Plasmonic Slot Waveguide: Dispersion & Field Map (2D)

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)—

Wall / center field ratio—

How it works

This is the 2D companion of the 3D plasmonic slot-waveguide scene. It solves the same transcendental metal-insulator-metal (MIM) gap-plasmon dispersion relation independently, with its own complex Newton–Raphson root-finder, but visualizes it two different ways instead of a 3D instanced-bar scene:

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)
ε_m(ω) = 1 − ω_p² / (ω² + iωγ)   (Drude model)

Top panel — dispersion diagram. The solver is re-run across the entire gap range (5–150 nm) every time you move the wavelength, index or metal control, tracing live curves of n_eff(d) and propagation length L_p(d). The marker shows where your current gap sits on that curve — the 3D scene only ever shows a single point at a time.
Bottom panel — 2D field heatmap. A genuine intensity map |E(y,z)|, animated by superposing the transverse mode profile with the propagating phase e^{i(β'z−ωt)} and the real decay envelope e^−β''z, colour-mapped pixel by pixel — not a bar chart, an actual field image.
Wall / center field ratio. The fundamental gap-plasmon mode is not flat: for a real (non-imaginary) κ_d, cosh(κ_dy) grows away from the gap center, so the field genuinely bows outward and peaks at the metal walls rather than in the middle. This ratio (cosh(κ_d·d/2)/cosh(0)) makes that bowing an explicit, checkable number — it climbs toward 1 (flat) as the gap narrows and grows above 1 as the gap widens, exactly the opposite intuition a "beam profile" mental model would suggest.

Confinement/loss trade-off, verified: narrowing the gap always raises n_eff and always shortens L_p — there is no parameter regime where you get tighter confinement for free.

n_eff(d) curve L_p(d) curve Field intensity |E|