2) Consider a uniform fibre Bragg grating (FBG) written in silica f...

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2) Consider a uniform fibre Bragg grating (FBG) written in silica fibre, of length Lgr = 7mm, effective periodic index modulation δn = 10‾⁴, and Bragg wavelength λB = 1550nm. a. Calculate the value of the coupling coefficient K, in the FBG. (in units of m‾¹ b. Considering a waveguide refractive index of n = 1.4489 for the silica fibre at 1550nm, what is the grating period of the FBG? (in units of nm) c. What is the full bandwidth Δλ of the FBG? (in units of nm) 3) Consider an FBG with parameters described in 2), but in this case of varying grating length, Lgr. a. Calculate the values of K, Δλ, and peak reflection, for i. Lgr = 1mm ii. Lgy = 4mm 111. Lgr = 10mm iv. Lgy = 15mm 4) Consider a single-mode silica optical fibre similar to those described in the lectures (Lecture 1.1 through to Lecture 1.5). a. Calculate the absolute wavelength of an FBG written in such a silica fibre, with a Bragg wavelength of 1545nm @ 25 °C when exposed to absolute temperatures of i. -55 °C ii. 20 °C iii. 75 °C Assume that the FBG is not subjected to any axial strain, and that it is not bonded to, or embedded in, any material. b. For the FBG described under 4) a) 111., calculate the relative wavelength shift when exposed to axial strain values of 1. -2000 μstrain 11. -100 - μstrain 111. 135 μstrain iv. 850 μstrain 1 μstrain= 10‾⁶ 5) Consider an FBG with a length of 1cm, a peak reflectivity of 29% and a Brag wavelength of 1040.25nm, at a temperature of 25°C. The FBG is written in a polymer fibre as opposed to a silica fibre. The polymer fibre has the following material parameters for a wavelength of - -1040nm Poisson's ratio: Vp SII 0.34 Photoelastic coefficients: P11 = 0.300 and P12 = 0.297 Refractive index: n=1.49 = Thermal expansion coefficient: ap = Thermo-optic coefficient: = a. Under isothermal conditions of 25 °C, calculate the relative wavelength shift of the FBG when it is exposed to axial strain values of 1. -2000 ustrain 11. - -100 ustrain 111. 335 ustrain b. Calculate the absolute wavelength of the FBG when exposed to absolute temperatures of i. -55 °C 11. 20 °C 111. 75 °C Assume that the FBG is not subjected to any axial strain, and that it is not bonded to, or embedded in, any material. Also assume that the thermal expansion and thermo-optic coefficients are constant across the entire temperature range in question. c. Calculate the absolute wavelength of the FBG if it is perfectly bonded to an aluminium plate, and the aluminium plate subsequently is exposed to a uniform absolute temperature of -55°C. - (The thermal expansion coefficient of aluminium is a = 23 x d. In relation to the configuration discussed under 5) c., comment on what the effects of reducing the length of the FBG to 5mm would be on the absolute wavelength, the full bandwidth, and the peak reflectivity of the FBG.

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