Abstract

When surface plasmons are excited at a metal-dielectric interface, the electromagnetic field takes a very large value near the interface. If the dielectric is a nonlinear Kerr medium, then the effect of nonlinearity can be greatly amplified due to the field enhancement. In this paper, we calculate the lateral shift of p wave beams incident on metal-dielectric multilayer systems in the Otto configuration in a numerically exact manner, using the invariant imbedding method of wave propagation in nonlinear stratified media. In the linear case, we find that the lateral shift becomes very large at the incident angles where the surface plasmons are excited. As the nonlinearity is turned on, the value of the lateral shift changes rapidly. We find that even a small change of the intensity of the incident wave can cause a huge change of the lateral shift. We propose that this phenomenon can be applied to designing precise optical switches operating at small powers.

© 2008 Optical Society of America

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  3. E. Ozbay, "Plasmonics: Merging photonics and electronics at nanoscale dimensions," Science 311, 189-193 (2006).
    [CrossRef] [PubMed]
  4. A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, "Nano-optics of surface plasmon polaritons," Phys. Rep. 408, 131-314 (2005).
    [CrossRef]
  5. S. A. Maier and H. A. Atwater, "Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures," J. Appl. Phys. 98, 011101 (2005).
    [CrossRef]
  6. K. A. Willets and R. P. Van Duyne, "Localized surface plasmon resonance spectroscopy and sensing," Annu. Rev. Phys. Chem. 58, 267-297 (2007).
    [CrossRef]
  7. X. D. Hoa, A. G. Kirk, and M. Tabrizian, "Towards integrated and sensitive surface plasmon resonance biosensors: A review of recent progress," Biosens. Bioelectron. 23, 151-160 (2007).
    [CrossRef] [PubMed]
  8. J. R. Sambles and R. A. Innes, "A comment on nonlinear optics using surface plasmon-polaritons," J. Mod. Opt. 35, 791-797 (1988).
    [CrossRef]
  9. I. I. Smolyaninov, A. V. Zayats, A. Gungor, and C. C. Davis, "Single-photon tunneling via localized surface plasmons," Phys. Rev. Lett. 88, 187402 (2002).
    [CrossRef] [PubMed]
  10. N.-C. Panoiu and R. M. Osgood, Jr., "Subwavelength nonlinear plasmonic nanowire," Nano Lett. 4, 2427-2430 (2004).
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  11. G. A. Wurtz, R. Pollard, and A. V. Zayats, "Optical bistability in nonlinear surface-plasmon polaritonic crystals," Phys. Rev. Lett. 97, 057402 (2006).
    [CrossRef] [PubMed]
  12. Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, "Subwavelength discrete solitons in nonlinear metamaterials," Phys. Rev. Lett. 99, 153901 (2007).
    [PubMed]
  13. X. Yin and L. Hesselink, "Goos-Hänchen shift surface plasmon resonance sensor," Appl. Phys. Lett. 89, 261108 (2006).
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  14. L. Chen, Z. Cao, F. Ou, H. Li, Q. Shen, and H. Qiao, "Observation of large positive and negative lateral shifts of a reflected beam from symmetrical metal-cladding waveguides," Opt. Lett. 32, 1432-1434 (2007).
    [CrossRef] [PubMed]
  15. G. I. Babkin and V. I. Klyatskin, "Theory of wave propagation in nonlinear inhomogeneous media," Sov. Phys. JETP 52, 416-420 (1980).
  16. B. Doucot and R. Rammal, "Invariant-imbedding approach to localization. II. Non-linear random media," J. Phys. (Paris) 48, 527-546 (1987).
    [CrossRef]
  17. K. Kim, D. K. Phung, F. Rotermund, and H. Lim, "Propagation of electromagnetic waves in stratified media with nonlinearity in both dielectric and magnetic responses," Opt. Express 16, 1150-1164 (2008).
    [CrossRef] [PubMed]
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  20. R. Rammal and B. Doucot, "Invariant-imbedding approach to localization. I. General framework and basic equations," J. Phys. (Paris) 48, 509-526 (1987).
    [CrossRef]
  21. K. Kim, "Reflection coefficient and localization length of waves in one-dimensional random media," Phys. Rev. B 58, 6153-6160 (1998).
    [CrossRef]
  22. K. Kim, D.-H. Lee, and H. Lim, "Theory of the propagation of coupled waves in arbitrarily inhomogeneous stratified media," Europhys. Lett. 69, 207-213 (2005).
    [CrossRef]
  23. K. Kim and D.-H. Lee, "Invariant imbedding theory of mode conversion in inhomogeneous plasmas. I. Exact calculation of the mode conversion coefficient in cold, unmagnetized plasmas," Phys. Plasmas 12, 062101 (2005).
    [CrossRef]
  24. K. Kim and D.-H. Lee, "Invariant imbedding theory of mode conversion in inhomogeneous plasmas. II. Mode conversion in cold, magnetized plasmas with perpendicular inhomogeneity," Phys. Plasmas 13, 042103 (2006).
    [CrossRef]
  25. K. Kim, F. Rotermund, and H. Lim, "Disorder-enhanced transmission of a quantum mechanical particle through a disordered tunneling barrier in one dimension: Exact calculation based on the invariant imbedding method," Phys. Rev. B 77, 024203 (2008).
    [CrossRef]
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  27. A. S. L. Gomes, E. L. F. Filho, C. B. de Araújo, D. Rativa, R. E. de Araujo, K. Sakaguchi, F. P. Mezzapesa, I. C. S. Carvalho, and P. G. Kazansky, "Third-order nonlinear optical properties of bismuth-borate glasses measured by conventional and thermally managed eclipse Z scan," J. Appl. Phys. 101, 033115 (2007).
    [CrossRef]
  28. T. E. O. Screen, K. B. Lawton, G. S. Wilson, N. Dolney, R. Ispasoiu, T. GoodsonIII, S. J. Martin, D. D. C. Bradley, and H. L. Anderson, "Synthesis and third order nonlinear optics of a new soluble conjugated porphyrin polymer," J. Mater. Chem. 11, 312-320 (2001).
    [CrossRef]

