Abstract

We analyze the angular steering of self-confined light beams, i.e., spatial solitons, in nematic liquid crystals exploiting both their electro-optic response and reorientational nonlinearity. A bias-induced interface is obtained with comb electrodes in a planar cell, applying two distinct voltages to control the spatial distribution of the optic axis. The configuration allows spatial solitons to propagate in a plane and maximize their deflection via refraction and total internal reflection, with an overall deflection of 70° in standard E7.

© 2011 Optical Society of America

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  1. D.-K. Yang and S.-T. Wu, Fundamentals of Liquid Crystals Devices (Wiley, 2006).
    [CrossRef]
  2. J. Margerum, J. Nimoy, and S. Yong, Appl. Phys. Lett. 17, 51 (1970).
    [CrossRef]
  3. L. K. Cotter, T. J. Drabik, R. J. Dillon, and M. A. Handschy, Opt. Lett. 15, 291 (1990).
    [CrossRef] [PubMed]
  4. P. Valley, D. Mathine, M. Dodge, J. Schwiegerling, and N. Peyghambarian, Opt. Lett. 35, 336 (2010).
    [CrossRef] [PubMed]
  5. I. C. Khoo, Phys. Rep. 471, 221 (2009).
    [CrossRef]
  6. M. Peccianti, C. Conti, and G. Assanto, Phys. Rev. E 68, R025602 (2003).
    [CrossRef]
  7. A. Fratalocchi and G. Assanto, Appl. Phys. Lett. 86, 051109 (2005).
    [CrossRef]
  8. A. d’Alessandro, R. Asquini, M. Trotta, R. Beccherelli, and I. C. Khoo, Appl. Phys. Lett. 97, 093302 (2010).
    [CrossRef]
  9. G. Assanto and M. Karpierz, Liq. Cryst. 36, 1161 (2009).
    [CrossRef]
  10. M. Peccianti and G. Assanto, Opt. Lett. 26, 1690 (2001).
    [CrossRef]
  11. A. Pasquazi, A. Alberucci, M. Peccianti, and G. Assanto, Appl. Phys. Lett. 87, 261104 (2005).
    [CrossRef]
  12. A. Piccardi, A. Alberucci, U. Bortolozzo, S. Residori, and G. Assanto, IEEE Photon. Technol. Lett. 22, 694 (2010).
    [CrossRef]
  13. M. Peccianti, A. Fratalocchi, and G. Assanto, Opt. Express 12, 6524 (2004).
    [CrossRef] [PubMed]
  14. D. Scrymgeour, A. Sharan, V. Gopalan, K. Gahagan, J. Casson, R. Sander, J. Robinson, P. Chandramani, and F. Kiamilev, Appl. Phys. Lett. 81, 3140 (2002).
    [CrossRef]
  15. S. Davis, G. Farca, S. Rommel, A. Martin, and M. Anderson, Proc. SPIE 6971, 69710G (2008).
    [CrossRef]
  16. A. Piccardi, M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, Appl. Phys. Lett. 94, 091106 (2009).
    [CrossRef]
  17. A. Alberucci, A. Piccardi, M. Peccianti, M. Kaczmarek, and G. Assanto, Phys. Rev. A 82, 023806 (2010).
    [CrossRef]
  18. N. Tabiryan and B. Zeldovich, Mol. Cryst. Liq. Cryst. 62, 237 (1980).
    [CrossRef]
  19. M. Peccianti, G. Assanto, A. Luca, C. Umeton, and I. C. Khoo, Appl. Phys. Lett. 77, 7 (2000).
    [CrossRef]
  20. A. Alberucci, A. Piccardi, U. Bortolozzo, S. Residori, and G. Assanto, Opt. Lett. 35, 390 (2010).
    [CrossRef] [PubMed]
  21. M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, Phys. Rev. Lett. 98, 113902 (2007).
    [CrossRef] [PubMed]
  22. M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, Nat. Phys. 2, 737 (2006).
    [CrossRef]

