420
10 Wavelength Division Multiplexing (WDM)
Fig. 10.24 The behavior of
the resonant wavelengths in a
Fabry–Perot cavity for three
values of the mirror
reflectivity based on the Airy
function
FSR
Passband
FSR λ = λ F S R =
λ
2
2n D
(10.56)
Here λ is the wavelength at the transmission peak.
Drill Problem 10.5 (a) If an engineer wants to use a material with a refractive
index n = 1.50 to make an etalon with an FSR of FSR = 50 GHz, show
that the etalon thickness should be 2.0 mm. (b) If this etalon is to be used at
1550 nm, show that the corresponding FSR in terms of wavelength is FSR
= 0.40 nm.
Another important parameter of an etalon is the measure of the full width of the
transmission passband at its half-maximum value, which is designated by δλ and
is called the full-width half-maximum (FWHM). The FSR is related to the FWHM
through the ratio
F =
λ F S R
δλ
(10.57)
The parameter F is known as the finesse of the filter. For mirror reflectivities greater
than 0.5, F can be approximated by the expression
F ≈
π (R 1 R 2 )
1/4
1 −
√
R 1 R 2
(10.58)
Here R 1 and R 2 are the reflectivities of the etalon mirrors. This shows that the major
factor influencing the finesse is the reflectivity of the mirrors; mirrors that have greater
reflectivities yield a higher finesse. Absorption within the device, especially within
the mirrors, reduces the sharpness of the filter peaks. Etalons with high finesse show