2008

K. Kim, D. K. Phung, F. Rotermund, and H. Lim, "Propagation of electromagnetic waves in stratified media with nonlinearity in both dielectric and magnetic responses," Opt. Express 16, 1150-1164 (2008).
[CrossRef] [PubMed]

K. Kim, F. Rotermund, and H. Lim, "Disorder-enhanced transmission of a quantum mechanical particle through a disordered tunneling barrier in one dimension: Exact calculation based on the invariant imbedding method," Phys. Rev. B 77, 024203 (2008).
[CrossRef]

2007

A. S. L. Gomes, E. L. F. Filho, C. B. de Araújo, D. Rativa, R. E. de Araujo, K. Sakaguchi, F. P. Mezzapesa, I. C. S. Carvalho, and P. G. Kazansky, "Third-order nonlinear optical properties of bismuth-borate glasses measured by conventional and thermally managed eclipse Z scan," J. Appl. Phys. 101, 033115 (2007).
[CrossRef]

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, "Subwavelength discrete solitons in nonlinear metamaterials," Phys. Rev. Lett. 99, 153901 (2007).
[PubMed]

L. Chen, Z. Cao, F. Ou, H. Li, Q. Shen, and H. Qiao, "Observation of large positive and negative lateral shifts of a reflected beam from symmetrical metal-cladding waveguides," Opt. Lett. 32, 1432-1434 (2007).
[CrossRef] [PubMed]

K. A. Willets and R. P. Van Duyne, "Localized surface plasmon resonance spectroscopy and sensing," Annu. Rev. Phys. Chem. 58, 267-297 (2007).
[CrossRef]

X. D. Hoa, A. G. Kirk, and M. Tabrizian, "Towards integrated and sensitive surface plasmon resonance biosensors: A review of recent progress," Biosens. Bioelectron. 23, 151-160 (2007).
[CrossRef] [PubMed]

2006

E. Ozbay, "Plasmonics: Merging photonics and electronics at nanoscale dimensions," Science 311, 189-193 (2006).
[CrossRef] [PubMed]

G. A. Wurtz, R. Pollard, and A. V. Zayats, "Optical bistability in nonlinear surface-plasmon polaritonic crystals," Phys. Rev. Lett. 97, 057402 (2006).
[CrossRef] [PubMed]

X. Yin and L. Hesselink, "Goos-Hänchen shift surface plasmon resonance sensor," Appl. Phys. Lett. 89, 261108 (2006).
[CrossRef]

K. Kim and D.-H. Lee, "Invariant imbedding theory of mode conversion in inhomogeneous plasmas. II. Mode conversion in cold, magnetized plasmas with perpendicular inhomogeneity," Phys. Plasmas 13, 042103 (2006).
[CrossRef]

2005

K. Kim, D.-H. Lee, and H. Lim, "Theory of the propagation of coupled waves in arbitrarily inhomogeneous stratified media," Europhys. Lett. 69, 207-213 (2005).
[CrossRef]

K. Kim and D.-H. Lee, "Invariant imbedding theory of mode conversion in inhomogeneous plasmas. I. Exact calculation of the mode conversion coefficient in cold, unmagnetized plasmas," Phys. Plasmas 12, 062101 (2005).
[CrossRef]

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, "Nano-optics of surface plasmon polaritons," Phys. Rep. 408, 131-314 (2005).
[CrossRef]

