Abstract

We theoretically studied nonlinear interactions between surface plasmon polariton (SPP) and conventional waveguide mode in nonlinear hybrid waveguide and proposed a possible method to enhance SPP wave via optical parametric amplification (OPA). The phase matching condition of this OPA process is fulfilled by carefully tailoring the dispersions of SPP and guided mode. The influences of incident intensity and phase of guided wave on the OPA process are comprehensively analyzed. It is found that not only a strong enhancement of SPP but also modulations on this enhancement can be achieved. This result indicates potential applications in nonlinear optical integration and modulations.

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  1. J. J. Burke, G. I. Stegeman, and T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B Condens. Matter 33(8), 5186–5201 (1986).
    [CrossRef] [PubMed]
  2. I. De Leon and P. Berini, “Theory of surface plasmon-polariton amplification in planar structures incorporating dipolar gain media,” Phys. Rev. B 78, 161401 (2008).
    [CrossRef]
  3. D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90(2), 027402 (2003).
    [CrossRef] [PubMed]
  4. R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
    [CrossRef] [PubMed]
  5. T. Holmgaard and S. I. Bozhevolnyi, “Theoretical analysis of dielectric-loaded surface plasman-polariton waveguides,” Phys. Rev. B 75(24), 245405 (2007).
    [CrossRef]
  6. T. Holmgaard, J. Gosciniak, and S. I. Bozhevolnyi, “Long-range dielectric-loaded surface plasmon-polariton waveguides,” Opt. Express 18(22), 23009–23015 (2010).
    [CrossRef] [PubMed]
  7. R. W. Boyd, Nonlinear Optics (Elsevier Science, 2003).
  8. R. A. Baumgartner and R. Byer, “Optical parametric amplification,” IEEE J. Quantum Electron. 15(6), 432–444 (1979).
    [CrossRef]
  9. J. Armstrong, N. Bloembergen, J. Ducuing, and P. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
    [CrossRef]
  10. S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278(5339), 843–846 (1997).
    [CrossRef]
  11. H. J. Simon, D. E. Mitchell, and J. G. Watson, “Optical Second-Harmonic Generation with Surface Plasmons in Silver Films,” Phys. Rev. Lett. 33(26), 1531–1534 (1974).
    [CrossRef]
  12. H. J. Simon, R. E. Benner, and J. G. Rako, “Optical second harmonic generation with surface plasmons in piezoelectric crystals,” Opt. Commun. 23(2), 245–248 (1977).
    [CrossRef]
  13. S. Palomba and L. Novotny, “Nonlinear excitation of surface plasmon polaritons by four-wave mixing,” Phys. Rev. Lett. 101(5), 056802 (2008).
    [CrossRef] [PubMed]
  14. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
    [CrossRef]
  15. G. Lifante, Integrated Photonics: Fundamentals (Wiley, England, 2003).
  16. 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(16), 13502–13515 (2009).
    [CrossRef] [PubMed]
  17. R. H. Stolen, M. A. Bösch, and C. Lin, “Phase matching in birefringent fibers,” Opt. Lett. 6(5), 213–215 (1981).
    [CrossRef] [PubMed]
  18. T. Sugita, K. Mizuuchi, Y. Kitaoka, and K. Yamamoto, “31%-efficient blue second-harmonic generation in a periodically poled MgO:LiNbO3 waveguide by frequency doubling of an AlGaAs laser diode,” Opt. Lett. 24(22), 1590–1592 (1999).
    [CrossRef]
  19. H. Jiang, G. H. Li, and X. Y. Xu, “Highly efficient single-pass second harmonic generation in a periodically poled MgO:LiNbO3 waveguide pumped by a fiber laser at 1111.6 nm,” Opt. Express 17(18), 16073–16080 (2009).
    [CrossRef] [PubMed]
  20. Y. L. Lee, T. J. Eom, W. Shin, B.-A. Yu, D.-K. Ko, W.-K. Kim, and H.-Y. Lee, “Characteristics of a multi-mode interference device based on Ti:LiNbO3 channel waveguide,” Opt. Express 17(13), 10718–10724 (2009).
    [CrossRef] [PubMed]
  21. A. R. Davoyan, I. V. Shadrivov, and Y. S. Kivshar, “Quadratic phase matching in nonlinear plasmonic nanoscale waveguides,” Opt. Express 17(22), 20063–20068 (2009).
    [CrossRef] [PubMed]
  22. Z. J. Wu, X. K. Hu, Z. Y. Yu, W. Hu, F. Xu, and Y. Q. Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82(15), 155107 (2010).
    [CrossRef]
  23. G. J. Edwards and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16(4), 373–375 (1984).
    [CrossRef]

