Abstract

The robustness of nematicons, i. e. spatial solitons in nematic liquid crystals, can be exploited to implement counter-intuitive negative reflection and refraction schemes for optical signal manipulation at interfaces.

© 2007 Optical Society of America

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References

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  1. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Pergamon Press, London, 1959)
    [PubMed]
  2. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
    [CrossRef] [PubMed]
  3. R. W. Ziolkowski and E. Heyman, "Wave propagation in media having negative permittivity and permeability,' Phys. Rev. E 64, 056625 (2001).
    [CrossRef]
  4. V. G. Veselago, "The electrodynamics of substances with simultaneously negative value of ε and μ," Sov. Phys. Usp. 10, 509-514 (1968).
    [CrossRef]
  5. V. Lindell, S. A. Tretyakov, K. I. Nikoskinen, and S. Ilvonen, "Bw media - media with negative parameters, capable of supporting backward waves," Microwave Opt. Technol. Lett. 31, 129-131 (2001).
    [CrossRef]
  6. Y. Zhang, B. Fluegel, and A. Mascarenhas, "Total Negative Refraction in Real Crystals for Ballistic Electrons and Light," Phys. Rev. Lett. 91, 157404 (2003).
    [CrossRef] [PubMed]
  7. X. L. Chen, Ming He, YinXiao Du, W. Y. Wang, and D. F. Zhang, "Negative refraction: An intrinsic property of uniaxial crystals," Phys. Rev. 72, 113111 (2005).
    [CrossRef]
  8. Z. Liu, Z. Lin, and S. T. Chui, "Negative refraction and omnidirectional total transmission at a planar interface associated with a uniaxial medium," Phys. Rev. B 69, 115402 (2004).
    [CrossRef]
  9. E. Bartholinus, Experimenta crystalli islandici disdiaclastici quibus mira & insolita refractio detegitur, (Hafniæ, Denmark 1669).
  10. C. Huygens, Traitè de Lumiere (Acad. des Sciènce, Paris, 1690).
  11. H. LaFey, "The Vikings," Natl. Geogr. 137, 528-530 (1970).
  12. C. Roslund and C. Beckman, "Disputing Viking navigation by polarized skylight," Appl. Opt. 33, 4754-4755 (1994).
    [CrossRef] [PubMed]
  13. H. Motz and H. Kogelnik, "Electromagnetic radiation from sources embedded in an infinite anisotropic medium and the significance of the Poynting vector,’’ in "Electromagnetic Theory and Antennas," Section B, paper no. 14, Copenhagen, Denmark, June 25-30, 1962.
  14. G. D. Boyd, A. Ashkin, J. M. Dziedzic, and D. A. Kleinman, "Second-harmonic generation of light with double refraction," Phys. Rev. 137, 1305-1309 (1965).
    [CrossRef]
  15. Y. S. Kivshar and G. P. Agrawal, Optical Solitons (Academic, London, 2003).
  16. M. Peccianti, G. Assanto, A. De 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]
  17. M. Peccianti, K. A. Brzdąkiewicz, and G. Assanto, "Nonlocal spatial soliton interactions in bulk nematic liquid crystals," Opt. Lett. 27, 1460-1462 (2002).
    [CrossRef]
  18. G. Assanto and M. Peccianti, "Spatial solitons in nematic liquid crystals," IEEE J. Quantum Electron. 39, 13-21 (2003).
    [CrossRef]
  19. C. Conti, M. Peccianti, and G. Assanto, "Route to nonlocality and observation of accessible solitons," Phys. Rev. Lett. 91, 073901 (2003).
    [CrossRef] [PubMed]
  20. 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]
  21. I. C. Khoo, Liquid Crystals: Physical Properties and Nonlinear Optical Phenomena (Wiley, New York, 1995).
  22. G. Assanto, M. Peccianti, and C. Conti, "Nematicons: optical spatial solitons in nematic liquid crystals," Opt. Photonics. News 14, 44-48 (2003).
    [CrossRef]
  23. O. P. Pishnyaka and O. D. Lavrentovich, "Electrically controlled negative refraction in a nematic liquid crystal," Appl. Phys. Lett. 89, 251103 (2006).
    [CrossRef]
  24. M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, "Routing of highly anisotropic spatial solitons and modulational instability in liquid crystals," Nature 432, 733-737 (2004).
    [CrossRef] [PubMed]
  25. A. Alberucci, M. Peccianti, G. Assanto, G. Coschignano, A. De Luca, and C. Umeton, "Self-healing generation of spatial solitons in liquid crystals," Opt. Lett. 30, 1381-1383 (2005).
    [CrossRef] [PubMed]
  26. M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, "Tunable refraction and reflection of self-confined light beams," Nat. Phys. 2, 737-741 (2006).
    [CrossRef]
  27. M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, "Nonspecular total internal reflection of spatial solitons at the interface between highly birefringent media," Phys. Rev. Lett. 98, 113902 (2007)
    [CrossRef] [PubMed]
  28. M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, "Nonlinear shift of spatial solitons at a graded dielectric interface," Opt. Lett. 32, 271-273 (2007).
    [CrossRef] [PubMed]
  29. Handbook of Laser Science and Technology: Optical Materials, ed. M. J. Weber (CRC Press, New York, 1995).

