Abstract

We analyze phase matching in metal-dielectric nonlinear structures which support highly localized plasmon polariton modes. We reveal that quadratic phase matching between the plasmon modes of different symmetries becomes possible in planar waveguide geometries. We discuss the example of a nonlinear LiNbO3 waveguide sandwiched between two silver plates, and demonstrate that second-harmonic generation can be achieved for interacting plasmonic modes.

© 2009 Optical Society of America

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References

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  1. A. D. Boardman, L. Pavlov, and S. Tanev, eds., Advanced Photonics with Second-order Optically Nonlinear Processes (Kluwer Academic, Dordretch, The Netherlands, 1998).
    [CrossRef]
  2. R. W. Boyd, Nonlinear Optics (Elsevier Science, USA 2003).
  3. A. Di Falco, C. Conti, and G. Assanto "Quadratic phase matching in slot waveguides," Opt. Lett. 31,3146-3148 (2006).
    [CrossRef] [PubMed]
  4. H. Ishikawa and T. Kondo "Birefringent Phase matching in thin rectangular high-index-contrast waveguides," Appl. Phys. Express 2, 042202 (2009).
    [CrossRef]
  5. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer-Verlag, Berlin 2007).
  6. E. N. Economou, "Surface plasmons in thin films," Phys. Rev. 182, 539-554 (1969).
    [CrossRef]
  7. J. J. Burke, G. I Stegeman, and T. Tamir, "Surface-polariton-like waves guided by thin, lossy metal films," Phys. Rev. B 33, 5186-5201 (1986).
    [CrossRef]
  8. B. Prade, J. Y. Vinet, and A. Mysyrowicz, "Guided optical waves in planar heterostructures with negative dielectric constant," Phys. Rev. B 44,13556-13572 (1991).
    [CrossRef]
  9. J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, "Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localkization," Phys. Rev. B 73, 035407 (2006).
    [CrossRef]
  10. Y. Satuby and M. Orenstein, "Surface plasmon polariton waveguides: From multimode stripe to a slot geometry," Appl. Phys. Lett. 90, 251104 (2007).
    [CrossRef]
  11. N.-N. Feng and L. Dal Negro, "Plasmon mode transformation in modulated-index metal-dielectric slot waveguides," Opt. Lett. 32, 3086-3088 (2007).
    [CrossRef] [PubMed]
  12. P. Neutens, P. Van Dorpe, I. De Vlaminck, L. Lagae, and G. Borghs, "Electrical detection of confined gap plasmons in metalinsulatormetal waveguides," Nat. Photonics 3, 283-286 (2009).
    [CrossRef]
  13. J. C. Quail and H. J. Simon "Second-harmonic generation with phase-matched long-range and short range surface plasmon polaritons," J. Appl. Phys. 56, 2589-2591 (1984).
    [CrossRef]
  14. G. I. Stegeman, J. J. Burke, and D. G. Hall "Nonlinear optics of long range surface plasmons," Appl. Phys. Lett. 41, 906-908 (1982).
    [CrossRef]
  15. P. B. Johnson and R. W. Christy, "Optical constants of nobel metals," Phys. Rev. B 6, 4370-4379 (1972).
    [CrossRef]
  16. R. S. Weis and T. K. Gaylord, "Lithium Niobate: Summary of physical properties and crystal structure," Appl. Phys. A 37, 191-203 (1985).
    [CrossRef]
  17. A. R. Davoyan, I. V. Shadrivov, and Yu. S. Kivshar, "Nonlinear plasmonic slot waveguides," Opt. Express 16, 21209-21214 (2008).
    [CrossRef] [PubMed]
  18. A. R. Davoyan, I. V. Shadrivov, and Yu. S. Kivshar, "Nonlinear plasmonic slot waveguides: erratum," Opt. Express 17, 4833 (2009).
    [CrossRef]
  19. Z. Ruan, G. Veronis, K. L. Vodopyanov, M. M. Fejer, and S. Fan, "Enhancement of optics-to-THz conversion efficiency by metallic slot waveguides", Opt. Express 17, 13502-13515 (2009).
    [CrossRef] [PubMed]

2009

P. Neutens, P. Van Dorpe, I. De Vlaminck, L. Lagae, and G. Borghs, "Electrical detection of confined gap plasmons in metalinsulatormetal waveguides," Nat. Photonics 3, 283-286 (2009).
[CrossRef]

