Microring Weight Banks

Do the floor-plan arithmetic for the mesh ONN. A 64×64 weight matrix needs roughly 4,000 MZIs at a few hundred micrometres each — square centimetres of silicon for one layer. Now recall the microring resonator: a circle of waveguide ten micrometres across whose transmission at its resonant wavelength can be tuned continuously between "almost everything" and "almost nothing". A tunable transmission is a multiplication. A device that multiplies one wavelength and ignores all others is precisely the weight element the wavelength crossbar left unnamed — and it is a hundred times smaller than an MZI. This lesson builds a layer of neurons out of rings: the broadcast-and-weight architecture, the most compact analog weighting scheme photonics has produced — and then pays its very real bills: tuning power, thermal drift, and the feedback loops that never sleep.

A ring as an analog weight

Near resonance, a single all-pass ring's through-port transmission is a Lorentzian notch. Writing \delta for the detuning from resonance and \kappa for the linewidth (FWHM), a critically coupled ring gives

T(\delta) \;=\; 1 - \frac{1}{1 + (2\delta/\kappa)^2},

which runs from T = 0 on resonance to T \to 1 far away. The weight is set by where you park the resonance: nudge the ring (thermally, or with a junction) so that the signal wavelength sits at the chosen detuning, and the ring transmits the chosen fraction. Put several rings along one bus waveguide, each resonant near a different WDM channel, and you have a weight bank: one ring per channel, each weighting its own colour, all sharing a single waveguide.

Play with the slider and notice two things. First, tuning ring 2 changes channel 2's transmission smoothly — a genuine analog weight, resolution limited only by how finely you can steer the resonance. Second, push the detuning far enough and ring 2's notch starts encroaching on its neighbour's channel: inter-channel crosstalk is a geometric fact of Lorentzian tails, and it is what limits how densely channels can be packed (a rule of thumb: spacing of a few linewidths keeps the tails below the precision floor).

One more piece completes the weight: sign. A ring has a second output — the drop port — and what leaves it is exactly what the through port lost. Send through and drop to a balanced pair of photodetectors wired in opposition and the output current is proportional to T_{\text{thru}} - T_{\text{drop}} \in [-1, +1]: a full signed weight from one ring, with the subtraction done by Kirchhoff's current law.

Broadcast-and-weight: a photonic neuron

The architecture that assembles this into a network was proposed by Tait and colleagues at Princeton. All N neuron outputs, each on its own wavelength, are multiplexed onto one shared bus — the broadcast: every neuron's signal physically reaches every other neuron, an all-to-all fan-out that costs one waveguide. Each receiving neuron taps the bus through its own bank of N rings — the weight — and its balanced detector pair sums the weighted channels into one current: the neuron's net input \sum_j w_j x_j, computed by filtering and photodetection. That current then drives the neuron's own light source or modulator (the nonlinearity — next lesson's subject), which launches the result back onto the bus at the neuron's wavelength. An N-neuron recurrent layer thus needs N^2 rings but only one waveguide of interconnect — compare the wiring nightmare of an electronic all-to-all fabric.

	MZI mesh (coherent)	Ring weight bank (WDM)
Weight element size	~100–300 µm per MZI	~10 µm per ring
Signed weights	Native (phase)	Balanced through − drop detection
Needs phase coherence	Yes — one laser, stable paths	No — computes in power
Parallelism axis	Space (N waveguides)	Colour (N wavelengths, 1 waveguide)
Matrix type	Unitary natively; arbitrary via SVD	Arbitrary rows directly
Chief overhead	Calibrating 2 phases per MZI	Tuning and locking every ring

The bill: tuning, drift, locking

Now the honest accounting. A fabricated ring never resonates exactly where the mask said — nanometre-scale thickness variation shifts resonances by whole linewidths — so every ring needs an actuator, almost always a resistive heater. Three costs follow.

Static power. Parking a ring costs continuous heater power — typically a few milliwatts. A 32-neuron all-to-all layer has 32^2 = 1{,}024 rings; at 3 mW each that is 3 W of heat before a single MAC is performed. Amortise it at a 10 GHz symbol rate and the tuning alone contributes 3\,\mathrm{mW} / 10\,\mathrm{GHz} = 0.3\ \mathrm{pJ} per symbol per ring — already larger than the per-MAC figures photonic papers advertise. (This is why undercut thermal isolation and non-volatile phase-change weights are active research: lesson 7 will put these numbers in the full ledger.)

Drift. Silicon's refractive index moves with temperature; a ring resonance drifts by roughly 10 GHz per kelvin. With linewidths of tens of gigahertz, a one-degree ambient swing re-writes your entire weight matrix. So, third cost: locking. Each ring carries a monitor (a photodiode tap, or the balanced pair itself), and a feedback loop continuously dithers the heater to hold the resonance at its commanded offset. The weights of a broadcast-and-weight processor are not "set and forget" — they are actively servoed, forever, and the control electronics is part of the machine.

Broadcast-and-weight was born in a neuromorphic lab, and the resemblance to biology is not decoration. A cortical neuron fans out to thousands of others over shared bundles; the WDM bus does the same with wavelength standing in for axonal identity. The Princeton group pushed the analogy to spiking: an excitable semiconductor laser fires an optical pulse when its summed, weighted input crosses threshold — dynamics mathematically close to a biological neuron's, but about a hundred million times faster (nanosecond spikes versus millisecond ones). The pitch is not "photonics beats GPUs at ResNets"; it is that some computations — radio-frequency front-ends, control loops, physics experiments — need microsecond-scale intelligence that clocked digital pipelines cannot deliver, and a fast analog substrate can. The spiking side of this story is picked up in photonic spiking neurons.

It is tempting to read "high-Q resonance" as pure win: sharper resonance, finer wavelength selectivity, denser channels. But a weight parked on the slope of a sharp Lorentzian inherits that slope as a noise amplifier. The steeper \mathrm{d}T/\mathrm{d}f, the more a fixed jitter in resonance position — thermal fluctuation, heater-driver noise, a neighbour's heater bleeding across (thermal crosstalk means the weights are coupled: setting w_5 nudges w_4 and w_6) — converts into transmission error, i.e. weight error. A sharper ring is a better filter and a worse-behaved weight. Real designs therefore choose moderate Q deliberately, and quote weight precision under closed-loop lock: measured broadcast-and-weight banks achieve roughly 5–9 bits of weight accuracy — a number to remember when lesson 5 asks how many bits the whole analog chain can honestly claim.

Where this goes next

Mesh or ring bank, coherent or WDM — every architecture so far computes the linear part of a layer, and then hands an electrical current to "the nonlinearity" as if that were a detail. It is not a detail. It is the oldest open wound in optical computing, and the next lesson opens it properly: why photons refuse to gate photons, and what every workaround — O/E/O stages, saturable absorbers, electro-optic activations — really costs.