Spectral shadowing is a distortion of a downstream FBG spectrum that results from light having to pass twice through the upstream FBG. From Eq. (1), if the Bragg wavelength of the ath FBG (a Ͻ i) is slightly offset from the ith FBG, it appears that the spectrum of the ith FBG is shifted further in the direction of the actual Bragg wavelength. For example, if the Bragg wavelength of the distal FBG in a 50-FBG serial array is 1550 nm, the rest of the FBGs are aligned to the same wavelength, but have an offset from 1 pm to 300 pm. The Bragg wavelength shift of the distal FBG due to this effect is shown in Figure 2. It is found that the maximum wavelength detection error is 18 pm when the reflectivity of the distal FBG is 1% and the FWHM of FBGs is 0.1 nm.Multiple reflection [3] results if the light reflected from an FBG arrives in the detection-time window allotted to another downstream FBG, because of delays associated with multiple reflection paths. We consider only first-order crosstalk pulses, which are those that undogo a total of three reflections in the array and are the strongest stray pulses generated. The secondorder multiple reflections are reduced relative to the primary signal by the 4 th power of reflectivity, and so on for the higher-order reflections. The graphical representation of the first-order multiple reflection processes shown in Figure 3. Here, the optical paths leading to primary FBG signal and all the possible first-order crosstalk pulses for the 4 th and 5 th FBG in a serial FBG sensor array are shown. If we assume the reflected power from FBGs are balanced and the Bragg wavelength of FBGs (from 1 to i Ϫ 1) are aligned to the Bragg wavelength of ith FBG, the wavelength detection error of the ith FBG due to the multiple reflection crosstalk isFor example, if for the Bragg wavelength all FBGs are aligned to the same wavelength and the reflected power from them is balanced, the wavelength detection error of the distal FBG due to multiple reflection in a 50-FBG sensor array is shown in Figure 4. The wavelength detection error is 12 pm when the reflectivity of the distal FBG is 1% and the FWHM of FBGs are 0.1 nm.
CONCLUSIONThe computer simulation results of the intrinsic crosstalk of a TDM FBG serial sensor array have been reported. The mathematical formula of the multiple reflections in this topology is derived.The maximum wavelength detection error is 18 pm and 12 pm for the spectral shadowing and multiple reflection effect, respectively, when the reflectivity of the distal FBG is 1%.
ACKNOWLEDGMENTThe authors would like to acknowledge support from the Hong Kong CERG, research grant no. PolyU5109/99E, and the Hong Kong Polytechnic University, research grant no. G-YW54.
PARALLEL-PLATE WAVEGUIDES WITH KRONIG-PENNEY MORPHOLOGY AS PHOTONIC BAND-GAP FILTERS