. Gorbach, I. V. Iorsh, I. V. Shadrivov, and Y. S. Kivshar, “Nonlinear switching with a graphene coupler,” Phys. Rev. B 88, 045443 (2013).
[Crossref]

Jeyaratnam, J.

C. M. de Sterke, I. V. Kabakova, I. Uddin, J. Jeyaratnam, and B. A. Malomed, “Spontaneous symmetry breaking in a double-defect nonlinear grating,” Phys. Rev. A 88, 033825 (2013).
[Crossref]

Jisha, C. P.

C. P. Jisha, Y. Lin, T.-D. Lee, and R.-K. Lee, “Crescent waves in optical cavities,” Phys. Rev. Lett. 107, 183902 (2011).
[Crossref]

Kabakova, I. V.

C. M. de Sterke, I. V. Kabakova, I. Uddin, J. Jeyaratnam, and B. A. Malomed, “Spontaneous symmetry breaking in a double-defect nonlinear grating,” Phys. Rev. A 88, 033825 (2013).
[Crossref]

Kaczmarek, M.

N. Kravets, A. Piccardi, A. Alberucci, O. Buchnev, M. Kaczmarek, and G. Assanto, “Bistability with optical beams propagating in a reorientational medium,” Phys. Rev. Lett. 113, 023901 (2014).
[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]

Kang, J.

Kavokin, A. V.

J. J. Baumberg, A. V. Kavokin, S. Christopoulos, A. J. D. Grundy, R. Butté, G. Christmann, D. D. Solnyshkov, G. Malpuech, G. Baldassarri Höger von Högersthal, E. Feltin, J.-F. Carlin, and N. Grandjean, “Spontaneous polarization buildup in a room-temperature polariton laser,” Phys. Rev. Lett. 101, 136409 (2008).
[Crossref]

Kevrekidis, P.

P. Kevrekidis, Z. Chen, B. Malomed, D. Frantzeskakis, and M. Weinstein, “Spontaneous symmetry breaking in photonic lattices: theory and experiment,” Phys. Lett. A 340, 275–280 (2005).
[Crossref]

Khoo, I. C.

I. C. Khoo, “Nonlinear optics of liquid crystalline materials,” Phys. Rep. 471, 221–267 (2009).
[Crossref]

M. Peccianti, G. Assanto, A. D. Luca, 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]

Kim, D. Y.

Kitano, M.

T. Yabuzaki, T. Okamoto, M. Kitano, and T. Ogawa, “Optical bistability with symmetry breaking,” Phys. Rev. A 29, 1964–1972 (1984).
[Crossref]

Kivshar, Y. S.

M. Liu, D. A. Powell, I. A. Shadrivov, M. Lapine, and Y. S. Kivshar, “Spontaneous chiral symmetry breaking in metamaterials,” Nat. Commun. 5, 4441 (2014).

D. A. Smirnova, A. V. Gorbach, I. V. Iorsh, I. V. Shadrivov, and Y. S. Kivshar, “Nonlinear switching with a graphene coupler,” Phys. Rev. B 88, 045443 (2013).
[Crossref]

Kleman, M.

P. E. Cladis and M. Kleman, “Non-singular disclinations,” J. Phys. 33, 591–598 (1972).
[Crossref]

Kockaert, P.

C. Cambournac, T. Sylvestre, H. Maillotte, B. Vanderlinden, P. Kockaert, P. Emplit, and M. Haelterman, “Symmetry-breaking instability of multimode vector solitons,” Phys. Rev. Lett. 89, 083901 (2002).
[Crossref]

Kravets, N.

N. Kravets, A. Piccardi, A. Alberucci, O. Buchnev, M. Kaczmarek, and G. Assanto, “Bistability with optical beams propagating in a reorientational medium,” Phys. Rev. Lett. 113, 023901 (2014).
[Crossref]

A. Piccardi, A. Alberucci, N. Kravets, O. Buchnev, and G. Assanto, “Power-controlled transition from standard to negative refraction in reorientational soft matter,” Nat. Commun. 5, 5533–5541 (2014).
[Crossref]

Lapine, M.

M. Liu, D. A. Powell, I. A. Shadrivov, M. Lapine, and Y. S. Kivshar, “Spontaneous chiral symmetry breaking in metamaterials,” Nat. Commun. 5, 4441 (2014).

