How a silicon wire guides light, and what the 220-nanometre platform makes cheap and what it makes hard: guided modes and group index, loss and bends, getting light on and off the chip, splitters and couplers, interferometers and rings, temperature and fabrication sensitivity, and the wavelength grids and multiplexers that put many channels on one fibre.
Concepts used here, and where they are explained. Each links to a glossary entry: this series glossary, or the glossaries of Fourier Optics for Inference, Compute in Transit, LLM Inference Simulators and FHE Accelerator Simulators for concepts those series already explain.
Silicon photonics builds optical circuits with the same wafers, lithography and etch tools as CMOS electronics. Silicon is transparent at the two telecom windows, 1310 nm and 1550 nm, because its bandgap corresponds to shorter wavelengths, so photons at 1310 and 1550 nm are not absorbed; germanium, grown on the same wafer, absorbs there and makes the detector. What silicon cannot do well is emit light, so the laser usually comes from elsewhere (deck 03).
What the platform gives
Wafer-scale manufacturing on 200 and 300 mm lines, with process control inherited from electronics.
High index contrast (silicon against oxide, slide 02): sub-micron waveguides and bends of a few micrometres, so thousands of devices fit on a die.
A full device set: couplers, splitters, filters, modulators, germanium detectors and heaters on one chip.
What it costs
No native laser: silicon's bandgap is indirect.
Sensitivity: the same contrast that shrinks devices makes them sensitive to nanometre width errors and to temperature (slide 10).
A large mode mismatch to fibre, which makes coupling and packaging a major part of the cost (slide 06).
Polarisation dependence: TE and TM modes behave very differently in a thin silicon layer.
Overviews: Soref, “The past, present, and future of silicon photonics” (IEEE JSTQE 12, 2006); Thomson et al., “Roadmap on silicon photonics” (J. Opt. 18, 073003, 2016). This series is the foundation for the data-centre and AI-processing series, which link its glossary for device physics.
02
The SOI Platform and Its Index Contrast
The common platform is a 220 nm silicon device layer on 2 µm of buried oxide: the foundry platforms surveyed in a 2013 review (imec, CEA-Leti and IHP among them) all use it (Nanophotonics, 2013). Thicker layers (300 nm and more, and micrometre-scale SOI) exist for lower loss and polarisation independence.
Index contrast: silicon's index is about 3.48 at 1550 nm (from Li's dispersion data, J. Phys. Chem. Ref. Data 9, 561, 1980) and fused silica's about 1.44 (Malitson's Sellmeier fit, JOSA 55, 1205, 1965). The widget on slide 04 evaluates both fits live: 3.476 and 1.444 at 1550 nm.
Why it matters: a contrast of Δn ≈ 2 confines light to a cross-section a quarter of a micrometre high, so bends can be a few micrometres in radius. Glass waveguides, with a contrast of a few per cent, need far larger bends.
The 2 µm BOX keeps the guided mode's evanescent tail away from the silicon substrate, which would otherwise draw light out (substrate leakage).
03
Guided Modes: Strip and Rib Waveguides
Light stays in a high-index core by total internal reflection. Solving Maxwell's equations for the cross-section gives a discrete set of guided modes, each a field pattern that propagates unchanged as exp(iβz). The effective index neff = β/k0 lies between the cladding and core indices: the more of the mode sits in the silicon, the closer neff is to 3.48.
Strip (wire) waveguide
Etched through the full 220 nm. Strongest confinement, tightest bends (radius of a few µm).
The guided field touches the etched sidewalls, so sidewall roughness scatters light: losses of a few dB/cm (slide 05).
Used for routing, compact rings and dense circuits.
Rib (ridge) waveguide
Partially etched, leaving a slab. The mode is pushed into the slab sideways, so it sees less sidewall: lower loss.
Bends must be larger, or light leaks into the slab.
The slab lets electrical contacts reach the core: modulators and some detectors are rib structures (deck 02).
Single-mode condition. Above a certain width the waveguide also guides a first higher-order mode, which couples to the fundamental at every bend and junction. Routing waveguides are kept single-mode; the widget finds the cut-off for a 220 nm strip near 0.5 µm at 1550 nm.
Polarisation. In a 220 nm layer the TE-like mode (electric field in the wafer plane) is well confined and the TM-like mode is not; most silicon circuits are designed for TE, and a fibre's random polarisation has to be split and rotated at the input.
Design references: Bogaerts and Chrostowski, “Silicon photonics circuit design: methods, tools and challenges” (Laser Photonics Rev. 12, 1700237, 2018).
04
Interactive: A Strip Waveguide, Solved
A two-dimensional finite-difference mode solver for an oxide-clad silicon strip, running in your browser. It solves the semi-vectorial equation for the TE-like field Ex on a 20 nm grid, with silicon and oxide indices from Li's and Malitson's dispersion fits, and derives everything else by re-solving: the group index from two wavelengths, the sensitivities from perturbed widths, heights and silicon index (dn/dT = 1.8×10−4 K−1, Komma et al., APL 101, 041905, 2012), and the fibre coupling loss from the overlap with a Gaussian of the SMF-28 Ultra mode-field diameter (9.2 µm at 1310 nm, 10.4 µm at 1550 nm, Corning PI-1424).
