Two coherent slits, but each is polarised at an angle φ from the other. As the polarisations become orthogonal the two paths stop interfering — the fringes fade, leaving only the diffraction envelope. That is Fresnel–Arago's third law, and it is the mechanism real which-path experiments use. Drag φ and watch the pattern, its measured profile, and the path/fringe balance respond together.
Green light (550 nm) through a double slit. The grey line marks the detector where the profile at right is measured.
D² + V² ≤ 1 has this same form.
Classical scalar wave optics, computed exactly: Young interference, single-slit
diffraction, and Fresnel–Arago polarisation coherence. The code sums complex field
amplitudes and displays |E|² — there are no photons, no detection events
and no collapse anywhere in it.
The fringe patterns are nonetheless identical to the single-photon quantum
predictions, because a single-photon amplitude obeys the same wave equation — which is
why polarising the slits is exactly how real which-path experiments are done. What the
quantum version adds is the measurement content: entanglement with a marker degree of
freedom, discrete detections, and the coincidence structure of a quantum eraser. None of
that is simulated here, so D is defined geometrically as |sin φ|
rather than derived from the distinguishability of quantum states.
Each slit's bright cone opens at ±10.6°, so the two cones only overlap beyond 67 µm past the barrier — yet fringes are visible long before that. The cone is only the bright core: a slit's diffraction pattern carries on outward in side lobes (4.7%, 1.7%, 0.8% … of the peak) and never truly ends. Each slit's light therefore reaches the other's cone immediately, through those tails.
Measured at the centre of the upper cone, for light coming from the lower slit:
| distance past barrier | arrives via | amplitude |
|---|---|---|
| 10 µm | side lobe #6 | 1.3% |
| 30 µm | side lobe #4 | 9.1% |
| 120 µm | side lobe #2 | 9.9% |
| 190 µm (detector) | central lobe | 35.2% |
Interference scales as the product 2·|E₁|·|E₂|, not as the
weaker beam's intensity — so even a 9% amplitude produces an ~18% brightness ripple.
Faint, but visible. Past 67 µm the central lobes finally overlap, the ratio jumps
to 35%, and the fringes sharpen markedly. That change of contrast across the image is
the two regimes meeting.