Narrow Bandpass Filter
Multiple-cavity Fabry-Perot filter with long quarter-wave mirrors: a narrow, flat-topped pass band, its FWHM, peak transmittance and ripple.
Peak transmittance
99.69 %
Ripple peaks at 1549.586 and 1550.414 nm
Transmittance at λ₀
95.74 %
FWHM
1.134 nm
1549.433 – 1550.567 nm
λ₀ / FWHM
1366
Resolving power (Q), not a finesse
Layers: 77; mirror zone (infinite stack) 1345.2 – 1828.3 nm
Each cavity is (HL)p S (LH)p with a half-wave spacer S; cavities are coupled by a quarter-wave L layer. Exact transfer matrix at normal incidence from air, lossless and non-dispersive layers, back surface ignored. FWHM: from λ₀ outward to where T first falls to half the peak, found by bisection. There are no matching layers, so the peak T is below 100 % and a multi-cavity pass band ripples (Macleod, Thin-Film Optical Filters, ch. 8).
Model and references
Exact. The equations are exact within the stated assumptions, or are a standard's tabulated values. The results are as good as the inputs. About the tiers
Transfer matrix of (HL)^p S (LH)^p cavities with half-wave spacers and quarter-wave couplers, normal incidence, constant lossless indices, back surface ignored. FWHM by bisection, not from the plot grid.
- Macleod H. A. (2010). Thin-Film Optical Filters, 4th ed., ch. 2 and ch. 8 (multiple-cavity band-pass filters). CRC Press. doi:10.1201/9781420073034