Abstract

We study the properties of bright and vortex solitons in thermal media with nonuniform thermal conductivity and homogeneous refractive index, whereby the local modulation of the thermal conductivity strongly affects the entire refractive index distribution. While regions where the thermal conductivity is increased effectively expel light, self-trapping may occur in the regions with reduced thermal conductivity, even if such regions are located close to the material boundary. As a result, strongly asymmetric self-trapped beams may form inside a ring with reduced thermal conductivity and perform persistent rotary motion. Also, such rings are shown to support stable vortex solitons, which may feature strongly noncanonical shapes.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. A. Akhmanov, D. P. Krindach, A. V. Migulin, A. P. Sukhorukov, and R. V. Khokhlov, IEEE J. Quantum Electron. QE-4, 568 (1968).
    [CrossRef]
  2. A. P. Sukhorukov, Sov. Phys. Usp. 13, 410 (1970).
    [CrossRef]
  3. A. M. Deykoon and G. A. Swartzlander, J. Opt. Soc. Am. B 18, 804 (2001).
    [CrossRef]
  4. D. Briedis, D. Petersen, D. Edmundson, W. Krolikowski, and O. Bang, Opt. Express 13, 435 (2005).
    [CrossRef]
  5. A. I. Yakimenko, Y. A. Zaliznyak, and Y. Kivshar, Phys. Rev. E 71, 065603(R) (2005).
    [CrossRef]
  6. C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, Phys. Rev. Lett. 95, 213904 (2005).
    [CrossRef]
  7. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Opt. Express 15, 9378 (2007).
    [CrossRef]
  8. C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, Nat. Phys. 2, 769 (2006).
    [CrossRef]
  9. I. A. Kolchugina, V. A. Mironov, and A. M. Sergeev, JETP Lett. 31, 304 (1980).
  10. C. Rotschild, M. Segev, Z. Xu, Y. V. Kartashov, L. Torner, and O. Cohen, Opt. Lett. 31, 3312 (2006).
    [CrossRef]
  11. D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, J. Opt. A 11, 094014 (2009).
    [CrossRef]
  12. S. Skupin, O. Bang, D. Edmundson, and W. Krolikowski, Phys. Rev. E 73, 066603 (2006).
    [CrossRef]
  13. A. I. Yakimenko, V. M. Lashkin, and O. O. Prikhodko, Phys. Rev. E 73, 066605 (2006).
    [CrossRef]
  14. B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, Opt. Lett. 32, 154 (2007).
    [CrossRef]
  15. A. Minovich, D. Neshev, A. Dreischuh, W. Krolikowski, and Y. Kivshar, Opt. Lett. 32, 1599 (2007).
    [CrossRef]
  16. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Opt. Express 15, 16217 (2007).
  17. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Opt. Lett. 33, 1774 (2008).
    [CrossRef]
  18. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Opt. Lett. 34, 283 (2009).
    [CrossRef]
  19. S. Narayana and Y. Sato, Phys. Rev. Lett. 108, 214303 (2012).
    [CrossRef]
  20. T. Han, T. Yuan, B. Li, and C.-W. Qiu, Science reports 3, 1593 (2013).
    [CrossRef]
  21. M. Maldovan, Phys. Rev. Lett. 110, 025902 (2013).
    [CrossRef]

2013

T. Han, T. Yuan, B. Li, and C.-W. Qiu, Science reports 3, 1593 (2013).
[CrossRef]

M. Maldovan, Phys. Rev. Lett. 110, 025902 (2013).
[CrossRef]

2012

S. Narayana and Y. Sato, Phys. Rev. Lett. 108, 214303 (2012).
[CrossRef]

2009

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Opt. Lett. 34, 283 (2009).
[CrossRef]

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, J. Opt. A 11, 094014 (2009).
[CrossRef]

2008

2007

2006

C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, Nat. Phys. 2, 769 (2006).
[CrossRef]

