Abstract

We present an analytical study of a third-harmonic generation process by surface plasmon polaritons at a Kerr-nonlinear-metal/dielectric interface. Using a planar silver/vacuum interface, we obtain a solution to the frequency-tripling process, showing a semibound third-harmonic surface wave. Unlike the fundamental surface-bound mode, the nonlinear signal radiates into the metal, while remaining bound at the dielectric side of the interface. The propagation of the tripled frequency wave into the metal is generally lossy, except within a narrow range of ultraviolet frequencies, where it is minimally attenuated. The latter is enabled by a transparency window that is unique to the permittivity of silver.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. Nkoma, R. Loudon, and D. R. Tilley, J. Phys. C 7, 3547 (1974).
    [CrossRef]
  2. X. D. Hoa, A. G. Kirk, and M. Tabrizian, Biosens. Bioelectron. 23, 151 (2007).
    [CrossRef]
  3. K. M. Mayer and J. H. Hafner, Chem. Rev. 111, 3828 (2011).
    [CrossRef]
  4. M. L. Brongersma, R. Zia, and J. A. Schuller, Appl. Phys. A 89, 221 (2007).
    [CrossRef]
  5. W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, Nano Lett. 4, 1085 (2004).
    [CrossRef]
  6. S. A. Maier, Opt. Express 14, 1957 (2006).
    [CrossRef]
  7. S. Palomba and L. Novotny, Phys. Rev. Lett. 101, 056802 (2008).
    [CrossRef]
  8. K. A. Willets and R. P. Van Duyne, Annu. Rev. Phys. Chem. 58, 267 (2007).
    [CrossRef]
  9. A. K. Sarychev, V. A. Shubin, and V. M. Shalaev, Phys. Rev. B 60, 16389 (1999).
    [CrossRef]
  10. R. W. Boyd, Nonlinear Optics (Academdic, 2008).
  11. P. Ginzburg, A. Hayat, N. Berkovitch, and M. Orenstein, Opt. Lett. 35, 1551 (2010).
    [CrossRef]
  12. A. Marini, M. Conforti, G. Della Valle, H. W. Lee, Tr. X. Tran, W. Chang, M. A. Schmidt, S. Longhi, P. St. J. Russell, and F. Biancalana, New J. Phys. 15, 013033 (2013).
    [CrossRef]
  13. P. Ginzburg, A. V. Krasavin, and A. V. Zayats, New J. Phys. 15, 013031 (2013).
    [CrossRef]
  14. D. Mihalache, G. I. Stegeman, C. T. Seaton, E. M. Wright, R. Zanoni, A. D. Boardman, and T. Twardowski, Opt. Lett. 12, 187 (1987).
    [CrossRef]
  15. P. Gadenne, F. Brouers, V. M. Shalaev, and A. K. Sarychev, J. Opt. Soc. Am. B 15, 68 (1998).
    [CrossRef]
  16. G. T. Boyd, Z. H. Yu, and Y. R. Shen, Phys. Rev. B 33, 7923 (1986).
    [CrossRef]
  17. P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
    [CrossRef]
  18. E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, 1985).
  19. T. Y. F. Tsang, Phys. Rev. A 52, 4116 (1995).
    [CrossRef]

2013 (2)

A. Marini, M. Conforti, G. Della Valle, H. W. Lee, Tr. X. Tran, W. Chang, M. A. Schmidt, S. Longhi, P. St. J. Russell, and F. Biancalana, New J. Phys. 15, 013033 (2013).
[CrossRef]

P. Ginzburg, A. V. Krasavin, and A. V. Zayats, New J. Phys. 15, 013031 (2013).
[CrossRef]

2011 (1)

K. M. Mayer and J. H. Hafner, Chem. Rev. 111, 3828 (2011).
[CrossRef]

2010 (1)

2008 (1)

S. Palomba and L. Novotny, Phys. Rev. Lett. 101, 056802 (2008).
[CrossRef]

2007 (3)

K. A. Willets and R. P. Van Duyne, Annu. Rev. Phys. Chem. 58, 267 (2007).
[CrossRef]

M. L. Brongersma, R. Zia, and J. A. Schuller, Appl. Phys. A 89, 221 (2007).
[CrossRef]

X. D. Hoa, A. G. Kirk, and M. Tabrizian, Biosens. Bioelectron. 23, 151 (2007).
[CrossRef]

2006 (1)

