Estimate Fabry–Perot etalon finesse from reflectivity or linewidth. Convert spacing and index into FSR values. Export results fast, validate setups, and compare measurements easily.
Finesse definition: F = FSR / FWHM, where FSR is the free spectral range and FWHM is the resonance linewidth.
Reflectivity-limited finesse: FR = π√R / (1 − R), using power reflectivity R (0<R<1).
FSR in frequency: FSRν = c / (2 n L), with spacing L and refractive index n.
FSR in wavelength (approx): ΔλFSR ≈ λ² / (2 n L) around center wavelength λ.
| Case | Method | Inputs | Key outputs |
|---|---|---|---|
| 1 | Reflectivity + parameters | R=95%, L=5 mm, n=1.0003, λ=1550 nm | FR≈61.2, FSR≈29.97 GHz, linewidth≈490 MHz |
| 2 | Measured (frequency) | FSR=30 GHz, FWHM=0.2 GHz | F≈150 |
| 3 | Measured (wavelength) | ΔλFSR=150 pm, ΔλFWHM=3 pm | F≈50 |
Etalon finesse (F) describes how sharply a Fabry-Perot resonance is defined. It is the ratio of free spectral range (FSR) to the resonance linewidth (FWHM). Higher finesse separates nearby modes better, improving filtering and wavelength discrimination. In practice, finesse also sets peak contrast and stability requirements.
For a plane-parallel etalon, the frequency spacing is FSR = c/(2 n L). In air (n about 1), L = 5 mm gives an FSR near 30 GHz, while 1 mm gives about 150 GHz. Smaller spacing increases spacing but can raise alignment sensitivity. For solid etalons, higher n reduces FSR proportionally.
Reflectivity drives the ideal finesse through F_R = pi*sqrt(R)/(1-R). Going from R = 0.90 to 0.95 increases F_R from about 30 to about 61, while R = 0.99 pushes F_R above 300. Coating choice therefore dominates performance in many laboratory filters.
Real devices rarely reach F_R because surface figure, parallelism, and beam divergence broaden resonances. A practical way to combine limits is 1/F_eff^2 = 1/F_R^2 + 1/F_defect^2 + 1/F_aperture^2. If a defect-limited finesse is 200, it can cap performance even with very high reflectivity.
Around a chosen wavelength, the approximate wavelength FSR is Delta-lambda_FSR about lambda^2/(2 n L). At 1550 nm and L = 5 mm, Delta-lambda_FSR is roughly 0.24 nm. The linewidth in wavelength follows Delta-lambda_FWHM = Delta-lambda_FSR/F, useful for spectrometer comparisons. For narrowband telecom filtering, pm-scale linewidths are common when finesse is high.
In experiments, finesse is often extracted from a frequency sweep: measure the distance between adjacent peaks (FSR) and the peak width at half maximum (FWHM). Keep both values in the same units (for example, GHz). A clean scan with FSR = 30 GHz and FWHM = 0.2 GHz yields F = 150.
Low-finesse etalons (F about 10 to 50) are common in broadband filtering and sensor interrogation, where throughput matters. Mid-range values (F about 50 to 200) suit tunable lasers and spectral cleanup. Very high finesse requires stable mechanics, narrow beams, and careful control of temperature and vibration. Plan mounts to minimize drift, and record temperature during measurements.
Use F = FSR/FWHM. Measure adjacent peak spacing for FSR and the peak full width at half maximum for FWHM, in the same unit, then divide.
Higher reflectivity makes the cavity store light longer, narrowing resonances. In the ideal case F_R = pi*sqrt(R)/(1-R), so F rises rapidly as R approaches 1.
Effective finesse is the practical value after including broadening from defects, wedge, and beam divergence. The calculator combines limits using an inverse-square sum, so the smallest limiting finesse usually dominates.
Yes. If you have wavelength-domain FSR and linewidth, finesse is still F = FSR/FWHM. Keep both in the same wavelength unit (pm, nm, or um) before dividing.
The wavelength FSR shown is an approximation around the selected center wavelength. It is accurate for small spacings relative to lambda and narrow scan ranges; for wide tuning, use frequency-domain analysis.
FSR scales as 1/(nL). Increasing spacing or refractive index reduces FSR. For example, doubling L halves the frequency FSR, making resonances closer together.
Target depends on required selectivity and throughput. Many practical optical filters use F between 30 and 150. Going higher demands better coatings, smaller divergence, and better thermal and mechanical stability.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.