Abstract
The propagation length of surface plasmon polaritons (SPP) is limited by the internal losses in the metal and the radiation losses due to the structure imperfections at the interface. These losses can be compensated by introducing material with optical gain (active medium) in the system. The required gain for complete loss compensation depends not only on the dissipative properties of the metal but also on the geometry of the structure. The geometry factor can weaken the gain requirements and one promising system, in this respect, is a metal layer embedded in an active medium. Here we present an analytical solution for this system, which allows to find the curves of exact loss compensation in the complex plane of the dielectric function of the gain medium. These curves determine the minimum required gain of the active medium for lossless SPP propagation. The solution is given for both modes of SPP propagation. This approach is then illustrated and discussed for silver and gold layers embedded in an active media.
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References
Berini, P.: Figures of merit for surface plasmon waveguides. Opt. Express 14(26), 13030–13042 (2006). https://doi.org/10.1364/oe.14.013030
Berini, P., De Leon, I.: Surface plasmon-polariton amplifiers and lasers. Nat. Photonics 6(1), 16–24 (2012). https://doi.org/10.1038/nphoton.2011.285
Burke, J.J., Stegeman, G.I., Tamir, T.: Surface-polariton-like waves guided by thin. Lossy Metal-Films Phys. Rev. B 33(8), 5186–5201 (1986). https://doi.org/10.1103/PhysRevB.33.5186
De Leon, I., Berini, P.: Amplification of long-range surface plasmons by a dipolar gain medium. Nat. Photonics 4(6), 382–387 (2010). https://doi.org/10.1038/Nphoton.2010.37
Gather, M.C., Meerholz, K., Danz, N., Leosson, K.: Net optical gain in a plasmonic waveguide embedded in a fluorescent polymer. Nat. Photonics 4(7), 457–461 (2010). https://doi.org/10.1038/nphoton.2010.121
Johnson, P.B., Christy, R.W.: Optical constants of the noble metals. Phys. Rev. B 6(12), 4370–4379 (1972)
Karami Keshmarzi, E., Tait, R.N., Berini, P.: Single-mode surface plasmon distributed feedback lasers. Nanoscale 10(13), 5914–5922 (2018). https://doi.org/10.1039/c7nr09183d
Kéna-Cohen, S., Stavrinou, P.N., Bradley, D.D.C., Maier, S.A.: Confined surface plasmon-polariton amplifiers. Nano Lett. 13(3), 1323–1329 (2013). https://doi.org/10.1021/nl400134v
Kumar, A., Yu, S.F., Li, X.F., Lau, S.P.: Surface plasmonic lasing via the amplification of coupled surface plasmon waves inside dielectric-metal-dielectric waveguides. Opt. Express 16(20), 16113–16123 (2008). https://doi.org/10.1364/Oe.16.016113
Leosson, K.: Optical amplification of surface plasmon polaritons: review. J. Nanophotonics 6(1), 061801 (2012)
Liu, L., Han, Z.H., He, S.L.: Novel surface plasmon waveguide for high integration. Opt. Express 13(17), 6645–6650 (2005). https://doi.org/10.1364/Opex.13.006645
Maier, S.A.: Plasmonics: Fundamentals and Applications. Springer, New York (2007)
Meng, X., Kildishev, A.V., Fujita, K., Tanaka, K., Shalaev, V.M.: Wavelength-tunable spasing in the visible. Nano Lett. 13(9), 4106–4112 (2013). https://doi.org/10.1021/nl4015827
Nezhad, M.P., Tetz, K., Fainman, Y.: Gain assisted propagation of surface plasmon polaritons on planar metallic waveguides. Opt. Express 12(17), 4072–4079 (2004). https://doi.org/10.1364/Opex.12.004072
Noginov, M.A., Podolskiy, V.A., Zhu, G., Mayy, M., Bahoura, M., Adegoke, J.A., Ritzo, B.A., Reynolds, K.: Compensation of loss in propagating surface plasmon polariton by gain in adjacent dielectric medium. Opt. Express 16(2), 1385–1392 (2008). https://doi.org/10.1364/Oe.16.001385
Norrman, A., Setala, T., Friberg, A.T.: Surface-plasmon polariton solutions at a lossy slab in a symmetric surrounding. Opt. Express 22(4), 4628–4648 (2014). https://doi.org/10.1364/Oe.22.004628
Ozbay, E.: Plasmonics: merging photonics and electronics at nanoscale dimensions. Science 311(5758), 189–193 (2006). https://doi.org/10.1126/science.1114849
Raether, H.: Surface-plasmons on smooth and rough surfaces and on gratings. Springer Trac. Mod. Phys. 111, 1–133 (1988)
Rao, R.J., Tang, T.T.: Study on active surface plasmon waveguides and design of a nanoscale lossless surface plasmon waveguide. J. Opt. Soc. Am. B 28(5), 1258–1265 (2011). https://doi.org/10.1364/Josab.28.001258
Russev, S.C., Tsutsumanova, G.G., Tzonev, A.N.: Conditions for loss compensation of surface plasmon polaritons propagation on a metal/gain medium boundary. Plasmonics 7(1), 151–157 (2012). https://doi.org/10.1007/s11468-011-9288-2
Sarid, D.: Long-range surface-plasma waves on very thin metal films. Phys. Rev. Lett. 47(26), 1927–1930 (1981)
Seidel, J., Grafstrom, S., Eng, L.: Stimulated emission of surface plasmons at the interface between a silver film and an optically pumped dye solution. Phys. Rev. Lett. 94(17), 177401 (2005). https://doi.org/10.1103/Physrevlett.94.177401
Sidiropoulos, T.P.H., Röder, R., Geburt, S., Hess, O., Maier, S.A., Ronning, C., Oulton, R.F.: Ultrafast plasmonic nanowire lasers near the surface plasmon frequency. Nat. Phys. 10(11), 870–876 (2014). https://doi.org/10.1038/nphys3103
Suárez, I., Ferrando, A., Marques-Hueso, J., Díez, A., Abargues, R., Rodríguez-Cantó, P.J., Martínez-Pastor, J.P.: Propagation length enhancement of surface plasmon polaritons in gold nano-/microwaveguides by the interference with photonic modes in the surrounding active dielectrics. Nanophotonics 6(5), 1109–1120 (2017). https://doi.org/10.1515/nanoph-2016-0166
Wong, W.R., Berini, P.: Integrated multichannel Young’s interferometer sensor based on long-range surface plasmon waveguides. Opt. Express 27(18), 25470–25484 (2019). https://doi.org/10.1364/oe.27.025470
Zakharian, A.R., Moloney, J.V., Mansuripur, M.: Surface plasmon polaritons on metallic surfaces. Opt. Express 15(1), 183–197 (2007). https://doi.org/10.1364/Oe.15.000183
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The concept of the study was given by Stoyan C. Russev. Calculations were performed by Atanas N. Tzonev. All authors contributed to the analysis of the results. Visualisation was performed by Gichka G. Tsutsumanova. The first draft of the manuscript was written by Atanas N. Tzonev and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.
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Tzonev, A.N., Tsutsumanova, G.G. & Russev, S.C. Conditions for loss compensation of surface plasmon polaritons in a metal layer surrounded by an active dielectric: an analytic solution. Opt Quant Electron 52, 313 (2020). https://doi.org/10.1007/s11082-020-02434-1
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DOI: https://doi.org/10.1007/s11082-020-02434-1