The dolmen antenna (one straight "bright" rod flanked by two parallel "dark" rods) is the textbook plasmonic realization of Fano interference. The bright rod couples directly to the incident field and radiates strongly (broad linewidth γ₁); the dark rods form a quadrupole-like mode that barely radiates on its own (narrow linewidth γ₂) but couples to the bright rod at strength g through their shared near field. Driven classical coupled-oscillator equations for complex amplitudes a₁ (bright), a₂ (dark) at drive detuning ω̃ from the bright resonance:
(ω̃ + iγ₁) a₁ − g·a₂ = E₀
(ω̃ − δ + iγ₂) a₂ − g·a₁ = 0
⇒ a₁ = E₀ / [ (ω̃ + iγ₁) − g² / (ω̃ − δ + iγ₂) ]
a₂ = g·a₁ / (ω̃ − δ + iγ₂)
Because the dark mode is only reached indirectly, its response has a much narrower, phase-shifted resonance than the bright mode. Their interference in a₁ produces the classic asymmetric Fano lineshape: a resonant peak sitting right next to a sharp transparency dip at ω̃ = δ (here δ = 0), where the two radiation pathways cancel almost completely — exactly the induced-transparency behaviour used in plasmonic biosensors and slow-light metamaterials.
- Drive detuning — sweeps the incident light's frequency across the resonance; the 3D dipoles pulse with the resulting amplitude and relative phase.
- Coupling g — set by the bright–dark gap distance; larger g widens and deepens the interference dip.
- Dark-mode damping γ₂ — how "dark" (subradiant) the quadrupole mode is; smaller γ₂ gives a sharper, deeper dip — the hallmark of a high-Q Fano resonance.
- Bright-mode damping γ₁ — the antenna's own radiative linewidth, which sets the overall width of the background resonance the dip sits inside.
The glowing points between the rods are the near-field "hot spots" — their brightness tracks the product of the two mode amplitudes, the same field enhancement exploited in surface-enhanced spectroscopy.