Inside a Photonic Link: Modulators, Detectors and Constellations

Topics We'll Cover

The hardware of a photonic link module (arXiv:2608.21536, Kundu et al.), from the bits the host sends to the bits it gets back. FOptInf 01 introduced the module; this deck explains each part of its signal chain, with the signal drawn as a constellation at every stage. Click a block to jump to its slide.

• Light Is a Carrier; a Photodiode Sees Only Power
• The Mach–Zehnder Modulator
• The Transfer Curve and Three Bias Points
• “Quadrature” Has Two Meanings
• The Textbook Coherent Transmitter
• Why Quadrature Bias Suits Unsigned Bits
• Holding the Bias Point
• Direct and Coherent Detection
• Constellations Through the Chain
• The DFT Alphabet
• Calibration: Rotation and Distortion
• From PAM5 and PAM3 to PAM4
• The Receiver: What a TIA Does
• The Noise Budget
• Skew: Four Lanes Summed Before Any Decision
• What a Simulator Needs From All This
• What to Take Away

Labels used on every slide: paper stated in arXiv:2608.21536; patent stated in a patent the paper cites; textbook standard physics or a published paper; derived arithmetic shown on the slide; inference this deck's reading, not stated by any source; illustrative a parameter chosen for the model, not measured. Numbers come from analysis/link_hw/results.md.

Light Is a Carrier; a Photodiode Sees Only Power

Light at 1550 nm is a carrier at about 193 THz. Its field E(t) = A·cos(2πft + φ) has an amplitude A, which can be negative, and a phase φ, exactly like an RF carrier. No electronics can follow 193 THz: a photodiode's current is proportional to the power |E|², averaged over many cycles. textbook

• To send data, change the field's amplitude or phase: modulation (slides 02–05).
• To read back a sign or a phase, compare against a reference wave: coherent detection (slide 08). The same problem in free-space optics: FOptInf 01, slide 10.

The Mach–Zehnder Modulator

Phase is easy to change in silicon; amplitude is not. A voltage across a pn junction in the waveguide moves free carriers and shifts the refractive index (plasma dispersion: tens of GHz, but weak); a heater does the same through the thermo-optic effect (strong, but microseconds). A phase change alone is invisible to a photodiode. An interferometer makes it visible: split the light into two arms, shift their phases, and recombine, so the fields add. textbook

• V_π is the drive that moves Δφ by π, from full power to none. Silicon depletion modulators have V_π·L of a few V·cm (one design: 3.1 V·cm at 2 V reverse bias, Félix Rosa et al., Adv. Radio Sci. 15, 2017), so a mm-scale modulator needs several volts: hence a driver amplifier. textbook
• The module: four MZMs from the foundry's process design kit, fed by linear “Direct-Drive MZM Drivers”, with thermo-optic phase shifters for phase control. paper

The Transfer Curve and Three Bias Points

The power transfer curve is a raised cosine. As with a transistor, you choose a DC operating point (the bias, set by a slow phase shifter inside the arms) and the data swings either side of it. Three bias points matter. textbook

Source: results.md, section “Drive ±0.22 Vπ”

At ±0.22 V_π the field step is 0.677 at null against 0.479 at quadrature (of the maximum field): the field is steepest at null, the power at quadrature.

“Quadrature” Has Two Meanings

• The module's calibration patent means the first: its first calibration step is “setting a quadrature of the modulators (transmitters)”, so that “the quadrature point of all the modulators in the input channels can be matched” (WO2025168828A1, a patent cited by the paper). patent
• The module's receivers use the second idea in a simpler way: each detector reads one projection, chosen by its LO phase (slide 08), rather than both I and Q at once.

The Textbook Coherent Transmitter

Every coherent long-haul transceiver writes its data with an IQ modulator: two MZMs, each biased at null so it is a signed, carrier-free modulator, combined 90° apart so the output is one complex field E = I + jQ. textbook (Seimetz, High-Order Modulation for Optical Fiber Transmission, 2009; Kikuchi, J. Lightwave Technol. 34, 2016)

• Why null, for coherent formats: the field is signed, so symbols sit symmetrically round the origin; no laser power or receiver range is spent on a carrier; and for a small drive the field slope is steepest at null (slide 03).
• The photonic link module does not do this. Its inputs are unsigned bits on single MZMs at quadrature (slide 06), and the complex values appear only after the optical Fourier transform (slide 10).