C. Rotschild, M. Segev, Z. Xu, Y. V. Kartashov, L. Torner, and O. Cohen, Opt. Lett. 31, 3312 (2006).
[CrossRef]

S. Skupin, O. Bang, D. Edmundson, and W. Krolikowski, Phys. Rev. E 73, 066603 (2006).
[CrossRef]

A. I. Yakimenko, V. M. Lashkin, and O. O. Prikhodko, Phys. Rev. E 73, 066605 (2006).
[CrossRef]

2005

D. Briedis, D. Petersen, D. Edmundson, W. Krolikowski, and O. Bang, Opt. Express 13, 435 (2005).
[CrossRef]

A. I. Yakimenko, Y. A. Zaliznyak, and Y. Kivshar, Phys. Rev. E 71, 065603(R) (2005).
[CrossRef]

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef]

2001

1980

I. A. Kolchugina, V. A. Mironov, and A. M. Sergeev, JETP Lett. 31, 304 (1980).

1970

A. P. Sukhorukov, Sov. Phys. Usp. 13, 410 (1970).
[CrossRef]

1968

S. A. Akhmanov, D. P. Krindach, A. V. Migulin, A. P. Sukhorukov, and R. V. Khokhlov, IEEE J. Quantum Electron. QE-4, 568 (1968).
[CrossRef]

Akhmanov, S. A.

S. A. Akhmanov, D. P. Krindach, A. V. Migulin, A. P. Sukhorukov, and R. V. Khokhlov, IEEE J. Quantum Electron. QE-4, 568 (1968).
[CrossRef]

Alfassi, B.

Bang, O.

S. Skupin, O. Bang, D. Edmundson, and W. Krolikowski, Phys. Rev. E 73, 066603 (2006).
[CrossRef]

D. Briedis, D. Petersen, D. Edmundson, W. Krolikowski, and O. Bang, Opt. Express 13, 435 (2005).
[CrossRef]

Briedis, D.

Buccoliero, D.

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, J. Opt. A 11, 094014 (2009).
[CrossRef]

Carmon, T.

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef]

Christodoulides, D. N.

Cohen, O.

C. Rotschild, M. Segev, Z. Xu, Y. V. Kartashov, L. Torner, and O. Cohen, Opt. Lett. 31, 3312 (2006).
[CrossRef]

C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, Nat. Phys. 2, 769 (2006).
[CrossRef]

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef]

Desyatnikov, A. S.

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, J. Opt. A 11, 094014 (2009).
[CrossRef]

Deykoon, A. M.

Dreischuh, A.

Edmundson, D.

S. Skupin, O. Bang, D. Edmundson, and W. Krolikowski, Phys. Rev. E 73, 066603 (2006).
[CrossRef]

D. Briedis, D. Petersen, D. Edmundson, W. Krolikowski, and O. Bang, Opt. Express 13, 435 (2005).
[CrossRef]

Han, T.

T. Han, T. Yuan, B. Li, and C.-W. Qiu, Science reports 3, 1593 (2013).
[CrossRef]

Kartashov, Y. V.

Khokhlov, R. V.

S. A. Akhmanov, D. P. Krindach, A. V. Migulin, A. P. Sukhorukov, and R. V. Khokhlov, IEEE J. Quantum Electron. QE-4, 568 (1968).
[CrossRef]

Kivshar, Y.

A. Minovich, D. Neshev, A. Dreischuh, W. Krolikowski, and Y. Kivshar, Opt. Lett. 32, 1599 (2007).
[CrossRef]

A. I. Yakimenko, Y. A. Zaliznyak, and Y. Kivshar, Phys. Rev. E 71, 065603(R) (2005).
[CrossRef]

Kivshar, Y. S.

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, J. Opt. A 11, 094014 (2009).
[CrossRef]

Kolchugina, I. A.

I. A. Kolchugina, V. A. Mironov, and A. M. Sergeev, JETP Lett. 31, 304 (1980).

Krindach, D. P.

S. A. Akhmanov, D. P. Krindach, A. V. Migulin, A. P. Sukhorukov, and R. V. Khokhlov, IEEE J. Quantum Electron. QE-4, 568 (1968).
[CrossRef]

Krolikowski, W.