Lee, R.-K.

C. P. Jisha, Y. Lin, T.-D. Lee, and R.-K. Lee, “Crescent waves in optical cavities,” Phys. Rev. Lett. 107, 183902 (2011).
[Crossref]

Lee, T.-D.

C. P. Jisha, Y. Lin, T.-D. Lee, and R.-K. Lee, “Crescent waves in optical cavities,” Phys. Rev. Lett. 107, 183902 (2011).
[Crossref]

Leuchs, G.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[Crossref]

Levenson, A.

P. Hamel, S. Haddadi, F. Raineri, P. Monnier, G. Beaudoin, I. Sagnes, A. Levenson, and A. M. Yacomotti, “Spontaneous mirror-symmetry breaking in coupled photonic-crystal nanolasers,” Nat. Photonics 9, 311–315 (2015).
[Crossref]

Libchaber, A.

E. Braun, L. P. Faucheux, and A. Libchaber, “Strong self-focusing in nematic liquid crystals,” Phys. Rev. A 48, 611–622 (1993).
[Crossref]

Lin, Y.

C. P. Jisha, Y. Lin, T.-D. Lee, and R.-K. Lee, “Crescent waves in optical cavities,” Phys. Rev. Lett. 107, 183902 (2011).
[Crossref]

Liu, M.

M. Liu, D. A. Powell, I. A. Shadrivov, M. Lapine, and Y. S. Kivshar, “Spontaneous chiral symmetry breaking in metamaterials,” Nat. Commun. 5, 4441 (2014).

Luca, A. D.

M. Peccianti, G. Assanto, A. D. Luca, 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]

Madani, A.

J. Beeckman, A. Madani, P. J. M. Vanbrabant, P. Henneaux, S.-P. Gorza, and M. Haelterman, “Switching and intrinsic position bistability of soliton beams in chiral nematic liquid crystals,” Phys. Rev. A 83, 033832 (2011).

Maillotte, H.

C. Cambournac, T. Sylvestre, H. Maillotte, B. Vanderlinden, P. Kockaert, P. Emplit, and M. Haelterman, “Symmetry-breaking instability of multimode vector solitons,” Phys. Rev. Lett. 89, 083901 (2002).
[Crossref]

Malomed, B.

P. Kevrekidis, Z. Chen, B. Malomed, D. Frantzeskakis, and M. Weinstein, “Spontaneous symmetry breaking in photonic lattices: theory and experiment,” Phys. Lett. A 340, 275–280 (2005).
[Crossref]

Malomed, B. A.

B. A. Malomed, “Nonlinear optics: Symmetry breaking in laser cavities,”Nat. Photonics 9, 287–289 (2015).
[Crossref]

C. M. de Sterke, I. V. Kabakova, I. Uddin, J. Jeyaratnam, and B. A. Malomed, “Spontaneous symmetry breaking in a double-defect nonlinear grating,” Phys. Rev. A 88, 033825 (2013).
[Crossref]

X. Shi, B. A. Malomed, F. Ye, and X. Chen, “Symmetric and asymmetric solitons in a nonlocal nonlinear coupler,” Phys. Rev. A 85, 053839 (2012).
[Crossref]

M. Matuszewski, B. A. Malomed, and M. Trippenbach, “Spontaneous symmetry breaking of solitons trapped in a double-channel potential,” Phys. Rev. A 75, 063621 (2007).
[Crossref]

Malpuech, G.

J. J. Baumberg, A. V. Kavokin, S. Christopoulos, A. J. D. Grundy, R. Butté, G. Christmann, D. D. Solnyshkov, G. Malpuech, G. Baldassarri Höger von Högersthal, E. Feltin, J.-F. Carlin, and N. Grandjean, “Spontaneous polarization buildup in a room-temperature polariton laser,” Phys. Rev. Lett. 101, 136409 (2008).
[Crossref]

Matuszewski, M.

M. Matuszewski, B. A. Malomed, and M. Trippenbach, “Spontaneous symmetry breaking of solitons trapped in a double-channel potential,” Phys. Rev. A 75, 063621 (2007).
[Crossref]

Mitchell, D. J.

