Plasmonic Nanofocusing: Adiabatic Tip Compression

Tip & Metal

Metal Gold (Au)

Vacuum wavelength λ₀ 600 nm

Base radius r₀ 45 nm

Taper half-angle θ 6.0°

Live Readouts

λ_spp at base

— nm

λ_spp at tip

— nm

Field enhancement

—×

Propagation length

— μm

Tip apex radius

— nm

How it works

A surface plasmon polariton (SPP) is a light wave bound to a metal–dielectric interface. Its wavenumber follows the standard dispersion relation, with the metal's permittivity given by the free-electron (Drude) model:

k_spp = k₀ √( εm·εd / (εm + εd) )
εm(ω) = 1 − ωp² / (ω² + iωγ)
k₀ = 2π/λ₀,  ω = 2πc/λ₀

On a taper, geometry adds a second effect: as the local radius r shrinks toward the metal's skin depth δ = λ₀/(2π√|Re εm|), the effective mode index rises steeply (adiabatic nanofocusing, Stockman 2004):

n(r) ≈ Re(n_spp) · (1 + δ/r)
λ_spp(r) = λ₀ / n(r)

Because the mode slows down and squeezes into a smaller cross-section at the same time, energy-flux conservation along the taper forces the near-field intensity to pile up at the apex:

|E(r)|² ∝ n(r)/r   (relative to the base)
L_spp = 1 / (2k₀·Im n_spp)   — Ohmic loss length

Metal — switches the Drude parameters ωp, γ (gold vs. silver; silver has lower loss, so it focuses further before decaying).
λ₀, r₀, θ — set the driving wavelength and the cone's geometry, which together fix how compressed the wave gets before it hits the ~2 nm apex floor (below that, nonlocal/quantum effects the model doesn't capture take over).
Send Wave Pulse — launches a visible wavefront so you can watch the ring spacing (local λ_spp) shrink and the glow (field enhancement) brighten as it nears the tip.

This is the working principle behind apertureless near-field microscopy (s-SNOM), tip-enhanced Raman spectroscopy (TERS) and plasmonic photothermal probes — all use a sharp metal tip to funnel visible-light energy into a spot far smaller than the diffraction limit.

Tapered metal tip SPP wavefronts Apex field hot spot

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