Why Quadrature Bias Suits Unsigned Bits

At quadrature each lane's field is E₀ + d·x, with x a bit (0 or 1): a constant carrier E₀ (the '0' level) plus a data step d. The optical Fourier transform is linear, and the DFT of a constant lands only in bin k = 0. derived

The patent's word is quadrature (slide 04) patent; the reasons in the right-hand box are this deck's, not the patent's.

Holding the Bias Point

Bias points drift with temperature and ageing, so a slow loop holds them. What the loop can measure depends on where it is holding. textbook

Source: results.md, section “3. Holding the bias”

• The module's patent uses the same idea with a different signal: a “slowly varying” perturbation on a separate monitor channel, compared with its expected time average. A discrepancy in the amplitude means amplitude drift; a discrepancy “in the derivative or gradient” means phase drift (WO2025168828A1). patent
• The paper: the microcontroller “reacts to slow-speed time averaged sensor data from PDs using ADCs built in the microcontroller and sets PS using DACs in the microcontroller”. paper

Direct and Coherent Detection

Direct detection is one photodiode measuring power: enough for intensity data, blind to sign and phase. Coherent detection mixes the signal E_s with a local oscillator (LO) of the same frequency in a 2×2 coupler and subtracts the two photodiode currents (a balanced pair): textbook

The module: one of the laser's seven channels becomes the LO, through a slow MZI “to control both phase and intensity”, split four ways with a phase shifter each; each copy is mixed with one transform output, and “All coherent homodyne detection techniques used in the PIC use balanced PDs.” paper Self-homodyne, in the terms above. derived

Constellations Through the Chain

One input vector, followed from the FPGA's transmitter to the decoded answer, with the signal drawn as a constellation at every stage. Choose any of the 16 inputs; tick the box to see the illustrative uncalibrated phases. The stages follow the paper and patents; the numbers are illustrative (parameters in section 1 of results.md). illustrative

The worked example, input [1, 0, 1, 1]:

Source: results.md, section “4. Constellations through the chain”

• Each lane leaves its MZM as one of two positive fields (stage 2), so the input constellation is two points on the real axis. The transform turns four of those into sums and differences: two real five-level outputs and two 3×3 complex grids that mirror each other (stage 4). Each homodyne detector projects one output onto its LO axis (three real, one imaginary), so the constellation collapses to levels (stage 5).
• The carrier costs output 1 dynamic range: its first 130.0 µA of current carries no data. A level step is 36.6 µA.

The DFT Alphabet

The transform computes a 4-point DFT, X_k = Σ_n x_n·(−j)^kn, whose only weights are 1, −j, −1 and j. With bits for inputs, the outputs take a small, fixed set of values: the module's output alphabet. derived

Source: results.md, section “5. The DFT alphabet”

• The outputs are signed although the inputs are not, so the receivers must be coherent: an intensity detector would lose the sign.
• Why four detectors suffice. For real inputs X₃ = X₁* (conjugate symmetry), and X₀, X₂ are real. Reading Re X₀, Re X₁, Re X₂ and Im X₃ recovers all four outputs: three detectors read real parts and one reads an imaginary part, the receiver arrangement a patent cited by the paper describes (WO2025168827A1). patent derived
• The same patent states the PAM5 (outputs 1 and 3) and 3-level-per-axis (outputs 2 and 4) alphabet patent; the enumeration above checks it.

Calibration: Rotation and Distortion

Every optical path has its own phase, set by fabrication and temperature. Phase errors before the transform and after it do different damage, which is why calibration fixes them in a fixed order. Toggle either kind and step through the calibration.

Source: results.md, section “7. Calibration”

• Order matters: each step fixes a reference the next one needs, like calibrating a scope before measuring with it. The animation idealises each step as removing its own errors exactly.
• The pass criterion is a decision margin: the claimed threshold is “less than a half of the difference between the 0 and 1 binary signal state”, exactly the condition for a correct level decision. patent
• In service, reference vectors are inserted as marker frames; a frame that fails is re-applied once, and a second failure pauses the stream for recalibration. patent Thermo-optic shifters settle in microseconds (Harris et al., arXiv:1410.3616), textbook, so the loop tracks slow thermal drift. inference

From PAM5 and PAM3 to PAM4

“The transmitted data to the module is restricted to binary (NRZ) levels. This is to compress the photonic computed result to PAM4”, and the results return on the QSFP56 port's receive lanes. paper But outputs 1 and 3 have five levels (slide 10), and PAM4 has four.

