Analysis Of Spatial Power Distribution Of Sampled Fiber Gratings

The sampled FBGs (SFBGs), also known as superstructure sampled FBGs, have been widely used in dense wavelength division multiplexing (DWDM) systems, multi-wavelength laser and optical sensing systems due to its multi-channel characteristic. Currently, researches on SFBGs mainly focus on their amplitude-frequency responses and phase-frequency responses. However, there is few research concentrates on the power distribution of SFBGs along the grating length, i.e., the characteristic of SFBGs in the spatial domain. Such a stationary power distribution might be beneficial for numerous applications, such as fiber laser, microwave photonics and optical sensor, and so on. In this thesis, deep analysis is provided in order to demonstrate the spatial power distribution of SFBGs.In this thesis, the history of fiber grating is first introduced, especially five kinds of applications of FBGs (WDM multiplexer, dispersion compensators, microwave filters, fiber laser and optical sensor). Brief introductions are given on the history of SFBGs, including the advantage and disadvantage of sampled methods and the applications of SFBGs. In the meanwhile, deep illustrations on the structure of FBGs and the coupled-mode theory are provided in chapter two. Then basic structure and classification of sampled fiber grating (amplitude sampling, phase-only sampling and amplitude-assisted phase sampling, etc.) are demonstrated, and the transfer matrix method of SFBGs and the Fourier theory are introduced.Secondly, the fundamental theory of field distribution inside fiber gratings is demonstrated, and two theoretical models (rectangular sampling method and Fourier series method) based on the structure of SFBGs are proposed to analyze the spatial power distribution. Moreover, all the results obtained from these two models are equivalently identical and capable of revealing the spatial power distribution of SFBGs. In the first model (rectangular sampling method), the spatial power distribution of sinc-SFBG with eight channels is analyzed. The results indicate the first model applies not only to rectangular sampling, but also to more complicated sampling methods. In the second model (Fourier series method), the spatial power distribution is obtained for each channel and this model is able to provide higher calculation efficiency for analyzing the spatial power distribution of SFBGs. In addition, the influences of the duty cycle on the spatial power distribution are discussed as well.Afterwards, two kinds of phase sampling approaches (phase-only sampling and amplitude-assisted phase sampling) are discussed. The impacts of the refractive index modulation depth, the number of phase-shift and the insertion points of phase-shifts on the amplitude response and the spatial power distribution of these two kinds of phase SFBG are analyzed. For single channel phase-sampled SFBG, the peaks of power distribution curve are increased with the increase of the number of phase-shifts. While for multiple-channel phase-sampled SFBG, the trends of the power distributions before and after the point of phase-shifts are opposite.This thesis focuses on analyzing the spatial power distribution of SFBGs. The research methods and results might be significant for the future studies.