0.50
0.22
10
Effective index
—
Group index
—
First higher mode
—
Power in core
—
Ring FSR
—
Shift per nm of width
—
Shift per nm of height
—
Shift per kelvin
—
Butt-coupled to SMF
—
Limits: semi-vectorial, not fully vectorial, so neff and ng are approximate (a full-vector solver is needed near cut-off and for TM); oxide cladding all round; the temperature shift counts silicon's thermo-optic coefficient only and neglects the oxide's; the fibre overlap assumes the fibre is butted straight onto the chip facet with no taper. Sensitivities are resonance shifts of a ring or filter: dλ = (λ/ng)·dneff.
Sidewall roughness dominates loss in strips; a wider or shallower-etched guide pulls the field off the sidewalls and loses an order of magnitude less, at the cost of bend radius. Circuits often route in wide, low-loss guides and taper to single-mode only where they must.
Bends radiate as the mode is pushed outward; with silicon's contrast the loss is already small at a 2 µm radius.
Group index. Pulses and the spacing of filter resonances follow the group index ng = neff − λ dneff/dλ, not neff. In a silicon wire the waveguide's own dispersion is strong: the solver on slide 04 gives neff ≈ 2.5 but ng ≈ 4.0 for 500 × 220 nm at 1550 nm. Every free spectral range and delay in this deck uses ng.
06
Getting Light On and Off the Chip
A standard single-mode fibre carries a mode about 10 µm across (10.4 µm at 1550 nm, Corning's datasheet); a silicon wire's mode is about half a micrometre. Butting one onto the other loses around 20 dB (slide 04 computes it). Two families of coupler fix the mismatch:
Grating coupler
Edge coupler
Where the fibre goes
Above the wafer, anywhere on the die
At the chip edge, after dicing and facet preparation
Wafer-level test
Yes, before dicing
No
Bandwidth and polarisation
Narrow, polarisation-dependent (a diffraction condition)
Broad, can be low in polarisation dependence
Best reported (examples)
−0.58 dB, 71 nm 3-dB bandwidth, with an apodised grating and a bonded aluminium mirror (Ding et al., Opt. Lett. 39, 5348, 2014)
About 0.36 dB (TM) and 0.66 dB (TE) per connection, a silicon taper below 15 nm wide inside a polymer guide (Pu et al., Opt. Commun. 283, 3678, 2010)
The trade, in Marchetti et al.'s review: edge couplers give higher efficiency and broader bandwidth but need more complex assembly; grating couplers suit volume manufacture and wafer-scale testing (Photonics Research 7, 201, 2019). The records above are research results; production couplers are typically worse, and packaging tolerances add loss (deck 03).
The inverse taper works by narrowing the silicon until the mode no longer fits and spreads into a larger cladding guide; Almeida, Panepucci and Lipson's 40 µm nanotaper improved coupling by an order of magnitude (Opt. Lett. 28, 1302, 2003).
07
Splitters and Directional Couplers
Directional coupler. Two parallel guides exchange power through their evanescent fields. With coupling coefficient κ and length L, the cross-port fraction is sin2(κL): full transfer at κL = π/2, a 50:50 split at π/4. Because κ depends on the gap, width and wavelength, the split ratio drifts with fabrication and across a band.
Multimode interference (MMI) coupler. A wide section supports several modes whose interference re-images the input as one or more copies at set lengths (self-imaging). MMIs are more tolerant of width errors and wavelength than directional couplers, at the cost of footprint and some excess loss.
Y-branch. A slow, symmetric split; broadband and nominally 50:50.
All three are passive, lossless in principle, and reciprocal: a 50:50 combiner fed in phase delivers all the light to one output, but fed with uncorrelated inputs it loses half. That is why an interferometer, not a combiner, is the building block of the next three slides.
08
The Mach–Zehnder Interferometer as a Filter
The transfer function. Light split into two arms and recombined interferes: with a phase difference Δφ, the bar port carries cos2(Δφ/2) of the power. A length difference ΔL gives Δφ = 2πneffΔL/λ, which varies with wavelength, so the output is a raised cosine in wavelength.
Free spectral range FSR = λ2/(ngΔL): the group index, because neff itself changes with λ. A cascade of such stages (a lattice filter) flattens the passband and sharpens the edges; it is one of the WDM multiplexers of slide 12.
The same structure, balanced and with a phase shifter in one arm, is a switch or a modulator: heat one arm to swap the outputs, or drive a carrier-depletion phase shifter at tens of GHz (deck 02).
Meshes of MZIs implement any N×N unitary, the discrete Fourier transform included: Reck et al.'s triangular arrangement (PRL 73, 58, 1994) and Clements et al.'s rectangular one, with half the optical depth (Optica 3, 1460, 2016). The Fourier Optics for Inference series uses them as an on-chip alternative to a lens (FOptInf 01, integrated-photonic alternatives).
