598 Appendix I 2. The reflectivity of the grating at the Bragg wavelength, l B , is À Á R ¼ tanh 2 k ac L g : The reflectivity, r, in % is: rð%Þ ¼ 1 À 10 À 3. The group delay in a chirped grating is t ¼ 2n g L g ; cDl g Tdip ðdBÞ 10 ðA1:7Þ ðA1:8Þ where T dip is the transmission dip in dBs at the Bragg wavelength. ðA1:9Þ where, Dl g is the chirp bandwidth of the grating, c is the speed of light, and n g is the group index of the mode. A.1.2 LPGs 4. The bandwidth of a LPG between the peak and the first zero is Dl LPG ¼ l 2 resonance Dn eff L g r ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4k n!01 L g ; p ðA1:10Þ where the ln cladding mode has an effective refractive index difference to the core LP 01 mode of Dn eff . k is the coupling constant for the selected mode interaction. A.2 MATERIAL PROPERTIES­BASED PARAMETERS The dependence of the Bragg wavelength of an FBG in SMF28 on the temper- ature is typically $16 pm- C, and the strain dependence is $10 nm/%. In high germania-boron co-doped fiber, the thermal sensitivity of an FBG is $10 pm-K À1 , and the strain coefficient is 0.95 pm/me. The thermal dependence of the stress-optic coefficient is 0.21 Æ 0.03 fm me À1 K À1 [1]. The thermal expansion coefficient of silica is $10 À6 K À1 . The thermo-optic coefficient of SMF28 is $9.2 Â 10 À6 ­ K À1 .