Moerner, W. E.

Monnier, P.

P. Hamel, S. Haddadi, F. Raineri, P. Monnier, G. Beaudoin, I. Sagnes, A. Levenson, and A. M. Yacomotti, “Spontaneous mirror-symmetry breaking in coupled photonic-crystal nanolasers,” Nat. Photonics 9, 311–315 (2015).
[Crossref]

Mullin, T.

G. I. Blake, T. Mullin, and S. J. Tavener, “The Freedericksz transition as a bifurcation problem,” Dynam. Stab. Syst. 14, 299–331 (1999).
[Crossref]

Musevic, I.

M. Nikkhou, M. Skarabot, S. Copar, M. Ravnik, S. Zumer, and I. Musevic, “Light-controlled topological charge in a nematic liquid crystal,” Nat. Phys. 11, 183–187 (2015).
[Crossref]

Nikkhou, M.

M. Nikkhou, M. Skarabot, S. Copar, M. Ravnik, S. Zumer, and I. Musevic, “Light-controlled topological charge in a nematic liquid crystal,” Nat. Phys. 11, 183–187 (2015).
[Crossref]

Ogawa, T.

T. Yabuzaki, T. Okamoto, M. Kitano, and T. Ogawa, “Optical bistability with symmetry breaking,” Phys. Rev. A 29, 1964–1972 (1984).
[Crossref]

Okamoto, T.

T. Yabuzaki, T. Okamoto, M. Kitano, and T. Ogawa, “Optical bistability with symmetry breaking,” Phys. Rev. A 29, 1964–1972 (1984).
[Crossref]

Ong, H. L.

H. L. Ong, “Optically induced Freedericksz transition and bistability in a nematic liquid crystal,” Phys. Rev. A 28, 2393–2407 (1983).
[Crossref]

Orlov, S.

D. Engin, S. Orlov, M. Segev, G. C. Valley, and A. Yariv, “Order-disorder phase transition and critical slowing down in photorefractive self-oscillators,” Phys. Rev. Lett. 74, 1743–1746 (1995).

Pasquazi, A.

K. Gallo, A. Pasquazi, S. Stivala, and G. Assanto, “Parametric solitons in two-dimensional lattices of purely nonlinear origin,” Phys. Rev. Lett. 100, 053901 (2008).
[Crossref]

Peccianti, M.

M. Peccianti and G. Assanto, “Nematicons,” Phys. Rep. 516, 147–208 (2012).
[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]

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

M. Peccianti, G. Assanto, A. D. Luca, 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]

Piccardi, A.

N. Kravets, A. Piccardi, A. Alberucci, O. Buchnev, M. Kaczmarek, and G. Assanto, “Bistability with optical beams propagating in a reorientational medium,” Phys. Rev. Lett. 113, 023901 (2014).
[Crossref]

A. Piccardi, A. Alberucci, N. Kravets, O. Buchnev, and G. Assanto, “Power-controlled transition from standard to negative refraction in reorientational soft matter,” Nat. Commun. 5, 5533–5541 (2014).
[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]

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

Pieranski, P.

C. Williams, P. Pierański, and P. E. Cladis, “Nonsingular s = + 1 screw disclination lines in nematics,” Phys. Rev. Lett. 29, 90–92 (1972).
[Crossref]

Poladian, L.

Powell, D. A.

M. Liu, D. A. Powell, I. A. Shadrivov, M. Lapine, and Y. S. Kivshar, “Spontaneous chiral symmetry breaking in metamaterials,” Nat. Commun. 5, 4441 (2014).

Prost, J.

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

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[Crossref]

Raineri, F.

P. Hamel, S. Haddadi, F. Raineri, P. Monnier, G. Beaudoin, I. Sagnes, A. Levenson, and A. M. Yacomotti, “Spontaneous mirror-symmetry breaking in coupled photonic-crystal nanolasers,” Nat. Photonics 9, 311–315 (2015).
[Crossref]

Ravnik, M.

M. Nikkhou, M. Skarabot, S. Copar, M. Ravnik, S. Zumer, and I. Musevic, “Light-controlled topological charge in a nematic liquid crystal,” Nat. Phys. 11, 183–187 (2015).
[Crossref]

Residori, S.

