Abstract

A theoretical study is presented for parametric compensation of power losses in surface plasmon polaritons (SPPs) along single metal–dielectric interfaces. An optical or near-infrared signal SPP with subwavelength transverse confinement and an idler SPP with 2–3 times longer wavelength are amplified parametrically by a broadside laser pump. Despite the fact that Drude losses are much higher than parametric gain, there is more than tenfold enhancement of the signal SPP propagation length, albeit at a reduced but detectable signal power level. Numerical results are presented for a silver surface interfaced with a polymer/dye or porous silicon layer that allow phase matching of the noncollinear parametric process.

© 2013 Optical Society of America

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References

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    [CrossRef]

2012 (5)

P. Berini and I. De Leon, “Surface plasmon-polariton amplifiers and lasers,” Nat. Photonics 6, 16–24 (2012).
[CrossRef]

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6, 737–748 (2012).
[CrossRef]

K. Leosson, “Optical amplification of surface plasmon polaritons: review,” J. Nanophoton. 6, 61801–61809 (2012).
[CrossRef]

S. B. Hasan, C. Rockstuhl, T. Pertsch, and F. Lederer, “Second-order nonlinear frequency conversion processes in plasmonic slot waveguides,” J. Opt. Soc. Am. B 29, 1606–1611 (2012).
[CrossRef]

A. T. Georges and N. E. Karatzas, “Optimizing the excitation of surface plasmon polaritons by difference-frequency generation on a gold surface,” Phys. Rev. B 85, 155442–155446 (2012).
[CrossRef]

2011 (3)

2010 (4)

2009 (1)

J. Grandidier, G. Colas des Francs, S. Massenot, A. Bouhelier, L. Markey, J.-C. Weeber, Ch. Finot, and A. Dereux, “Gain-assisted propagation in a plasmonic waveguide at telecom wavelength,” Nano Lett. 9, 2935–2939 (2009).
[CrossRef]

2008 (1)

2005 (2)

J. Seidel, S. Grafstrom, and L. Eng, “Stimulated emission of surface plasmons at the interface between a silver film and an optically pumped dye solution,” Phys. Rev. Lett. 94, 177401–177404 (2005).
[CrossRef]

A. F. Mansour, M. H. El Gazaly, M. Gaber, and R. M. Ahmed, “Characterization of polymer films for fluorescent solar-concentrator applications,” Int. J. Polym. Mater. 54, 237–246 (2005).
[CrossRef]

2004 (1)

D. Krause, C. W. Teplin, and C. T. Rogers, “Optical surface second harmonic generation measurements of isotropic thin-film metals: gold, silver, copper, aluminum, and tantalum,” J. Appl. Phys. 96, 3626–3634 (2004).
[CrossRef]

Adegoke, J. A.

Ahmed, R. M.

A. F. Mansour, M. H. El Gazaly, M. Gaber, and R. M. Ahmed, “Characterization of polymer films for fluorescent solar-concentrator applications,” Int. J. Polym. Mater. 54, 237–246 (2005).
[CrossRef]

Albrektsen, O.

Bahoura, M.

Berini, P.

P. Berini and I. De Leon, “Surface plasmon-polariton amplifiers and lasers,” Nat. Photonics 6, 16–24 (2012).
[CrossRef]

Bolger, R. M.

Bouhelier, A.

J. Grandidier, G. Colas des Francs, S. Massenot, A. Bouhelier, L. Markey, J.-C. Weeber, Ch. Finot, and A. Dereux, “Gain-assisted propagation in a plasmonic waveguide at telecom wavelength,” Nano Lett. 9, 2935–2939 (2009).
[CrossRef]

Bozhevolnyi, S. I.

Colas des Francs, G.

J. Grandidier, G. Colas des Francs, S. Massenot, A. Bouhelier, L. Markey, J.-C. Weeber, Ch. Finot, and A. Dereux, “Gain-assisted propagation in a plasmonic waveguide at telecom wavelength,” Nano Lett. 9, 2935–2939 (2009).
[CrossRef]

Danz, N.

M. C. Gather, K. Meerholz, N. Danz, and K. Leosson, “Net optical gain in a plasmonic waveguide embedded in a fluorescent,” Nat. Photonics 4, 457–461 (2010).
[CrossRef]

De Leon, I.

