2004

We demonstrate an inverse scattering algorithm for reconstructing the structure of lossy fiber Bragg gratings. The algorithm enables us to extract the profiles of the refractive index and the loss coefficient along the grating from the grating transmission spectrum and from the reflection spectra, measured from both sides of the grating. Such an algorithm can be used to develop novel distributed evanescent-wave fiber Bragg sensors that measure the change in both the refractive index and the attenuation coefficient of the medium surrounding the grating. The algorithm can also be used to analyze and to design fiber Bragg gratings written in fiber amplifiers. A novel method to overcome instability problems in extracting the parameters of the lossy grating is introduced. The new method also makes it possible to reduce the spectral resolution needed to accurately extract the grating parameters. [Read more…]

Fig. 1 Reconstruction of a grating with a chirped Gaussian coupling coefficient, 𝑞(𝑧)=600 exp[−105(𝑧−𝐿/2)2(2.5+20𝑖)] m−1 and with a sinusoidal loss profile 𝛼=70[1−cos(10𝜋𝑧/𝐿)] m−1 written in the region [0, L=1 cm]. The reconstructed parameters (solid curves) are compared with the original parameters (dashed curves). The reflection spectra, obtained from both sides of the grating, and the transmission spectrum were sampled over a bandwidth of 10 nm with a spectral resolution of 0.02 nm.

Amir Rosenthal and Moshe Horowitz, “Inverse scattering algorithm for reconstructing lossy fiber Bragg gratings,” J. Opt. Soc. Am. A 21, 552-560 (2004)

We demonstrate theoretically a new method to accurately interpolate the complex reflection spectrum of fiber Bragg gratings with a finite length at any desired frequency resolution. The required sampling resolution is significantly smaller than can be expected by directly using the sampling theorem for obtaining a low-error characterization of the reflection spectrum. A further decrease in the required sampling resolution by a factor of two is obtained by sampling both the complex reflection and the complex transmission functions. The new reconstruction technique may enable to significantly reduce the time needed to characterize fiber Bragg gratings and to interrogate fiber Bragg sensors. [Read more…]

Fig. 1 (a) The reflectivity and (b) the impulse response function of a uniform fiber Bragg grating with a maximum reflectivity of 99% and a length of L=4 mm . The sampled points used to characterize the reflection function with a sampling period of Δλ=0.1 nm are marked in the figure.

Amir Rosenthal and Moshe Horowitz, “New technique to accurately interpolate the complex reflection spectrum of fiber Bragg gratings,” IEEE Journal of Quantum Electronics ( Volume: 40 , Issue: 8 , Aug. 2004 )