Research On Optical Computing And Pulse Shaper Based On Transmissive Fiber Bragg Gratings

As an ideal optical waveguide,devices based on fiber have advantages like low loss,small size,anti-electromagnetic interference and relatively low price compared with other waveguide devices.Among all fiber optical devices,fiber gratings have more and more applications in optical sensing,fiber communication and optical computing due to their unique regulation of light waves.Fiber gratings can be divided into Fiber Bragg Gratings(FBG)and Long-Period Fiber Gratings(LPG)according to the size of the grating period.Compared with LPG,FBG has higher tolerance to the surrounding environment and are more suitable for practical applications.According to the working mode,FBG can be divided into reflective FBG and transmissive FBG.Compared with reflective FBG,transmissive FBG does not require an additional optical circulator or coupler,reducing cost and system complexity.This thesis focuses on the design and application of novel FBGs and uses them in optical computing and optical pulse shaping areas.The main contents of the thesis include:1)Theoretically analyzed various algorithms for synthesizing FBG,including mapping algorithm,layer-peeling algorithm and optimization algorithm.The mapping algorithm mainly includes space-to-time mapping method and space-to-frequency-to-time mapping method.The space-to-time mapping algorithm is only applicable to weak reflection FBG;the space-to-frequency-to-time mapping method is applicable to weak to medium reflection FBG.Layer-peeling method includes discrete layer-peeling algorithm and continuous layer-peeling algorithm,in which the discrete layer-peeling algorithm is more commonly used because it runs faster.The optimization algorithm mainly includes genetic algorithm,Newton algorithm,quasi-Newton algorithm and trust region method.The genetic algorithm is an evolutionary algorithm and has global optimization features but slow convergence while Newton algorithm,quasi-Newton algorithm and trust region method are all iterative algorithms and have local optimization features but fast convergence.2)All-optical fractional-order temporal differentiators with bandwidths reaching terahertz(THz)values are demonstrated with transmissive fiber Bragg gratings.Since the designed fractional-order differentiator is a minimum phase function,the reflective phase of the designed function can be chosen arbitrarily.As examples,we first design several 0.5th-order differentiators with bandwidths reaching the THz range for comparison.The reflective phases of the 0.5th-order differentiators are chosen to be linear phase,quadratic phase,cubic phase,and biquadratic phase,respectively.We find that both the maximum coupling coefficient and the spatial resolution of the designed grating increase when the reflective phase varies from quadratic function to cubic function to biquadratic function.Furthermore,when the reflective phase is chosen to be a quadratic function,the obtained grating coupling coefficient and period are more likely to be achieved in practice.Then we design fractional-order differentiators with different orders when the reflective phase is chosen to be a quadratic function.We see that when the designed order of the differentiator increases,the obtained maximum coupling coefficient also increases while the oscillation of the coupling coefficient decreases.3)All-optical arbitrary-order temporal differentiators are demonstrated with phase-modulated fiber Bragg gratings(PM-FBGs)in transmission for the first time.The transmissive PM-FBGs are designed by employing a novel two-step nonlinear optimization method,which consists of unconstrained nonlinear optimization method step and constrained nonlinear optimization method step.Specifically,the first unconstrained nonlinear step is used to get appropriate parameters as input to the second step,while the second constrained nonlinear step is employed to generate more accurate result based on the output of the first step.The proposed method does not impose much restriction on the initial input parameters and also improves the result accuracy compared with previous one-step nonlinear optimization method.Examples of 0.5th-order,first-order,and second-order differentiators are designed and numerically simulated.The numerical results show that the designed PM-FBG differentiators are very accurate with a bandwidth up to 500 GHz.4)We show analytically and numerically that a practically realizable phase-shift fiber Bragg grating(PS-FBG)can function as a temporal first-order optical differentiator and a temporal first-order optical integrator at the same time.The PS-FBG working in reflection implements the differentiation and working in transmission implements the integration.We provide both the generalized conditions for a PS-FBG functioning as a first-order optical differentiator and a first-order optical integrator.The proposed PS-FBG can perform the time differential and integral of the complex envelope of an input optical signal with high accuracy,respectively.5)We propose all-optical arbitrary-order Hilbert transformers using phase-modulated fiber Bragg gratings(PM-FBGs)in transmission.For demonstration,we have designed and numerically simulated 0.5th-order,first-order and 1.5th-order photonic Hilbert transformers,respectively.The profiles of those PM-FBGs are obtained using Quasi-Newton optimization algorithm.The numerical results show that the designed three Hilbert transformers are all very accurate with bandwidths up to 500 GHz.6)Customized ultrahigh repetition rate pulse bursts are demonstrated with PM-FBGs in transmission.Examples of three,four and eight replicas with a repetition rate of 100 GHz in one period of the input pulse are designed and numerically simulated.The simulation results show that the designed PM-FBGs can function as pulse bursts generator very well.7)We introduce the FBG fabrication system based on UV laser direct writing technology.The system uses phase mask and acousto-optic modulator to realize the fabrication of arbitrary FBG.Both of the pulse bursts generator and first-order optical differentiator were fabricated using this system,and the measured transmission spectrum response of the fabricated gratings were consistent with the simulation results.Finally,this pulse bursts generator FBG is applied to the pattern conversion from the return-to-zero on-off keying(RZ-OOK)to the non-return to zero on-off keying(NRZ-OOK),and the experimental verification is carried out.The experimental results show that the device we designed perform pattern conversion very well.