Ebbesen's 1998 discovery: a metal film perforated with a periodic array of holes much smaller than the light's wavelength transmits far more light at certain wavelengths than the classical Bethe theory of diffraction through a single subwavelength aperture predicts (Bethe: T ∝ (d/λ)⁴, vanishingly small). The extra light is carried by surface plasmon polaritons (SPPs) bound to the metal–dielectric interface, which the periodic lattice couples to free-space light whenever the grating momentum matches the SPP dispersion:
SPP resonance (square lattice, order i,j):
λ(i,j) = (P / √(i²+j²)) · √[ εm(λ)·εd / (εm(λ)+εd) ] (solved self-consistently)
Free-electron metal (simplified Drude, no damping):
εm(λ) = 1 − (λ / λp)² λp = bulk plasma wavelength
Bethe single-aperture baseline:
T_Bethe(λ) ∝ (d/λ)⁴ · (d/P)²
- Period P — drag the top-down lattice or watch the side panel: the lattice constant sets which wavelengths satisfy the momentum-matching condition; larger P pushes SPP resonances to longer λ.
- Hole diameter d — controls how strongly the lattice couples free-space light into SPPs (transmission amplitude) and how quickly that coupling re-radiates the energy back out (resonance linewidth, drawn as peak width in the spectrum panel).
- Medium index nd — the dielectric on the exit side; raising it (air → water → glass) red-shifts every resonance, the basis of EOT refractive-index biosensors.
- Metal — sets the plasma wavelength λp, i.e. how negative εm is at a given λ, which shifts and reshapes the resonance ladder.
- Probe wavelength λ — where on the spectrum you are reading the live transmission, driving the photon-stream colour and pass-through rate in the side panel, and compared against the classical Bethe limit.