Page 304 - Optofluidics Fundamentals, Devices, and Applications

278 Cha pte r T w e l v e

If there is no absorption and no scattering of the light waves at the
two reflecting surfaces, the sum of the intensities of the transmit-
ted and reflected light must be equal to 1. Using Eqs. (12-22) and
(12-26):
ϕ
T 2 + K sin 2 ⎛ ⎞
⎜ ⎟

I + I = 1 ( − R) 2 ⎝ ⎠ 2 ⎯⎯⎯ →1 QED (12-27)
R RT+=1
ϕ
T R ⎛ ⎞
1 + K sin 2 ⎜ ⎟
⎝ ⎠ 2
Other characteristics describing a Fabry-Perot resonator are similar to
a ring resonator. The free spectral range (FSR) is given by
λ λ 2 2 nd
FSR = m = λ = (12-28)
m
m + 1 2 nd m
The FWHM is defined as the full width at half maximum and is the
same as in the case of the ring resonator. The quality factor is given in
terms of the finesse (F). The finesse of a resonator gives information
about the quality of the reflecting surfaces and the spectral resolution
of a Fabry-Perot resonator. The finesse is given by

F = FSR (12-29)
FWHM

The reflection finesse is given by

π R ⎛ ⎞π
F = = ⎜ ⎟ K (12-30)
R 1 − R ⎝ ⎠ 2

In the ideal case, the finesse is identical with the refection finesse. In
practical cases another finesse is present, the so-called surface finesse
F . The relation between all of them is given by
S
1 1 1
= + (12-31)
F 2 F 2 F 2
R S
The maximum intensity of a single peak is in the ideal case equal to
the intensity of the incident wave I . Due to absorption (A) and/or
0
scattering, this intensity will be weakened and is given by

⎡ A ⎤ 2 T 2
+
I = I 1 − ⎥ = I due to the fact that RT + A = 1
⎢
+
max 0 ⎣ AT⎦ 0 ( − R) 2
1
(12-32)