Page 619 - Introduction to Information Optics

10.3. Distributed Fiber-Optic Sensors

Incident UV
laser beam Silica glass
phase mask
Grating
corrugations

Fiber
Diffracted beams

-1 order +1 order
Zero order
(< 3% of throughput)
Fig. 10.21. Fabrication of fiber Bragg grating using the phase mask approach.

One of the most important properties of fiber Bragg grating is wavelength-
selective reflection. Assume that a broadband light is coupled into a fiber with
fiber Bragg grating inside. Light that has a wavelength matching the Bragg
condition will be reflected back. Light that has a wavelength not matching the
Bragg condition will be transmitted through the fiber, as shown in Fig. 10.22.
Mathematically the Bragg condition is given by

1 B = 2n eff , (10.30)

where A B is the Bragg grating wavelength that will be reflected back from the
Bragg grating, and n eff is the effective refractive index of the fiber core at
wavelength A B.
For the uniform Bragg grating, the reflectivity and spectral width of the fiber
Bragg grating were quantitatively analyzed [38,39]. The refractive index
profile for the uniform Bragg grating with grating period, A, is given by

n(z) — n 0 + An cos(27iz/A), (10.31)

where An is the amplitude of the induced refractive index perturbation (typical
5
3
values 10 ~ ~ 10 ~ ), n 0 is the average refractive index, and z is the distance
along the fiber longitudinal axis. The reflectivity for this grating can be shown
to be [38]
2
2
Q sinh (SL)
R(L, A) = 2 2 2 (10.32)
sinh (SL) + S cosh (SL)