Abstract

We address the formation of optical surface waves at the very edge of semiconductor materials illuminated by modulated light beams that generate thermal waves rapidly fading in the bulk material. We find families of thresholdless surface waves existing owing to the combined action of thermally-induced refractive index modulations and instantaneous Kerr-type nonlinearity.

© 2008 Optical Society of America

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References

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  1. H.E.Ponath and G.I.Stegeman, eds., Nonlinear Surface Electromagnetic Phenomena (North-Holland, 1991).
  2. D. Mihalache, M. Bertolotti, and C. Sibilia, Prog. Opt. 27, 229 (1989).
  3. K. G. Makris, S. Suntsov, D. N. Christodoulides, and G. I. Stegeman, Opt. Lett. 30, 2466 (2005).
    [CrossRef] [PubMed]
  4. S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Haché, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, Phys. Rev. Lett. 96, 063901 (2006).
    [CrossRef] [PubMed]
  5. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 96, 073901 (2006).
    [CrossRef] [PubMed]
  6. M. I. Molina, R. A. Vicencio, and Y. S. Kivshar, Opt. Lett. 31, 1693 (2006).
    [CrossRef] [PubMed]
  7. C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, Phys. Rev. Lett. 97, 083901 (2006).
    [CrossRef] [PubMed]
  8. E. Smirnov, M. Stepic, C. E. Rüter, D. Kip, and V. Shandarov, Opt. Lett. 31, 2338 (2006).
    [CrossRef] [PubMed]
  9. X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
    [CrossRef] [PubMed]
  10. A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, Phys. Rev. Lett. 98, 173903 (2007).
    [CrossRef]
  11. A.Mandelis, ed., Photoacoustic and Thermal Wave Phenomena in Semiconductors (North-Holland, 1987).
  12. P. S. Dobal, H. D. Bist, S. K. Mehta, and R. K. Jain, Appl. Phys. Lett. 65, 2469 (1994).
    [CrossRef]
  13. F. G. Della Corte, G. Cocorullo, M. Iodice, and I. Rendina, Appl. Phys. Lett. 77, 1614 (2000).
    [CrossRef]
  14. D. E. Aspnes, S. M. Kelso, and R. A. Logan, J. Appl. Phys. 60, 754 (1986).
    [CrossRef]

2007

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef] [PubMed]

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, Phys. Rev. Lett. 98, 173903 (2007).
[CrossRef]

2006

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Haché, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 96, 073901 (2006).
[CrossRef] [PubMed]

M. I. Molina, R. A. Vicencio, and Y. S. Kivshar, Opt. Lett. 31, 1693 (2006).
[CrossRef] [PubMed]

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

E. Smirnov, M. Stepic, C. E. Rüter, D. Kip, and V. Shandarov, Opt. Lett. 31, 2338 (2006).
[CrossRef] [PubMed]

2005

2000

F. G. Della Corte, G. Cocorullo, M. Iodice, and I. Rendina, Appl. Phys. Lett. 77, 1614 (2000).
[CrossRef]

1994

P. S. Dobal, H. D. Bist, S. K. Mehta, and R. K. Jain, Appl. Phys. Lett. 65, 2469 (1994).
[CrossRef]

1989

D. Mihalache, M. Bertolotti, and C. Sibilia, Prog. Opt. 27, 229 (1989).

1986

D. E. Aspnes, S. M. Kelso, and R. A. Logan, J. Appl. Phys. 60, 754 (1986).
[CrossRef]

Appl. Phys. Lett.

P. S. Dobal, H. D. Bist, S. K. Mehta, and R. K. Jain, Appl. Phys. Lett. 65, 2469 (1994).
[CrossRef]

F. G. Della Corte, G. Cocorullo, M. Iodice, and I. Rendina, Appl. Phys. Lett. 77, 1614 (2000).
[CrossRef]

J. Appl. Phys.

D. E. Aspnes, S. M. Kelso, and R. A. Logan, J. Appl. Phys. 60, 754 (1986).
[CrossRef]

Opt. Lett.

Phys. Rev. Lett.

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef] [PubMed]

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, Phys. Rev. Lett. 98, 173903 (2007).
[CrossRef]

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Haché, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 96, 073901 (2006).
[CrossRef] [PubMed]

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

Prog. Opt.

D. Mihalache, M. Bertolotti, and C. Sibilia, Prog. Opt. 27, 229 (1989).

Other

H.E.Ponath and G.I.Stegeman, eds., Nonlinear Surface Electromagnetic Phenomena (North-Holland, 1991).

A.Mandelis, ed., Photoacoustic and Thermal Wave Phenomena in Semiconductors (North-Holland, 1987).

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Figures (4)

Fig. 1
Fig. 1

Spatial profiles of thermal waves for (a) different moments of time t at τ = 16 and (b) different modulation periods τ at t = τ 8 . (c) Maximal surface temperature as a function of modulation period τ at t = τ 8 . (d) Complex spatial profile of the surface wave created by three heat sources with the parameters ( τ 1 = 160 , φ 1 = 3 π 4 , I 1 = 0.04 ), ( τ 2 = 16 , φ 2 = 5 π 4 , I 2 = 0.16 ), and ( τ 3 = 1 , φ 3 = 3 π 4 , I 3 = 0.80 ) at t = 0 .

Fig. 2
Fig. 2

Linear surface modes supported by the refractive index profile induced by thermal wave at t = τ 8 for τ = 16 . (a) Propagation constants versus modulation depth p. (b) Profiles of the first three linear modes at p = 60 corresponding to points marked by circles in (a).

Fig. 3
Fig. 3

Steering of near-surface soliton q ( η , 0 ) = sech ( η η 0 ) by thermal wave at η 0 = 4 , τ = 64 , and p = 5.5 . (a) Superimposed field modulus distributions for solitons in the time moments t 1 = τ 8 and t 2 = 5 τ 8 . (b) Soliton center displacements versus time at different propagation distances.

Fig. 4
Fig. 4

Nonlinear surface modes supported by thermally induced refractive index profiles at t = τ 8 for τ = 16 . (a) Profiles of fundamental modes with different b at p = 20 . (b) Energy flow versus b for fundamental and dipole modes at p = 20 . Points marked by circles correspond to profiles shown in (a). (c) Profiles of dipole and triple-mode solutions at b = 4 , p = 60 . (d) Real part of perturbation growth rate for triple-mode solution at p = 60 .

Equations (2)

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T t 2 T η 2 = 1 2 exp ( α η ) [ 1 + cos ( Ω t ) ] ,
i q ξ = 1 2 2 q η 2 q 2 q p T ( η , t ) q ,

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