2010

A. d’Alessandro, R. Asquini, M. Trotta, R. Beccherelli, and I. C. Khoo, Appl. Phys. Lett. 97, 093302 (2010).
[CrossRef]

A. Alberucci, A. Piccardi, M. Peccianti, M. Kaczmarek, and G. Assanto, Phys. Rev. A 82, 023806 (2010).
[CrossRef]

A. Piccardi, A. Alberucci, U. Bortolozzo, S. Residori, and G. Assanto, IEEE Photon. Technol. Lett. 22, 694 (2010).
[CrossRef]

P. Valley, D. Mathine, M. Dodge, J. Schwiegerling, and N. Peyghambarian, Opt. Lett. 35, 336 (2010).
[CrossRef] [PubMed]

A. Alberucci, A. Piccardi, U. Bortolozzo, S. Residori, and G. Assanto, Opt. Lett. 35, 390 (2010).
[CrossRef] [PubMed]

2009

A. Piccardi, M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, Appl. Phys. Lett. 94, 091106 (2009).
[CrossRef]

G. Assanto and M. Karpierz, Liq. Cryst. 36, 1161 (2009).
[CrossRef]

I. C. Khoo, Phys. Rep. 471, 221 (2009).
[CrossRef]

2008

S. Davis, G. Farca, S. Rommel, A. Martin, and M. Anderson, Proc. SPIE 6971, 69710G (2008).
[CrossRef]

2007

M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, Phys. Rev. Lett. 98, 113902 (2007).
[CrossRef] [PubMed]

2006

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, Nat. Phys. 2, 737 (2006).
[CrossRef]

D.-K. Yang and S.-T. Wu, Fundamentals of Liquid Crystals Devices (Wiley, 2006).
[CrossRef]

2005

A. Fratalocchi and G. Assanto, Appl. Phys. Lett. 86, 051109 (2005).
[CrossRef]

A. Pasquazi, A. Alberucci, M. Peccianti, and G. Assanto, Appl. Phys. Lett. 87, 261104 (2005).
[CrossRef]

2004

2003

M. Peccianti, C. Conti, and G. Assanto, Phys. Rev. E 68, R025602 (2003).
[CrossRef]

2002

D. Scrymgeour, A. Sharan, V. Gopalan, K. Gahagan, J. Casson, R. Sander, J. Robinson, P. Chandramani, and F. Kiamilev, Appl. Phys. Lett. 81, 3140 (2002).
[CrossRef]

2001

2000

M. Peccianti, G. Assanto, A. Luca, C. Umeton, and I. C. Khoo, Appl. Phys. Lett. 77, 7 (2000).
[CrossRef]

1990

1980

N. Tabiryan and B. Zeldovich, Mol. Cryst. Liq. Cryst. 62, 237 (1980).
[CrossRef]

1970

J. Margerum, J. Nimoy, and S. Yong, Appl. Phys. Lett. 17, 51 (1970).
[CrossRef]

Alberucci, A.

A. Alberucci, A. Piccardi, U. Bortolozzo, S. Residori, and G. Assanto, Opt. Lett. 35, 390 (2010).
[CrossRef] [PubMed]

A. Piccardi, A. Alberucci, U. Bortolozzo, S. Residori, and G. Assanto, IEEE Photon. Technol. Lett. 22, 694 (2010).
[CrossRef]

A. Alberucci, A. Piccardi, M. Peccianti, M. Kaczmarek, and G. Assanto, Phys. Rev. A 82, 023806 (2010).
[CrossRef]

A. Pasquazi, A. Alberucci, M. Peccianti, and G. Assanto, Appl. Phys. Lett. 87, 261104 (2005).
[CrossRef]

Anderson, M.

S. Davis, G. Farca, S. Rommel, A. Martin, and M. Anderson, Proc. SPIE 6971, 69710G (2008).
[CrossRef]

Asquini, R.

A. d’Alessandro, R. Asquini, M. Trotta, R. Beccherelli, and I. C. Khoo, Appl. Phys. Lett. 97, 093302 (2010).
[CrossRef]

Assanto, G.

