Each emission angle launches a full ring of rays (true 3-D), traced with the Monte-Carlo physics (Snell + Fresnel/AR + TIR at the silicon lens, specular metals, porous ground + qubit absorber), then projected orthographically onto the x–z plane. Geometry constants come directly from the reference Monte-Carlo simulation.
The silicon lens is standard geometric ray optics — no wave/interference
effects. At every silicon surface (the ellipsoidal dome and the flat) the tracer applies
Snell refraction with nSi = √εr ≈ 3.42,
total internal reflection when sin2θt ≥ 1, and a
Fresnel reflect/transmit split (or a fixed 3 % AR residual). Metals (dish,
lid, cavity walls) are specular mirrors losing 1−Rmat per bounce. The chip
plane carries the central qubit absorber (red) inside a porous ground plane
(reflect Rgp, transmit the rest).
Frequency enters only twice, both lumped: (1) the diffraction blur
σθ = 0.437 λ/Rcurv on each launched ray, and
(2) the absorber radius Rant = λ/(2π√εeff).
Everything else (the Si index, AR residual, wall reflectivity) is frequency-independent.
Why this version traces in 3-D. An earlier 2-D version drew only the meridional slice, in which a single rim ray crosses the focus and leaves — so the centre only lit up for rays that start near the axis. That is a slice artefact. The real system is axisymmetric: a ring of light at polar angle θ sends rays toward the focal point on the axis from all azimuths. Here each θ launches a full ring (true 3-D trace), and the 3-D paths are projected orthographically onto the x–z plane (the y-coordinate is dropped). Rays whose azimuth is near 90°/270° move in the y–z plane, so they project right onto the central axis — and the whole ring converges on the focal point. That is why, even with the slider at the rim (θ near 90°), the centre still concentrates: it reproduces the 3-D Monte-Carlo, where every emission annulus focuses onto the central qubit (validated: outer-annulus 60–89° collects ~21 % on the central absorber vs ~0.01 % if it were unfocused).
First pass vs recycling. The first pass is actually a broad spot (r50 ≈ 2 mm, ~ the whole lens flat); the tight central concentration builds up over many recycling passes (the sealed cat’s-eye keeps refocusing un-absorbed light back to the centre). Turn Rmat down and the rays fade into the walls before that can happen — which is why wall reflectivity is the dominant lever for collection.
What does “show secondary reflections (partial / leak)” do? At every surface that physically splits a ray into two paths, the tracer can either follow only the dominant outgoing path (default) or fork off the partial side-path as a separate, lower-intensity ray. Ticking the box enables the side-paths. There are two such surfaces in this model:
RF of the amplitude reflects and the rest transmits. With the
AR coating on (default), this residual is forced to 3 % per crossing;
without it, the full Fresnel formula is used. Off — only the transmitted ray
continues. On — the calculator additionally emits the partially-reflected ray
at intensity RF · iincoming and traces it
separately, so you can see ghost reflections bouncing back into the silicon and the
cavity.Rgp of the rays back toward the lens
and transmits the rest into the metal cavity behind it. Off — only the reflected
path is shown. On — the transmitted "leak" path is also traced at intensity
(1 − Rgp) · iincoming, switching
medium as it crosses (vacuum ↔ silicon).In both cases the physics is identical whether the box is ticked or not — the tracer's bookkeeping of energy on the primary path already accounts for the lost amplitude. The toggle is purely a visualisation switch: it makes the partially-reflected and leaked sub-rays visible so you can see where the energy goes, at the cost of a denser canvas. Secondary paths are capped at two levels of forking so the recursion doesn't run away.