Skip to main content
Log in

Numerical Study of Gain-Assisted Terahertz Hybrid Plasmonic Waveguide

  • Published:
Plasmonics Aims and scope Submit manuscript

Abstract

A numerical transfer matrix method (TMM) is applied to investigate hybrid surface plasmon polaritons (HySPPs) waveguide structure, which consists of a high permittivity dielectric fiber separated from a metal surface with a low permittivity dielectric gap. The results obtained from the TMM agree well with those from the finite element method but with a faster calculation speed. As a demonstration example, we have systematically investigated the propagation properties of the gain-assisted HySPPs waveguide in the terahertz regime by using this method, studying the influences of structure parameters, frequency, temperature, and material gain. The results manifest that the effective index and the propagation loss decrease with the increase of temperature. In addition, as the frequency increases, the effective index increases and the propagation loss shows a peak. Furthermore, lossless propagation can be achieved when certain gain materials are applied into the HySPPs structure. Our method provides an efficient approach to investigate HySPPs waveguide and other plasmonic devices.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Raether H (1988) Surface plasmons on smooth and rough surfaces and on gratings. Springer, Berlin

    Google Scholar 

  2. Barnes WL, Dereux A, Ebbesen TW (2003) Surface plasmon subwavelength optics. Nature 424(6950):824–830

    Article  CAS  Google Scholar 

  3. Wang QJ, Yan C, Diehl L, Hentschel M, Wiersig J, Yu N, Pflügl C, Belkin MA, Edamura T, Yamanishi M, Kan H, Capasso F (2009) Deformed microcavity quantum cascade lasers with directional emission. New J Phys 11(12):125018

    Article  Google Scholar 

  4. Li XF, Yu SF (2010) Extremely high sensitive plasmonic refractive index sensors based on metallic grating. Plasmonics 5(4):389–394

    Article  Google Scholar 

  5. Bozhevolnyi SI, Volkov VS, Devaux E, Laluet JY, Ebbesen TW (2006) Channel plasmon subwavelength waveguide components including interferometers and ring resonators. Nature 440(7083):508–511

    Article  CAS  Google Scholar 

  6. Grandidier J, Massenot S, des Francs GC, Bouhelier A, Weeber JC, Markey L, Dereux A, Renger J, González MU, Quidant R (2008) Dielectric-loaded surface plasmon polariton waveguides: figures of merit and mode characterization by image and Fourier plane leakage microscopy. Phys Rev B 78(24):245419

    Article  Google Scholar 

  7. Veronis G, Fan SH (2005) Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides. Appl Phys Lett 87(13):131102

    Article  Google Scholar 

  8. He XY (2009) Numerical analysis of the propagation properties of subwavelength semiconductor slit in the terahertz region. Opt Express 17(17):15359–15371

    Article  CAS  Google Scholar 

  9. Oulton RF, Sorger VJ, Genov DA, Pile DFP, Zhang X (2008) A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation. Nat Photonics 2(8):496–500

    Article  CAS  Google Scholar 

  10. Oulton RF, Sorger VJ, Zentgraf T, Ma RM, Gladden C, Dai L, Bartal G, Zhang X (2009) Plasmon lasers at deep subwavelength scale. Nature 461(7264):629–632

    Article  CAS  Google Scholar 

  11. Zhang J, Cai L, Bai W, Xu Y, Song G (2011) Hybrid plasmonic waveguide with gain medium for lossless propagation with nanoscale confinement. Opt Lett 36(12):2312–2314

    Article  CAS  Google Scholar 

  12. Zheng YJ, Liu H, Wang SM, Li T, Cao JX, Li L, Zhu C, Wang Y, Zhu SN, Zhang X (2011) Selective optical trapping based on strong plasmonic coupling between gold nanorods and slab. Appl Phys Lett 98(8):083117

    Article  Google Scholar 

  13. Yang XD, Liu YM, Oulton RF, Yin XB, Zhang X (2011) Optical forces in hybrid plasmonic waveguides. Nano Lett 11(2):321–328

    Article  CAS  Google Scholar 

  14. Ta VD, Chen R, Sun HD (2011) Wide-range coupling between surface plasmon polariton and cylindrical dielectric waveguide mode. Opt Express 19(14):13598–13603

    Article  Google Scholar 

  15. Zou CL, Sun FW, Xiao YF, Dong CH, Chen XD, Cui JM, Gong Q, Han ZF, Guo GC (2010) Plasmon modes of silver nanowire on a silica substrate. Appl Phys Lett 97(18):183102

    Article  Google Scholar 

  16. Wang X, Belyanin AA, Crooker SA, Mittleman DM, Kono J (2010) Interference-induced terahertz transparency in a semiconductor magneto-plasma. Nat Phys 6(2):126–130

