Engineering & Science
Fabry-Perot Etalon: Free Spectral Range (FSR), Reflective Finesse & Linewidth
Calculate optical cavity Free Spectral Range FSR = c / (2 * n * L) in GHz, mirror Reflective Finesse F = (PI() * SQRT(R)) / (1 - R), and transmission peak FWHM = FSR / F.
Design laser cavities, telecom DWDM filters, and LIGO-style optical resonators!
A Fabry-Perot interferometer (or solid fused-silica etalon of thickness L and refractive index n between two parallel mirrors of power reflectivity R) transmits razor-sharp Airy resonance peaks separated in frequency by the Free Spectral Range: FSR = c / (2 * n * L), where c = 299,792,458 m/s! Dividing Hz by 10^9 expresses FSR directly in gigahertz (GHz): for a L = 5 mm (0.005 m) fused-silica etalon (n = 1.45), longitudinal modes repeat every FSR = 20.675 GHz!
How sharp is each resonance peak relative to mode spacing? Reflective Finesse F = (PI() * SQRT(R)) / (1 - R) equals the ratio of FSR to peak full-width at half-maximum linewidth (FWHM = FSR / F)! At R = 0.95 (95% mirror reflectivity), Finesse is 61.24 (FWHM = 0.338 GHz = 338 MHz), whereas upgrading to dielectric coatings with R = 0.99 boosts Finesse 5-fold to 312.58!
| 5 mm Fused-Silica Etalon (n = 1.45) | Mirror Reflectivity R | Free Spectral Range FSR | Reflective Finesse F & Linewidth |
|---|---|---|---|
| Standard Laser Mode Etalon | R = 0.95 (95%) | 20.675 GHz | F = 61.24 | FWHM = 0.338 GHz |
| High-Finesse Reference Cavity | R = 0.99 (99%) | 20.675 GHz (Same FSR!) | F = 312.58 | FWHM = 0.066 GHz |
| Invalid Reflectivity R >= 1 | 1 - R = 0 Division Check | Guarded Singularity | "Invalid Etalon Parameters" |
Free Spectral Range FSR = c / (2 * n * L) in Gigahertz (GHz)
Evaluates (299792458 / (2 * n * L_m)) / 10^9 in GHz at normal incidence.
=IF(OR(B2 <= 0, B3 < 1), "Invalid Etalon Parameters", ROUND((299792458 / (2 * B3 * B2)) / 1000000000, 3))Reflective Finesse F = (PI() * SQRT(R)) / (1 - R)
Computes Airy reflective finesse for mirror reflectivity 0 < R < 1.
=IF(OR(B4 <= 0, B4 >= 1), "Invalid Etalon Parameters", ROUND((PI() * SQRT(B4)) / (1 - B4), 2))Try the example
Use the original values or change them to test your understanding.