R. Barboza, U. Bortolozzo, G. Assanto, E. Vidal-Henriquez, M. G. Clerc, and S. Residori, “Harnessing optical vortices in soft matter lattices,” Phys. Rev. Lett. 111, 093902 (2013).
[Crossref]

Rowland, D. R.

Sagnes, I.

P. Hamel, S. Haddadi, F. Raineri, P. Monnier, G. Beaudoin, I. Sagnes, A. Levenson, and A. M. Yacomotti, “Spontaneous mirror-symmetry breaking in coupled photonic-crystal nanolasers,” Nat. Photonics 9, 311–315 (2015).
[Crossref]

Segev, M.

D. Engin, S. Orlov, M. Segev, G. C. Valley, and A. Yariv, “Order-disorder phase transition and critical slowing down in photorefractive self-oscillators,” Phys. Rev. Lett. 74, 1743–1746 (1995).

Shadrivov, I. A.

M. Liu, D. A. Powell, I. A. Shadrivov, M. Lapine, and Y. S. Kivshar, “Spontaneous chiral symmetry breaking in metamaterials,” Nat. Commun. 5, 4441 (2014).

Shadrivov, I. V.

D. A. Smirnova, A. V. Gorbach, I. V. Iorsh, I. V. Shadrivov, and Y. S. Kivshar, “Nonlinear switching with a graphene coupler,” Phys. Rev. B 88, 045443 (2013).
[Crossref]

Shen, Y. R.

S. D. Durbin, S. M. Arakelian, and Y. R. Shen, “Optical-field-induced birefringence and Freedericksz transition in a nematic liquid crystal,” Phys. Rev. Lett. 47, 1411–1414 (1981).
[Crossref]

Shi, X.

X. Shi, B. A. Malomed, F. Ye, and X. Chen, “Symmetric and asymmetric solitons in a nonlocal nonlinear coupler,” Phys. Rev. A 85, 053839 (2012).
[Crossref]

Skarabot, M.

M. Nikkhou, M. Skarabot, S. Copar, M. Ravnik, S. Zumer, and I. Musevic, “Light-controlled topological charge in a nematic liquid crystal,” Nat. Phys. 11, 183–187 (2015).
[Crossref]

Smirnova, D. A.

D. A. Smirnova, A. V. Gorbach, I. V. Iorsh, I. V. Shadrivov, and Y. S. Kivshar, “Nonlinear switching with a graphene coupler,” Phys. Rev. B 88, 045443 (2013).
[Crossref]

Snyder, A. W.

Solnyshkov, D. D.

J. J. Baumberg, A. V. Kavokin, S. Christopoulos, A. J. D. Grundy, R. Butté, G. Christmann, D. D. Solnyshkov, G. Malpuech, G. Baldassarri Höger von Högersthal, E. Feltin, J.-F. Carlin, and N. Grandjean, “Spontaneous polarization buildup in a room-temperature polariton laser,” Phys. Rev. Lett. 101, 136409 (2008).
[Crossref]

Stegeman, G. I.

Stivala, S.

K. Gallo, A. Pasquazi, S. Stivala, and G. Assanto, “Parametric solitons in two-dimensional lattices of purely nonlinear origin,” Phys. Rev. Lett. 100, 053901 (2008).
[Crossref]

Sylvestre, T.

C. Cambournac, T. Sylvestre, H. Maillotte, B. Vanderlinden, P. Kockaert, P. Emplit, and M. Haelterman, “Symmetry-breaking instability of multimode vector solitons,” Phys. Rev. Lett. 89, 083901 (2002).
[Crossref]

Tavener, S. J.

G. I. Blake, T. Mullin, and S. J. Tavener, “The Freedericksz transition as a bifurcation problem,” Dynam. Stab. Syst. 14, 299–331 (1999).
[Crossref]

Torruellas, W. E.

Trippenbach, M.

M. Matuszewski, B. A. Malomed, and M. Trippenbach, “Spontaneous symmetry breaking of solitons trapped in a double-channel potential,” Phys. Rev. A 75, 063621 (2007).
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Supplementary Material (1)

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Figures (7)

Fig. 1.
Fig. 1.