S. A. Maier and H. A. Atwater, "Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures," J. Appl. Phys. 98, 011101 (2005).
[CrossRef]

2004

N.-C. Panoiu and R. M. Osgood, Jr., "Subwavelength nonlinear plasmonic nanowire," Nano Lett. 4, 2427-2430 (2004).
[CrossRef]

2003

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

2002

I. I. Smolyaninov, A. V. Zayats, A. Gungor, and C. C. Davis, "Single-photon tunneling via localized surface plasmons," Phys. Rev. Lett. 88, 187402 (2002).
[CrossRef] [PubMed]

2001

T. E. O. Screen, K. B. Lawton, G. S. Wilson, N. Dolney, R. Ispasoiu, T. GoodsonIII, S. J. Martin, D. D. C. Bradley, and H. L. Anderson, "Synthesis and third order nonlinear optics of a new soluble conjugated porphyrin polymer," J. Mater. Chem. 11, 312-320 (2001).
[CrossRef]

1998

K. Kim, "Reflection coefficient and localization length of waves in one-dimensional random media," Phys. Rev. B 58, 6153-6160 (1998).
[CrossRef]

1994

V. I. Klyatskin, "The imbedding method in statistical boundary-value wave problems," Prog. Opt. 33, 1-127 (1994).
[CrossRef]

1988

J. R. Sambles and R. A. Innes, "A comment on nonlinear optics using surface plasmon-polaritons," J. Mod. Opt. 35, 791-797 (1988).
[CrossRef]

1987

R. Rammal and B. Doucot, "Invariant-imbedding approach to localization. I. General framework and basic equations," J. Phys. (Paris) 48, 509-526 (1987).
[CrossRef]

B. Doucot and R. Rammal, "Invariant-imbedding approach to localization. II. Non-linear random media," J. Phys. (Paris) 48, 527-546 (1987).
[CrossRef]

1980

G. I. Babkin and V. I. Klyatskin, "Theory of wave propagation in nonlinear inhomogeneous media," Sov. Phys. JETP 52, 416-420 (1980).

Anderson, H. L.

T. E. O. Screen, K. B. Lawton, G. S. Wilson, N. Dolney, R. Ispasoiu, T. GoodsonIII, S. J. Martin, D. D. C. Bradley, and H. L. Anderson, "Synthesis and third order nonlinear optics of a new soluble conjugated porphyrin polymer," J. Mater. Chem. 11, 312-320 (2001).
[CrossRef]

Atwater, H. A.

S. A. Maier and H. A. Atwater, "Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures," J. Appl. Phys. 98, 011101 (2005).
[CrossRef]

Babkin, G. I.

G. I. Babkin and V. I. Klyatskin, "Theory of wave propagation in nonlinear inhomogeneous media," Sov. Phys. JETP 52, 416-420 (1980).

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

Bartal, G.

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, "Subwavelength discrete solitons in nonlinear metamaterials," Phys. Rev. Lett. 99, 153901 (2007).
[PubMed]

Bradley, D. D. C.

T. E. O. Screen, K. B. Lawton, G. S. Wilson, N. Dolney, R. Ispasoiu, T. GoodsonIII, S. J. Martin, D. D. C. Bradley, and H. L. Anderson, "Synthesis and third order nonlinear optics of a new soluble conjugated porphyrin polymer," J. Mater. Chem. 11, 312-320 (2001).
[CrossRef]

Cao, Z.

Carvalho, I. C. S.

A. S. L. Gomes, E. L. F. Filho, C. B. de Araújo, D. Rativa, R. E. de Araujo, K. Sakaguchi, F. P. Mezzapesa, I. C. S. Carvalho, and P. G. Kazansky, "Third-order nonlinear optical properties of bismuth-borate glasses measured by conventional and thermally managed eclipse Z scan," J. Appl. Phys. 101, 033115 (2007).
[CrossRef]

Chen, L.

Davis, C. C.

I. I. Smolyaninov, A. V. Zayats, A. Gungor, and C. C. Davis, "Single-photon tunneling via localized surface plasmons," Phys. Rev. Lett. 88, 187402 (2002).
[CrossRef] [PubMed]

de Araujo, R. E.

A. S. L. Gomes, E. L. F. Filho, C. B. de Araújo, D. Rativa, R. E. de Araujo, K. Sakaguchi, F. P. Mezzapesa, I. C. S. Carvalho, and P. G. Kazansky, "Third-order nonlinear optical properties of bismuth-borate glasses measured by conventional and thermally managed eclipse Z scan," J. Appl. Phys. 101, 033115 (2007).
[CrossRef]

de Araújo, C. B.

