Modulators and Detectors

Topics We'll Cover

• What a Modulator Has to Do
• The Plasma-Dispersion Effect
• Depletion, Injection and MOS Capacitors
• The Mach–Zehnder Modulator
• Travelling-Wave Electrodes and Driver Energy
• Ring Modulators
• Interactive: Ring and Mach–Zehnder Modulators
• Keeping a Ring on Resonance
• Beyond Plasma Dispersion
• Germanium Photodiodes
• Bandwidth, Dark Current and Avalanche Gain
• From Photocurrent to Bits
• Direct and Coherent Detection
• What to Take Away

What a Modulator Has to Do

• Extinction ratio and OMA. The receiver decides between levels, so what matters is the difference between them, the optical modulation amplitude (OMA). A modulator can give more OMA by swinging deeper, at the price of insertion loss on the high level. The interactive on slide 07 shows the trade.
• PAM4 sends two bits per symbol, so a lane runs at half the symbol rate of NRZ: 400GBASE-DR4 carries 100 Gb/s per lane as PAM4 at 53.125 GBd (IEEE 802.3bs). For the same OMA each of its three eyes is a third as tall, which costs 10·log₁₀3 ≈ 4.8 dB of optical power at the same noise.
• TDECQ. IEEE 802.3bs grades PAM4 transmitters by TDECQ, the optical power penalty a transmitter's eye costs a reference receiver with a reference equaliser, rather than by extinction ratio alone.
• The rest of the specification: electro-optic bandwidth (tens of GHz), drive voltage the electronics can deliver (a CMOS driver's swing), energy per bit, footprint, optical bandwidth and temperature range. No silicon modulator wins on all of them, which is why there are two families (slides 04–06).

The Plasma-Dispersion Effect

Silicon's crystal is centrosymmetric, so it has no linear (Pockels) electro-optic effect, the effect lithium-niobate modulators use. The practical handle is free carriers: adding electrons or holes lowers the refractive index and adds absorption. Soref and Bennett derived the size of the effect from absorption data by a Kramers–Kronig analysis; about 10¹⁸ cm⁻³ of carriers changes the index by about 1.5×10⁻³ at 1.3 µm (IEEE JQE 23, 123, 1987). The empirical fit used at 1550 nm (concentrations in cm⁻³, α in cm⁻¹):

• Worked through the fit: 10¹⁸ cm⁻³ each of electrons and holes gives Δn ≈ −8.8×10⁻⁴ from electrons and −2.1×10⁻³ from holes, a total of −3.0×10⁻³, and Δα = 14.5 cm⁻¹, about 63 dB/cm of extra loss.
• Holes are the better bargain: more index change per unit of absorption, which is why junctions are placed and doped to sweep holes through the mode.
• The effect is weak. An index change of 10⁻³ needs about 775 µm of path for a π phase shift at 1550 nm (λ/(2Δn)), which is why silicon Mach–Zehnder modulators are millimetres long and rings use resonance to multiply a small shift.
• Nedeljkovic, Soref and Mashanovich refitted the 1.3 and 1.55 µm expressions and extended them to longer wavelengths (IEEE Photonics J. 3, 1171, 2011); the review by Reed et al. covers the modulator designs built on the effect (Nature Photon. 4, 518, 2010).

Depletion, Injection and MOS Capacitors

VπL figures: Rahim et al.'s comparison of silicon modulator technologies (Adv. Photonics 3, 024003, 2021). The MOS-capacitor modulator of Liu et al. (Intel) exceeded 1 GHz when the previous best silicon modulator reached about 20 MHz (Nature 427, 615, 2004).

• Depletion won for high-speed links because its speed does not depend on carrier lifetime. Its weakness is efficiency: it needs long devices or resonance.
• The doping that makes the junction also absorbs light (slide 02), so every design trades phase efficiency against optical loss in the phase shifter.

The Mach–Zehnder Modulator

The balanced form of the interferometer of deck 01, slide 08, with a depletion phase shifter in each arm. Driven push–pull (one arm advanced, the other retarded) and biased at quadrature, half-way down the cos² curve, where the response to drive is steepest and most linear.

