Plasmonic Slot Waveguide: Subwavelength Mode Confinement

Gap Waveguide

Dielectric gap width d 40 nm

Free-space wavelength λ₀ 650 nm

Dielectric index n_d 1.45

Metal

Mode (live)

Effective index n_eff—

Propagation length L_p—

Gap / λ₀ (confinement)—

How it works

A thin dielectric gap sandwiched between two metal half-spaces (a metal-insulator-metal, or MIM, waveguide) supports a bound "gap plasmon" mode with no cutoff width — unlike an ordinary dielectric waveguide, it keeps guiding light however narrow the gap gets. Its fundamental (symmetric) mode satisfies the transcendental dispersion relation:

tanh(κ_d · d/2) = −(ε_d κ_m) / (ε_m κ_d)
κ_d = √(β² − ε_d k₀²),   κ_m = √(β² − ε_m k₀²)
k₀ = 2π/λ₀,   β = β' + iβ''  (complex propagation constant)

This simulator solves that equation live by complex Newton–Raphson every time a slider moves. The metal's permittivity ε_m(ω) comes from the free-electron Drude model,

ε_m(ω) = 1 − ω_p² / (ω² + iωγ)

with plasma frequency ω_p and collision rate γ fit to gold or silver (a standard teaching simplification — real gold deviates below ~550 nm due to interband d-band transitions, which the free-electron model ignores).

n_eff = Re(β)/k₀ — how much the mode's wavelength shrinks inside the gap versus free space; it climbs sharply as d narrows.
Propagation length L_p = 1/(2·Im(β)) — the distance over which guided power falls by 1/e. Tighter confinement always costs propagation length: the field bars along the waveguide decay visibly faster for a narrow gap and barely decay at all for a wide one.
The bars extending sideways from the metal plates show the transverse mode profile — roughly uniform across the gap and exponentially evanescent (∝ e^{−κ_m x}) inside each metal, the same evanescent tail that lets the mode beat the diffraction limit.

This confinement/loss trade-off is the central design problem in nanophotonic plasmonic circuitry — routing light through structures far smaller than its own wavelength always trades propagation distance for mode size.

Metal (gold/silver) Gap-plasmon field |E|

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