    Article  CAS  Google Scholar 

  17. Wang QJ, Yan C, Yu N, Unterhinninghofen J, Wiersig J, Pflügl C, Diehl L, Edamurac T, Yamanishi M, Kan H, Capasso F (2010) Whispering-gallery mode resonators for highly unidirectional laser action. PNAS 107(52):22407–22412

    Article  CAS  Google Scholar 

  18. Cao JC (2003) Interband impact ionization and nonlinear absorption of terahertz radiation in semiconductor heterostructures. Phys Rev Lett 91(23):237401

    Article  CAS  Google Scholar 

  19. Yu NF, Wang QJ, Kats MA, Fan FA, Khanna SP, Li LH, Davies AG, Linfield EH, Capasso F (2010) Designer spoof surface plasmon structures collimate terahertz laser beams. Nat Mater 9(9):730–735

    Article  CAS  Google Scholar 

  20. Singh R, Rockstuhl C, Lederer F, Zhang WL (2009) Coupling between a dark and a bright eigenmode in a terahertz metamaterial. Phys Rev B 79(8):085111

    Article  Google Scholar 

  21. Wright AR, Cao JC, Zhang C (2009) Enhanced optical conductivity of bilayer grapheme nanoribbons in the terahertz regime. Phys Rev Lett 103(20):207401

    Article  CAS  Google Scholar 

  22. Wang KL, Mittleman DM (2004) Metal wires for terahertz wave guiding. Nature 432(7015):376–379

    Article  CAS  Google Scholar 

  23. Wang KL, Mittleman DM (2006) Dispersion of surface plasmon polaritons on metal wires in the terahertz frequency range. Phys Rev Lett 96(15):157401

    Article  Google Scholar 

  24. He XY (2009) Investigation of terahertz Sommerfeld wave propagation along conical metal wire. J Opt Soc Am B 26(9):A23–A28

    Article  CAS  Google Scholar 

  25. He XY (2010) Investigation of terahertz surface waves of a metallic nanowire. J Opt Soc Am B 27(11):2298–2303

    Article  CAS  Google Scholar 

  26. Snyder AW, Love JD (1983) Optical waveguide theory. Chapman & Hall, New York

    Google Scholar 

  27. Yang F, Sambles JR, Bradberry GW (1991) Long-range surface modes supported by thin films. Phys Rev B 44(11):5855–5872

    Article  Google Scholar 

  28. Lü JT, Cao JC (2006) Confined optical phonon modes and electron-phonon interactions in wurtzite GaN/ZnO quantum wells. Phys Rev B 73(19):195326

    Article  Google Scholar 

  29. Ordal MA, Bell RJ, Alexander RW, Long LL, Querry MR (1985) Optical properties of fourteen metals in the infrared and far infrared: Al, Co, Cu, Au, Fe, Pb, Mo, Ni, Pd, Pt, Ag, Ti, V, and W. Appl Opt 24(24):4493–4499

    Article  CAS  Google Scholar 

  30. Azad AK, Zhao Y, Zhang WL (2005) Transmission properties of terahertz pulses through an ultrathin subwavelength silicon hole array. Appl Phys Lett 86(14):141102

    Article  Google Scholar 

  31. Vinh NQ, Ha NN, Gregorkiewicz T (2007) Photonic properties of Er-doped crystalline silicon. Proc IEEE 97(7):1269–1283

    Article  Google Scholar 

  32. Adam TN, Troeger RT, Ray SK, Lü PC, Kolodzeya J (2003) Terahertz electroluminescence from boron-doped silicon devices. Appl Phys Lett 83(9):1713–1715

    Article  CAS  Google Scholar 

  33. Pavlov SG, Zhukavin RK, Orlova EE, Shastin VN, Kirsanov AV, Hübers HW, Auen K, Riemann H (2000) Stimulated emission from donor transitions in silicon. Phys Rev Lett 84(22):5220–5223

    Article  CAS  Google Scholar 

  34. Rana F (2008) Graphene terahertz plasmon oscillators. IEEE Trans Nanotechnol 7(1):91–99

    Article  Google Scholar 

  35. Li DB, Ning CZ (2009) Giant modal gain, amplified surface plasmon-polariton propagation, and slowing down of energy velocity in a metal-semiconductor-metal structure. Phys Rev B 80(15):153304

    Article  Google Scholar 

Download references

Acknowledgments

This work is supported by A*STAR SERC under grant no. 082-101-0016 and Nanyang Technological University, Singapore, under grant no. M58040017. HE XY would like to thank Mr. Tao Liu for many helpful discussions.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Qi Jie Wang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

He, X.Y., Wang, Q.J. & Yu, S.F. Numerical Study of Gain-Assisted Terahertz Hybrid Plasmonic Waveguide. Plasmonics 7, 571–577 (2012). https://doi.org/10.1007/s11468-012-9344-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11468-012-9344-6

Keywords

Navigation