2007 (2)

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, "Nonspecular total internal reflection of spatial solitons at the interface between highly birefringent media," Phys. Rev. Lett. 98, 113902 (2007)
[CrossRef] [PubMed]

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, "Nonlinear shift of spatial solitons at a graded dielectric interface," Opt. Lett. 32, 271-273 (2007).
[CrossRef] [PubMed]

2006 (2)

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, "Tunable refraction and reflection of self-confined light beams," Nat. Phys. 2, 737-741 (2006).
[CrossRef]

O. P. Pishnyaka and O. D. Lavrentovich, "Electrically controlled negative refraction in a nematic liquid crystal," Appl. Phys. Lett. 89, 251103 (2006).
[CrossRef]

2005 (2)

X. L. Chen, Ming He, YinXiao Du, W. Y. Wang, and D. F. Zhang, "Negative refraction: An intrinsic property of uniaxial crystals," Phys. Rev. 72, 113111 (2005).
[CrossRef]

A. Alberucci, M. Peccianti, G. Assanto, G. Coschignano, A. De Luca, and C. Umeton, "Self-healing generation of spatial solitons in liquid crystals," Opt. Lett. 30, 1381-1383 (2005).
[CrossRef] [PubMed]

2004 (3)

Z. Liu, Z. Lin, and S. T. Chui, "Negative refraction and omnidirectional total transmission at a planar interface associated with a uniaxial medium," Phys. Rev. B 69, 115402 (2004).
[CrossRef]

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, "Routing of highly anisotropic spatial solitons and modulational instability in 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]

2003 (4)

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

Y. Zhang, B. Fluegel, and A. Mascarenhas, "Total Negative Refraction in Real Crystals for Ballistic Electrons and Light," Phys. Rev. Lett. 91, 157404 (2003).
[CrossRef] [PubMed]

G. Assanto and M. Peccianti, "Spatial solitons in nematic liquid crystals," IEEE J. Quantum Electron. 39, 13-21 (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]

2002 (1)

2001 (2)

R. W. Ziolkowski and E. Heyman, "Wave propagation in media having negative permittivity and permeability,' Phys. Rev. E 64, 056625 (2001).
[CrossRef]

V. Lindell, S. A. Tretyakov, K. I. Nikoskinen, and S. Ilvonen, "Bw media - media with negative parameters, capable of supporting backward waves," Microwave Opt. Technol. Lett. 31, 129-131 (2001).
[CrossRef]

2000 (2)

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

M. Peccianti, G. Assanto, A. De 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]

1994 (1)

1970 (1)

H. LaFey, "The Vikings," Natl. Geogr. 137, 528-530 (1970).

1968 (1)

V. G. Veselago, "The electrodynamics of substances with simultaneously negative value of ε and μ," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

1965 (1)

G. D. Boyd, A. Ashkin, J. M. Dziedzic, and D. A. Kleinman, "Second-harmonic generation of light with double refraction," Phys. Rev. 137, 1305-1309 (1965).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

O. P. Pishnyaka and O. D. Lavrentovich, "Electrically controlled negative refraction in a nematic liquid crystal," Appl. Phys. Lett. 89, 251103 (2006).
[CrossRef]

M. Peccianti, G. Assanto, A. De 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]

IEEE J. Quantum Electron. (1)

G. Assanto and M. Peccianti, "Spatial solitons in nematic liquid crystals," IEEE J. Quantum Electron. 39, 13-21 (2003).
[CrossRef]

Microwave Opt. Technol. Lett. (1)

V. Lindell, S. A. Tretyakov, K. I. Nikoskinen, and S. Ilvonen, "Bw media - media with negative parameters, capable of supporting backward waves," Microwave Opt. Technol. Lett. 31, 129-131 (2001).
[CrossRef]

Nat. Phys. (1)

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, "Tunable refraction and reflection of self-confined light beams," Nat. Phys. 2, 737-741 (2006).
[CrossRef]

Natl. Geogr. (1)

H. LaFey, "The Vikings," Natl. Geogr. 137, 528-530 (1970).

Nature (1)

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, "Routing of highly anisotropic spatial solitons and modulational instability in liquid crystals," Nature 432, 733-737 (2004).
[CrossRef] [PubMed]

Opt. Lett. (3)

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. Rev. (2)