2010

Z. J. Wu, X. K. Hu, Z. Y. Yu, W. Hu, F. Xu, and Y. Q. Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82(15), 155107 (2010).
[CrossRef]

T. Holmgaard, J. Gosciniak, and S. I. Bozhevolnyi, “Long-range dielectric-loaded surface plasmon-polariton waveguides,” Opt. Express 18(22), 23009–23015 (2010).
[CrossRef] [PubMed]

2009

2008

I. De Leon and P. Berini, “Theory of surface plasmon-polariton amplification in planar structures incorporating dipolar gain media,” Phys. Rev. B 78, 161401 (2008).
[CrossRef]

S. Palomba and L. Novotny, “Nonlinear excitation of surface plasmon polaritons by four-wave mixing,” Phys. Rev. Lett. 101(5), 056802 (2008).
[CrossRef] [PubMed]

2007

T. Holmgaard and S. I. Bozhevolnyi, “Theoretical analysis of dielectric-loaded surface plasman-polariton waveguides,” Phys. Rev. B 75(24), 245405 (2007).
[CrossRef]

2003

D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90(2), 027402 (2003).
[CrossRef] [PubMed]

1999

1997

S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278(5339), 843–846 (1997).
[CrossRef]

1986

J. J. Burke, G. I. Stegeman, and T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B Condens. Matter 33(8), 5186–5201 (1986).
[CrossRef] [PubMed]

1984

G. J. Edwards and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16(4), 373–375 (1984).
[CrossRef]

1981

1979

R. A. Baumgartner and R. Byer, “Optical parametric amplification,” IEEE J. Quantum Electron. 15(6), 432–444 (1979).
[CrossRef]

1977

H. J. Simon, R. E. Benner, and J. G. Rako, “Optical second harmonic generation with surface plasmons in piezoelectric crystals,” Opt. Commun. 23(2), 245–248 (1977).
[CrossRef]

1974

H. J. Simon, D. E. Mitchell, and J. G. Watson, “Optical Second-Harmonic Generation with Surface Plasmons in Silver Films,” Phys. Rev. Lett. 33(26), 1531–1534 (1974).
[CrossRef]

1972

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

1962

J. Armstrong, N. Bloembergen, J. Ducuing, and P. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[CrossRef]

Armstrong, J.

J. Armstrong, N. Bloembergen, J. Ducuing, and P. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[CrossRef]

Bartal, G.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
[CrossRef] [PubMed]

Baumgartner, R. A.

R. A. Baumgartner and R. Byer, “Optical parametric amplification,” IEEE J. Quantum Electron. 15(6), 432–444 (1979).
[CrossRef]

Benner, R. E.

H. J. Simon, R. E. Benner, and J. G. Rako, “Optical second harmonic generation with surface plasmons in piezoelectric crystals,” Opt. Commun. 23(2), 245–248 (1977).
[CrossRef]

Bergman, D. J.

D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90(2), 027402 (2003).
[CrossRef] [PubMed]

Berini, P.

I. De Leon and P. Berini, “Theory of surface plasmon-polariton amplification in planar structures incorporating dipolar gain media,” Phys. Rev. B 78, 161401 (2008).
[CrossRef]

Bloembergen, N.

