Guide
How to design a silicon ring filter
Drop one 100 GHz channel from an eight-channel grid
One optical fiber carries many wavelength channels at once. At a node of the network one of them has to come off the fiber while the rest travel on. A ring resonator is the smallest silicon filter that does it: light at the ring's resonance crosses from the input bus into the ring and leaves at the drop port, and every other channel stays on the bus and leaves at the through port. (New to ring filters? The Academy's ring resonator tutorial covers the free spectral range, the drop and through ports, and critical coupling.)
By the end of this guide you will have that filter for an eight-channel, 100 GHz grid: its waveguide, its radius and its coupling gap, checked against every line of the spec.
Two numbers make this filter: the ring's radius and the gap between the ring and its bus waveguides. The radius comes straight from the channel plan. The gap is the hard one. Too wide a gap and the bandwidth is too narrow for the channel; too narrow a gap and the neighbors leak into the drop port. Between the two is a window 38 nm wide, and where that window sits depends on how accurately the coupling is computed.
Every step runs on this page, in widgets built from three tools: the PIC Waveguide Mode Solver, the PIC Directional Coupler Simulator and the Ring Resonator Calculator. Each step also says how to do the same thing in the tool itself.
The spec
The channel plan is the ITU-T fixed grid: channels at 193.1 + n × 0.1 THz, and eight of them, n = 0 to 7. The parameter names are the ones ITU-T G.671 uses for an optical add-drop multiplexer. G.671 leaves the values to the system designer, so the values below are ours.
| Parameter | Value | Where it comes from |
|---|---|---|
| Channel grid | 100 GHz spacing, 8 channels from 193.1 to 193.8 THz | ITU-T G.694.1; the count is ours |
| Free spectral range | more than 800 GHz | no second resonance on another channel of the plan |
| 3-dB bandwidth (the passband) | at least 10 GHz | ours |
| Adjacent and non-adjacent isolation | at least 20 dB | ours |
| Input-to-drop insertion loss | at most 1 dB | ours |
| Through-port extinction of the dropped channel | at least 20 dB | ours |
| Propagation loss | 1.48 dB/cm | a published silicon foundry figure (Siew et al., 2021) |
| Mode | TE0 | ours |
The waveguide is a 500 × 220 nm silicon strip on oxide, with oxide above as well. Oxide cladding is a deliberate choice: with air above, the same strip couples much more weakly at the same gap, and the 10 GHz bandwidth would need a far narrower gap.
Step 1
The waveguide: its modes and its group index
Set the top cladding to SiO₂ and solve. In practice the strip is single-mode for TE. TE0 is the ring's mode, with an effective index of 2.4469. TE1 sits at cutoff: its effective index, 1.494, is barely above the oxide's 1.444, so its field spreads far into the oxide. TM0 is guided, but a TE input does not excite it. (What guided modes and the effective index are.)
How to do it in the tool
In the PIC Waveguide Mode Solver: Preset, SOI Strip 220; Top Cladding, SiO₂; Wavelength (nm), 1550; Engine, Full-vectorial; Mesh (nm), Standard. The Guided Modes table lists TE0 at 2.4469, TM0 and TE1.
The number the ring needs is the group index. It sets both the ring's free spectral range and its bandwidth, which both scale as 1/n_g. Run the wavelength sweep and read n_g at 1550 nm: 4.1948.
How to do it in the tool
In the PIC Waveguide Mode Solver, open vs Wavelength: λ min (nm) 1500, λ max (nm) 1600, Number of points 11. On Full-vectorial at Standard, n_g at 1550 nm reads 4.1948.
Carried to the next steps: n_eff and n_g at 1550 nm.
Step 2
The radius, from the channel plan
The ring repeats its resonance every free spectral range. If a second resonance lands on another channel of the plan, the filter drops that channel too. The plan spans 700 GHz, from channel 0 to channel 7. The FSR has to be at least 800 GHz, the span plus one channel spacing, so that the next resonance sits a full spacing past the far channel rather than on it. With n_g = 4.1948 that holds for any radius up to 14.2 µm. Take R = 10 µm: the FSR is 1137 GHz.
What goes wrong with a bigger ring. A bigger ring couples more strongly at the same gap (κ² = 0.0719 at 140 nm for R = 20 µm, against 0.0369 at 10 µm), which would move the gap window to a wider, easier gap. At R = 20 µm the FSR falls to 569 GHz. The next resonance then lands 31 GHz from channel 6 of the plan, and that channel reaches the drop port only 13.2 dB below the dropped one, against the 20 dB spec. The adjacent channels still pass (22.7 dB), so the check most people run first passes while the plan fails. Set R to 20 in the widget and watch the comb walk onto the grid.
The loss. Type 1.48 dB/cm and no bend loss: at R = 10 µm the bend loss of TE0 is below the Mode Solver's floor of 6e-7 dB per 90° (under 4e-4 dB/cm), far under the propagation loss, so the ring's loss is the waveguide's.
How to do it in the tool
In the Ring Resonator Calculator: Add-drop; Radius, center line (µm), 10; Propagation loss (dB/cm), 1.48; Effective index n_eff and Group index n_g from step 1. The card's FSR reads 9.14 nm and 1137 GHz.
Carried to the next step: R.
Step 3
The gap
Sweep the gap. The window is two-sided. At this group index and loss, the bandwidth reaches 10 GHz at κ² = 0.0262, and the neighbors reach −20 dB at κ² = 0.0523. Every κ² in between meets both lines. On the Full-vectorial curve that window is a gap of 121 nm to 159 nm. (How the coupler computes a ring-bus arc.)