X. L. Chen, Ming He, YinXiao Du, W. Y. Wang, and D. F. Zhang, "Negative refraction: An intrinsic property of uniaxial crystals," Phys. Rev. 72, 113111 (2005).
[CrossRef]

G. D. Boyd, A. Ashkin, J. M. Dziedzic, and D. A. Kleinman, "Second-harmonic generation of light with double refraction," Phys. Rev. 137, 1305-1309 (1965).
[CrossRef]

Phys. Rev. B (1)

Z. Liu, Z. Lin, and S. T. Chui, "Negative refraction and omnidirectional total transmission at a planar interface associated with a uniaxial medium," Phys. Rev. B 69, 115402 (2004).
[CrossRef]

Phys. Rev. E (1)

R. W. Ziolkowski and E. Heyman, "Wave propagation in media having negative permittivity and permeability,' Phys. Rev. E 64, 056625 (2001).
[CrossRef]

Phys. Rev. Lett. (5)

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Y. Zhang, B. Fluegel, and A. Mascarenhas, "Total Negative Refraction in Real Crystals for Ballistic Electrons and Light," Phys. Rev. Lett. 91, 157404 (2003).
[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, "Nonspecular total internal reflection of spatial solitons at the interface between highly birefringent media," Phys. Rev. Lett. 98, 113902 (2007)
[CrossRef] [PubMed]

Sov. Phys. Usp. (1)

V. G. Veselago, "The electrodynamics of substances with simultaneously negative value of ε and μ," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Other (7)

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Pergamon Press, London, 1959)
[PubMed]

E. Bartholinus, Experimenta crystalli islandici disdiaclastici quibus mira & insolita refractio detegitur, (Hafniæ, Denmark 1669).

C. Huygens, Traitè de Lumiere (Acad. des Sciènce, Paris, 1690).

I. C. Khoo, Liquid Crystals: Physical Properties and Nonlinear Optical Phenomena (Wiley, New York, 1995).

Handbook of Laser Science and Technology: Optical Materials, ed. M. J. Weber (CRC Press, New York, 1995).

Y. S. Kivshar and G. P. Agrawal, Optical Solitons (Academic, London, 2003).

H. Motz and H. Kogelnik, "Electromagnetic radiation from sources embedded in an infinite anisotropic medium and the significance of the Poynting vector,’’ in "Electromagnetic Theory and Antennas," Section B, paper no. 14, Copenhagen, Denmark, June 25-30, 1962.

Supplementary Material (1)

» Media 1: MOV (345 KB)     

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Figures (7)

Fig. 1.
Fig. 1.

Sketch of the NLC cell geometry: (a) 3D view from the top; (b) xy cross sectional view with the indication of the (transparent) electrodes for the application of an external (low frequency) voltage V.

Fig. 2.
Fig. 2.

(a) Double refraction at the isotropic-uniaxial input interface. In refraction the y component of the wavevector is conserved. (b) From the ISWN we can obtain the direction of the emerging o- and e-wavevectors k o and k e , respectively, and the associated Poynting vectors S o and S e .

Fig. 3.
Fig. 3.

Example of double refraction in NLC: the o-wave (upper beam) undergoes positive refraction and diffracts. Owing to walk-off and all-optical reorientation, the self-trapped e-beam becomes a nematicon and propagates with negative refraction (towards y<0).

Fig. 4.
Fig. 4.

Effects of external voltage V on the propagation of a nematicon. As the bias increases making ξ larger, (a) the electro-optic reorientation increases the extraordinary index, decreasing Φe ; (b) walk-off reaches a maximum and then decreases towards zero; (c) x and y components of S are altered by anisotropic refraction.

Fig. 5.
Fig. 5.

Effects of external voltage V (movie: steering.mov, 345KB) on the propagation of a nematicon: a voltage ramp is applied from V=0 V and reaches V=2 V after 25 s. The e-ray nematicon progressively approaches the o-beam (faint diffractive components at t=0 s, top left photograph) as ξ increases and , consequently, δ tends to zero. [Media 1]

Fig. 6.
Fig. 6.

Scheme of negative reflection at an NLC-metal interface. In the presence of high birefringence, the director distribution can be arranged in order to obtain both incident and reflected Poynting vectors belonging to the same quadrant. (a) Basic configuration and (b) sketch of ISWN: the transverse wavevectors are conserved and the Poynting vectors belong to the same (incidence) quadrant.

Fig. 7.
Fig. 7.

Principle of operation of an optical resonator in an anisotropic medium.

Equations (5)

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

cos ( θ ) = cos ( θ 0 ) cos ( ξ )
cos ( δ ) = cos ( δ yz ) cos ( δ x )
tan 2 ( δ yz ) = tan 2 ( δ ) tan 2 ξ sin 2 θ 0 + 1
S e x s = sin ( δ x )
S e y s = sin ( Φ e δ yz )

Metrics