H. Ishikawa and T. Kondo "Birefringent Phase matching in thin rectangular high-index-contrast waveguides," Appl. Phys. Express 2, 042202 (2009).
[CrossRef]

A. R. Davoyan, I. V. Shadrivov, and Yu. S. Kivshar, "Nonlinear plasmonic slot waveguides: erratum," Opt. Express 17, 4833 (2009).
[CrossRef]

Z. Ruan, G. Veronis, K. L. Vodopyanov, M. M. Fejer, and S. Fan, "Enhancement of optics-to-THz conversion efficiency by metallic slot waveguides", Opt. Express 17, 13502-13515 (2009).
[CrossRef] [PubMed]

2008

2007

N.-N. Feng and L. Dal Negro, "Plasmon mode transformation in modulated-index metal-dielectric slot waveguides," Opt. Lett. 32, 3086-3088 (2007).
[CrossRef] [PubMed]

Y. Satuby and M. Orenstein, "Surface plasmon polariton waveguides: From multimode stripe to a slot geometry," Appl. Phys. Lett. 90, 251104 (2007).
[CrossRef]

2006

A. Di Falco, C. Conti, and G. Assanto "Quadratic phase matching in slot waveguides," Opt. Lett. 31,3146-3148 (2006).
[CrossRef] [PubMed]

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, "Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localkization," Phys. Rev. B 73, 035407 (2006).
[CrossRef]

1991

B. Prade, J. Y. Vinet, and A. Mysyrowicz, "Guided optical waves in planar heterostructures with negative dielectric constant," Phys. Rev. B 44,13556-13572 (1991).
[CrossRef]

1986

J. J. Burke, G. I Stegeman, and T. Tamir, "Surface-polariton-like waves guided by thin, lossy metal films," Phys. Rev. B 33, 5186-5201 (1986).
[CrossRef]

1985

R. S. Weis and T. K. Gaylord, "Lithium Niobate: Summary of physical properties and crystal structure," Appl. Phys. A 37, 191-203 (1985).
[CrossRef]

1984

J. C. Quail and H. J. Simon "Second-harmonic generation with phase-matched long-range and short range surface plasmon polaritons," J. Appl. Phys. 56, 2589-2591 (1984).
[CrossRef]

1982

G. I. Stegeman, J. J. Burke, and D. G. Hall "Nonlinear optics of long range surface plasmons," Appl. Phys. Lett. 41, 906-908 (1982).
[CrossRef]

1972

P. B. Johnson and R. W. Christy, "Optical constants of nobel metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

1969

E. N. Economou, "Surface plasmons in thin films," Phys. Rev. 182, 539-554 (1969).
[CrossRef]

Assanto, G.

Atwater, H. A.

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, "Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localkization," Phys. Rev. B 73, 035407 (2006).
[CrossRef]

Borghs, G.

P. Neutens, P. Van Dorpe, I. De Vlaminck, L. Lagae, and G. Borghs, "Electrical detection of confined gap plasmons in metalinsulatormetal waveguides," Nat. Photonics 3, 283-286 (2009).
[CrossRef]

Burke, J. J.

J. J. Burke, G. I Stegeman, and T. Tamir, "Surface-polariton-like waves guided by thin, lossy metal films," Phys. Rev. B 33, 5186-5201 (1986).
[CrossRef]

G. I. Stegeman, J. J. Burke, and D. G. Hall "Nonlinear optics of long range surface plasmons," Appl. Phys. Lett. 41, 906-908 (1982).
[CrossRef]

Christy, R. W.

P. B. Johnson and R. W. Christy, "Optical constants of nobel metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

Conti, C.

Dal Negro, L.

Davoyan, A. R.

De Vlaminck, I.

P. Neutens, P. Van Dorpe, I. De Vlaminck, L. Lagae, and G. Borghs, "Electrical detection of confined gap plasmons in metalinsulatormetal waveguides," Nat. Photonics 3, 283-286 (2009).
[CrossRef]

Di Falco, A.

Dionne, J. A.

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, "Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localkization," Phys. Rev. B 73, 035407 (2006).
[CrossRef]

Economou, E. N.

E. N. Economou, "Surface plasmons in thin films," Phys. Rev. 182, 539-554 (1969).
[CrossRef]

Fan, S.

Fejer, M. M.

Feng, N.-N.

Gaylord, T. K.

