Etalon Free Spectral Range Calculator

Etalon FSR Article

1) What the free spectral range represents

An etalon forms a short interferometric cavity that transmits only discrete resonant frequencies. The free spectral range (FSR) is the separation between neighboring transmission peaks. In frequency units it is typically expressed in GHz or THz, while in wavenumber it may be written in cm⁻¹. A larger FSR means fewer resonances inside a given optical bandwidth, which simplifies filtering and mode selection in lasers.

2) Thickness and index set the scale

The dominant term is the optical round trip, 2nL. If you double the spacing L, the FSR halves. If you increase refractive index from 1.00 to 1.50 at fixed thickness, the FSR drops by one third. For example, an air-spaced 10 mm etalon gives roughly 15 GHz spacing, while a 1 mm glass etalon (n ≈ 1.45) reaches about 103 GHz, matching typical laboratory filter components.

3) Angle tuning and cosine dependence

Changing incidence angle modifies the effective path length by cos(θ). Small angles provide gentle tuning without changing hardware. At 5° the cosine factor is about 0.996, so the FSR changes by only a few tenths of a percent. Larger angles increase sensitivity but also raise alignment demands and may introduce polarization or walk-off effects in practical optics.

4) Linking FSR to wavelength spacing

Many users think in nanometers rather than hertz. The wavelength spacing depends on the chosen center wavelength λ₀ through Δλ ≈ λ₀²/(2nLcosθ). This is why the same etalon has a larger Δλ in the infrared than in the visible. At 1550 nm, a 10 mm air etalon yields around 0.12 nm, whereas at 633 nm the same cavity produces a much smaller Δλ.

5) Order number as a quick consistency check

The interference order m ≈ 2nLcosθ/λ₀ helps sanity-check geometry. For millimeter-scale cavities at near‑IR wavelengths, m is often in the thousands to tens of thousands. If your computed order is unexpectedly small, revisit unit selections and confirm that L is not entered in the wrong scale.

6) Reflectivity, finesse, and linewidth

Reflectivity controls how sharp each transmission peak becomes. With an entered reflectivity R, this calculator estimates finesse F ≈ π√R/(1−R) and an approximate linewidth δν ≈ FSR/F. As a reference, R = 0.90 gives F ≈ 29.8, so a 15 GHz FSR corresponds to about 0.50 GHz linewidth.

7) Practical selection guidelines

Choose a large FSR when you want aggressive mode suppression or coarse comb spacing. Choose a smaller FSR for dense spectral sampling, such as calibrating spectrometers. Combine FSR with linewidth to ensure peaks are narrow enough for your resolution target but not so narrow that temperature drift dominates performance.

8) Reporting and documentation

Engineering workflows often require repeatable records. After calculation, export CSV for quick spreadsheets or PDF for lab notebooks and design reviews. Keep notes on L, n, angle, and λ₀, because small differences in units can move results by orders of magnitude. This page is designed for fast iteration across scenarios.

FAQs

1) What is a typical FSR range for lab etalons?

Millimeter to centimeter cavities often produce FSR values from a few GHz up to hundreds of GHz. Very thin plates can reach the THz range, especially in air-spaced configurations.

2) Why does increasing thickness reduce the FSR?

FSR is inversely proportional to the optical path length 2nLcosθ. A thicker cavity stores more phase per round trip, so resonances occur more closely spaced in frequency.

3) When is the Δλ approximation reliable?

The Δλ expression assumes small spacing compared with the center wavelength. It is accurate for many optical filters where Δλ is much less than λ₀, but large spacings warrant frequency-based comparisons.

4) Does refractive index vary with wavelength?

Yes. Many materials are dispersive, so n changes with λ. Use an index value appropriate to your operating wavelength, especially for broadband designs or precision spectrometer work.

5) What reflectivity should I enter for finesse estimates?

Use the intensity reflectivity of the etalon surfaces at your wavelength. If coatings differ on each side, a more detailed model is needed, but a single representative R gives useful first estimates.

6) How does angle tuning affect alignment?

Angle tuning changes effective path length, but it can also shift beam position and polarization response. Small angles are typically easier to manage and keep results closer to the ideal cosine model.

7) Why do my measured peaks differ from the calculator?

Real systems include dispersion, wedge errors, temperature drift, and non-normal incidence inside the medium. Verify units, use the correct n at λ₀, and consider calibration against a known reference source.