A. S. L. Gomes, E. L. F. Filho, C. B. de Araújo, D. Rativa, R. E. de Araujo, K. Sakaguchi, F. P. Mezzapesa, I. C. S. Carvalho, and P. G. Kazansky, "Third-order nonlinear optical properties of bismuth-borate glasses measured by conventional and thermally managed eclipse Z scan," J. Appl. Phys. 101, 033115 (2007).
[CrossRef]

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

Dolney, N.

T. E. O. Screen, K. B. Lawton, G. S. Wilson, N. Dolney, R. Ispasoiu, T. GoodsonIII, S. J. Martin, D. D. C. Bradley, and H. L. Anderson, "Synthesis and third order nonlinear optics of a new soluble conjugated porphyrin polymer," J. Mater. Chem. 11, 312-320 (2001).
[CrossRef]

Doucot, B.

B. Doucot and R. Rammal, "Invariant-imbedding approach to localization. II. Non-linear random media," J. Phys. (Paris) 48, 527-546 (1987).
[CrossRef]

R. Rammal and B. Doucot, "Invariant-imbedding approach to localization. I. General framework and basic equations," J. Phys. (Paris) 48, 509-526 (1987).
[CrossRef]

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

Filho, E. L. F.

A. S. L. Gomes, E. L. F. Filho, C. B. de Araújo, D. Rativa, R. E. de Araujo, K. Sakaguchi, F. P. Mezzapesa, I. C. S. Carvalho, and P. G. Kazansky, "Third-order nonlinear optical properties of bismuth-borate glasses measured by conventional and thermally managed eclipse Z scan," J. Appl. Phys. 101, 033115 (2007).
[CrossRef]

Genov, D. A.

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, "Subwavelength discrete solitons in nonlinear metamaterials," Phys. Rev. Lett. 99, 153901 (2007).
[PubMed]

Gomes, A. S. L.

A. S. L. Gomes, E. L. F. Filho, C. B. de Araújo, D. Rativa, R. E. de Araujo, K. Sakaguchi, F. P. Mezzapesa, I. C. S. Carvalho, and P. G. Kazansky, "Third-order nonlinear optical properties of bismuth-borate glasses measured by conventional and thermally managed eclipse Z scan," J. Appl. Phys. 101, 033115 (2007).
[CrossRef]

Goodson, T.

T. E. O. Screen, K. B. Lawton, G. S. Wilson, N. Dolney, R. Ispasoiu, T. GoodsonIII, S. J. Martin, D. D. C. Bradley, and H. L. Anderson, "Synthesis and third order nonlinear optics of a new soluble conjugated porphyrin polymer," J. Mater. Chem. 11, 312-320 (2001).
[CrossRef]

Gungor, A.

I. I. Smolyaninov, A. V. Zayats, A. Gungor, and C. C. Davis, "Single-photon tunneling via localized surface plasmons," Phys. Rev. Lett. 88, 187402 (2002).
[CrossRef] [PubMed]

Hesselink, L.

X. Yin and L. Hesselink, "Goos-Hänchen shift surface plasmon resonance sensor," Appl. Phys. Lett. 89, 261108 (2006).
[CrossRef]

Hoa, X. D.

X. D. Hoa, A. G. Kirk, and M. Tabrizian, "Towards integrated and sensitive surface plasmon resonance biosensors: A review of recent progress," Biosens. Bioelectron. 23, 151-160 (2007).
[CrossRef] [PubMed]

Innes, R. A.

J. R. Sambles and R. A. Innes, "A comment on nonlinear optics using surface plasmon-polaritons," J. Mod. Opt. 35, 791-797 (1988).
[CrossRef]

Ispasoiu, R.

T. E. O. Screen, K. B. Lawton, G. S. Wilson, N. Dolney, R. Ispasoiu, T. GoodsonIII, S. J. Martin, D. D. C. Bradley, and H. L. Anderson, "Synthesis and third order nonlinear optics of a new soluble conjugated porphyrin polymer," J. Mater. Chem. 11, 312-320 (2001).
[CrossRef]

Kazansky, P. G.

A. S. L. Gomes, E. L. F. Filho, C. B. de Araújo, D. Rativa, R. E. de Araujo, K. Sakaguchi, F. P. Mezzapesa, I. C. S. Carvalho, and P. G. Kazansky, "Third-order nonlinear optical properties of bismuth-borate glasses measured by conventional and thermally managed eclipse Z scan," J. Appl. Phys. 101, 033115 (2007).
[CrossRef]

Kim, K.

