Page 620 - Introduction to Information Optics

604 10. Sensing with Optics

Bragg grating
Cladding Fiber core

I
Index modulation

Wavelength

Fig. 10.22. Illustration of a uniform fiber Bragg grating and its wavelength-selective reflection
property.

where R(L, A) is the reflectance as a function of wavelength, A, and fiber length,
L; O is the coupling coefficient; A/? = ft — 7r/A is the detuning wave vector;
/? = 2nn 0/A is the propagation constant; A is the Bragg grating period; and
2
2
S — ^/Q — A/? . For the single mode sinusoidal modulated grating as de-
scribed by Eq. (10.14), the coupling constant, Q, is given by

(10.33)

where M p is the fraction of the fiber mode power contained by the fiber core,
which can be approximately expressed as

2
M = 1 — F~ , (10.34)

where V is the normalized frequency of the fiber and given by
2na

where a is the core radius, and n co and n cl are the core and cladding refractive
indices, respectively. At the Bragg grating center wavelength, the detuning