Choose the gap. Aim at the window's geometric center, κ² = 0.0370; the geometric center leaves the same factor of margin to both lines. On the Full-vectorial curve that κ² sits at a gap of 140 nm. Take 140 nm: κ² = 0.0369 at 1550 nm.
Toggle: the Effective index engine. The browser's Effective index engine is quick, and it is the wrong tool for this gap. It puts TE0's effective index at 2.4932 against the Full-vectorial 2.4469, and its group index 4.0306 is 3.9 % low, an error that carries straight into the FSR and the bandwidth. On the gap it is further off. Its window is 166 nm to 207 nm, which does not overlap the Full-vectorial one; 6.7 nm separate them. Across the window its κ² runs 2.1 to 2.4 times the Full-vectorial one at the same gap. Take the gap at the center of its window, 186 nm: the Full-vectorial engine reads κ² = 0.0162 there, a bandwidth of 6.3 GHz, outside the spec. Type that κ² into the ring widget in step 4 and the bandwidth line turns red. (How the two engines and their meshes work.)
What a gap below the window does. At 115 nm the coupler gives κ² = 0.0584. The bandwidth widens to 22.2 GHz, and the neighbors rise to 19.0 dB below the drop, past the 20 dB line. Type 115 into the widget and watch the neighbor channels climb in the drop spectrum.
How to do it in the tool
In the PIC Directional Coupler Simulator: Preset, SOI Strip 220 (oxide-clad); Coupling region, Ring-bus arc, R 10 µm; TE, 1550 nm. Tick Parameter sweep and sweep the gap. Type 0.0370 into Target κ²: Full-vectorial gives about 140 nm, Effective index about 186 nm. At gap 140 nm, Full-vectorial κ² reads 0.0369.
Carried to the next step: the gap, 140 nm.
Step 4
Checking the gap across the band
κ² is not one number. The coupling grows with wavelength: across 1500 to 1600 nm the arc's κ² at 140 nm rises from 0.0245 to 0.0572, a factor of 2.33. A ring draws many resonances, and each one sees the κ² at its own wavelength, so the ring takes the coupler's whole wavelength sweep rather than one value. (How the ring reads κ² between wavelengths.)
The result. Light at the channel's wavelength leaves through the ring's drop port with a 3-dB bandwidth of 14.5 GHz and 0.23 dB of loss. The neighboring channels, 100 GHz away on either side, reach the drop port 22.6 dB weaker than the channel itself, and the through port loses the channel by 31.5 dB. The next resonance of the ring sits 1137 GHz away, past the far end of the grid, so the ring answers to one channel only.
About this sweep's mesh
This sweep was computed on the Coarse mesh. At 1550 nm its κ² differs by +2.3 % from the Standard mesh value the gap was chosen on; the card and spectrum use the Coarse values.
With the sweep in the ring, the card's resonance sits at 1551.72 nm, where the ring reads κ² = 0.0383 (the sweep runs at Coarse, which reads κ² at 1550 nm about 2.3 % above step 3's Standard run; see About this sweep's mesh). Read the card against the spec:
| Spec line | The filter | |
|---|---|---|
| FSR > 800 GHz | 1137 GHz | pass |
| 3-dB bandwidth ≥ 10 GHz | 14.5 GHz | pass |
| Adjacent isolation ≥ 20 dB (±100 GHz, worse side) | 22.6 dB | pass |
| Non-adjacent isolation ≥ 20 dB (worst channel, ±200 GHz) | 28.2 dB | pass |
| Drop loss ≤ 1 dB | 0.23 dB | pass |
| Through-port extinction ≥ 20 dB | 31.5 dB | pass |
| Coupling | the badge reads Critically coupled | pass |
The badge reads Critically coupled: the through port falls to −31.5 dB at the resonance, inside the badge's −30 dB line. Two identical couplers would be exactly critical in a ring without loss; the waveguide's 1.48 dB/cm loss is what leaves the through port at −31.5 dB rather than at zero.
The bandwidth changes with κ² across the plotted range. Look at the first and last resonances in the spectrum: the one at 1533.7 nm has a 12.5 GHz bandwidth, and the one at 1570.2 nm has 17.0 GHz, against the card's 14.5 GHz. That is why the badge adds that the regime differs at other resonances in the plotted range.
How to do it in the tool
In the PIC Directional Coupler Simulator, on your ring-bus arc at gap 140 nm: Engine, Full-vectorial; Mesh, Coarse; tick Wavelength sweep, λ min 1500 nm, λ max 1600 nm. Run, then Save. In the Ring Resonator Calculator: Import from Directional Coupler, pick the design, Apply. The card's 3-dB bandwidth reads 14.5 GHz.
Step 5
Your design in the tool
Your filter is finished on this page. To keep working on it in the Ring Resonator Calculator, follow the link. The link carries every value you set on this page: send it to a colleague and it opens your ring, computed, with no account needed.
Why the resonance is not on 193.1 THz yet. The resonance lands where the waveguide's effective index puts it, and fabrication moves that index: Rizzo et al. put foundries' 3σ width variation at ±10 nm. A heater on the ring moves the resonance onto the grid.
Sources
- ITU-T G.694.1 (10/2020), Spectral grids for WDM applications: DWDM frequency grid, §6 and §7, Table 1.
- ITU-T G.671 (11/2025), Transmission characteristics of optical components and subsystems, §3.2.2 and Table 6.1.
- S. Y. Siew et al., "Review of silicon photonics technology and platform development," J. Lightwave Technol. 39, 4374 (2021), Fig. 6.
- A. Rizzo et al., arXiv:2205.11481 (2022), p. 2, the width-variation statement.