In this work a numerical analysis of the group delay response of the Bragg gratings written in tapered fibers is presented. In particular, a structure that is written in fiber that consist of two tapered transitions is considered. Similarly, to the single sided self-apodized gratings, a significant reduction of the group delay oscillations occurs due to the expansion of the modal field in the tapered region. Moreover, as a result of the symmetrical shape of the described structure, reduction of these oscillations occurs irrespective of the feeding direction of light. Both, tapered transitions slope and Bragg grating chirp are taken into account in respect to the limitations of the fabrication process.
In this paper an extensive study of the spectral response of the Fibonacci like Bragg gratings, that consist of multiple phase shifts, is presented. Namely in the presented analysis, for a grating with given physical parameters, a periodical structure is divided into N sections of constant length. For each section it is assumed that number of phase shifts is both distributed uniformly, and the index of section corresponds to the number of phase shifts in such a way, that for each next section number of phase shifts grows in accordance to the Fibonacci sequence. Both, symmetrical and asymmetrical structures are analyzed. For purpose of this analysis, a Coupled Mode Theory (CMT) together with Transfer Matrix Method (TMM) is employed.
This paper focuses on numerical analysis of the technological imperfections of the Bragg grating inscription process in the fiber. For such purposes, a Rouard method that allows for simulating a Bragg gratings section-by-section has been employed. The analysis presented in the paper includes considerations on the period instability of the grating together with variance of induced by UV exposure changes of the refractive index. As a result, an impact of these imperfections on the spectral responses has been examined, for both Gauss and Johnson distributions. The general motivation of this work is a proposition for novel process of the phase mask fabrication, what is also described in the following paper.
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