R. S. Weis and T. K. Gaylord, "Lithium Niobate: Summary of physical properties and crystal structure," Appl. Phys. A 37, 191-203 (1985).
[CrossRef]

Hall, D. G.

G. I. Stegeman, J. J. Burke, and D. G. Hall "Nonlinear optics of long range surface plasmons," Appl. Phys. Lett. 41, 906-908 (1982).
[CrossRef]

Ishikawa, H.

H. Ishikawa and T. Kondo "Birefringent Phase matching in thin rectangular high-index-contrast waveguides," Appl. Phys. Express 2, 042202 (2009).
[CrossRef]

Johnson, P. B.

P. B. Johnson and R. W. Christy, "Optical constants of nobel metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

Kivshar, Yu. S.

Kondo, T.

H. Ishikawa and T. Kondo "Birefringent Phase matching in thin rectangular high-index-contrast waveguides," Appl. Phys. Express 2, 042202 (2009).
[CrossRef]

Lagae, L.

P. Neutens, P. Van Dorpe, I. De Vlaminck, L. Lagae, and G. Borghs, "Electrical detection of confined gap plasmons in metalinsulatormetal waveguides," Nat. Photonics 3, 283-286 (2009).
[CrossRef]

Mysyrowicz, A.

B. Prade, J. Y. Vinet, and A. Mysyrowicz, "Guided optical waves in planar heterostructures with negative dielectric constant," Phys. Rev. B 44,13556-13572 (1991).
[CrossRef]

Neutens, P.

P. Neutens, P. Van Dorpe, I. De Vlaminck, L. Lagae, and G. Borghs, "Electrical detection of confined gap plasmons in metalinsulatormetal waveguides," Nat. Photonics 3, 283-286 (2009).
[CrossRef]

Orenstein, M.

Y. Satuby and M. Orenstein, "Surface plasmon polariton waveguides: From multimode stripe to a slot geometry," Appl. Phys. Lett. 90, 251104 (2007).
[CrossRef]

Polman, A.

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, "Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localkization," Phys. Rev. B 73, 035407 (2006).
[CrossRef]

Prade, B.

B. Prade, J. Y. Vinet, and A. Mysyrowicz, "Guided optical waves in planar heterostructures with negative dielectric constant," Phys. Rev. B 44,13556-13572 (1991).
[CrossRef]

Quail, J. C.

J. C. Quail and H. J. Simon "Second-harmonic generation with phase-matched long-range and short range surface plasmon polaritons," J. Appl. Phys. 56, 2589-2591 (1984).
[CrossRef]

Ruan, Z.

Satuby, Y.

Y. Satuby and M. Orenstein, "Surface plasmon polariton waveguides: From multimode stripe to a slot geometry," Appl. Phys. Lett. 90, 251104 (2007).
[CrossRef]

Shadrivov, I. V.

Simon, H. J.

J. C. Quail and H. J. Simon "Second-harmonic generation with phase-matched long-range and short range surface plasmon polaritons," J. Appl. Phys. 56, 2589-2591 (1984).
[CrossRef]

Stegeman, G. I

J. J. Burke, G. I Stegeman, and T. Tamir, "Surface-polariton-like waves guided by thin, lossy metal films," Phys. Rev. B 33, 5186-5201 (1986).
[CrossRef]

Stegeman, G. I.

G. I. Stegeman, J. J. Burke, and D. G. Hall "Nonlinear optics of long range surface plasmons," Appl. Phys. Lett. 41, 906-908 (1982).
[CrossRef]

Sweatlock, L. A.

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, "Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localkization," Phys. Rev. B 73, 035407 (2006).
[CrossRef]

Tamir, T.

J. J. Burke, G. I Stegeman, and T. Tamir, "Surface-polariton-like waves guided by thin, lossy metal films," Phys. Rev. B 33, 5186-5201 (1986).
[CrossRef]

Van Dorpe, P.

P. Neutens, P. Van Dorpe, I. De Vlaminck, L. Lagae, and G. Borghs, "Electrical detection of confined gap plasmons in metalinsulatormetal waveguides," Nat. Photonics 3, 283-286 (2009).
[CrossRef]

Veronis, G.

Vinet, J. Y.

B. Prade, J. Y. Vinet, and A. Mysyrowicz, "Guided optical waves in planar heterostructures with negative dielectric constant," Phys. Rev. B 44,13556-13572 (1991).
[CrossRef]

Vodopyanov, K. L.

Weis, R. S.

