Design Of All-optical Temporal Integrator Based On Fiber Bragg Grating Fabry-perot Cavity

The applications of fiber gratings are more and more popular in opticalcommunication and optical fiber sensors because of its advantages of small cubage,low cost, good compatibility to fiber systems, low insertion loss, simple fabricationand so on. They can be used to make fiber laser, semiconductor laser and ring laseretc with accurate wavelength and power. Fiber gratings can be used in fiber sensorsystems as temperature sensors, strain sensors, pressure sensors, refractive indexsensors, filtering, devices of dispersion compensation, gain flattening oferbium-doped fiber amplifiers and so on.As the rising volume of global communications and the limited computer dataprocessing capacity, the requirement of AON (All Optical Network) and opticalcomputer for people is very strong. And all-optical temporal integrators are the basicbuilding blocks of optical computer. So the research for the all-optical temporalintegrators has become very important.The main work of this thesis is to establish Design of all-optical temporalintegrator based on Fiber Bragg Grating Fabry-Perot Cavity from theory, using thecoupled mode theory and the transfer matrix model was derived transfer functionexpression, and derived using the results of the matlab term numerical simulation, thefinal analysis of the results obtained and discussed, draw some important conclusions.In this way, the transmissivity of the F-P cavity under these boundary conditionsis Where the parameter is the maximumtransmissivity of F-P, the parameter F is called finesse of the transmission spectrum fringe, F=4Re/(1-Re)2,and Re=Rexp(-2αd) is defined as the effective reflectivity of the single FBG.Fig1:The amplitude of response and the phase of response of the simulated integrator and ideal integratorA uniform FBG operated in reflection provides the time integral of the electric field of an input arbitrary optical signal over a time window fixed by the round-trip light propagation time along the total grating length. The reflection Spectrum and corresponding impulse response of FBGs are a shown in FigureFig3:The Reflection Spectrum of FBGs and corresponding impulse response with different FBG LengthsThe transmission spectrum of an FP-FGB cavity with cavity length of lmm,3mm and5mm grating length of3mm and corresponding impulse response is showing in Figure4 Fig4:Transmission Spectrum of FP-FBGs and corresponding impulse responseThe theory of FBG and FP_FBG integrator is almost the same, for FPFBGs, If fl(t) is the input signal to an ideal temporal integrator then the output can be expressed as f2(t)=∫-αtf1(τ)dτ (2)The spectral impulse response of ideal integrator is given by h(t)=u(t)(3)Where u(t) is the step response. Thisideal impulse response cannot be obtained practically and by using Lorentzian approximation the impulse response can be written as h1(t)∝exp(-t/τ)u(t), Where τ is the time constant, The Fabry-Perot FBG filter exhibits exponentially decaying impulse response given by h1(t)∝exp(-kt)u(t), Where k=(c/2Ln)ln(r2γ).’L’ is the cavity length,’n’ is the refractive index of cavity,’Y’is the gain in the cavity, and ’r’ is the reflectivity of the gratings. From equations we can infer that a FP-FBG cavity behaves like a temporal optical integrator when the reflectivity of the gratings are high and loses of reflecting surfaces are compensated by the cavity gain. Figure6shows the magnitude and impulse responses of FP-FBG integrator with cavity length lmm, reflectivity of99%and FBG length of3mm along with that of an RC integrator with a resistance of about1K Q and capacitor value of1μF. For higher frequencies the phase plot of FP-FBG integrator differs significantly from that of an RC integrator owing to the limits introduced by the bandwidth as well as finesse of the cavity.Fig5:Magnitude Plot of FP-FBG integrator and RC integratorThe functionality of the designed integrator can be tested by applying different inputs to the integrator. Here a single70ps Gaussian pulse, two Gaussian pulsesin phase and two Gaussian pulses shifted by pi are used as inputs. The output obtained for the said inputs is given in fig (6-8). The outputs are compared with that of an ideal integrator.Fig6:Response of FBG and FP-FBG integrator to a single Gaussian pulse. Fig7:Response of FBGs and FP-FBG integrators to Gaussian pulses shifted by pi Fig8:Response of FBG and FP-FBG integrator to Gaussian pulses in phase...