2004 (1)

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, Nano Lett. 4, 1085 (2004).
[CrossRef]

1999 (1)

A. K. Sarychev, V. A. Shubin, and V. M. Shalaev, Phys. Rev. B 60, 16389 (1999).
[CrossRef]

1998 (1)

1995 (1)

T. Y. F. Tsang, Phys. Rev. A 52, 4116 (1995).
[CrossRef]

1987 (1)

1986 (1)

G. T. Boyd, Z. H. Yu, and Y. R. Shen, Phys. Rev. B 33, 7923 (1986).
[CrossRef]

1974 (1)

J. Nkoma, R. Loudon, and D. R. Tilley, J. Phys. C 7, 3547 (1974).
[CrossRef]

1972 (1)

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Berkovitch, N.

Biancalana, F.

A. Marini, M. Conforti, G. Della Valle, H. W. Lee, Tr. X. Tran, W. Chang, M. A. Schmidt, S. Longhi, P. St. J. Russell, and F. Biancalana, New J. Phys. 15, 013033 (2013).
[CrossRef]

Boardman, A. D.

Boyd, G. T.

G. T. Boyd, Z. H. Yu, and Y. R. Shen, Phys. Rev. B 33, 7923 (1986).
[CrossRef]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academdic, 2008).

Brongersma, M. L.

M. L. Brongersma, R. Zia, and J. A. Schuller, Appl. Phys. A 89, 221 (2007).
[CrossRef]

Brouers, F.

Chang, W.

A. Marini, M. Conforti, G. Della Valle, H. W. Lee, Tr. X. Tran, W. Chang, M. A. Schmidt, S. Longhi, P. St. J. Russell, and F. Biancalana, New J. Phys. 15, 013033 (2013).
[CrossRef]

Christy, R. W.

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Conforti, M.

A. Marini, M. Conforti, G. Della Valle, H. W. Lee, Tr. X. Tran, W. Chang, M. A. Schmidt, S. Longhi, P. St. J. Russell, and F. Biancalana, New J. Phys. 15, 013033 (2013).
[CrossRef]

Della Valle, G.

A. Marini, M. Conforti, G. Della Valle, H. W. Lee, Tr. X. Tran, W. Chang, M. A. Schmidt, S. Longhi, P. St. J. Russell, and F. Biancalana, New J. Phys. 15, 013033 (2013).
[CrossRef]

Fang, N.

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, Nano Lett. 4, 1085 (2004).
[CrossRef]

Gadenne, P.

Ginzburg, P.

P. Ginzburg, A. V. Krasavin, and A. V. Zayats, New J. Phys. 15, 013031 (2013).
[CrossRef]

P. Ginzburg, A. Hayat, N. Berkovitch, and M. Orenstein, Opt. Lett. 35, 1551 (2010).
[CrossRef]

Hafner, J. H.

K. M. Mayer and J. H. Hafner, Chem. Rev. 111, 3828 (2011).
[CrossRef]

Hayat, A.

Hoa, X. D.

X. D. Hoa, A. G. Kirk, and M. Tabrizian, Biosens. Bioelectron. 23, 151 (2007).
[CrossRef]

Johnson, P. B.

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Kirk, A. G.

X. D. Hoa, A. G. Kirk, and M. Tabrizian, Biosens. Bioelectron. 23, 151 (2007).
[CrossRef]

Krasavin, A. V.

P. Ginzburg, A. V. Krasavin, and A. V. Zayats, New J. Phys. 15, 013031 (2013).
[CrossRef]

Lee, H. W.

A. Marini, M. Conforti, G. Della Valle, H. W. Lee, Tr. X. Tran, W. Chang, M. A. Schmidt, S. Longhi, P. St. J. Russell, and F. Biancalana, New J. Phys. 15, 013033 (2013).
[CrossRef]

Longhi, S.

A. Marini, M. Conforti, G. Della Valle, H. W. Lee, Tr. X. Tran, W. Chang, M. A. Schmidt, S. Longhi, P. St. J. Russell, and F. Biancalana, New J. Phys. 15, 013033 (2013).
[CrossRef]

Loudon, R.

J. Nkoma, R. Loudon, and D. R. Tilley, J. Phys. C 7, 3547 (1974).
[CrossRef]

Luo, Q.

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, Nano Lett. 4, 1085 (2004).
[CrossRef]

Maier, S. A.

