Many wavelengths, one mesh

Part II’s chip lets W wavelengths share each unit’s mesh: rings put a different colour on each modulator, the mesh transforms them all in the same pass, and demux filters separate them again at the receivers. Until v0.4 the simulator modelled that only as a loss, a shared laser, extra heaters and extra area; nothing in the transform depended on the colour. In a real mesh every phase is an optical path length divided by a wavelength, so one set of heater settings is exactly right for one colour only. Every other channel sees a slightly different 4-point transform. In a link that hardly matters; in compute it is an arithmetic error.

Channels sit on a uniform grid around λ₀ = 1,310 nm illustrative (spacing 200 GHz illustrative by default; experiment 17 sweeps from one to 32 channels on four frequency grids and a coarse 20 nm grid). Each nominal phase of the mesh, the couplers’ internal π/2 and the −π/2 twiddle, is part designed into the waveguide and part set by a heater (0.5 illustrative). A designed phase scales with n_g/n_eff = 1.7 illustrative, a heater-set phase as 1/λ (thermo-optic dispersion ignored), a combined slope of 1.35 (δ is the channel’s offset from λ₀ over λ₀). At δ = 0 the model is v0.3’s mesh exactly; the site’s port reproduces the simulator’s per-channel errors, and its frame tests check that.

One set of heaters serves every channel. The simulator calibrates it at the centre wavelength or by least squares over all channels (the default, least_squares illustrative), and compares the alternative of a separate mesh per wavelength. Exact mode is judged through v0.3’s stacked receiver at 112 GBd: a reference receiver gives the ideal transform 10 dB of margin, and a channel passes while it keeps 6 dB. Approximate mode reruns experiment 16’s FFT with each channel’s transform. A plan must also fit one free spectral range of the modulator and demux rings, $\text{FSR} = \lambda_0^2 / (n_g\, 2\pi R)$ with R = 5 um illustrative.

The error is small, deterministic and cannot be calibrated away. A plan of 16 channels at 200 GHz spans 18.32 nm (edge δ = 0.006555) and leave the worst channel 0.01558 off the DFT, normalised (centre calibration 0.01554). Least squares gains nothing: its largest heater correction is 3.442 × 10⁻⁵ rad, because on a grid centred on λ₀ the first-order errors cancel in the mean and the centre setting is already optimal. The error is a tilt across the band.

Exact mode barely notices; the rings bind first. That plan costs 0.04545 dB of margin, and the worst channel keeps the design margin for channels within ±81.72 nm of λ₀ (largest swept plan inside the O-band: 80 nm). The ring FSR is far narrower: 14.01 nm at 5 um, so at most 8 of the swept channel counts fit at 200 GHz (a 9.159 nm plan); 3 µm rings would give 23.34 nm. One laser still feeds U × W = 20 at 4 λ and 6 dB, as in v0.3 (20).

Approximate mode is where it costs. Per stage, the wavelength error passes v0.3’s random phase error of 0.01 rad once the edge channel is ±5.525 nm from λ₀ (10.65 channels at 200 GHz). Over a whole chained FFT the wavelength error is coherent, the same at every stage, so it costs more bits than the random error from 8 channels. At the design SNR with 8 bits converters the worst of 32 channels keeps 2.558 bits at S = 6 against 3.198 bits for one wavelength; 4 λ costs little (2.731 bits and 3.19 bits against 2.74 bits and 3.198 bits). Precision-limited (60 dB, 16 bits converters) the worst of 32 keeps 2.901 bits against 5.055 bits without the wavelength term.

Fabrication and the LO path matter more than dispersion.

A per-channel output trim helps, but only where a receiver reads the mesh. Per-channel LOs after the demux filters can set one phase per output port per channel (off by default, false illustrative). It cuts the worst error at 16 channels from 0.01558 to 0.01102, and at 32 from 0.03227 to 0.02282. With S = 1 every stage ends at a receiver, so precision-limited bits at 32 channels rise from 2.493 bits to 3.73 bits; with S = 6 the trim corrects only the last stage of each chained block, not the stages inside it, and the gain shrinks (2.901 bits to 3.09 bits).

So: sharing one mesh between wavelengths looks fine for links and for exact, decided arithmetic, as long as the plan fits the ring FSR. For analogue compute it holds only over a few nanometres, unless the phases are made achromatic or each wavelength gets its own mesh, at about W times the area and heater power. This does not change Part II’s break-even picture (chapter 13), which is set by exact mode; it narrows how far approximate mode (chapter 17) can lean on wavelengths for throughput.

Every new parameter is illustrative until a source is opened. Measured data would settle:

• the mesh waveguides’ real n_g/n_eff and how each nominal phase splits between the design and the heater (the worst error at 16 × 200 GHz runs from 0.01154 to 0.01846 over the swept n_g/n_eff);
• whether the mesh’s couplers are directional couplers, whose drift would dominate, or MMIs;
• the ring radius and group index of the O-band modulator and demux rings, which set the FSR that binds first;
• whether per-channel LO trim is in the architecture, or the signal and LO paths are matched to a fraction of a micrometre.

Not modelled: ring spectra beyond the FSR check, thermo-optic dispersion, polarisation and crosstalk between channels. See the method page for every parameter with its tag and swept range.