Design Of All-optical Temporal Differentiators Based On Phase-shifted Long-period Fiber Gratings

With the continuous progress and development of human society, computer andcommunications equipment development gradually the essential information tool inPeople’s Daily life. In today’s communication and computing fields, based on theelectronic technology of communication networks are almost reached the limit speed.As a result, people expect through the optical fiber grating technology research anddesign, the light of the computer as soon as possible into People’s Daily lives, and letall optical communication network become a new carrier of information exchange andtransmission.All-optical temporal differentiator is an important part of opticalcomputers can be any light wave waveform of the input differential signal time,compared with traditional electronics differentiator, all-optical time differentiator isfar superior to traditional electronics differentiator inside the processing speed. So,for the all-optical temporal differentiator of research work has the very vitalsignificance, also has a role in promoting in the realization of the optical computerand all-optical communication network.Communication is the main direction of futureall optical communication network, so to speak, and the development of all-optical time differentiator is the key technology of all-optical network. Its super charactersuch as bandwidth, low loss, high speed, will gradually by the attention of people,make it has great application value in the field of optical fiber communication, bring arevolutionary change in human life.This paper put forward based on phase-shifted long-period fiber gratingall-optical time differentiator of analysis and design work. For long period fibergrating to realize all-optical time differentiator operation, need to transfer through thefilter, so find the filter transfer function is very important.On this basis, the filtertransfer function to make use of MATLAB simulation, to find the ideal transmissionspectrum and phase change of the spectrum, and the time, to simulate thedifferentiator theory put forward by the analysis of spectrum, for the next deeperresearch, provide theoretical support.This paper consists of four chapters:Chapter1: First of all,according to the paper’s design idea, in the first chapterrespectively introduced the history and development of optical fiber communication,optical fiber grating according to the classification of different parameter has carriedon the detailed introduction, and its application in the field of communication andsensing has carried on the simple introduction. Chapter2:On the basis of in the first chapter,detailed introduces gratingcoupled-mode theory of optical fiber and optical waveguide theory, and the transfermatrix method is used for related introduction. For the rest of the time can providetheoretical basis for research work.Chapter3:On the basis of chapter2was introduced About fiber grating theory,long period fiber grating are introduced separately the coupling principle, producingmethod of long period fiber grating and the application of long period fiber grating inthe related field, through the introduction to these features, for the production of fibergrating and the grating device options provide advice.Chapter4:On the basis of the former three chapters, and mainly introducedbased on phase-shifted long period fiber grating is put forward the order1timedifferentiator and N order differentiator of research methods, through the coupledmode theory and transfer matrix method of theory analysis, According to the coupledmode equations, we in the symmetric position of long period fiber grating π phaseshift. However long period fiber grating receiving mode for cladding mode, it will bedifficult to retrieve the output signal, so we use the filter transfer function to transfer.Let us assume an arbitrary optical signal spectrally centered at the opticalfrequencyω0(carrier frequency). The signal’s time-domain representation can be mathematically described as follows:where x(t)is the analytic representation, and xe(t)is the complex temporal envelope ofthe optical signal.Notice that it is assumed that the slow-varying envelope approximation alwaysholds for the involved optical signals (i.e., the spectral bandwidth of the signal underanalysis is much smaller than the carrier frequency). At this point, if x (t)as the inputsignal, then the corresponding approximate ideal differentiator output signal y (t)canbe represented as:In the range of frequency domain, through Fourier change between the input andoutput of the approximate expressions for the:where X e(ω)and Ye (ω)are the Fourier transforms (complex spectra) of the input andoutput temporal envelopes, xe(t)and ye(t), respectively.In this notation,ω=ωopt ω0is the baseband angular frequency variable, withω optbeing the optical angular frequency variable. Thus,in terms of the signals’ analytic representations:By type can be seen on the input optical signal is independent, meaning that forany input optical wave is established. This means that what we call the timedifferentiator based on long period fiber grating operation can be provided through alinear filter spectral transmission function to realize. Both, the ideal transfer functioncan be represented as:Uniform type is on long period fiber grating under the condition of full coupling,the linear relationship of transmissionthe expression.It for the first time the realizationof the differentiator is necessary, and it needs injection π phase shift in the resonantfrequencyω R, and the resonance frequencyω Rzero transfer. Such long period fibergrating devices will be able to as a first-order time differentiator to input any of theoptical pulse differential operation. It is worth noting that the transfer function in thecenterω0for the limited spectrum bandwidth of continuous existence, its role will beto determine the processing speed of the differentiator. In addition, filter transferfunction has two main characteristics: one, in the baseband frequency range, the linearchange; Second, in the center of the signal frequencyω0zero transmission function; And these two characteristics need to be in the center frequencyω0insertionπphaseshift can be achieved. Fig a and b, respectively, for the ideal transfer function of thetransmission spectrum and phase spectrum lines.In theory, we choose long period fiber grating length L=8.9cm, periodΛ=415μm, wavelength1540nm, use sine function and cosine function,and gaussianpulse as input, the output of the transmission line, respectively, as follows: Fig.c input cosine and sine function and the gaussian pulse of first-order long periodGrating tempole differentiatorFor N-order long period fiber grating photonic temporal differentiator iscomposed of multiple segments, each segment is a uniform long-period fiber grating.So N-order photonic temporal differentiator be able to get through with the transferfunction of the filter. That is to say, the transfer function can be written as:Assumes that the coupling coefficient is120m1, type optical fiber for the SMF-28,wavelengths is1550nm,period is495μ m,respectivelythe,input signal is half widthvalue of400fs with two peaks of the gaussian pulse and pulse "S" type. For N=2,there are: We can get the ideal second-order differentiator phase-shift grating to3:1ratio, whichis respectively19.6and6.5mm, as shown in the figure below.Fig.d Input double-peak gaussian pulse and "S" type pulse of2-order long period fibergrating photonic temporal differentiatorFrom energy efficiency and the differentiator error rate on the numericalsimulation, we increase the differentiator grating reflectivity will improve theefficiency of energy, however, differential error rate will also increase. As a result, thesame as the all-optical time order differentiator, need to achieve a balance betweenenergy efficiency and differential of error rate. The differentiator model can be any light wave differential, processing speed has reached the GHz, greatly improves theprocessing speed than traditional computers.