J. Armstrong, N. Bloembergen, J. Ducuing, and P. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[CrossRef]

Bösch, M. A.

Bozhevolnyi, S. I.

T. Holmgaard, J. Gosciniak, and S. I. Bozhevolnyi, “Long-range dielectric-loaded surface plasmon-polariton waveguides,” Opt. Express 18(22), 23009–23015 (2010).
[CrossRef] [PubMed]

T. Holmgaard and S. I. Bozhevolnyi, “Theoretical analysis of dielectric-loaded surface plasman-polariton waveguides,” Phys. Rev. B 75(24), 245405 (2007).
[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 Condens. Matter 33(8), 5186–5201 (1986).
[CrossRef] [PubMed]

Byer, R.

R. A. Baumgartner and R. Byer, “Optical parametric amplification,” IEEE J. Quantum Electron. 15(6), 432–444 (1979).
[CrossRef]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Dai, L.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
[CrossRef] [PubMed]

Davoyan, A. R.

De Leon, I.

I. De Leon and P. Berini, “Theory of surface plasmon-polariton amplification in planar structures incorporating dipolar gain media,” Phys. Rev. B 78, 161401 (2008).
[CrossRef]

Ducuing, J.

J. Armstrong, N. Bloembergen, J. Ducuing, and P. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[CrossRef]

Edwards, G. J.

G. J. Edwards and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16(4), 373–375 (1984).
[CrossRef]

Eom, T. J.

Fan, S.

Fejer, M. M.

Gladden, C.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
[CrossRef] [PubMed]

Gosciniak, J.

Holmgaard, T.

T. Holmgaard, J. Gosciniak, and S. I. Bozhevolnyi, “Long-range dielectric-loaded surface plasmon-polariton waveguides,” Opt. Express 18(22), 23009–23015 (2010).
[CrossRef] [PubMed]

T. Holmgaard and S. I. Bozhevolnyi, “Theoretical analysis of dielectric-loaded surface plasman-polariton waveguides,” Phys. Rev. B 75(24), 245405 (2007).
[CrossRef]

Hu, W.

Z. J. Wu, X. K. Hu, Z. Y. Yu, W. Hu, F. Xu, and Y. Q. Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82(15), 155107 (2010).
[CrossRef]

Hu, X. K.

Z. J. Wu, X. K. Hu, Z. Y. Yu, W. Hu, F. Xu, and Y. Q. Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82(15), 155107 (2010).
[CrossRef]

Jiang, H.

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Kim, W.-K.

Kitaoka, Y.

Kivshar, Y. S.

Ko, D.-K.

Lawrence, M.

G. J. Edwards and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16(4), 373–375 (1984).
[CrossRef]

Lee, H.-Y.

Lee, Y. L.

Li, G. H.

Lin, C.

Lu, Y. Q.

Z. J. Wu, X. K. Hu, Z. Y. Yu, W. Hu, F. Xu, and Y. Q. Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82(15), 155107 (2010).
[CrossRef]

Ma, R. M.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
[CrossRef] [PubMed]

Ming, N. B.

S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278(5339), 843–846 (1997).
[CrossRef]

Mitchell, D. E.

H. J. Simon, D. E. Mitchell, and J. G. Watson, “Optical Second-Harmonic Generation with Surface Plasmons in Silver Films,” Phys. Rev. Lett. 33(26), 1531–1534 (1974).
[CrossRef]

Mizuuchi, K.

Novotny, L.

S. Palomba and L. Novotny, “Nonlinear excitation of surface plasmon polaritons by four-wave mixing,” Phys. Rev. Lett. 101(5), 056802 (2008).
[CrossRef] [PubMed]

Oulton, R. F.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
[CrossRef] [PubMed]

Palomba, S.

