Large range wavelength demodulation for ultra-short fiber Bragg gratings based on an arrayed waveguide grating and a convex optimization algorithm

A wavelength demodulation method for ultra-short fiber Bragg grating (US-FBG) sensors based on an arrayed waveguide grating (AWG) and a convex optimization algorithm is proposed and demonstrated. Instead of measuring the output power ratio of the two adjacent AWG channels as previously done, in this work the wavelength demodulation is realized by reconstructing the US-FBG spectrum. The principle of spectral reconstruction involves using an AWG to sample the spectral information of US-FBG and constructing underdetermined matrix equations with the obtained prior information on transmission responses and the detected output power from multiple AWG channels. A convex optimization algorithm is then used to solve the underdetermined matrix equation to obtain the reconstructed US-FBG spectrum. Finally, the US-FBG is demodulated by tracking the peak of the reconstructed spectrum. In a proof-of-concept experiment, axial strain is applied to a US-FBG sensor with the bandwidth of 1.14 nm to change its peak wavelength. The experimental findings demonstrate that a wavelength demodulation accuracy of better than 4 pm can be achieved using only five consecutive AWG channels to sample the spectrum. The proposed method expands the types of FBG sensors that can be demodulated, overcoming the limitation of the conventional AWG-based method on the demodulation range. This method holds promise for achieving high-precision, wide-range, flexible, and cost-effective demodulation with rapid speed.