Strip vs rib waveguide
The two standard cross-sections of integrated waveguides: fully etched strip for tight confinement and small bends; partially etched rib for lower loss and the slab access that electrical devices need.
The two standard cross-sections of an integrated waveguide are made from the same guiding layer with two etch depths. A strip waveguide, also called a channel waveguide or photonic wire, is etched through the whole layer, leaving a rectangular core surrounded by cladding. A rib waveguide, or ridge waveguide, is etched only part way, leaving a thin slab of the core material on either side of a raised core. In 220 nm silicon on insulator, where both are standard, a 500 nm wide strip bends through 90° with negligible radiation at a radius of 1.5 µm, while a rib of the same width on a 90 nm slab needs a radius of about 8 µm to keep the radiation loss to 0.01 dB. In exchange the rib's slab lowers the propagation loss and gives an electrical path to the core, which the doped junctions of silicon modulators need.
Compared
| Strip | Rib, 90 nm slab | Rib, 150 nm slab | |
|---|---|---|---|
| Etch depth | 220 nm | 130 nm | 70 nm |
| Effective index | 2.446 | 2.568 | 2.685 |
| Group index | 4.18 | 3.88 | 3.75 |
| Radius for 0.01 dB per 90° | 1 µm or less | about 8 µm | about 55 µm |
| Single-mode below a width of | about 450 nm | about 480 nm | about 700 nm |
| Electrical access to the core | none | through the slab | through the slab |
The values are computed at 1550 nm for the TE-like mode of 500 nm wide waveguides in 220 nm silicon with oxide cladding, using a full-vectorial finite-difference mode solver; the bend losses are radiation losses, computed with a conformal transformation of the bend (Heiblum and Harris).
Strip waveguides
The strip has the full index contrast of silicon against oxide, 3.48 against 1.44, on all four sides, so its mode is tightly confined and bends sharply. For a 500 × 220 nm strip the computed radiation loss is 0.0003 dB per 90° at a 1.5 µm radius and negligible from 2 µm upward. At such radii the larger loss is the mismatch between the straight mode and the bent mode, which shifts outward in the bend: 0.16 dB at each junction between a straight section and a 1.5 µm bend, 0.09 dB at 2 µm and 0.04 dB at 3 µm. A small lateral offset at the junction, or a bend whose curvature grows gradually, reduces it. Dense routing, small ring resonators, directional couplers and compact multimode interference couplers are therefore made in strips.
The same contrast makes the strip sensitive to sidewall roughness. The mode presses against two etched walls the full 220 nm tall, and scattering from their roughness is the main source of propagation loss in silicon strips. A second TE mode is guided once the strip is wider than about 450 nm, so routing strips are kept near 500 nm or narrower, where that mode is only barely guided.
Rib waveguides
In a rib the mode sits mostly under the raised core but spreads into the slab on either side, so less of it meets the etched walls, which are also shorter: 130 nm on a 90 nm slab. Roughness scattering is lower accordingly, and ribs have lower propagation loss than strips made in the same layer; typical values for both are in the propagation loss entry. The rib's mode is also larger, with a computed effective area of 0.18 µm² on a 90 nm slab and 0.24 µm² on a 150 nm slab against 0.15 µm² for the strip, which lowers the peak intensity and with it the two-photon and free-carrier absorption at high power.
The slab is what makes the rib the waveguide of active silicon devices. Doped regions in the slab on either side of the core form a lateral p-n or p-i-n junction across the waveguide, with the metal contacts on the slab far enough from the core not to absorb the light. Carrier-depletion Mach-Zehnder and microring modulators, carrier-injection phase shifters and variable optical attenuators are built this way, all using the plasma dispersion effect.
The price is weaker lateral confinement. In a bend, light leaks sideways into the slab, whose own guided mode carries it away once the bend is tight enough. Computed for 500 nm ribs, the radiation loss per 90° falls from 0.30 dB at a 5 µm radius to 0.012 dB at 8 µm and 0.001 dB at 10 µm on a 90 nm slab, and from 0.57 dB at 30 µm to 0.019 dB at 50 µm on a 150 nm slab. The slab can also carry scattered light to neighboring structures.
Higher-order modes leak into the slab in the same way, which keeps a rib single-mode up to a larger width than a strip in the same layer: about 480 nm on a 90 nm slab and about 700 nm on a 150 nm slab, against about 450 nm for the strip. In thick silicon layers with shallow etches the effect is strong enough for ribs several micrometers wide to stay single-mode, the condition analyzed by Soref and colleagues. TM-like light behaves differently in a thin-slab rib: its effective index lies below that of the slab's TE mode, and at most widths it leaks sideways into that mode (Webster and colleagues), one reason rib circuits in 220 nm silicon are normally used in TE.
Using both
Circuits use both cross-sections, joined by strip-to-rib converters in which the slab widens gradually from the edges of the core so that the mode changes shape without scattering. A common arrangement routes and bends in strips and changes to rib for modulators and phase shifters, where the slab contacts are needed, and for long straight runs, where its lower loss counts.
Common questions
What is the difference between a strip and a rib waveguide?
A strip is etched through the whole guiding layer and is surrounded by cladding; a rib is etched part way and keeps a thin slab on either side. The strip confines light more tightly and bends more sharply; the rib has lower loss and lets electrical contacts reach the core through the slab.
What is the minimum bend radius of a silicon waveguide?
For a 500 × 220 nm strip, radiation loss is negligible down to about a 1.5 µm radius, and the practical limit is set by the mismatch loss at the junctions and by fabrication. A rib with a 90 nm slab needs about 8 µm for 0.01 dB per 90°, and one with a 150 nm slab about 55 µm.
Why are silicon modulators made in rib waveguides?
Because the slab carries current to a junction across the core. The doped regions and their contacts sit on the slab on either side, away from the light, which a strip surrounded by oxide does not allow.
Does a rib or a strip waveguide have lower loss?
The rib, when both are made in the same silicon layer, because less of its mode meets the etched sidewalls whose roughness causes most of the loss.
References: R. A. Soref, J. Schmidtchen, and K. Petermann, "Large single-mode rib waveguides in GeSi-Si and Si-on-SiO2," IEEE Journal of Quantum Electronics 27, 1971 (1991). M. A. Webster, R. M. Pafchek, A. Mitchell, and T. L. Koch, "Width dependence of inherent TM-mode lateral leakage loss in silicon-on-insulator ridge waveguides," IEEE Photonics Technology Letters 19, 429 (2007). M. Heiblum and J. H. Harris, "Analysis of curved optical waveguides by conformal transformation," IEEE Journal of Quantum Electronics 11, 75 (1975). L. Chrostowski and M. Hochberg, Silicon Photonics Design (Cambridge University Press, 2015). Z. Zhu and T. G. Brown, "Full-vectorial finite-difference analysis of microstructured optical fibers," Optics Express 10, 853 (2002), for the mode solver.