Marini, A.

A. Marini, M. Conforti, G. Della Valle, H. W. Lee, Tr. X. Tran, W. Chang, M. A. Schmidt, S. Longhi, P. St. J. Russell, and F. Biancalana, New J. Phys. 15, 013033 (2013).
[CrossRef]

Mayer, K. M.

K. M. Mayer and J. H. Hafner, Chem. Rev. 111, 3828 (2011).
[CrossRef]

Mihalache, D.

Nkoma, J.

J. Nkoma, R. Loudon, and D. R. Tilley, J. Phys. C 7, 3547 (1974).
[CrossRef]

Novotny, L.

S. Palomba and L. Novotny, Phys. Rev. Lett. 101, 056802 (2008).
[CrossRef]

Orenstein, M.

Palomba, S.

S. Palomba and L. Novotny, Phys. Rev. Lett. 101, 056802 (2008).
[CrossRef]

Russell, P. St. J.

A. Marini, M. Conforti, G. Della Valle, H. W. Lee, Tr. X. Tran, W. Chang, M. A. Schmidt, S. Longhi, P. St. J. Russell, and F. Biancalana, New J. Phys. 15, 013033 (2013).
[CrossRef]

Sarychev, A. K.

A. K. Sarychev, V. A. Shubin, and V. M. Shalaev, Phys. Rev. B 60, 16389 (1999).
[CrossRef]

P. Gadenne, F. Brouers, V. M. Shalaev, and A. K. Sarychev, J. Opt. Soc. Am. B 15, 68 (1998).
[CrossRef]

Schmidt, M. A.

A. Marini, M. Conforti, G. Della Valle, H. W. Lee, Tr. X. Tran, W. Chang, M. A. Schmidt, S. Longhi, P. St. J. Russell, and F. Biancalana, New J. Phys. 15, 013033 (2013).
[CrossRef]

Schuller, J. A.

M. L. Brongersma, R. Zia, and J. A. Schuller, Appl. Phys. A 89, 221 (2007).
[CrossRef]

Seaton, C. T.

Shalaev, V. M.

A. K. Sarychev, V. A. Shubin, and V. M. Shalaev, Phys. Rev. B 60, 16389 (1999).
[CrossRef]

P. Gadenne, F. Brouers, V. M. Shalaev, and A. K. Sarychev, J. Opt. Soc. Am. B 15, 68 (1998).
[CrossRef]

Shen, Y. R.

G. T. Boyd, Z. H. Yu, and Y. R. Shen, Phys. Rev. B 33, 7923 (1986).
[CrossRef]

Shubin, V. A.

A. K. Sarychev, V. A. Shubin, and V. M. Shalaev, Phys. Rev. B 60, 16389 (1999).
[CrossRef]

Srituravanich, W.

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, Nano Lett. 4, 1085 (2004).
[CrossRef]

Stegeman, G. I.

Sun, C.

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, Nano Lett. 4, 1085 (2004).
[CrossRef]

Tabrizian, M.

X. D. Hoa, A. G. Kirk, and M. Tabrizian, Biosens. Bioelectron. 23, 151 (2007).
[CrossRef]

Tilley, D. R.

J. Nkoma, R. Loudon, and D. R. Tilley, J. Phys. C 7, 3547 (1974).
[CrossRef]

Tran, Tr. X.

A. Marini, M. Conforti, G. Della Valle, H. W. Lee, Tr. X. Tran, W. Chang, M. A. Schmidt, S. Longhi, P. St. J. Russell, and F. Biancalana, New J. Phys. 15, 013033 (2013).
[CrossRef]

Tsang, T. Y. F.

T. Y. F. Tsang, Phys. Rev. A 52, 4116 (1995).
[CrossRef]

Twardowski, T.

Van Duyne, R. P.

K. A. Willets and R. P. Van Duyne, Annu. Rev. Phys. Chem. 58, 267 (2007).
[CrossRef]

Willets, K. A.

K. A. Willets and R. P. Van Duyne, Annu. Rev. Phys. Chem. 58, 267 (2007).
[CrossRef]

Wright, E. M.

Yu, Z. H.

G. T. Boyd, Z. H. Yu, and Y. R. Shen, Phys. Rev. B 33, 7923 (1986).
[CrossRef]

Zanoni, R.

Zayats, A. V.