P. Berini and I. De Leon, “Surface plasmon-polariton amplifiers and lasers,” Nat. Photonics 6, 16–24 (2012).
[CrossRef]

Dereux, A.

J. Grandidier, G. Colas des Francs, S. Massenot, A. Bouhelier, L. Markey, J.-C. Weeber, Ch. Finot, and A. Dereux, “Gain-assisted propagation in a plasmonic waveguide at telecom wavelength,” Nano Lett. 9, 2935–2939 (2009).
[CrossRef]

Dickson, W.

El Gazaly, M. H.

A. F. Mansour, M. H. El Gazaly, M. Gaber, and R. M. Ahmed, “Characterization of polymer films for fluorescent solar-concentrator applications,” Int. J. Polym. Mater. 54, 237–246 (2005).
[CrossRef]

Eng, L.

J. Seidel, S. Grafstrom, and L. Eng, “Stimulated emission of surface plasmons at the interface between a silver film and an optically pumped dye solution,” Phys. Rev. Lett. 94, 177401–177404 (2005).
[CrossRef]

Finot, Ch.

J. Grandidier, G. Colas des Francs, S. Massenot, A. Bouhelier, L. Markey, J.-C. Weeber, Ch. Finot, and A. Dereux, “Gain-assisted propagation in a plasmonic waveguide at telecom wavelength,” Nano Lett. 9, 2935–2939 (2009).
[CrossRef]

Gaber, M.

A. F. Mansour, M. H. El Gazaly, M. Gaber, and R. M. Ahmed, “Characterization of polymer films for fluorescent solar-concentrator applications,” Int. J. Polym. Mater. 54, 237–246 (2005).
[CrossRef]

Gather, M. C.

M. C. Gather, K. Meerholz, N. Danz, and K. Leosson, “Net optical gain in a plasmonic waveguide embedded in a fluorescent,” Nat. Photonics 4, 457–461 (2010).
[CrossRef]

Georges, A. T.

A. T. Georges and N. E. Karatzas, “Optimizing the excitation of surface plasmon polaritons by difference-frequency generation on a gold surface,” Phys. Rev. B 85, 155442–155446 (2012).
[CrossRef]

A. T. Georges, “Theory of nonlinear excitation of surface plasmon polaritons by four-wave mixing,” J. Opt. Soc. Am. B 28, 1603–1606 (2011).
[CrossRef]

Grafstrom, S.

J. Seidel, S. Grafstrom, and L. Eng, “Stimulated emission of surface plasmons at the interface between a silver film and an optically pumped dye solution,” Phys. Rev. Lett. 94, 177401–177404 (2005).
[CrossRef]

Gramotnev, D. K.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4, 83–91 (2010).
[CrossRef]

Grandidier, J.

J. Grandidier, G. Colas des Francs, S. Massenot, A. Bouhelier, L. Markey, J.-C. Weeber, Ch. Finot, and A. Dereux, “Gain-assisted propagation in a plasmonic waveguide at telecom wavelength,” Nano Lett. 9, 2935–2939 (2009).
[CrossRef]

Hasan, S. B.

Hickey, S. G.

Karatzas, N. E.

A. T. Georges and N. E. Karatzas, “Optimizing the excitation of surface plasmon polaritons by difference-frequency generation on a gold surface,” Phys. Rev. B 85, 155442–155446 (2012).
[CrossRef]

Kauranen, M.

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6, 737–748 (2012).
[CrossRef]

Krasavin, A. V.

Krause, D.

D. Krause, C. W. Teplin, and C. T. Rogers, “Optical surface second harmonic generation measurements of isotropic thin-film metals: gold, silver, copper, aluminum, and tantalum,” J. Appl. Phys. 96, 3626–3634 (2004).
[CrossRef]

Lederer, F.

Leosson, K.

K. Leosson, “Optical amplification of surface plasmon polaritons: review,” J. Nanophoton. 6, 61801–61809 (2012).
[CrossRef]

M. C. Gather, K. Meerholz, N. Danz, and K. Leosson, “Net optical gain in a plasmonic waveguide embedded in a fluorescent,” Nat. Photonics 4, 457–461 (2010).
[CrossRef]

Li, L.

