This article proposes an unequivocal method of labeling and numbering the cladding modes propagating in single-mode opticalwaveguides with tilted periodic structures. The unambiguous determination of individual propagating modes in this type of optical fiber is crucial for their use in sensory systems. The selection of the appropriate spectral range and mode determines the sensitivity and measuring range of tilted fiber Bragg grating (TFBG) sensors. The measurement methods proposed by individual research teams using TFBGs as transducers are usually based on the selection of specific modes. Unification of the labeling of modes and their numbering enables comparison of the basic metrological parameters of individual measurement methods and reproduction and verification of the proposed sensors and methods in the laboratories of other scientific and research centers.

In the paper, an indirect method for the identification of the final shape of the freshly executed jet-grouted column is developed. The method relies on the backward analysis of the temperatures measured inside the column, along the trace of the injecting pipe. Temperature changes in the column are caused by the hydration process of the cementitious grout. 2D axisymmetric unsteady heat conduction initial-boundary value problem is solved for finding the column shape which fits best the reference temperature measurements. The model of the column is solved using the finite element method. The search is performed using the global evolutionary optimization algorithm called differential evolution. It is shown that the proposed method can provide an accurate prediction of the column shape if only the model reflects the physical reality well. The advantage over previous results is that the cylindrical shape of the column does not have to be assumed anymore, and the full profile of the column along its length can be accurately identified.