S. Palomba and L. Novotny, “Nonlinear excitation of surface plasmon polaritons by four-wave mixing,” Phys. Rev. Lett. 101(5), 056802 (2008).
[CrossRef] [PubMed]

Pershan, P.

J. Armstrong, N. Bloembergen, J. Ducuing, and P. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[CrossRef]

Rako, J. G.

H. J. Simon, R. E. Benner, and J. G. Rako, “Optical second harmonic generation with surface plasmons in piezoelectric crystals,” Opt. Commun. 23(2), 245–248 (1977).
[CrossRef]

Ruan, Z.

Shadrivov, I. V.

Shin, W.

Simon, H. J.

H. J. Simon, R. E. Benner, and J. G. Rako, “Optical second harmonic generation with surface plasmons in piezoelectric crystals,” Opt. Commun. 23(2), 245–248 (1977).
[CrossRef]

H. J. Simon, D. E. Mitchell, and J. G. Watson, “Optical Second-Harmonic Generation with Surface Plasmons in Silver Films,” Phys. Rev. Lett. 33(26), 1531–1534 (1974).
[CrossRef]

Sorger, V. J.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
[CrossRef] [PubMed]

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 Condens. Matter 33(8), 5186–5201 (1986).
[CrossRef] [PubMed]

Stockman, M. I.

D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90(2), 027402 (2003).
[CrossRef] [PubMed]

Stolen, R. H.

Sugita, T.

Tamir, T.

J. J. Burke, G. I. Stegeman, and T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B Condens. Matter 33(8), 5186–5201 (1986).
[CrossRef] [PubMed]

Veronis, G.

Vodopyanov, K. L.

Watson, J. G.

H. J. Simon, D. E. Mitchell, and J. G. Watson, “Optical Second-Harmonic Generation with Surface Plasmons in Silver Films,” Phys. Rev. Lett. 33(26), 1531–1534 (1974).
[CrossRef]

Wu, Z. J.

Z. J. Wu, X. K. Hu, Z. Y. Yu, W. Hu, F. Xu, and Y. Q. Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82(15), 155107 (2010).
[CrossRef]

Xu, F.

Z. J. Wu, X. K. Hu, Z. Y. Yu, W. Hu, F. Xu, and Y. Q. Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82(15), 155107 (2010).
[CrossRef]

Xu, X. Y.

Yamamoto, K.

Yu, B.-A.

Yu, Z. Y.

Z. J. Wu, X. K. Hu, Z. Y. Yu, W. Hu, F. Xu, and Y. Q. Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82(15), 155107 (2010).
[CrossRef]

Zentgraf, T.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
[CrossRef] [PubMed]

Zhang, X.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
[CrossRef] [PubMed]

Zhu, S. N.

S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278(5339), 843–846 (1997).
[CrossRef]

Zhu, Y. Y.

S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278(5339), 843–846 (1997).
[CrossRef]

IEEE J. Quantum Electron.

R. A. Baumgartner and R. Byer, “Optical parametric amplification,” IEEE J. Quantum Electron. 15(6), 432–444 (1979).
[CrossRef]

Nature

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
[CrossRef] [PubMed]

Opt. Commun.

H. J. Simon, R. E. Benner, and J. G. Rako, “Optical second harmonic generation with surface plasmons in piezoelectric crystals,” Opt. Commun. 23(2), 245–248 (1977).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Quantum Electron.

G. J. Edwards and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16(4), 373–375 (1984).
[CrossRef]

Phys. Rev.

J. Armstrong, N. Bloembergen, J. Ducuing, and P. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[CrossRef]

Phys. Rev. B

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

T. Holmgaard and S. I. Bozhevolnyi, “Theoretical analysis of dielectric-loaded surface plasman-polariton waveguides,” Phys. Rev. B 75(24), 245405 (2007).
[CrossRef]

Z. J. Wu, X. K. Hu, Z. Y. Yu, W. Hu, F. Xu, and Y. Q. Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82(15), 155107 (2010).
[CrossRef]

I. De Leon and P. Berini, “Theory of surface plasmon-polariton amplification in planar structures incorporating dipolar gain media,” Phys. Rev. B 78, 161401 (2008).
[CrossRef]

Phys. Rev. B Condens. Matter

J. J. Burke, G. I. Stegeman, and T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B Condens. Matter 33(8), 5186–5201 (1986).
[CrossRef] [PubMed]

Phys. Rev. Lett.