Li, T.

Liebscher, L.

Lu, F. F.

Maier, S. A.

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

Mansour, A. F.

A. F. Mansour, M. H. El Gazaly, M. Gaber, and R. M. Ahmed, “Characterization of polymer films for fluorescent solar-concentrator applications,” Int. J. Polym. Mater. 54, 237–246 (2005).
[CrossRef]

Markey, L.

J. Grandidier, G. Colas des Francs, S. Massenot, A. Bouhelier, L. Markey, J.-C. Weeber, Ch. Finot, and A. Dereux, “Gain-assisted propagation in a plasmonic waveguide at telecom wavelength,” Nano Lett. 9, 2935–2939 (2009).
[CrossRef]

Massenot, S.

J. Grandidier, G. Colas des Francs, S. Massenot, A. Bouhelier, L. Markey, J.-C. Weeber, Ch. Finot, and A. Dereux, “Gain-assisted propagation in a plasmonic waveguide at telecom wavelength,” Nano Lett. 9, 2935–2939 (2009).
[CrossRef]

Mayy, M.

Meerholz, K.

M. C. Gather, K. Meerholz, N. Danz, and K. Leosson, “Net optical gain in a plasmonic waveguide embedded in a fluorescent,” Nat. Photonics 4, 457–461 (2010).
[CrossRef]

Nielsen, M. G.

Noginov, M. A.

Palik, E. D.

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

Pertsch, T.

Podolskiy, V. A.

Radko, I. P.

Reynolds, K.

Ritzo, B. A.

Rockstuhl, C.

Rogers, C. T.

D. Krause, C. W. Teplin, and C. T. Rogers, “Optical surface second harmonic generation measurements of isotropic thin-film metals: gold, silver, copper, aluminum, and tantalum,” J. Appl. Phys. 96, 3626–3634 (2004).
[CrossRef]

Seidel, J.

J. Seidel, S. Grafstrom, and L. Eng, “Stimulated emission of surface plasmons at the interface between a silver film and an optically pumped dye solution,” Phys. Rev. Lett. 94, 177401–177404 (2005).
[CrossRef]

Shen, Y. R.

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, 1984).

Skryabin, D. V.

Stockman, M. I.

M. I. Stockman, “Nanoplasmonics: the physics behind the applications,” Phys. Today 64(2), 39–44 (2011).
[CrossRef]

Teplin, C. W.

D. Krause, C. W. Teplin, and C. T. Rogers, “Optical surface second harmonic generation measurements of isotropic thin-film metals: gold, silver, copper, aluminum, and tantalum,” J. Appl. Phys. 96, 3626–3634 (2004).
[CrossRef]

Weeber, J.-C.

J. Grandidier, G. Colas des Francs, S. Massenot, A. Bouhelier, L. Markey, J.-C. Weeber, Ch. Finot, and A. Dereux, “Gain-assisted propagation in a plasmonic waveguide at telecom wavelength,” Nano Lett. 9, 2935–2939 (2009).
[CrossRef]

Xie, Z. D.

Xu, J.

Zayats, A. V.

Zhu, G.

Zhu, S. N.

Zhu, Y. Y.

Int. J. Polym. Mater. (1)

A. F. Mansour, M. H. El Gazaly, M. Gaber, and R. M. Ahmed, “Characterization of polymer films for fluorescent solar-concentrator applications,” Int. J. Polym. Mater. 54, 237–246 (2005).
[CrossRef]

J. Appl. Phys. (1)

D. Krause, C. W. Teplin, and C. T. Rogers, “Optical surface second harmonic generation measurements of isotropic thin-film metals: gold, silver, copper, aluminum, and tantalum,” J. Appl. Phys. 96, 3626–3634 (2004).
[CrossRef]

J. Nanophoton. (1)

K. Leosson, “Optical amplification of surface plasmon polaritons: review,” J. Nanophoton. 6, 61801–61809 (2012).
[CrossRef]

J. Opt. Soc. Am. B (2)

Nano Lett. (1)

J. Grandidier, G. Colas des Francs, S. Massenot, A. Bouhelier, L. Markey, J.-C. Weeber, Ch. Finot, and A. Dereux, “Gain-assisted propagation in a plasmonic waveguide at telecom wavelength,” Nano Lett. 9, 2935–2939 (2009).
[CrossRef]