K. Kim, F. Rotermund, and H. Lim, "Disorder-enhanced transmission of a quantum mechanical particle through a disordered tunneling barrier in one dimension: Exact calculation based on the invariant imbedding method," Phys. Rev. B 77, 024203 (2008).
[CrossRef]

K. Kim, D. K. Phung, F. Rotermund, and H. Lim, "Propagation of electromagnetic waves in stratified media with nonlinearity in both dielectric and magnetic responses," Opt. Express 16, 1150-1164 (2008).
[CrossRef] [PubMed]

K. Kim and D.-H. Lee, "Invariant imbedding theory of mode conversion in inhomogeneous plasmas. II. Mode conversion in cold, magnetized plasmas with perpendicular inhomogeneity," Phys. Plasmas 13, 042103 (2006).
[CrossRef]

K. Kim, D.-H. Lee, and H. Lim, "Theory of the propagation of coupled waves in arbitrarily inhomogeneous stratified media," Europhys. Lett. 69, 207-213 (2005).
[CrossRef]

K. Kim and D.-H. Lee, "Invariant imbedding theory of mode conversion in inhomogeneous plasmas. I. Exact calculation of the mode conversion coefficient in cold, unmagnetized plasmas," Phys. Plasmas 12, 062101 (2005).
[CrossRef]

K. Kim, "Reflection coefficient and localization length of waves in one-dimensional random media," Phys. Rev. B 58, 6153-6160 (1998).
[CrossRef]

Kirk, A. G.

X. D. Hoa, A. G. Kirk, and M. Tabrizian, "Towards integrated and sensitive surface plasmon resonance biosensors: A review of recent progress," Biosens. Bioelectron. 23, 151-160 (2007).
[CrossRef] [PubMed]

Klyatskin, V. I.

V. I. Klyatskin, "The imbedding method in statistical boundary-value wave problems," Prog. Opt. 33, 1-127 (1994).
[CrossRef]

G. I. Babkin and V. I. Klyatskin, "Theory of wave propagation in nonlinear inhomogeneous media," Sov. Phys. JETP 52, 416-420 (1980).

Lawton, K. B.

T. E. O. Screen, K. B. Lawton, G. S. Wilson, N. Dolney, R. Ispasoiu, T. GoodsonIII, S. J. Martin, D. D. C. Bradley, and H. L. Anderson, "Synthesis and third order nonlinear optics of a new soluble conjugated porphyrin polymer," J. Mater. Chem. 11, 312-320 (2001).
[CrossRef]

Lee, D.-H.

K. Kim and D.-H. Lee, "Invariant imbedding theory of mode conversion in inhomogeneous plasmas. II. Mode conversion in cold, magnetized plasmas with perpendicular inhomogeneity," Phys. Plasmas 13, 042103 (2006).
[CrossRef]

K. Kim and D.-H. Lee, "Invariant imbedding theory of mode conversion in inhomogeneous plasmas. I. Exact calculation of the mode conversion coefficient in cold, unmagnetized plasmas," Phys. Plasmas 12, 062101 (2005).
[CrossRef]

K. Kim, D.-H. Lee, and H. Lim, "Theory of the propagation of coupled waves in arbitrarily inhomogeneous stratified media," Europhys. Lett. 69, 207-213 (2005).
[CrossRef]

Li, H.

Lim, H.

K. Kim, D. K. Phung, F. Rotermund, and H. Lim, "Propagation of electromagnetic waves in stratified media with nonlinearity in both dielectric and magnetic responses," Opt. Express 16, 1150-1164 (2008).
[CrossRef] [PubMed]

K. Kim, F. Rotermund, and H. Lim, "Disorder-enhanced transmission of a quantum mechanical particle through a disordered tunneling barrier in one dimension: Exact calculation based on the invariant imbedding method," Phys. Rev. B 77, 024203 (2008).
[CrossRef]

K. Kim, D.-H. Lee, and H. Lim, "Theory of the propagation of coupled waves in arbitrarily inhomogeneous stratified media," Europhys. Lett. 69, 207-213 (2005).
[CrossRef]

Liu, Y.

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, "Subwavelength discrete solitons in nonlinear metamaterials," Phys. Rev. Lett. 99, 153901 (2007).
[PubMed]

Maier, S. A.

S. A. Maier and H. A. Atwater, "Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures," J. Appl. Phys. 98, 011101 (2005).
[CrossRef]

Maradudin, A. A.

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, "Nano-optics of surface plasmon polaritons," Phys. Rep. 408, 131-314 (2005).
[CrossRef]

Martin, S. J.

T. E. O. Screen, K. B. Lawton, G. S. Wilson, N. Dolney, R. Ispasoiu, T. GoodsonIII, S. J. Martin, D. D. C. Bradley, and H. L. Anderson, "Synthesis and third order nonlinear optics of a new soluble conjugated porphyrin polymer," J. Mater. Chem. 11, 312-320 (2001).
[CrossRef]

Mezzapesa, F. P.