D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90(2), 027402 (2003).
[CrossRef] [PubMed]

S. Palomba and L. Novotny, “Nonlinear excitation of surface plasmon polaritons by four-wave mixing,” Phys. Rev. Lett. 101(5), 056802 (2008).
[CrossRef] [PubMed]

H. J. Simon, D. E. Mitchell, and J. G. Watson, “Optical Second-Harmonic Generation with Surface Plasmons in Silver Films,” Phys. Rev. Lett. 33(26), 1531–1534 (1974).
[CrossRef]

Science

S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278(5339), 843–846 (1997).
[CrossRef]

Other

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

G. Lifante, Integrated Photonics: Fundamentals (Wiley, England, 2003).

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Figures (4)

Fig. 1
Fig. 1

(a) Schematic of a dielectric/dielectric/metal planar hybrid waveguide, where NLD1 and NLD2 represent the nonlinear dielectric with higher and lower refractive indices respectively; (b) The mode profiles of SPP (red) and TM1 (blue) in hybrid waveguide, which are revealed as Hy.

Fig. 2
Fig. 2

(a) Dispersion relations of SPP (red curve) and TM1 mode (blue curve) in hybrid waveguide. Inset shows the frequency vs. effective index. (b) Evolutions of normalized intensity of SPP (left logarithm scale) and TM1 (right linear scale) modes in propagations, where the incident initial intensities are defined as P SPP (0) = 1kW/cm and P TM1 (0) = 50MW/cm. A decay tendency of a pure SPP without amplification is also depicted as the dashed line.

Fig. 3
Fig. 3

(a) OPA efficiency and SPP peak position as a function of the incident intensity of TM1; (b) OPA efficiency and SPP peak position as a function of the incident intensity of seed SPP.

Fig. 4
Fig. 4

(a) Phase evolutions with different incident phases, where ψ(x) = Φ + 2φ 1(x)-φ 2(x); (b) OPA efficiency and SPP peak position as the functions of incident phase ψ(0), where P TM1 (0) = 50MW/cm and P SPP (0) = 1kW/cm; (c) Evolutions of SPP intensity as propagation in condition of different incident pumping phases.

Equations (9)

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

k 1 d = n π + tan 1 ( f 1 p k 1 ) + tan 1 ( f 2 q k 1 ) ,   n = 0 , 1 , 2...   ,
× E i = μ H i t , × H i = ε E i t + P i N L t ,
A 1 x = α 1 2 A 1 + i ω ε 0 4 κ 1 A 1 * A 2 e i ( β 2 2 β 1 ) x , A 2 x = α 2 2 A 2 + i ω ε 0 4 κ 2 A 1 2 e i ( β 2 2 β 1 ) x ,
κ 1 = d 33 E 2 , z ( E 1 , z * ) 2 d z = κ * ,
κ 2 = d 33 E 2 , z * ( E 1 , z ) 2 d z = κ ,
d | A 1 | d x = 1 2 | A 1 | [ α 1 + 1 2 ω ε 0 | κ | | A 2 | sin ψ ( x ) ] ,
d | A 2 | d x = 1 2 | A 2 | [ α 2 1 2 ω ε 0 | κ | | A 1 | 2 | A 2 | sin ψ ( x ) ] ,
d φ 1 d x   = 1 4 ω ε 0 | κ | | A 2 | cos ψ ( x ) ,
d φ 2 d x   = 1 4 ω ε 0 | κ | | A 1 | 2 | A 2 | cos ψ ( x ) .

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