Nat. Photonics (4)

M. C. Gather, K. Meerholz, N. Danz, and K. Leosson, “Net optical gain in a plasmonic waveguide embedded in a fluorescent,” Nat. Photonics 4, 457–461 (2010).
[CrossRef]

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4, 83–91 (2010).
[CrossRef]

P. Berini and I. De Leon, “Surface plasmon-polariton amplifiers and lasers,” Nat. Photonics 6, 16–24 (2012).
[CrossRef]

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6, 737–748 (2012).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. B (1)

A. T. Georges and N. E. Karatzas, “Optimizing the excitation of surface plasmon polaritons by difference-frequency generation on a gold surface,” Phys. Rev. B 85, 155442–155446 (2012).
[CrossRef]

Phys. Rev. Lett. (1)

J. Seidel, S. Grafstrom, and L. Eng, “Stimulated emission of surface plasmons at the interface between a silver film and an optically pumped dye solution,” Phys. Rev. Lett. 94, 177401–177404 (2005).
[CrossRef]

Phys. Today (1)

M. I. Stockman, “Nanoplasmonics: the physics behind the applications,” Phys. Today 64(2), 39–44 (2011).
[CrossRef]

Other (4)

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

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, 1984).

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

http://refractiveindex.info .

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Figures (4)

Fig. 1.
Fig. 1.

Schematic diagram for parametric amplification of SPPs on a silver–dielectric interface. kp, ki, and ks are the wave vectors of the incident laser pump and the idler and signal SPPs, respectively. The curves labeled Eix(z) and Esx(z) display the relative transverse field localization of the idler (infrared) and signal (visible) SPPs.

Fig. 2.
Fig. 2.

Log–log plot of the normalized amplitudes of the signal and idler SPPs versus propagation distance on a silver-PMMA/dye interface. The solid curves correspond to calculations from Eqs. (10) and (11), the dotted ones show the amplitudes in the absence of parametric coupling between the two SPPs, and the dashed one represents parametric compensation of losses in the signal SPP.

Fig. 3.
Fig. 3.

Plot of the normalized peak intensity of the signal SPP versus the angle of incidence of the laser pump beam at a propagation distance of x=1mm.

Fig. 4.
Fig. 4.

Same as Fig. 2 but for different wavelengths and a silver-porous silicon interface.

Equations (13)

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

Eν(x,z,t)=Aν(x)Eν(z)ei(ωνtkνx)+c.c.,
Eν(z)={[Eνx,dx^+Eνz,dz^]eανdz,z>0,[Eνx,mx^+Eνz,mz^]eανmz,z<0,
kν=kvikv=ωνcϵνdϵνmϵνd+ϵνm.
Pν(2)(x,z,t)=Pνz,S(2)δ(z0)ei[ωνt(kpxkν*)x]z^+c.c.,
dA˜sdx=(ks+iΔk/2)A˜sκsiA˜i*,
dA˜idx=(ki+iΔk/2)A˜iκisA˜s*.
κνν=i(ων/c)22kνwνϵνd*ϵνm*χS(2)(ων)Epz,
wν=[2|ϵνd+ϵνm||ϵνm|]1ανd+ανd*+[2|ϵνd+ϵνm||ϵνd|]|ϵνd|2/|ϵνm|2ανm+ανm*,
sinθpϵpd=λpλsReϵsdϵsmϵsd+ϵsm+λpλiReϵidϵimϵid+ϵim,
A˜s(x)=e(ks+ki)x/2[A˜s0cosh(Sx)+Csinh(Sx)],
A˜i*(x)=1κsie(ks+ki)x/2{[12(kski+iΔk)A˜s0+SC]cosh(Sx)+[12(kski+iΔk)C+SA˜s0]sinh(Sx)},
C=1S[12(kski+iΔk)A˜s0+κsiA˜i0*],
A˜s(x)[(1g2(kski)2)A˜s0+κsikskiA˜i0*]e[ks+g2/(kski)]x+[g2(kski)2A˜s0κsikskiA˜i0*]e[kig2/(kski)]x.

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