A. S. L. Gomes, E. L. F. Filho, C. B. de Araújo, D. Rativa, R. E. de Araujo, K. Sakaguchi, F. P. Mezzapesa, I. C. S. Carvalho, and P. G. Kazansky, "Third-order nonlinear optical properties of bismuth-borate glasses measured by conventional and thermally managed eclipse Z scan," J. Appl. Phys. 101, 033115 (2007).
[CrossRef]

Osgood, R. M.

N.-C. Panoiu and R. M. Osgood, Jr., "Subwavelength nonlinear plasmonic nanowire," Nano Lett. 4, 2427-2430 (2004).
[CrossRef]

Ou, F.

Ozbay, E.

E. Ozbay, "Plasmonics: Merging photonics and electronics at nanoscale dimensions," Science 311, 189-193 (2006).
[CrossRef] [PubMed]

Panoiu, N.-C.

N.-C. Panoiu and R. M. Osgood, Jr., "Subwavelength nonlinear plasmonic nanowire," Nano Lett. 4, 2427-2430 (2004).
[CrossRef]

Phung, D. K.

Pollard, R.

G. A. Wurtz, R. Pollard, and A. V. Zayats, "Optical bistability in nonlinear surface-plasmon polaritonic crystals," Phys. Rev. Lett. 97, 057402 (2006).
[CrossRef] [PubMed]

Qiao, H.

Rammal, R.

B. Doucot and R. Rammal, "Invariant-imbedding approach to localization. II. Non-linear random media," J. Phys. (Paris) 48, 527-546 (1987).
[CrossRef]

R. Rammal and B. Doucot, "Invariant-imbedding approach to localization. I. General framework and basic equations," J. Phys. (Paris) 48, 509-526 (1987).
[CrossRef]

Rativa, D.

A. S. L. Gomes, E. L. F. Filho, C. B. de Araújo, D. Rativa, R. E. de Araujo, K. Sakaguchi, F. P. Mezzapesa, I. C. S. Carvalho, and P. G. Kazansky, "Third-order nonlinear optical properties of bismuth-borate glasses measured by conventional and thermally managed eclipse Z scan," J. Appl. Phys. 101, 033115 (2007).
[CrossRef]

Rotermund, F.

K. Kim, F. Rotermund, and H. Lim, "Disorder-enhanced transmission of a quantum mechanical particle through a disordered tunneling barrier in one dimension: Exact calculation based on the invariant imbedding method," Phys. Rev. B 77, 024203 (2008).
[CrossRef]

K. Kim, D. K. Phung, F. Rotermund, and H. Lim, "Propagation of electromagnetic waves in stratified media with nonlinearity in both dielectric and magnetic responses," Opt. Express 16, 1150-1164 (2008).
[CrossRef] [PubMed]

Sakaguchi, K.

A. S. L. Gomes, E. L. F. Filho, C. B. de Araújo, D. Rativa, R. E. de Araujo, K. Sakaguchi, F. P. Mezzapesa, I. C. S. Carvalho, and P. G. Kazansky, "Third-order nonlinear optical properties of bismuth-borate glasses measured by conventional and thermally managed eclipse Z scan," J. Appl. Phys. 101, 033115 (2007).
[CrossRef]

Sambles, J. R.

J. R. Sambles and R. A. Innes, "A comment on nonlinear optics using surface plasmon-polaritons," J. Mod. Opt. 35, 791-797 (1988).
[CrossRef]

Screen, T. E. O.

T. E. O. Screen, K. B. Lawton, G. S. Wilson, N. Dolney, R. Ispasoiu, T. GoodsonIII, S. J. Martin, D. D. C. Bradley, and H. L. Anderson, "Synthesis and third order nonlinear optics of a new soluble conjugated porphyrin polymer," J. Mater. Chem. 11, 312-320 (2001).
[CrossRef]

Shen, Q.

Smolyaninov, I. I.

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, "Nano-optics of surface plasmon polaritons," Phys. Rep. 408, 131-314 (2005).
[CrossRef]

I. I. Smolyaninov, A. V. Zayats, A. Gungor, and C. C. Davis, "Single-photon tunneling via localized surface plasmons," Phys. Rev. Lett. 88, 187402 (2002).
[CrossRef] [PubMed]

Tabrizian, M.

X. D. Hoa, A. G. Kirk, and M. Tabrizian, "Towards integrated and sensitive surface plasmon resonance biosensors: A review of recent progress," Biosens. Bioelectron. 23, 151-160 (2007).
[CrossRef] [PubMed]

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K. A. Willets and R. P. Van Duyne, "Localized surface plasmon resonance spectroscopy and sensing," Annu. Rev. Phys. Chem. 58, 267-297 (2007).
[CrossRef]

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K. A. Willets and R. P. Van Duyne, "Localized surface plasmon resonance spectroscopy and sensing," Annu. Rev. Phys. Chem. 58, 267-297 (2007).
[CrossRef]

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T. E. O. Screen, K. B. Lawton, G. S. Wilson, N. Dolney, R. Ispasoiu, T. GoodsonIII, S. J. Martin, D. D. C. Bradley, and H. L. Anderson, "Synthesis and third order nonlinear optics of a new soluble conjugated porphyrin polymer," J. Mater. Chem. 11, 312-320 (2001).
[CrossRef]

Wurtz, G. A.