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, J. Opt. A 11, 094014 (2009).
[CrossRef]

A. Minovich, D. Neshev, A. Dreischuh, W. Krolikowski, and Y. Kivshar, Opt. Lett. 32, 1599 (2007).
[CrossRef]

S. Skupin, O. Bang, D. Edmundson, and W. Krolikowski, Phys. Rev. E 73, 066603 (2006).
[CrossRef]

D. Briedis, D. Petersen, D. Edmundson, W. Krolikowski, and O. Bang, Opt. Express 13, 435 (2005).
[CrossRef]

Lashkin, V. M.

A. I. Yakimenko, V. M. Lashkin, and O. O. Prikhodko, Phys. Rev. E 73, 066605 (2006).
[CrossRef]

Li, B.

T. Han, T. Yuan, B. Li, and C.-W. Qiu, Science reports 3, 1593 (2013).
[CrossRef]

Maldovan, M.

M. Maldovan, Phys. Rev. Lett. 110, 025902 (2013).
[CrossRef]

Manela, O.

B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, Opt. Lett. 32, 154 (2007).
[CrossRef]

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef]

Migulin, A. V.

S. A. Akhmanov, D. P. Krindach, A. V. Migulin, A. P. Sukhorukov, and R. V. Khokhlov, IEEE J. Quantum Electron. QE-4, 568 (1968).
[CrossRef]

Minovich, A.

Mironov, V. A.

I. A. Kolchugina, V. A. Mironov, and A. M. Sergeev, JETP Lett. 31, 304 (1980).

Narayana, S.

S. Narayana and Y. Sato, Phys. Rev. Lett. 108, 214303 (2012).
[CrossRef]

Neshev, D.

Petersen, D.

Prikhodko, O. O.

A. I. Yakimenko, V. M. Lashkin, and O. O. Prikhodko, Phys. Rev. E 73, 066605 (2006).
[CrossRef]

Qiu, C.-W.

T. Han, T. Yuan, B. Li, and C.-W. Qiu, Science reports 3, 1593 (2013).
[CrossRef]

Rotschild, C.

B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, Opt. Lett. 32, 154 (2007).
[CrossRef]

C. Rotschild, M. Segev, Z. Xu, Y. V. Kartashov, L. Torner, and O. Cohen, Opt. Lett. 31, 3312 (2006).
[CrossRef]

C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, Nat. Phys. 2, 769 (2006).
[CrossRef]

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef]

Sato, Y.

S. Narayana and Y. Sato, Phys. Rev. Lett. 108, 214303 (2012).
[CrossRef]

Segev, M.

B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, Opt. Lett. 32, 154 (2007).
[CrossRef]

C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, Nat. Phys. 2, 769 (2006).
[CrossRef]

C. Rotschild, M. Segev, Z. Xu, Y. V. Kartashov, L. Torner, and O. Cohen, Opt. Lett. 31, 3312 (2006).
[CrossRef]

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef]

Sergeev, A. M.

I. A. Kolchugina, V. A. Mironov, and A. M. Sergeev, JETP Lett. 31, 304 (1980).

Skupin, S.

S. Skupin, O. Bang, D. Edmundson, and W. Krolikowski, Phys. Rev. E 73, 066603 (2006).
[CrossRef]

Sukhorukov, A. P.

A. P. Sukhorukov, Sov. Phys. Usp. 13, 410 (1970).
[CrossRef]

S. A. Akhmanov, D. P. Krindach, A. V. Migulin, A. P. Sukhorukov, and R. V. Khokhlov, IEEE J. Quantum Electron. QE-4, 568 (1968).
[CrossRef]

Swartzlander, G. A.

Torner, L.

Vysloukh, V. A.

Xu, Z.

Yakimenko, A. I.

A. I. Yakimenko, V. M. Lashkin, and O. O. Prikhodko, Phys. Rev. E 73, 066605 (2006).
[CrossRef]

A. I. Yakimenko, Y. A. Zaliznyak, and Y. Kivshar, Phys. Rev. E 71, 065603(R) (2005).
[CrossRef]

Yuan, T.

T. Han, T. Yuan, B. Li, and C.-W. Qiu, Science reports 3, 1593 (2013).
[CrossRef]

Zaliznyak, Y. A.