A. Alberucci, A. Piccardi, M. Peccianti, M. Kaczmarek, and G. Assanto, Phys. Rev. A 82, 023806 (2010).
[CrossRef]

A. Piccardi, A. Alberucci, U. Bortolozzo, S. Residori, and G. Assanto, IEEE Photon. Technol. Lett. 22, 694 (2010).
[CrossRef]

A. Alberucci, A. Piccardi, U. Bortolozzo, S. Residori, and G. Assanto, Opt. Lett. 35, 390 (2010).
[CrossRef] [PubMed]

G. Assanto and M. Karpierz, Liq. Cryst. 36, 1161 (2009).
[CrossRef]

A. Piccardi, M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, Appl. Phys. Lett. 94, 091106 (2009).
[CrossRef]

M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, Phys. Rev. Lett. 98, 113902 (2007).
[CrossRef] [PubMed]

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, Nat. Phys. 2, 737 (2006).
[CrossRef]

A. Pasquazi, A. Alberucci, M. Peccianti, and G. Assanto, Appl. Phys. Lett. 87, 261104 (2005).
[CrossRef]

A. Fratalocchi and G. Assanto, Appl. Phys. Lett. 86, 051109 (2005).
[CrossRef]

M. Peccianti, A. Fratalocchi, and G. Assanto, Opt. Express 12, 6524 (2004).
[CrossRef] [PubMed]

M. Peccianti, C. Conti, and G. Assanto, Phys. Rev. E 68, R025602 (2003).
[CrossRef]

M. Peccianti and G. Assanto, Opt. Lett. 26, 1690 (2001).
[CrossRef]

M. Peccianti, G. Assanto, A. Luca, C. Umeton, and I. C. Khoo, Appl. Phys. Lett. 77, 7 (2000).
[CrossRef]

Beccherelli, R.

A. d’Alessandro, R. Asquini, M. Trotta, R. Beccherelli, and I. C. Khoo, Appl. Phys. Lett. 97, 093302 (2010).
[CrossRef]

Bortolozzo, U.

A. Piccardi, A. Alberucci, U. Bortolozzo, S. Residori, and G. Assanto, IEEE Photon. Technol. Lett. 22, 694 (2010).
[CrossRef]

A. Alberucci, A. Piccardi, U. Bortolozzo, S. Residori, and G. Assanto, Opt. Lett. 35, 390 (2010).
[CrossRef] [PubMed]

Casson, J.

D. Scrymgeour, A. Sharan, V. Gopalan, K. Gahagan, J. Casson, R. Sander, J. Robinson, P. Chandramani, and F. Kiamilev, Appl. Phys. Lett. 81, 3140 (2002).
[CrossRef]

Chandramani, P.

D. Scrymgeour, A. Sharan, V. Gopalan, K. Gahagan, J. Casson, R. Sander, J. Robinson, P. Chandramani, and F. Kiamilev, Appl. Phys. Lett. 81, 3140 (2002).
[CrossRef]

Conti, C.

M. Peccianti, C. Conti, and G. Assanto, Phys. Rev. E 68, R025602 (2003).
[CrossRef]

Cotter, L. K.

d’Alessandro, A.

A. d’Alessandro, R. Asquini, M. Trotta, R. Beccherelli, and I. C. Khoo, Appl. Phys. Lett. 97, 093302 (2010).
[CrossRef]

Davis, S.

S. Davis, G. Farca, S. Rommel, A. Martin, and M. Anderson, Proc. SPIE 6971, 69710G (2008).
[CrossRef]

Dillon, R. J.

Dodge, M.

Drabik, T. J.

Dyadyusha, A.

A. Piccardi, M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, Appl. Phys. Lett. 94, 091106 (2009).
[CrossRef]

M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, Phys. Rev. Lett. 98, 113902 (2007).
[CrossRef] [PubMed]

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, Nat. Phys. 2, 737 (2006).
[CrossRef]

Farca, G.

S. Davis, G. Farca, S. Rommel, A. Martin, and M. Anderson, Proc. SPIE 6971, 69710G (2008).
[CrossRef]

Fratalocchi, A.

Gahagan, K.

D. Scrymgeour, A. Sharan, V. Gopalan, K. Gahagan, J. Casson, R. Sander, J. Robinson, P. Chandramani, and F. Kiamilev, Appl. Phys. Lett. 81, 3140 (2002).
[CrossRef]

Gopalan, V.