09
Ring Resonators: FSR, Q and Finesse
Resonance: when the round trip L = 2πR holds a whole number of wavelengths, neffL = mλ, light builds up in the ring. An all-pass ring removes those wavelengths from the bus (a notch); an add-drop ring routes them to a second bus (a band-pass filter).
Free spectral range FSR = λ2/(ngL). With ng ≈ 4.0, a 10 µm-radius ring at 1550 nm has an FSR of about 9.5 nm (computed on slide 04). Small rings have wide FSRs, which is what lets one ring per WDM channel share a bus.
Q factor = λ/ΔλFWHM, set by round-trip loss and by how strongly the ring couples to the bus; finesse = FSR/ΔλFWHM counts how many resolvable channels fit in one FSR. A loaded Q of 10,000 at 1550 nm is a 0.155 nm linewidth.
Critical coupling (coupling equal to round-trip loss) gives a deep notch: the basis of ring modulators (deck 02). The standard treatment, with all the transfer functions, is Bogaerts et al., “Silicon microring resonators” (Laser Photonics Rev. 6, 47, 2012).
10
Temperature and Fabrication Sensitivity
A filter's resonance moves by dλ = (λ/ng)·dneff whenever anything changes neff. In silicon, two things change it a lot.
Temperature
Silicon's thermo-optic coefficient is 1.8×10−4 K−1 at 300 K (Komma et al., APL 101, 041905, 2012).
The solver on slide 04 turns that into about 72 pm/K for a 500 × 220 nm strip at 1550 nm. A ring with a 0.155 nm linewidth (Q of 10,000) is pushed off its own resonance by about 2 K.
Hence heaters and control loops on every ring (deck 02) and their power in the link budget (deck 03).
Fabrication
The same solver gives about 0.5 nm of resonance shift per nanometre of width and about 1.3 nm per nanometre of silicon thickness, for 500 × 220 nm at 1550 nm. Narrower guides are more sensitive to width.
Thickness varies across a wafer as well as width; Lu et al. extracted both from 2,074 racetrack resonators on one 200 mm wafer to predict circuit yield (Opt. Express 25, 9712, 2017).
A few nanometres of variation therefore move a resonance by more than a WDM channel spacing at 100 GHz (0.8 nm at 1550 nm): rings are tuned after fabrication, not trusted to land.
The sensitivities in this slide are computed by the semi-vectorial solver and are approximate; a fully vectorial solver or measurement on a given process is the authority. Wider waveguides are less width-sensitive, which is one reason rings are often drawn wider than the single-mode width.
11
WDM Grids: CWDM, LAN-WDM and DWDM
Wavelength-division multiplexing (WDM) carries several channels on one fibre, each on its own wavelength. Standards fix the grid so that transmitters and receivers from different vendors agree.
Coarse grids let uncooled lasers drift without leaving their channel and need only simple filters; dense grids need temperature-controlled lasers and sharper filters, but fit many more channels in the band where fibre and amplifiers work best.
Data-centre optics around 1310 nm uses coarse grids or none: 400GBASE-DR4 (802.3bs) puts one PAM4 wavelength on each of four parallel fibres for 500 m, while 400GBASE-FR8 and LR8 put eight wavelengths on one duplex fibre for 2 and 10 km. The data-centre series takes this up.
12
Multiplexers: AWGs, Echelles, Rings and Lattices
Device
How it separates wavelengths
Strengths
Weaknesses
Arrayed waveguide grating (AWG)
Arms with stepped lengths tilt the phase front by wavelength; the output slab focuses each wavelength to its own port
Pathak et al. compared AWGs and echelle gratings on SOI and found AWGs better for dense channel spacing and echelles for coarse (IEEE Photonics J. 6, 4900109, 2014).
An AWG is integrated Fourier optics. Each slab is a free-propagation region that acts as a lens: the input slab spreads the field over the arms and the output slab Fourier-transforms the arms' phase-tilted field into a position. That is the on-chip analogue of the lens of FOptInf 01, the lens as a Fourier transformer.
13
What to Take Away
The 220 nm SOI platform trades sensitivity for density. An index contrast of about 2 gives sub-micron guides and micrometre bends, and makes every resonance move with nanometres of width and degrees of temperature.
Use the group index for every FSR and delay: about 4.0 against an neff of about 2.5 for a 500 × 220 nm strip (the interactive, slide 04).
Fibre coupling is a design problem of its own: about 20 dB butt-coupled, under 1 dB with the best research grating or edge couplers.
Interferometers and rings are the filters; their FSR, Q and finesse set how many WDM channels fit, and their sensitivity sets how much tuning power they cost.
WDM grids are standardised: CWDM (20 nm) and LAN-WDM for short reaches near 1310 nm, DWDM anchored at 193.1 THz for dense systems.
Next:deck 02 puts data on the light and takes it off again: modulators and photodiodes.