A. I. Yakimenko, Y. A. Zaliznyak, and Y. Kivshar, Phys. Rev. E 71, 065603(R) (2005).
[CrossRef]

IEEE J. Quantum Electron.

S. A. Akhmanov, D. P. Krindach, A. V. Migulin, A. P. Sukhorukov, and R. V. Khokhlov, IEEE J. Quantum Electron. QE-4, 568 (1968).
[CrossRef]

J. Opt. A

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, J. Opt. A 11, 094014 (2009).
[CrossRef]

J. Opt. Soc. Am. B

JETP Lett.

I. A. Kolchugina, V. A. Mironov, and A. M. Sergeev, JETP Lett. 31, 304 (1980).

Nat. Phys.

C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, Nat. Phys. 2, 769 (2006).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. E

S. Skupin, O. Bang, D. Edmundson, and W. Krolikowski, Phys. Rev. E 73, 066603 (2006).
[CrossRef]

A. I. Yakimenko, V. M. Lashkin, and O. O. Prikhodko, Phys. Rev. E 73, 066605 (2006).
[CrossRef]

A. I. Yakimenko, Y. A. Zaliznyak, and Y. Kivshar, Phys. Rev. E 71, 065603(R) (2005).
[CrossRef]

Phys. Rev. Lett.

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef]

S. Narayana and Y. Sato, Phys. Rev. Lett. 108, 214303 (2012).
[CrossRef]

M. Maldovan, Phys. Rev. Lett. 110, 025902 (2013).
[CrossRef]

Science reports

T. Han, T. Yuan, B. Li, and C.-W. Qiu, Science reports 3, 1593 (2013).
[CrossRef]

Sov. Phys. Usp.

A. P. Sukhorukov, Sov. Phys. Usp. 13, 410 (1970).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1.

Intensity (left), phase (center), and refractive index (right) distributions for vortex solitons in the inhomogeneous thermal medium at (a) b=1.8, m=1, (b) b=5.7, m=1, and (c) b=5.7, m=2. In all cases, δκ=0.7. The dashed line indicates the center of the ring with radius r=2, where the thermal conductivity is reduced. Notice the different scales in the right and the left panels.

Fig. 2.
Fig. 2.

(a) Energy flow U and integral width W of the vortex soliton solutions versus the propagation constant b at δκ=0.7. Circles correspond to the solutions shown in Figs. 1(a) and 1(b). (b) Energy flow of the vortex soliton solutions versus δκ for different b values. The dashed line corresponds to a uniform medium. (c) Energy flow and (d) energy fractions concentrated in the real and imaginary parts of the field versus nleft at b=4, δκ=0.7. Circles correspond to the solutions depicted in Fig. 3. In panels 2(a), 2(c), and 2(d), stable soliton branches are shown in black, while unstable branches are shown in red. In all cases, m=1.

Fig. 3.
Fig. 3.

Intensity and phase distributions for vortex solitons with m=1, b=4, δκ=0.7 at nleft=2.0 (a), and nleft=3.09 (b). Panel (c) shows the refractive index distribution induced by the vortex soliton depicted in panel (b). Panel (d) shows the refractive index distribution that occurs in the absence of any heating beam, for δκ=0.9, nleft=3.0. Notice the different scales in panels (a), (b) and panels (c), (d).

Fig. 4.
Fig. 4.

(a) Energy flow U versus b for a soliton trapped inside the ring with reduced thermal conductivity at r=3, δκ=0.9. (b) The cross sections of the soliton and the refractive index at ζ=0 corresponding to the circle in (a).

Fig. 5.
Fig. 5.

Intensity (top row) and refractive index (bottom row) distributions, at different distances, showing stable rotation of the fundamental soliton with b=8, δκ=0.9 and initial phase tilt αη=0.0, αζ=0.6, inside the ring with reduced thermal conductivity and radius r=3. The dashed line shows the trajectory of the soliton center, while the arrows show the direction of rotation and are simply to help the eye.

Equations (1)

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

iqξ=12(2qη2+2qζ2)nq,κηnη+κζnζ+κ(2nη2+2nζ2)=|q|2.

Metrics