D. Scrymgeour, A. Sharan, V. Gopalan, K. Gahagan, J. Casson, R. Sander, J. Robinson, P. Chandramani, and F. Kiamilev, Appl. Phys. Lett. 81, 3140 (2002).
[CrossRef]

Handschy, M. A.

Kaczmarek, M.

A. Alberucci, A. Piccardi, M. Peccianti, M. Kaczmarek, and G. Assanto, Phys. Rev. A 82, 023806 (2010).
[CrossRef]

A. Piccardi, M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, Appl. Phys. Lett. 94, 091106 (2009).
[CrossRef]

M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, Phys. Rev. Lett. 98, 113902 (2007).
[CrossRef] [PubMed]

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, Nat. Phys. 2, 737 (2006).
[CrossRef]

Karpierz, M.

G. Assanto and M. Karpierz, Liq. Cryst. 36, 1161 (2009).
[CrossRef]

Khoo, I. C.

A. d’Alessandro, R. Asquini, M. Trotta, R. Beccherelli, and I. C. Khoo, Appl. Phys. Lett. 97, 093302 (2010).
[CrossRef]

I. C. Khoo, Phys. Rep. 471, 221 (2009).
[CrossRef]

M. Peccianti, G. Assanto, A. Luca, C. Umeton, and I. C. Khoo, Appl. Phys. Lett. 77, 7 (2000).
[CrossRef]

Kiamilev, F.

D. Scrymgeour, A. Sharan, V. Gopalan, K. Gahagan, J. Casson, R. Sander, J. Robinson, P. Chandramani, and F. Kiamilev, Appl. Phys. Lett. 81, 3140 (2002).
[CrossRef]

Luca, A.

M. Peccianti, G. Assanto, A. Luca, C. Umeton, and I. C. Khoo, Appl. Phys. Lett. 77, 7 (2000).
[CrossRef]

Margerum, J.

J. Margerum, J. Nimoy, and S. Yong, Appl. Phys. Lett. 17, 51 (1970).
[CrossRef]

Martin, A.

S. Davis, G. Farca, S. Rommel, A. Martin, and M. Anderson, Proc. SPIE 6971, 69710G (2008).
[CrossRef]

Mathine, D.

Nimoy, J.

J. Margerum, J. Nimoy, and S. Yong, Appl. Phys. Lett. 17, 51 (1970).
[CrossRef]

Pasquazi, A.

A. Pasquazi, A. Alberucci, M. Peccianti, and G. Assanto, Appl. Phys. Lett. 87, 261104 (2005).
[CrossRef]

Peccianti, M.

A. Alberucci, A. Piccardi, M. Peccianti, M. Kaczmarek, and G. Assanto, Phys. Rev. A 82, 023806 (2010).
[CrossRef]

A. Piccardi, M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, Appl. Phys. Lett. 94, 091106 (2009).
[CrossRef]

M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, Phys. Rev. Lett. 98, 113902 (2007).
[CrossRef] [PubMed]

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, Nat. Phys. 2, 737 (2006).
[CrossRef]

A. Pasquazi, A. Alberucci, M. Peccianti, and G. Assanto, Appl. Phys. Lett. 87, 261104 (2005).
[CrossRef]

M. Peccianti, A. Fratalocchi, and G. Assanto, Opt. Express 12, 6524 (2004).
[CrossRef] [PubMed]

M. Peccianti, C. Conti, and G. Assanto, Phys. Rev. E 68, R025602 (2003).
[CrossRef]

M. Peccianti and G. Assanto, Opt. Lett. 26, 1690 (2001).
[CrossRef]

M. Peccianti, G. Assanto, A. Luca, C. Umeton, and I. C. Khoo, Appl. Phys. Lett. 77, 7 (2000).
[CrossRef]

Peyghambarian, N.

Piccardi, A.

A. Alberucci, A. Piccardi, M. Peccianti, M. Kaczmarek, and G. Assanto, Phys. Rev. A 82, 023806 (2010).
[CrossRef]

A. Piccardi, A. Alberucci, U. Bortolozzo, S. Residori, and G. Assanto, IEEE Photon. Technol. Lett. 22, 694 (2010).
[CrossRef]

A. Alberucci, A. Piccardi, U. Bortolozzo, S. Residori, and G. Assanto, Opt. Lett. 35, 390 (2010).
[CrossRef] [PubMed]

A. Piccardi, M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, Appl. Phys. Lett. 94, 091106 (2009).
[CrossRef]

Residori, S.

