Extraordinary Optical Transmission — Nanohole Array

Array & Material

Hole period P 600 nm

Hole diameter d 220 nm

Medium index n_d 1.00

Metal film

Probe wavelength λ 700 nm

Transmission Spectrum

Live Readouts

T(λ) — measured

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Bethe diffraction limit

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Enhancement over Bethe limit

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Nearest SPP mode λ(1,0)

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How it works

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) ]

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 — 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).
Medium index n_d — 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 λ_p, i.e. how negative ε_m 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 and comparing it against the classical Bethe limit.

Hole glow ∝ local transmission Metal film

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