Long Period Fiber Grating Differentiator Research

All-optical signal process is essential for the future high-speed all-optical network.All-optical differentiator is a key device in all-optical signal process, which can achievethe differentiation of optical signal in the time domain. In this dissertation, thelong-period fiber grating has been deep researched, and the feasibility of opticaldifferentiator based on mechanically long-period fiber grating is verified throughexperiment and simulation. The main contents are as follows:1. Characteristics of long-period fiber grating are analyzed. When considering thecoupling between the core mode and one of the cladding modes only, coupled modeequations is derived in detail from Maxwell’s equations, then response function of coremode and transmission matrix are obtained.2. According to the core response function of uniform long-period fiber gratingunder the conditions of full-coupling, first order differentiator based on mechanicallylong-period fiber grating is designed, and its performance is simulated and analyzedusing the spectrum measured by experiment.3. The second order differentiator based on mechanically long-period fiber gratingwith a shifted is designed, and its performance is simulated and analyzed using thespectrum measured by experiment. For the long-period fiber grating fabricated bymechanically is related to the light polarization state, the influence of the polarizationcan be eliminated by Faraday rotator. Studies show that Faraday rotator can make thedifferentiator order double, at the same time, the transmission ratio of LPFG at theresonance wavelength is closer to zero, which improves its accuracy.4. After analyzed the amplitude function and phase function of differentiatorresponse function, the program of fraction order differentiator based on mechanicallylong-period fiber grating is studied. The performance of0.6order differentiator issimulated and analyzed using the spectrum measured by experiment.5. The factors can lead to errors of the long period fiber grating differentiator areanalyzed, studies show that: i) grating resonance wavelength should be the same withthe center frequency of the input light signal, otherwise the spectrum in the center frequency after differentiation is not equal to zero; ii) when the resonance frequency offiber grating is different with the center frequency of input pulse, the spectrum afterdifferentiation is not symmetrical about the center frequency.