Formula used
A ring supports resonances separated by a free spectral range (FSR). Using group index ng and round-trip length L:
- L = 2πR for a circular ring.
- FSRf = c / (ng · L) in hertz.
- Trt = (ng · L) / c for round-trip time.
- FSRλ ≈ λ02 / (ng · L) near λ0.
The wavelength spacing expression is an approximation that is most accurate over narrow bandwidths around the chosen center wavelength.
How to use this calculator
- Select Use radius or Use round-trip length.
- Enter ng from simulation or measurement.
- Set the center wavelength for wavelength spacing output.
- Press Calculate to view results above the form.
- Use Download CSV or Download PDF for reports.
Example data table
| Radius (µm) | Group index ng | Center wavelength (nm) | FSR (GHz) | FSR (nm) approx |
|---|---|---|---|---|
| 50 | 4.0 | 1550 | ≈ 238.567 | ≈ 1.910 |
| 100 | 4.2 | 1310 | ≈ 113.607 | ≈ 0.648 |
| 25 | 3.8 | 1550 | ≈ 503.352 | ≈ 4.025 |
Example outputs are rounded and intended for quick reference.
Article
1) Why free spectral range is a key specification
Free spectral range (FSR) is the spacing between adjacent resonances of a ring resonator. It sets the channel grid for add-drop filters, determines how many resonances fit inside a source bandwidth, and helps prevent overlap with neighboring channels. Larger FSR simplifies channel planning, while smaller FSR increases spectral density for compact multiplexing.
2) Frequency-domain and wavelength-domain views
Rings are fundamentally periodic in optical frequency, so the most direct definition is in hertz: FSRf = c /(ngL). Many photonics labs view spectra in nanometers, so a narrowband conversion is useful: FSRλ ≈ λ02 /(ngL). The wavelength spacing changes slightly with center wavelength because the conversion is nonlinear.
3) Why the group index ng matters
FSR depends on group index because pulses and modulation envelopes propagate at the group velocity. For many integrated waveguides, ng can be noticeably higher than the effective index due to dispersion. Use a simulated or measured ng at the operating wavelength. Typical values in high-index contrast platforms often fall around 3.5 to 4.8, depending on geometry and cladding.
4) Round-trip length and geometry choices
The round-trip length L is the full optical path for one circulation. For a circular ring, L = 2πR. For racetrack layouts, add the straight sections to the curved arcs. Increasing R (or L) lowers the FSR, while shrinking the perimeter raises FSR but can increase bending loss and sensitivity to fabrication variations. The calculator supports either radius input or direct perimeter input for flexibility.
5) Interpreting practical numbers
As a reference, a ring with R = 50 µm and ng = 4 has L ≈ 314.159 µm and an FSR near 238.567 GHz. Around 1550 nm, the wavelength spacing estimate is about 1.91 nm. Doubling the radius roughly halves both the frequency and wavelength FSR values, which is a fast sanity check when iterating early layouts.
6) Temperature and wavelength tuning context
FSR is set by geometry and ng, so it is usually stable for a given design, but individual resonance positions shift with temperature and carrier injection. Thermal tuning can move resonances by small fractions of an FSR, enabling alignment to a laser grid. When comparing tunability, keep FSR separate from resonance shift rate; they answer different questions.
7) FSR versus linewidth, Q, and coupling
FSR describes spacing between modes; linewidth describes how sharp each mode is. A ring can have the same FSR but very different linewidths depending on propagation loss and coupling strength. High Q gives narrow resonances that are easier to separate, while over-coupling can broaden the response. Use FSR for channel planning, then evaluate Q and extinction for performance.
8) A recommended design workflow
Start with a target FSR based on your channel plan or sensor readout range. Use this calculator to pick an initial radius or perimeter given a realistic ng. Next, validate ng and loss with a waveguide mode solver, then revisit FSR if geometry changes. Finally, export CSV or PDF results to compare design variants and document decisions.
FAQs
1) What is the most reliable way to compute FSR?
Use the frequency-domain formula FSRf = c /(ngL) with a realistic group index at the operating wavelength. The wavelength spacing is a convenient approximation around the chosen center wavelength.
2) Should I use effective index or group index?
Use group index for FSR. Effective index can misestimate spacing when dispersion is significant. If you only have effective index, simulate or measure ng for better agreement with spectra.
3) How do I handle a racetrack resonator?
Enter the full round-trip length using the length mode. Compute L as the sum of both bends plus the straight sections. This directly maps to the resonance spacing without assuming a circular ring.
4) Why does FSR in nanometers depend on wavelength?
Resonances are periodic in frequency, not wavelength. Converting to nanometers introduces a nonlinear mapping, so the same FSR in hertz corresponds to slightly different nanometer spacing at different center wavelengths.
5) Does a higher Q change the FSR?
No. Q changes linewidth and resonance sharpness, not the spacing between resonances. FSR mainly depends on round-trip length and group index.
6) What inputs most strongly affect the result?
Perimeter (or radius) and group index dominate FSR. Center wavelength only affects the wavelength-domain spacing estimate. Keeping ng accurate is usually the biggest improvement you can make.
7) Why do my measurements differ from the estimate?
Differences typically come from ng mismatch, layout details that change L, or wavelength-dependent dispersion. Use measured FSR to back-calculate ng and refine your model for the next iteration.