• Vπ = VπL / L. At about 2 V·cm, a 2 mm phase shifter needs 10 V for a full π. CMOS drivers swing far less than that, so a practical silicon MZM uses a fraction of Vπ, accepting a lower extinction ratio and more insertion loss at the operating point. The interactive on slide 07 quantifies it.
• Broadband and tolerant. An MZM has no resonance, so its optical bandwidth spans the whole band and a few kelvin of drift do not matter: it suits CWDM and single-wavelength links and uncontrolled environments.
• Large and power-hungry. Millimetres of electrode need a travelling-wave design and a driver into a terminated line (slide 05).
• How fast silicon goes: Li et al. ran a silicon MZM at 100 Gb/s on–off keying with a 28 nm CMOS driver consuming 2.03 pJ/bit (Optica 7, 1514, 2020); Han et al. reached 110 GHz bandwidth with a slow-light all-silicon modulator 124 µm long and sent 112 Gb/s OOK (Sci. Adv. 9, eadi5339, 2023).

Travelling-Wave Electrodes and Driver Energy

• The driver usually dominates. Li et al.'s 100 Gb/s transmitter spent 2.03 pJ/bit in its CMOS driver (slide 04): orders of magnitude above the capacitive energy of a ring. The modulator choice decides what the driver must deliver (volts into a line, or a small swing into a capacitor).
• Miller's argument for optical interconnects to chips sets a target of about 10 fJ/bit for the optical output device itself (Proc. IEEE 97, 1166, 2009); the whole link budget is deck 03's subject.

Ring Modulators

Put a depletion junction in the ring of deck 01, slide 09: a small index change moves the whole resonance, and a sharp notch moves on or off the laser line. Resonance multiplies the weak plasma effect by the number of round trips the light makes.

• Photon lifetime. Light stays in a ring for about Q/ω, which limits how fast its output can change: the cavity's bandwidth is roughly f₀/Q, about 39 GHz for Q = 5,000 at 1550 nm. High Q gives a sharp notch and a large swing per volt, but slows the ring; designers pick Q for the data rate.
• Built-in WDM. Each ring only touches wavelengths near its resonance, so rings of slightly different sizes on one bus modulate different WDM channels with no separate multiplexer: the basis of dense optical I/O.
• The cost is control. A resonance that moves about 72 pm per kelvin (deck 01, slide 10) has to be locked to its laser (slide 08).

Interactive: Ring and Mach–Zehnder Modulators

Both modulators computed from their transfer functions: an all-pass ring, T = (a² − 2ra cosφ + r²)/(1 − 2ar cosφ + r²a²), and a push–pull MZM, T = cos²(Δφ/2). Choose the drive and watch extinction ratio, insertion loss and OMA trade against each other. The default ring loss, resonance shift per volt, capacitance and MZM arm loss are illustrative; the other defaults have sources: the ring's 72 pm/K is deck 01's solver result, the heater's 19.5 mW per π is Sun et al.'s measurement, and the MZM's 2 V·cm is Rahim et al.'s typical depletion value.

Limits: static transfer functions only (no electro-optic dynamics, chirp or noise); the ring's resonance shift is taken as linear in voltage and its extra loss from carriers is ignored; the MZM's phase is linear in voltage and its loss is the phase shifter's alone. Drive energy is ¼CV² per bit for the ring and V_pp²/(4R) per arm for the MZM's terminated electrodes, both before driver overhead. Group index 4.0 and 72 pm/K are from deck 01's solver for a 500 × 220 nm strip.

Keeping a Ring on Resonance

A ring modulator works only while its resonance sits a fraction of a linewidth from its laser. Fabrication offsets (deck 01, slide 10), the laser's own drift and the chip's temperature all move it. Padmaraju and Bergman divide the remedies into athermal designs, which cancel silicon's thermo-optic coefficient with a material of the opposite sign or with the circuit, and control-based ones, which measure and correct (Nanophotonics 3, 269, 2014).

• A π phase shift moves a ring's resonance by half its FSR. So a heater rated at 19.5 mW per π moves a ring with a 10 nm FSR by 5 nm, about 0.26 nm per milliwatt. Correcting a random fabrication offset can need up to a full FSR in the worst case: tens of milliwatts, per ring, continuously.
• Heaters only heat. A ring is designed to sit below its target and is warmed up to it, so the heater must cover the coldest operating point; the control loop then backs it off as the chip warms.
• Control loops sense a monitor photodiode or the modulator's own photocurrent and dither or track the operating point; Timurdogan et al. compensated their ring over 7.5 °C with an integrated heater for an extra 0.24 fJ/bit (Nature Commun. 5, 4008, 2014).
• Static tuning power, not modulation energy, is often the largest term in a ring-based link. Deck 03 puts it in the budget.

