A versatile numerical model for spectral transmission/reflection, group delay characteristic analysis, and design of tapered fiber Bragg gratings (TFBGs) is presented. This approach ensures flexibility with defining both distribution of refractive index change of the gratings (including apodization) and shape of the taper profile. Additionally, sensing and tunable dispersion properties of the TFBGs were fully examined, considering strain-induced effects. The presented numerical approach, together with Pareto optimization, were also used to design the best tanh apodization profiles of the TFBG in terms of maximizing its spectral width with simultaneous minimization of the group delay oscillations. Experimental verification of the model confirms its correctness. The combination of model versatility and possibility to define the other objective functions of Pareto optimization creates a universal tool for TFBG analysis and design.

In this paper, the new method of the determination of entries of the state matrices of the positive two-dimensional systems described by the second Fornasini-Marchesini model (IIF-M) using digraphs theory D ⁽²⁾ has been presented. For the proposed method parallel computing algorithm was constructed. Algorithm is based on GPGPU (General- Purpose Computing on Graphics Processing Units) computing method to gain needed speed and computational power for such solution. The proposed method was discussed and illustrated with numerical examples. Proposed solution allows digraphs construction for any positive two-dimensional system, regardless of its complexity.

A new concept for an optical fiber inclinometer based on tapered fiber Bragg grating (TFBG) is presented. The sensor was characterized by the experimental measurement of the dependence of inclination angle on the spectral response in fluctuating temperature conditions. The research showed that the TFBG made it possible to simultaneously measure both the inclination angle and temperature, and to operate as a temperature insensitive 0°-90° tilt sensor, in a different interrogation regime. Inscription of the FBG in the tapered optical fiber section offered not only sensor miniaturization, but also the possibility of temperature sensing by the fiber section adjacent to the inclination area. Moreover, due to the reflective mode of the TFBG, the sensor offers excellent sensitivity due to the double-loss operation.

This paper presents a series of further modifications to the parallel algorithm used for finding digraphs realisations of the characteristic polynomial. What distinguishes the mentioned algorithm from other state-of-the-art solutions is the ability to find a complete set of existing solutions, not just a few of them. Moreover, solutions found tend to be minimal in terms of a rank of matrices created. Due to a of large number of solutions tested and an NP-hard complexity of the problem, the parallel algorithm is incapable of finding solutions for more complicated problems in reasonable time. To address this problem additional modifications of the algorithm structure are proposed and explained. Modifications presented in this paper contribute to a reduction of a number of improper solutions that are created, and later tested and rejected, by the algorithm making it work in all cases, except the most trivial ones, at least by an order of magnitude faster.