SeeFields invisible electromagnetic world
Drag transmitters, phone or wallShift+drag to lift or lowerDrag floor to orbitCtrl+drag or right button to panScroll to zoomKeys R P W select · arrows move · Shift+↑↓ lift · 1–9 and 0 experiments
d = – m λ = –
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Frequency
900 MHz
2.4 GHz
5 GHz
28 GHz
Transmit power 20 dBm
Wall
Phone tilt 0°
Router height 0.64 m
Phone height 1.10 m
Zoom to antenna
Keyboard
R P W select router (R again: second router), phone, wall
Enter cycle selection; Esc clears it
← → ↑ ↓ move the selected object 5 cm, relative to the view
Shift+↑ ↓ lift or lower it 5 cm
Ctrl+arrows orbit the camera
− = zoom out, zoom in
1 … 9, 0 the experiments (0 is the tenth)
Z Y M zoom to antenna, why this number, math
Engineering model
Wavefronts: conceptual
What is and isn't modelled
Free-space path loss between two antennas. Router: a vertical half-wave dipole, 2.15 dBi peak, with its doughnut pattern G(θ) = 2.15 dBi + 20·log₁₀[cos(π/2·cosθ)/sinθ] applied to every ray when "Dipole pattern" is on (analytical). Phone: 0 dBi, isotropic.
Wall penetration: one slab at normal incidence, ITU-R P.2040-3 material constants, interface plus bulk loss. No multiple internal reflections.
Polarisation: router vertical, phone linear; mismatch loss cos²Δθ, saturating at 25 dB cross-polar discrimination.
Second transmitter: same frequency, phase-locked to the first, so the two waves add coherently. That is how a reflection or an antenna array behaves, not two independent routers. Floor shows the fringe pattern; when it would be finer than the screen can draw it shows average power instead.
Room reflections: the four room walls are 20 cm concrete. One bounce per wall by the image method, with the Fresnel coefficient Γ⊥ at the actual incidence angle, summed coherently with the direct path. The mottled floor is multipath fading.
Wall-edge diffraction: the wall is a semi-transparent screen with one knife edge, the nearest of its two vertical edges and its top edge. The direct ray is multiplied by W = D(ν) + T·(1 − D(ν)), where D(ν) = (1+j)/2·∫ᵥ^∞ e^(−jπt²/2) dt is the Fresnel-integral knife-edge factor (ν = ±√2·h/r₁, h the edge's distance from the line of sight, + in the shadow) and T the slab's transmission with its phase delay. Opaque wall: the ITU-R P.526 single knife edge. No wall: 1. Continuous across the shadow boundary, so the floor shows the edge's Fresnel ripples. Fresnel integrals by Heald's approximation, ±0.5 dB. Engineering model: one edge, no corner or double-edge terms, no diffraction on bounced rays.
Floor reflection: the floor is 20 cm concrete (P.2040 constants). One bounce by the image method, the image dipole co-directed, with the Fresnel coefficient Γ∥ = (εc·cosθ − √(εc − sin²θ))/(εc·cosθ + √(εc − sin²θ)) at the actual angle from the floor normal: +0.39 at normal incidence, zero at the Brewster angle tanθ_B = √ε′ (66° at 2.4 GHz), −1 at grazing. Summed coherently with the direct path, so the floor and the slice show the two-ray fading and the height lobes. A wall on the bounced path attenuates it (T), no diffraction. Analytical coefficient, engineering model (flat floor, no roughness, no surface wave).
Fresnel zone: the ellipsoid is the first Fresnel zone of the direct path, r = √(λ·d₁·d₂/d). Amber when the wall edge or the floor cuts into it. The wall case is the diffraction step above; the floor case is the floor reflection above when it is on, otherwise only a flag. Analytical geometry, exact edge distances.
Not modelled: the ceiling, double bounces (wall + floor, wall + wall), the wall's far edge, the phone's antenna pattern.
Inside one wavelength of the transmitter the far-field formula is invalid; the readout says so. The two rings on the floor mark λ/2π (reactive near field of a small antenna) and 1 λ (where this model starts applying the 1/r law). Zoom in to see them at true scale.
E / B vectors: a vertically polarised wave sampled along the direct path. E (amber) and B (teal) are in phase, perpendicular to each other and to the direction of travel k. Arrow length shows the instantaneous phase, not field strength; the 1/r decay is what the floor colour shows. Same slowed time as the wavefronts. Conceptual.
Floor colour is the same engineering model evaluated at every floor point using horizontal distance only, i.e. a map at antenna height. The vertical slice evaluates it with true 3D distance on the plane through the antenna tip and the phone. Rings are true-to-scale wavefront spacing (λ) but a conceptual animation.
3D wavefronts: spherical shells leaving the antenna tip, spaced 1 λ, same slowed time as the floor rings, fading by 2.5 m. The sphere is the phase front (a dipole's far-field phase fronts are spherical); with the pattern on, shell brightness follows the dipole's doughnut and vanishes along the axis. Conceptual animation, analytical shape. Hidden, like the rings, when λ is under a few pixels.
Heights: the readout uses the true 3D distance between the antenna tip and the phone, so lifting either changes the number. Shift+drag or the sliders.
Move the transmitter
Drag the router. Watch the phone.