Each metal nanorod is a point dipole with a resonant Lorentzian polarizability. Only the central feed rod is driven directly; the reflector and director rods are passive and radiate only because their neighbours' near field induces a dipole moment in them — the discrete-dipole / coupled-dipole approximation used for plasmonic arrays:
p_i = α_i · ( E_inc,i + Σ_j≠i G(r_ij) p_j )
α_i = 1 / (δ_i + iΓ)
G(r) = e^(ikr)·( k²/r + ik/r² − 1/r³ )
This page solves exactly the same linear system as the 3D version, but instead of rendering rods in space it puts the solved complex numbers themselves on screen: each p_i is a rotating vector (an Argand / phasor diagram) whose length is the dipole's amplitude and whose angle is its phase relative to the feed's drive. Drag the ring around the polar radiation plot (or use the angle slider) to pick a look direction φ; the scope panel below multiplies every rod's phasor by its extra path-length phase e^(ik·x_i·cosφ) and draws the resulting sinusoids — bold total, faint per-rod — so you can watch them add up along the forward director axis and cancel along the reflector axis, which is the front-to-back ratio made visible as literal wave cancellation rather than a lobe shape.
- Rod spacing d/λ — sets the phase delay between rods; too small and near-field coupling dominates, too large and grating lobes appear.
- Directors — leading (shorter) parasitic rods in front of the feed; more directors narrow and strengthen the forward lobe.
- δR / δD — how far reflector/directors are detuned from resonance; "Snap to optimal" sets the classic Yagi-Uda values.
- Observation angle φ — where the scope panel is "listening"; drag it to 0° (forward) or 180° (back) and watch the waveforms go from reinforcing to cancelling.
Real-world relevance: single-molecule and quantum-dot optical antennas built this way (Curto et al. 2010; Novotny & van Hulst) redirect a nanoemitter's normally isotropic light into a narrow forward beam.