A. Piccardi, A. Alberucci, U. Bortolozzo, S. Residori, and G. Assanto, IEEE Photon. Technol. Lett. 22, 694 (2010).
[CrossRef]

A. Alberucci, A. Piccardi, U. Bortolozzo, S. Residori, and G. Assanto, Opt. Lett. 35, 390 (2010).
[CrossRef] [PubMed]

Robinson, J.

D. Scrymgeour, A. Sharan, V. Gopalan, K. Gahagan, J. Casson, R. Sander, J. Robinson, P. Chandramani, and F. Kiamilev, Appl. Phys. Lett. 81, 3140 (2002).
[CrossRef]

Rommel, S.

S. Davis, G. Farca, S. Rommel, A. Martin, and M. Anderson, Proc. SPIE 6971, 69710G (2008).
[CrossRef]

Sander, R.

D. Scrymgeour, A. Sharan, V. Gopalan, K. Gahagan, J. Casson, R. Sander, J. Robinson, P. Chandramani, and F. Kiamilev, Appl. Phys. Lett. 81, 3140 (2002).
[CrossRef]

Schwiegerling, J.

Scrymgeour, D.

D. Scrymgeour, A. Sharan, V. Gopalan, K. Gahagan, J. Casson, R. Sander, J. Robinson, P. Chandramani, and F. Kiamilev, Appl. Phys. Lett. 81, 3140 (2002).
[CrossRef]

Sharan, A.

D. Scrymgeour, A. Sharan, V. Gopalan, K. Gahagan, J. Casson, R. Sander, J. Robinson, P. Chandramani, and F. Kiamilev, Appl. Phys. Lett. 81, 3140 (2002).
[CrossRef]

Tabiryan, N.

N. Tabiryan and B. Zeldovich, Mol. Cryst. Liq. Cryst. 62, 237 (1980).
[CrossRef]

Trotta, M.

A. d’Alessandro, R. Asquini, M. Trotta, R. Beccherelli, and I. C. Khoo, Appl. Phys. Lett. 97, 093302 (2010).
[CrossRef]

Umeton, C.

M. Peccianti, G. Assanto, A. Luca, C. Umeton, and I. C. Khoo, Appl. Phys. Lett. 77, 7 (2000).
[CrossRef]

Valley, P.

Wu, S.-T.

D.-K. Yang and S.-T. Wu, Fundamentals of Liquid Crystals Devices (Wiley, 2006).
[CrossRef]

Yang, D.-K.

D.-K. Yang and S.-T. Wu, Fundamentals of Liquid Crystals Devices (Wiley, 2006).
[CrossRef]

Yong, S.

J. Margerum, J. Nimoy, and S. Yong, Appl. Phys. Lett. 17, 51 (1970).
[CrossRef]

Zeldovich, B.

N. Tabiryan and B. Zeldovich, Mol. Cryst. Liq. Cryst. 62, 237 (1980).
[CrossRef]

Appl. Phys. Lett.

J. Margerum, J. Nimoy, and S. Yong, Appl. Phys. Lett. 17, 51 (1970).
[CrossRef]

A. Fratalocchi and G. Assanto, Appl. Phys. Lett. 86, 051109 (2005).
[CrossRef]

A. d’Alessandro, R. Asquini, M. Trotta, R. Beccherelli, and I. C. Khoo, Appl. Phys. Lett. 97, 093302 (2010).
[CrossRef]

D. Scrymgeour, A. Sharan, V. Gopalan, K. Gahagan, J. Casson, R. Sander, J. Robinson, P. Chandramani, and F. Kiamilev, Appl. Phys. Lett. 81, 3140 (2002).
[CrossRef]

A. Piccardi, M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, Appl. Phys. Lett. 94, 091106 (2009).
[CrossRef]

M. Peccianti, G. Assanto, A. Luca, C. Umeton, and I. C. Khoo, Appl. Phys. Lett. 77, 7 (2000).
[CrossRef]

A. Pasquazi, A. Alberucci, M. Peccianti, and G. Assanto, Appl. Phys. Lett. 87, 261104 (2005).
[CrossRef]

IEEE Photon. Technol. Lett.