P. Ginzburg, A. V. Krasavin, and A. V. Zayats, New J. Phys. 15, 013031 (2013).
[CrossRef]

Zhang, X.

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, Nano Lett. 4, 1085 (2004).
[CrossRef]

Zia, R.

M. L. Brongersma, R. Zia, and J. A. Schuller, Appl. Phys. A 89, 221 (2007).
[CrossRef]

Annu. Rev. Phys. Chem. (1)

K. A. Willets and R. P. Van Duyne, Annu. Rev. Phys. Chem. 58, 267 (2007).
[CrossRef]

Appl. Phys. A (1)

M. L. Brongersma, R. Zia, and J. A. Schuller, Appl. Phys. A 89, 221 (2007).
[CrossRef]

Biosens. Bioelectron. (1)

X. D. Hoa, A. G. Kirk, and M. Tabrizian, Biosens. Bioelectron. 23, 151 (2007).
[CrossRef]

Chem. Rev. (1)

K. M. Mayer and J. H. Hafner, Chem. Rev. 111, 3828 (2011).
[CrossRef]

J. Opt. Soc. Am. B (1)

J. Phys. C (1)

J. Nkoma, R. Loudon, and D. R. Tilley, J. Phys. C 7, 3547 (1974).
[CrossRef]

Nano Lett. (1)

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, Nano Lett. 4, 1085 (2004).
[CrossRef]

New J. Phys. (2)

A. Marini, M. Conforti, G. Della Valle, H. W. Lee, Tr. X. Tran, W. Chang, M. A. Schmidt, S. Longhi, P. St. J. Russell, and F. Biancalana, New J. Phys. 15, 013033 (2013).
[CrossRef]

P. Ginzburg, A. V. Krasavin, and A. V. Zayats, New J. Phys. 15, 013031 (2013).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. A (1)

T. Y. F. Tsang, Phys. Rev. A 52, 4116 (1995).
[CrossRef]

Phys. Rev. B (3)

G. T. Boyd, Z. H. Yu, and Y. R. Shen, Phys. Rev. B 33, 7923 (1986).
[CrossRef]

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

A. K. Sarychev, V. A. Shubin, and V. M. Shalaev, Phys. Rev. B 60, 16389 (1999).
[CrossRef]

Phys. Rev. Lett. (1)

S. Palomba and L. Novotny, Phys. Rev. Lett. 101, 056802 (2008).
[CrossRef]

Other (2)

R. W. Boyd, Nonlinear Optics (Academdic, 2008).

E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, 1985).

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 (3)

Fig. 1.
Fig. 1.

Normalized x-components of the fields in Eq. (5): (a) dielectric and (b) silver. The interface is at z=0. The field radiates into the metal [direction denoted in (b) by black arrow] while still evanescent in the dielectric.

Fig. 2.
Fig. 2.

Propagation angle of the ω3 signal in the metal, computed from Eq. (9), plotted against λSPP.

Fig. 3.
Fig. 3.

Propagation angle, ϑ, of the ω3 signal, obtained from Drude model (solid line) and measured permittivities (dots) [18]. The shaded area denotes the pump λSPP corresponding to a third harmonic in the UV window of silver.

Equations (15)

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

kx2=ω2c2ϵdϵmϵd+ϵm,
k(m,d)z2+kx2=ω2c2ϵm,d.
2E(r,ω)+ω2c2ϵmE(r,ω)=ω2ϵ0c2PNL(r,ω),
·[ϵmϵ0E(r,ω)+PNL(r,ω)]=0,
PjNL=3χ1212(3)Ej(E·E)+(χ1111(3)3χ1212(3))Ej3,
PxNL=Ex0[A(Ex0)2+B(Ez0)2]ei(q·rω3t),
PzNL=Ez0[A(Ez0)2+B(Ex0)2]ei(q·rω3t).
in the linear dielectric:Ed=Ed0eiKd·reiω3t,
in metal:Em=(Em0eiKm·r+Q0eiq·r)eiω3t.
Q0=ω32PNL(Km2q2)ϵ0c2,
Q0=PNLϵ0ϵm.
Qx0=Q0cosψq+Q0cosϕq,
Qz0=Q0sinψq+Q0sinϕq.
E(m,d)x0=Qx0(tanψqtanψd,m+tanϕd,m)Qz0(tanψdtanϕd)(tanψmtanϕm).
tanϑ=Re[Kmz]Re[Kmx].

Metrics