New Parameters Extracted from Tilted Fiber Bragg Grating Spectra for the Determination of the Refractive Index and Cut-Off Wavelength

Abstract

Tilted fiber Bragg grating (TFBG) is a very popular fiber optic element that is used as a sensor for various physical quantities. The calculation of the refractive index of a substance surrounding the TFBG is based on its spectrum demodulation, which consists of determining a certain parameter that is correlated with the sought quantity. The most commonly used parameter is the area created by the maxima and minima of the cladding mode resonances. In this article, we propose a new group of methods, which are based on calculating the parameters related to the spectrum differences between the local average values in the range of occurrence of the cladding modes. The basic parameter used in this group of methods is the mean absolute deviation from the local mean, which is characterized by the best linearity among the considered group of methods. The calculated parameters, in their cumulative form, can also be used to determine the cut-off wavelength, which can also indirectly indicate the refractive index value. The proposed approaches were compared, in terms of measurement resolution, to the most commonly used methods, such as the cladding modes’ envelope area and the spectral contour lengths.

Single- and Double-Comb Tilted Fibre Bragg Grating Refractive Index Demodulation Methods with Fourier Transform Pre-Processing

“…The first proposed algorithm of this type is an algorithm that calculates the value of the standard deviation between the spectrum amplitudes and the local mean of the spectrum [ 21 ]. Another parameter of this type is the determination of the average difference from the local average [ 22 ]. The spectrum contour length parameter can also be calculated [ 23 ]: where T i are measured spectrum points in the specified spectral range.…”

“…In the [ 22 ] article, it is proposed to use the curve created as a result of calculating the cumulative version of locally calculated parameters such as cumulative mean deviation from the local mean: where are spectrum points smoothed by the lowpass filter.…”

Relative humidity measurement sensor based on polyvinyl alcohol coated tilted fiber Bragg grating

“…The tilt of the grating planes is an important parameter that decides which set of the cladding modes are going to be excited. The tilt angle of 4 • was selected judiciously to cover the refractive index range of 1.47-1.34 that corresponds to the RH range 45%-95% [39,40]. While passing the UV output through the phase mask, a cylindrical lens was used to line focus onto the fiber.…”

Metrology and Measurement Systems

“…where ∆ i, j = θ i, j − θ D and (z i , z j ) are the critical points of the Airy's integral Ai(z) at which the rainbow's minima and maxima occur [30]. As (10) has no closed form, it is computed using an iterative procedure. The cladding diameter estimates can be made on the basis of maxima/minima spacing:…”

“…As precise quantitative understanding of the rainbow mechanism is necessary and the inverse problem (enabling to interpret data by relating the optical field back to the properties of interest in the object, see e.g. [8][9][10]) is decidedly non-trivial, the paper initially discusses modelling of scattered fields in the vicinity of the rainbow pattern. Central to this discussion is the fact that the coherence properties of the incident beam can be adjusted specifically to improve the stability of the inverse problem.…”