Source: results.md, section “6. Packing into PAM4”

16 distinct symbol patterns for 16 inputs; every input decodes back to itself. Parity alone settles every clipped case but 2; there the inverse DFT rules out the impossible candidate.

The Receiver: What a TIA Does

“The PDs in the PIC are packaged with Single Layer Capacitors (SLCs) and bonded with a TIA die.” paper A transimpedance amplifier (TIA) turns the balanced pair's difference current into a voltage. The SLCs give the photodiode bias an AC ground right at the diode, and a bare TIA die bonded beside the chip keeps the input capacitance and the bond-wire inductance small. inference

Source: results.md, section “9. The transimpedance limit”

The Noise Budget

Is there enough signal-to-noise? Three noise currents compete with the balanced pair's signal: the TIA's own noise (flat), shot noise (grows as √P_LO, like the signal) and the LO's intensity noise left after imperfect balance (grows as P_LO). A decision fails when noise crosses half a level step, so the figure of merit is Q = (step/2)/σ; Q ≈ 4.9 gives about 10⁻⁶ errors per decision. textbook

Source: results.md, section “8. Noise budget”

Source: results.md, section “Margins”

• The LO is split many ways. The laser feeds seven channels and the LO channel four detectors paper, so a laser of a few tens of mW leaves of the order of −5 dBm per detector pair. illustrative On a future stacked chip with many transform units the split is the limit: a simulator of that chip finds one 20 dBm laser feeds about 20 unit-wavelengths at a 6 dB margin (deck 05).
• The regime: at −5 dBm, TIA and shot noise are about equal. Best SNR 39.9 dB at 7.0 dBm LO; shot noise overtakes TIA noise above about −3.0 dBm. Below that, more LO buys SNR almost for free. That fits the patent setting the LO amplitude to maximum (slide 11) inference; photodiode saturation and residual RIN limit how far it can go.
• Output 1 is not noisier per step; its difficulty is range: the carrier offset plus four steps (about 7.6 steps from zero) must stay linear through the TIA. derived
• Bandwidth: the drivers and TIAs are built for up to 56 GBaud paper, four times the symbol rate, so the receiver's noise bandwidth can be several times the 7 GHz this signal needs. Unless something band-limits the noise, the margin shrinks:

Source: results.md, section “Noise bandwidth”

Skew: Four Lanes Summed Before Any Decision

In an ordinary four-lane link each lane has its own clock and data recovery, and lanes are deskewed digitally after decisions. Here the four lanes are added optically before any decision: near its edges a late lane still carries its previous bit, so the sum is partly the wrong answer and the eye closes. derived

Source: results.md, section “10. Skew”

At 14 GBaud a tenth of a unit interval is 7 ps; at 56 GBaud, which the module's drivers and TIAs support paper, it is 1.8 ps, which makes skew a first-order layout constraint for a faster chip. derived

What a Simulator Needs From All This

Each hardware effect on the previous slides becomes a term in a system model. A simulator of a link like this one is a chain of small, testable models, each with parameters that can be measured on the bench.

Every model on these slides is in analysis/link_hw/link_hw.py, first-order and labelled; a real simulator would add each block's measured transfer function. The system-level questions a link like this raises are the subject of the Compute in Transit series.

What to Take Away

• A photodiode sees power, not field. Sign and phase need an interferometer to write them (the MZM) and a reference to read them (the LO).
• Bias points are a design choice. Quadrature makes power linear and keeps both levels positive; null makes the field linear and signed. For unsigned bits into a DFT, quadrature's carrier costs only an offset on output 1.
• The DFT of bits has a tiny alphabet: five real levels on two outputs, 3×3 grids on the other two, mirror images. Three real readings and one imaginary recover everything, and saturation packs it into PAM4.
• Calibration is geometry: output errors rotate the constellation, input errors distort it, and the patent's order fixes the reference, then the receivers, then the transmitters, to within half a level step.
• The analogue limits are the receiver's: a linear TIA without automatic gain surprises, enough LO to beat the TIA's noise, a noise bandwidth matched to the symbol rate, and lane skew that would matter far more at 56 GBaud.

Where the module fits: FOptInf 01, the case study and its slab lens; what it could compute on in LLM training and inference traffic: Compute in Transit 01.