G. A. Wurtz, R. Pollard, and A. V. Zayats, "Optical bistability in nonlinear surface-plasmon polaritonic crystals," Phys. Rev. Lett. 97, 057402 (2006).
[CrossRef] [PubMed]

Yin, X.

X. Yin and L. Hesselink, "Goos-Hänchen shift surface plasmon resonance sensor," Appl. Phys. Lett. 89, 261108 (2006).
[CrossRef]

Zayats, A. V.

G. A. Wurtz, R. Pollard, and A. V. Zayats, "Optical bistability in nonlinear surface-plasmon polaritonic crystals," Phys. Rev. Lett. 97, 057402 (2006).
[CrossRef] [PubMed]

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, "Nano-optics of surface plasmon polaritons," Phys. Rep. 408, 131-314 (2005).
[CrossRef]

I. I. Smolyaninov, A. V. Zayats, A. Gungor, and C. C. Davis, "Single-photon tunneling via localized surface plasmons," Phys. Rev. Lett. 88, 187402 (2002).
[CrossRef] [PubMed]

Zhang, X.

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, "Subwavelength discrete solitons in nonlinear metamaterials," Phys. Rev. Lett. 99, 153901 (2007).
[PubMed]

Annu. Rev. Phys. Chem.

K. A. Willets and R. P. Van Duyne, "Localized surface plasmon resonance spectroscopy and sensing," Annu. Rev. Phys. Chem. 58, 267-297 (2007).
[CrossRef]

Appl. Phys. Lett.

X. Yin and L. Hesselink, "Goos-Hänchen shift surface plasmon resonance sensor," Appl. Phys. Lett. 89, 261108 (2006).
[CrossRef]

Biosens. Bioelectron.

X. D. Hoa, A. G. Kirk, and M. Tabrizian, "Towards integrated and sensitive surface plasmon resonance biosensors: A review of recent progress," Biosens. Bioelectron. 23, 151-160 (2007).
[CrossRef] [PubMed]

Europhys. Lett.

K. Kim, D.-H. Lee, and H. Lim, "Theory of the propagation of coupled waves in arbitrarily inhomogeneous stratified media," Europhys. Lett. 69, 207-213 (2005).
[CrossRef]

J. Appl. Phys.

A. S. L. Gomes, E. L. F. Filho, C. B. de Araújo, D. Rativa, R. E. de Araujo, K. Sakaguchi, F. P. Mezzapesa, I. C. S. Carvalho, and P. G. Kazansky, "Third-order nonlinear optical properties of bismuth-borate glasses measured by conventional and thermally managed eclipse Z scan," J. Appl. Phys. 101, 033115 (2007).
[CrossRef]

S. A. Maier and H. A. Atwater, "Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures," J. Appl. Phys. 98, 011101 (2005).
[CrossRef]

J. Mater. Chem.

T. E. O. Screen, K. B. Lawton, G. S. Wilson, N. Dolney, R. Ispasoiu, T. GoodsonIII, S. J. Martin, D. D. C. Bradley, and H. L. Anderson, "Synthesis and third order nonlinear optics of a new soluble conjugated porphyrin polymer," J. Mater. Chem. 11, 312-320 (2001).
[CrossRef]

J. Mod. Opt.

J. R. Sambles and R. A. Innes, "A comment on nonlinear optics using surface plasmon-polaritons," J. Mod. Opt. 35, 791-797 (1988).
[CrossRef]

J. Phys. (Paris)

B. Doucot and R. Rammal, "Invariant-imbedding approach to localization. II. Non-linear random media," J. Phys. (Paris) 48, 527-546 (1987).
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R. Rammal and B. Doucot, "Invariant-imbedding approach to localization. I. General framework and basic equations," J. Phys. (Paris) 48, 509-526 (1987).
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N.-C. Panoiu and R. M. Osgood, Jr., "Subwavelength nonlinear plasmonic nanowire," Nano Lett. 4, 2427-2430 (2004).
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Nature

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
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Opt. Express

Opt. Lett.

