Fabry-Pérot Filter
Fabry-Pérot etalon/filter transmission based on the Airy function. Explore how mirror reflectance and cavity spacing control spectral selectivity.
Nearest peak: λ_m (order m)
500.00 nm (order 3)
FSR: exact frequency c/(2nd)
199.9 THz
Neighbour peaks: λm+1 = 375.00 nm, λm−1 = 750.00 nm
≈ λ²/2nd (first order) = 166.67 nm
FWHM at the peak
11.9 nm
Finesse
14.05
Airy Function
T = 1 / (1 + F·sin²(δ/2))
δ = 4πnd/λ
Peaks: δ = 2πm, i.e. λ_m = 2nd/m
F = 4R/(1−R)²
FSR ≈ λ²/(2nd) (first order); exactly c/(2nd) in frequency
ℱ = π√F/2
FWHM = 4πnd[1/(2πm − w/2) − 1/(2πm + w/2)], w = 4 asin(1/√F)
Model and references
Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers
Ideal Airy etalon: two identical lossless mirrors of constant R, normal incidence, no mirror phase, absorption or dispersion. Dielectric-mirror cavities add a wavelength-dependent R and penetration depth.
- Born M., Wolf E. (1999). Principles of Optics, 7th ed., §7.6.1 (Airy formulae, half-intensity width). Cambridge University Press.
- Hecht E. (2016). Optics, 5th ed., §9.6 (Fabry-Perot interferometer).