Each channel carries frequency-bin-encoded photons at νi = ν₀ + iΔν. All channels are combined into one fiber (wavelength-division multiplexing), then a diffraction grating at the receiver separates them again by angle — the demultiplexer:
grating equation: sinθ = λ/d (normal incidence, order m = 1)
wavelength: λ = c/ν
resolving power: R = λ/Δλ = mN (N = illuminated grooves)
crosstalk: X ≈ exp(−Δθ² / 2σ²)
- Channels — how many frequency bins share the fiber; more channels need either wider spacing or a finer grating to stay separable.
- Channel spacing Δν — the frequency gap between neighboring channels; larger spacing gives larger angular separation Δθ at the grating.
- Groove density — sets both the dispersion (how much angle per unit wavelength) and, through the illuminated groove count, the angular beam width σ that each channel arrives with at the detector array — more grooves illuminated means higher resolving power R = mN, so σ shrinks as density rises.
- Crosstalk — modeled as the Gaussian overlap between a channel's diffracted beam and its neighbor's detector; when Δθ is small relative to σ, a photon can land in the wrong detector — visible below as a particle veering into an off-color detector. The inset spectrum panel plots each channel's Gaussian beam profile over angle so you can see the overlap directly, not just read it as a percentage.
Real quantum networks use exactly this frequency-multiplexing idea — dense wavelength-division multiplexing (DWDM) grids in the telecom C-band (~193 THz) let many entangled-photon or single-photon channels share one fiber between quantum repeater nodes, with arrayed-waveguide gratings playing the role of the grating here. This 2D view is the same top-down schematic the 3D version's camera looks down on — every source, the fiber, the grating and the detector arc all sit in one plane; drag to pan and scroll/pinch to zoom instead of orbiting.