Phys. Plasmas

K. Kim and D.-H. Lee, "Invariant imbedding theory of mode conversion in inhomogeneous plasmas. I. Exact calculation of the mode conversion coefficient in cold, unmagnetized plasmas," Phys. Plasmas 12, 062101 (2005).
[CrossRef]

K. Kim and D.-H. Lee, "Invariant imbedding theory of mode conversion in inhomogeneous plasmas. II. Mode conversion in cold, magnetized plasmas with perpendicular inhomogeneity," Phys. Plasmas 13, 042103 (2006).
[CrossRef]

Phys. Rep.

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, "Nano-optics of surface plasmon polaritons," Phys. Rep. 408, 131-314 (2005).
[CrossRef]

Phys. Rev. B

K. Kim, F. Rotermund, and H. Lim, "Disorder-enhanced transmission of a quantum mechanical particle through a disordered tunneling barrier in one dimension: Exact calculation based on the invariant imbedding method," Phys. Rev. B 77, 024203 (2008).
[CrossRef]

K. Kim, "Reflection coefficient and localization length of waves in one-dimensional random media," Phys. Rev. B 58, 6153-6160 (1998).
[CrossRef]

Phys. Rev. Lett.

I. I. Smolyaninov, A. V. Zayats, A. Gungor, and C. C. Davis, "Single-photon tunneling via localized surface plasmons," Phys. Rev. Lett. 88, 187402 (2002).
[CrossRef] [PubMed]

G. A. Wurtz, R. Pollard, and A. V. Zayats, "Optical bistability in nonlinear surface-plasmon polaritonic crystals," Phys. Rev. Lett. 97, 057402 (2006).
[CrossRef] [PubMed]

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, "Subwavelength discrete solitons in nonlinear metamaterials," Phys. Rev. Lett. 99, 153901 (2007).
[PubMed]

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V. I. Klyatskin, "The imbedding method in statistical boundary-value wave problems," Prog. Opt. 33, 1-127 (1994).
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R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic Press, 2003).

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Figures (5)

Fig. 1.
Fig. 1.

Reflectance versus incident angle in the linear (αw=0), focusing (αw=0.003) and defocusing (αw=-0.003) cases when λ=633 nm.

Fig. 2.
Fig. 2.

Spatial distributions of the normalized magnetic field intensity corresponding to the three reflectance minima shown in Fig. 1. The vertical dotted line represents the position of the metal-dielectric boundary. A p wave is assumed to be incident from the right side where z>L.

Fig. 3.
Fig. 3.

Dependencies of (a) the phase of the reflection coefficient and (b) the lateral shift on the incident angle when αw=0, ±0.0015, ±0.003.

Fig. 4.
Fig. 4.

(a) Phase of the reflection coefficient and (b) the real and imaginary parts of the reflection coefficient versus incident angle, when αw=-0.00199 and -0.002.

Fig. 5.
Fig. 5.

Lateral shift versus the nonlinearity parameter |α|w when θ=62.285°, 61°, 62°, 63° for both the focusing (a–d) and defocusing (e–h) cases.

Equations (10)

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d 2 H d z 2 1 ε ( z ) d ε d z d H d z + [ k 0 2 ε ( z ) q 2 ] H = 0 ,
ε ( z ) = { ε 1 if z > L ε L ( z ) + α ( z ) E ( z ) 2 if 0 z L , ε 2 if z < 0
H ( z ) = ν ε 1 [ e i p ( L z ) + r ( L ) e i p ( z L ) ] ,
1 p d r ( l ) d l = 2 i ε ( l ) ε 1 r ( l ) i 2 [ ε ( l ) ε 1 1 ] [ 1 ε 1 ε ( l ) tan 2 θ ] [ 1 + r ( l ) ] 2 ,
1 p d w ( l ) d l = Im { 2 ε ( l ) ε 1 [ ε ( l ) ε 1 1 ] [ 1 ε 1 ε ( l ) tan 2 θ ] [ 1 + r ( l ) ] } w ( l ) ,
ε ( l ) = ε L ( l ) + α ( l ) w ( l ) [ ε 1 2 ε ( l ) 2 1 + r ( l ) 2 sin 2 θ + 1 r ( l ) 2 cos 2 θ ] .
r ( 0 ) = ε 2 ε 1 cos θ ε 1 ε 2 ε 1 sin 2 θ ε 2 ε 1 cos θ + ε 1 ε 2 ε 1 sin 2 θ , w ( 0 ) = w 0 .
Δ = d Φ d q = λ 2 π ε 1 cos θ d Φ d θ ,
1 p u ( z , l ) l = i ε ( l ) ε 1 u ( z , l ) i 2 [ ε ( l ) ε 1 1 ] [ 1 ε 1 ε ( l ) tan 2 θ ] [ 1 + r ( l ) ] u ( z , l ) .
α w = 24 π 2 c 10 7 χ ( 3 ) I 0.079 χ ( 3 ) I ,

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