Beyond Plasma Dispersion

• Electro-absorption changes amplitude directly, so it needs no interferometer and no resonance: short, broadband within its window, and tolerant of temperature in a way rings are not. Its window is fixed by the germanium alloy, and moves with temperature.
• Pockels materials change phase without free carriers, so they avoid the loss that comes with plasma dispersion; that makes them attractive for coherent transmitters and very high symbol rates, where silicon depletion struggles.

Germanium Photodiodes

• Why germanium. Silicon is transparent at 1310 and 1550 nm (deck 01); germanium, a group-IV material that can be grown epitaxially on silicon, absorbs there. Its absorption weakens towards the long end of the C band; tensile strain from growth on silicon extends it, as Michel, Liu and Kimerling's review describes (Nature Photon. 4, 527, 2010).
• Waveguide coupling separates the two lengths that compete in a surface detector: light is absorbed along the device, while carriers only cross its thin height. Small volume means small capacitance and short transit.
• Responsivity R = ηqλ/(hc): at most 1.25 A/W at 1550 nm and 1.06 A/W at 1310 nm for a quantum efficiency η of 100%. Vivien et al. measured 0.8 A/W at 1550 nm (an external efficiency of about 64%), estimated an optical bandwidth up to 120 GHz for 10 µm devices, and received 40 Gb/s at zero bias (Opt. Express 20, 1096, 2012).

Bandwidth, Dark Current and Avalanche Gain

• Ge/Si APDs absorb in germanium and multiply in silicon, whose ionisation ratio is low. Kang et al. reported a gain–bandwidth product of 340 GHz, an effective k of 0.09 and a sensitivity of −28 dBm at 10 Gb/s, the highest gain–bandwidth product of any APD at 1,300 nm when published (Nature Photon. 3, 59, 2009).
• Gain is worth it when the receiver is amplifier-noise-limited, as most short links are; it is not worth it when the light is already plentiful, or when bias voltage is scarce.

From Photocurrent to Bits

• The transimpedance amplifier (TIA) turns microamps of photocurrent into a voltage. Its input-referred noise current, together with the detector's capacitance, sets the receiver's sensitivity: the smallest OMA that meets the target bit error ratio. Sensitivity is where the link budget ends (deck 03).
• Capacitance is the enemy twice: it limits bandwidth and it raises the noise the TIA adds. Miller argues that a detector with about 300 aF of total capacitance (diode, wiring and transistor input) could drive a logic gate without an amplifier, removing about 170 fJ/bit of receiver circuitry and allowing about 1 fJ/bit reception (J. Lightwave Technol. 35, 343, 2017). That is the case for putting detectors and electronics very close together (deck 03).
• PAM4 receivers must be linear, not limiting, keep three decision thresholds, and usually equalise with a feed-forward equaliser; the 4.8 dB eye penalty of slide 01 is paid here, and TDECQ measures a transmitter against a reference version of this receiver.
• Forward error correction relaxes the raw bit error ratio the receiver must reach, trading latency and logic for optical power; standards specify the FEC with the optics.

Direct and Coherent Detection

Silicon photonics serves both. IQ modulators are nested Mach–Zehnder modulators (slide 04); coherent receivers are 90° optical hybrids built from the couplers of deck 01, slide 07 feeding germanium photodiodes. The data-centre series picks up where each one fits.

What to Take Away

• Silicon modulates with free carriers. The plasma effect is weak (about 10⁻³ of index for 10¹⁸ cm⁻³) and lossy, so modulators are either long (MZMs) or resonant (rings).
• Depletion is the workhorse: fast because it does not wait on carrier lifetime, at about 2 V·cm.
• MZMs are broadband and robust but long, with terminated electrodes and drivers that cost picojoules per bit; rings are tiny and reach femtojoules but need heaters and control loops that can cost more than the modulation (the interactive, slide 07).
• Germanium makes the detector, waveguide-coupled for bandwidth, with Ge/Si APDs when the receiver is noise-limited. The receiver's sensitivity is where the link budget ends.
• Other materials (GeSi EAMs, thin-film lithium niobate) buy size, voltage or loss at the price of process complexity.
• Next: deck 03 brings in the laser, the package, and the energy-per-bit budget of a whole link.