**1. Introduction**

Into an increasing number of scientific, medical, industrial and military sensing and telecom‐ munication applications, optic fibers are used, which have a spatial periodic variation of the refractive index inscribed in the core, δn, periodic variation defined as grating, the fiber optic being denoted under the general name "fiber grating" [1–5]. There are two main types of such

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optic fibers: the fiber Bragg grating (FBG) ones and the long-period grating (LPG) kind [5–7]. In literature, FBGs are considered as short-period grating (300–700 nm), while LPGs as long ones (10–1000 μm). For both FBGs and LPGs, the amplitude of the core refractive index is extreme‐ ly small, in the range 0.0001–0.0005 or even smaller [5–12]. It is important to mention that only step index optic fibers for which the weakly guiding approximation relying on a very small difference between the values of the core and cladding refractive index, *nco*–*ncl*, is applicable are analyzed [5–7, 11–15]. Related to this, it has to be underlined the fact that the amplitude of the spatial periodic variation of the refractive index inscribed in the core is smaller than *nco*–*ncl* [11– 15]. The basic functions as sensors and/or wavelength filter of both FBG and LPG are accom‐ plished by controlled, observed and measured variations of optical fiber refractive indexes of the core (*nco*) andcladding (*ncl*)to whichthe refractive index ofthe ambient(*namb*)is added, where the optical fiber is mounted. Consequently, the spectral characteristics that can be observed in fiberreflection(FBG)andtransmission(LPG)gratingswillbedescribed[13–19].Foranimproved designof experimental setupsdedicatedtothe above-mentionedapplications,itisobvious that, for both FBG and LPG, the principles for understanding and tools for designing fiber gratings are emphasized [11–20]. The emphasized understanding principles and designing tools are applicable for the wide variety of optical properties that are possible in fiber gratings [19–28]. There are given examples related to the large number of fiber grating subtypes of both FBG and LPG, considering uniform, apodized, chirped, discrete phase-shifted and superstructure gratings; symmetric and tilted gratings; and cladding-mode and radiation-mode coupling gratings [20–33].

Both FBGs and LPGs are manufactured in single-mode silicate optic fiber by modifying in a periodic manner its core refractive index using UV-irradiation delivered by Ar or other UV laser [20]. Most commonly, the LPG is created by altering the core in a periodic manner, but another class of manufacturing methods physically deforms the fiber to create the required optical modulation [34–40]. These include the following: irradiation from a carbon dioxide laser, radiation with femtosecond pulses and writing by electric discharge, ion implantation, periodic ablation and/or annealing, corrugation of the cladding, micro-structuring of tapered fibers and dopant diffusion into the fiber core.