A. Piccardi, A. Alberucci, U. Bortolozzo, S. Residori, and G. Assanto, IEEE Photon. Technol. Lett. 22, 694 (2010).
[CrossRef]

Liq. Cryst.

G. Assanto and M. Karpierz, Liq. Cryst. 36, 1161 (2009).
[CrossRef]

Mol. Cryst. Liq. Cryst.

N. Tabiryan and B. Zeldovich, Mol. Cryst. Liq. Cryst. 62, 237 (1980).
[CrossRef]

Nat. Phys.

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, Nat. Phys. 2, 737 (2006).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rep.

I. C. Khoo, Phys. Rep. 471, 221 (2009).
[CrossRef]

Phys. Rev. A

A. Alberucci, A. Piccardi, M. Peccianti, M. Kaczmarek, and G. Assanto, Phys. Rev. A 82, 023806 (2010).
[CrossRef]

Phys. Rev. E

M. Peccianti, C. Conti, and G. Assanto, Phys. Rev. E 68, R025602 (2003).
[CrossRef]

Phys. Rev. Lett.

M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, Phys. Rev. Lett. 98, 113902 (2007).
[CrossRef] [PubMed]

Proc. SPIE

S. Davis, G. Farca, S. Rommel, A. Martin, and M. Anderson, Proc. SPIE 6971, 69710G (2008).
[CrossRef]

Other

D.-K. Yang and S.-T. Wu, Fundamentals of Liquid Crystals Devices (Wiley, 2006).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Device sketch. (a) Front view: the superposed gray-scale map represents the intensity of E L F (black is the highest). (b) Top view of the electrodes. (c) Distribution of the NLCs’ optic axis in the cell midplane x = L / 2 (bottom) and corresponding θ versus y (top). Inset: definition of θ. The red arrows indicate the orientation of the molecular director.

Fig. 2
Fig. 2

(a) Reorientation angle in the cell midplane x = L / 2 for V 1 = V 2 versus applied bias: each label indicates the corresponding background angle θ 0 . (b) Color map of θ in the plane x y . (c) Maximum change in θ ( x = L / 2 , y ) versus applied biases V 1 and V 2 . (d)–(f) θ distribution versus y in x = L / 2 for various V 2 ; the numeric labels on each line indicate the corresponding V 1 . The bias values refer to a thickness L = 100 μm .

Fig. 3
Fig. 3

(a) Nematicon evolution for P = 3 mW ; dashed and dotted white lines indicate the interface borders and the beam trajectory when θ L F = 10 ° , respectively. (b) Left, trajectories upon TIR for P = 0.5 mW (no symbols) and P = 3 mW (squares); right, dashed (solid) curves correspond to θ 2 = 90 ° ( 10 ° ). (c) Soliton output slope β versus θ 1 for θ 2 = 10 ° and (d) versus θ 2 for θ 1 = 10 ° . Here, the wavelength is 1064 nm , the input waist is 5 μm , and L = 100 μm .

Fig. 4
Fig. 4

(a) TIR region versus θ 1 and θ 2 . (b) Angle β versus θ 2 for α = 0 ° , (c)  25 ° , and (d)  70 ° ; the labels in each line indicate the corresponding θ 1 . (e) Maximum angular deflection of wave vector k and Poynting vector S versus α. We took θ 1 / 2 [ 0 , π / 2 ] , in line with Fig. 2.

Equations (4)

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

2 θ L F x 2 + 2 θ L F y 2 + γ L F sin ( 2 θ L F ) | E L F | 2 = 0 ,
2 i k 0 n 0 ( A z + tan δ A y ) + D y 2 A y 2 + k 0 2 Δ n e 2 A = 0 ,
2 ψ z 2 + 2 ψ y 2 ( π L ) 2 ψ + γ sin [ 2 ( θ L F + ψ δ ) ] | A | 2 = 0 ,
d 2 y d z 2 = n e n 0 2 n e y + d tan δ d z ,

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