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Lu F F, Zhang W D, Huang L G, Liang S H, Mao D et al. Mode evolution and nanofocusing of grating-coupled surface plasmon polaritons on metallic tip. Opto-Electron Adv 1, 180010 (2018). doi: 10.29026/oea.2018.180010
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Original Article Open Access
Mode evolution and nanofocusing of grating-coupled surface plasmon polaritons on metallic tip
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Abstract
We present a detailed analysis on mode evolution of grating-coupled surface plasmonic polaritons (SPPs) on a conical metal tip based on the guided-wave theory. The eigenvalue equations for SPPs modes are discussed, revealing that cylindrical metal waveguides only support TM01 and HEm1 surface modes. During propagation on the metal tip, the grating-coupled SPPs are converted to HE31, HE21, HE11 and TM01 successively, and these modes are sequentially cut off except TM01. The TM01 mode further propagates with drastically increasing effective mode index and is converted to localized surface plasmons (LSPs) at the tip apex, which is responsible for plasmonic nanofocusing. The gap-mode plasmons can be excited with the focusing TM01 mode by approaching a metal substrate to the tip apex, resulting in further enhanced electric field and reduced size of the plasmonic focus. -
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References
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Supplementary information for Mode evolution and nanofocusing of grating-coupled surface plasmon polaritons on metallic tip 
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Lu F F, Zhang W D, Huang L G, Liang S H, Mao D et al. Mode evolution and nanofocusing of grating-coupled surface plasmon polaritons on metallic tip. Opto-Electron Adv 1, 180010 (2018). doi: 10.29026/oea.2018.180010
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Figure 1.
Geometry of a conical silver tip with grating-assisted light coupling.
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Figure 2.
(a) Sketch map of SPPs excitation using a planar grating; (b) Dispersion relationship of SPPs and the grating coupling; (c) Reflection obtained from the field monitor located above the surface without grating; (d) Re(Hy) distribution of the grating-coupled SPPs generation and propagation along the silver-air interface with excitation wavelength at λ=632.8 nm and θ=28.5°.
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Figure 3.
Effective indices neff in real part (a) and imaginary part (b) of guided SPP modes versus the radius of cylindrical silver guide R. (c) Sketch map of a silver tip removing the diffracting grating. (d–j) Transverse modes intensity distributions of guided modes for R=1 μm.
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Figure 4.
(a) Transverse mode intensity distributions of the grating-coupled SPPs at R=1 μm; (b–g) Transverse mode intensity distributions of the hybrid mode at R=800, 750, 600, 350, 230, and 20 nm, respectively. (h) Electric field intensity distribution at the tip apex. (i) Transverse electric field intensity distribution at 1 nm below the tip apex.
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Figure 5.
Adiabatic parameter δ of TM01 mode versus R.
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Figure 6.
(a) Gap-mode configuration with the gap distance d=2 nm. (b) Electric field intensity and polarization distributions in the x-z plane. (c) Electric field intensity distribution in the x-y plane at 1 nm below the tip apex. (d) Comparison of electric field enhancement factor between the non-gap mode (Fig. 4(i)) and gap mode located at 1 nm below the apex of the silver tip.