Soliton-enhanced spontaneous symmetry breaking in uniaxials. (a) Geometry of relevant quantities in a uniaxial medium supporting spatial solitons: wavevector k (taken parallel to z ^ ) at angle θ with the optic axis n ^ , electric field E , and Poynting vector S at angle δ with k . (b) Parity-conserving beam propagation in the absence of noise. (c) Parity breaking due to reorientation of the optic axis in the presence of input noise and propagation of spatial solitons with walk-off.

Fig. 2.
Fig. 2.

Simulated soliton-enhanced SSB. Realizations of beam evolution in y z (upper panels) and corresponding NLC director distribution (lower graphs); the legends above indicate the input power densities. Stochastic white noise was added to the initial molecular distribution in order to initiate director motion.

Fig. 3.
Fig. 3.

Synopsis of nonlinear beam properties. (a) Absolute value of maximum soliton walk-off and orientation θ versus power density. (b) Beam trajectories corresponding to the five powers marked by symbols in (a):  0.8 Wmm 1 (blue line without symbols), 1.0 Wmm 1 (green line with squares), 1.2 Wmm 1 (red with triangles), 1.8 Wmm 1 (cyan with circles), and 2.9 Wmm 1 (magenta with crosses). (c) Absolute output displacement across y (line with circles) and z -averaged width (line with squares) of the beam versus power density.

Fig. 4.
Fig. 4.

Calculated free energy for four input powers (legends) versus reorientation angle θ m at the intensity peak. Oriented states are energetically favored for input powers above 20 mW.

Fig. 5.
Fig. 5.

Measured refraction of the nonlinear beam. Acquired beam trajectories at various powers for positive ( β = 3 ° , solid lines) and negative ( β = 3 ° , dashed lines) input tilts. The cases of 40 and 70 mW correspond to power-driven negative refraction. The optical wavelength is 1.064 μm, and the medium is the nematic E7.

Fig. 6.
Fig. 6.

Experimental assessment of SSB. (a) Top: the beam is incident normally to the uniform NLC with θ = 0 at powers below OFT. Center: positive and negative tilts of the input wavevector in y = 0 can aid nonlinear reorientation, leading—at high enough powers (HP)—to beam self-confinement and deflection with (power-dependent) negative refraction (the transverse velocity changes sign when crossing the input interface in z = 0 ). Bottom: the wavevector is brought back to normal incidence k z ^ keeping the input power above OFT: the beam maintains/remembers self-confinement and self-deflection. The blue ellipses indicate the local alignment of the molecular director. (b)–(e) Symmetry breaking in beam propagation as the director distribution is distorted through reorientation. (b), (d) Photographs of a P = 100 mW nonlinear beam undergoing (b) negative and (d) positive walk-off, respectively. (c) Linear diffraction for P = 2 mW . (e) Beam trajectories for various input powers. The curved trajectories for P = 40 mW (green lines) are caused by scattering losses that make optical reorientation fade away along z .

Fig. 7.
Fig. 7.

Hysteresis of beam position versus input tilt. Output beam position y out versus increasing (black squares) and decreasing (red circles) incidence angles β for an input power of 100 mW. The two (opposite) angles corresponding to the transitions (points b and d ) depend on power. The cycle was swept clockwise from a to d . The colored areas mark positive (light blue) and negative (pink) refraction, respectively.

Equations (4)

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2 A z 2 + 2 i k 0 n A z + 2 A x 2 + D y 2 A y 2 + k 0 2 Δ n e 2 ( θ ) A = 0 ,
2 θ + γ sin [ 2 ( θ δ ) ] ( | A | 2 | E s | 2 ) + 2 γ cos [ 2 ( θ δ ) ] Re ( E t E s * ) = 0 ,
y z 2 θ ( π L x ) 2 θ + γ sin [ 2 ( θ δ ) ] ( | A | 2 | E s | 2 ) + 2 γ cos [ 2 ( θ δ ) ] Re ( E t E s * ) = 0 ,
F = α κ 2 θ m 2 2 + n P 2 c n e 2 ( θ m ) P 2 c n + γ Z 0 sin [ 2 ( θ m δ m ) ] 4 π c n cos 2 δ m d n e d θ | θ m P 2 + 2 P c k 0 2 w sol 2 ,

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