Reconstruction of a fiber Bragg grating from noisy reflection data

source: © 2005 Optical Society of America

We develop a novel method that enables one to reconstruct the structure of highly reflecting fiber Bragg gratings from noisy reflection spectra. When the reflection spectrum is noisy and the grating reflectivity is high, noise in the Bragg zone of the reflection spectrum is amplified by the inverse scattering algorithms and prevents the reconstruction of the grating. Our method is based on regularizing the reflection spectrum in frequencies inside the Bragg zone by using the data on the grating spectrum outside the Bragg zone. The regularized reflection spectrum is used to reconstruct the grating structure by means of inverse scattering. Our method enables one to analyze gratings with a high reflectivity from a spectrum that contains a high level of noise. Such gratings could not be analyzed by using methods described in previous work [IEEE J. Quantum Electron. 39, 1238 (2003)]. [Read more…]

Fig. 1 Reconstruction of a uniform grating with coupling coefficient q = 500 m-1 and length L = 1 cm from a noisy reflection spectrum. The figure compares the reconstruction obtained with the method developed in Ref. 9 (solid curve) with a direct reconstruction by the ILP algorithm (dashed curve) and with a reconstruction by the method presented in this paper (dotted curve). The reflection spectrum of the grating was sampled with a bandwidth of 10 nm and resolution of 0.002 nm. The standard deviation of the noise variables, added to the complex reflection spectrum, was equal to 5 × 10-5. The ILP algorithm as well as the algorithm presented in this paper have accurately reconstructed the grating profile.

Amir Rosenthal and Moshe Horowitz, “Reconstruction of a fiber Bragg grating from noisy reflection data,” J. Opt. Soc. Am. A 22, 84-92 (2005)