R. S. Weis and T. K. Gaylord, "Lithium Niobate: Summary of physical properties and crystal structure," Appl. Phys. A 37, 191-203 (1985).
[CrossRef]

Appl. Phys. A

R. S. Weis and T. K. Gaylord, "Lithium Niobate: Summary of physical properties and crystal structure," Appl. Phys. A 37, 191-203 (1985).
[CrossRef]

Appl. Phys. Express

H. Ishikawa and T. Kondo "Birefringent Phase matching in thin rectangular high-index-contrast waveguides," Appl. Phys. Express 2, 042202 (2009).
[CrossRef]

Appl. Phys. Lett.

Y. Satuby and M. Orenstein, "Surface plasmon polariton waveguides: From multimode stripe to a slot geometry," Appl. Phys. Lett. 90, 251104 (2007).
[CrossRef]

G. I. Stegeman, J. J. Burke, and D. G. Hall "Nonlinear optics of long range surface plasmons," Appl. Phys. Lett. 41, 906-908 (1982).
[CrossRef]

J. Appl. Phys.

J. C. Quail and H. J. Simon "Second-harmonic generation with phase-matched long-range and short range surface plasmon polaritons," J. Appl. Phys. 56, 2589-2591 (1984).
[CrossRef]

Nat. Photonics

P. Neutens, P. Van Dorpe, I. De Vlaminck, L. Lagae, and G. Borghs, "Electrical detection of confined gap plasmons in metalinsulatormetal waveguides," Nat. Photonics 3, 283-286 (2009).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev.

E. N. Economou, "Surface plasmons in thin films," Phys. Rev. 182, 539-554 (1969).
[CrossRef]

Phys. Rev. B

J. J. Burke, G. I Stegeman, and T. Tamir, "Surface-polariton-like waves guided by thin, lossy metal films," Phys. Rev. B 33, 5186-5201 (1986).
[CrossRef]

B. Prade, J. Y. Vinet, and A. Mysyrowicz, "Guided optical waves in planar heterostructures with negative dielectric constant," Phys. Rev. B 44,13556-13572 (1991).
[CrossRef]

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, "Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localkization," Phys. Rev. B 73, 035407 (2006).
[CrossRef]

P. B. Johnson and R. W. Christy, "Optical constants of nobel metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

Other

A. D. Boardman, L. Pavlov, and S. Tanev, eds., Advanced Photonics with Second-order Optically Nonlinear Processes (Kluwer Academic, Dordretch, The Netherlands, 1998).
[CrossRef]

R. W. Boyd, Nonlinear Optics (Elsevier Science, USA 2003).

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer-Verlag, Berlin 2007).

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Figures (4)

Fig. 1.
Fig. 1.

(a) Schematic of a slot waveguide of the width a. (b) Dispersion relation for a 100nm thick lithium-niobate waveguide placed between two silver plates. Blue curve - symmetric branch, red curve - antisymmetric branch. The inset shows a typical profile of the magnetic field in the structure.

Fig. 2.
Fig. 2.

Plasmonic guide index versus the slot width for different FF wavelengths: (a) λ 0=840nm (εm =-23.4+i1.628) and (b) λ 0=1550nm (εm =-103.2+i8.11). Notations “s” and “a” stand for the symmetric and antisymmetric modes, respectively, and the indices ω and 2ω correspond to the fundamental and second harmonics, respectively.

Fig. 3.
Fig. 3.

(a) Free-space wavelength vs the slot width in the case of the exact phase matching in a plasmonic slot waveguide. (b) Efficiency of the second-harmonic generation as a function of the propagation distance (or the device length).

Fig. 4.
Fig. 4.

Structure of modes for the phase-matching in a plasmonic slot waveguide. The upper row corresponds to the field components of a symmetric mode at the fundamental frequency, lower row - an antisymmetric mode of the second-harmonic field.

Equations (5)

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

tanh(kda2)={(εzkmεmkd),symmetricmode,(εmkdεzkm),antisymmetricmode,
Pxω =d15[(Exω)*Ez2ω+(Ezω)*Ex2ω],Pzω=d31(Exω)*Ex2ω+d33(Ezω)*Ez2ω,
Px2ω=d15ExωEzω,Pz2ω=12[d31(Exω)2+d33(Ezω)2].
dΑ1dz=α1Α1+iΓ1Α1*Α2eiΔβz,
dΑ2dz=α2Α2+iΓ2Α12eiΔβz

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