基于线性啁啾光栅简化设计和频率-时间映射理论的任意波形产生技术研究

Arbitrary Waveform Generation Based on Simple Design of Linearly Chirped Fiber Bragg Grating and Frequency-to-Time Mapping

基于频率-时间映射理论,提出一种简单、全光纤任意波形产生方法。该方法简化了具有任意反射谱的线性啁啾光栅设计方法,结合啁啾光栅的色散特性,能够实现用户定义的任意波形脉冲信号。利用由传输损耗公式推导的折射率调制幅度与光栅反射率的关系,可实现具有任意形状反射谱的啁啾光栅的逆向设计;微调折射率调制幅度伸缩因子和折射率调制顶点的归一化光谱位置可优化反射谱形状,在保证高反射率的情况下(≥90%),设计误差可降低至10%以下。阐明啁啾光栅色散特性引入的频率-时间映射关系,将设计的光谱形状映射到时域波形,改变光栅设计参数,可灵活控制输出脉冲的形状和脉宽。基于Matlab和Optisystem仿真软件,以常用重要波形(三角形、锯齿形、矩形、梯形、高斯型、抛物型脉冲)为例验证了系统的可行性。该方法简单灵活,对任意波形产生和应用研究具有一定的参考价值。

Objective The arbitrary waveform generator(AWG)has been widely utilized in wireless communications,radar systems,and signal processing due to its benefits of high frequency and large bandwidth.More emphasis has been paid to creating commonly used pulses(triangular,sawtooth,rectangular,parabolic,and Gaussian).Conventional AWG,based on electronics,has a sampling rate up to a few tens of GHz,whereas photonic-assisted AWG,which can break the speed and bandwidth limits of electronics,has become a topic of interest.Compared with other photonic-assisted AWGs,spectral shaping and frequency-to-time mapping can realize arbitrary waveforms with the advantages of low loss,strong system reliability,and easy integration.To further simplify the AWG system based on spectral shaping and frequency-to-time mapping,linearly chirped fiber Bragg grating(LCFBG)is operated as both the spectral shaper and dispersion device for the generation of frequency-chirped and phase-coded pulses.For the generation of arbitrary waveforms,it is difficult to employ CFBG as both the spectral shaper and dispersion device because of the complicated design method and fabrication process of CFBG with an arbitrary spectral response.This paper proposes a simple allfiber method for arbitrary waveform generation based on the frequency-to-time mapping.The design scheme of CFBG with an arbitrary spectral response is simplified,and with the assistance of the dispersion characteristic of CFBG,the user-defined arbitrary waveform can be achieved accordingly.Methods This study proposes an all-fiber and straightforward method for arbitrary waveform generation based on frequency-to-time mapping.First,the design scheme of LCFBG with an arbitrary spectral response is simplified.The relationship between refractive index modulation amplitude and grating reflectivity is derived from the transmission loss formula.By adjusting the amplitude scaling factor M;and the normalized position of the spectral vertex of the refractive index modulation M;,the reflective spectral response can be optimized to achieve high reflectivity(≥90%)and low error(less than 10%).The effects of grating parameters,such as length and chirp coefficient,on reflection spectrum shape are analyzed.And then,frequency-to-time mapping introduced by the dispersion characteristic of LCFBG has been utilized to convert the designed reflection spectrum of LCFBG into a temporal waveform.In this way,the userdefined arbitrary waveform can be realized.Generated pulse shape and temporal width can be adjusted flexibly by redesigning the LCFBG,and the repetition rate is identical to that of the broadband optical source.This simple and flexible method may provide a useful reference for arbitrary waveform generation and application.Results and Discussions The system feasibility and performance are analyzed and verified on Matlab and Optisystem platforms.Triangular-shaped LCFBG is taken as an example to demonstrate the proposed design scheme of LCFBG.To realize target triangular-shaped LCFBG,we derive the refractive index modulation using the transmission loss formula and obtain the corresponding reflection spectrum via the transfer matrix method.The amplitude scaling factor M;and normalized position of a spectral vertex of the refractive index modulation M;is introduced to reduce the error between the target triangular-shaped spectrum and obtained reflection spectrum(Fig.2and Fig.3).In addition,the effects of grating length and chirp coefficient on the spectral bandwidth are analyzed(Fig.5and Fig.6).We explore the effects of the grating period and index modulation depth errors introduced in the grating fabrication process for practical applications.The grating period error has a more serious effect than index modulation depth error(Fig.7and Fig.8).Besides the triangular-shaped spectrum,the proposed LCFBG design scheme also caters to LCFBG with an arbitrary spectral response.We present the simulation results of LCFBGs with sawtooth-,rectangular-,trapezoidal-,Gaussian-,and parabolic-shaped spectra(Fig.4and Figs.9--11).User-defined arbitrary waveforms are then realized with the help of LCFBG’s dispersion characteristic.To examine and test the system viability,examples of commonly used key waveforms(triangular,sawtooth,rectangular,trapezoidal,Gaussian,and parabolic pulses)are employed(Fig.13 and Fig.14).Small amplitude oscillation on frequency-to-time mapped waveforms are induced by both limited uniform pieces in transfer matrix method and steep leading edge of the reflection spectrum.Conclusions Based on a simple design of LCFBG and frequency-to-time mapping,a low-cost,all-fiber scheme for arbitrary waveform generation is suggested in this paper.The relationship between grating reflectivity and refractive index modulation amplitude is derived from the transmission loss formula,leading to the reverse design of LCFBG with an arbitrary spectral response.The amplitude scaling factor M;and the normalized position of a spectral vertex of the refractive index modulation M;are introduced to optimize the reflective spectral response with high reflectivity(≥90%)and low error(≤10%);and yet,for designing LCFBG reflection spectrum with steep leading edge,the error will be higher.The dispersion characteristic of LCFBG maps the specified reflection spectrum into a temporal waveform.We tested the system’s practicality and performance using the Matlab and Optisystem platforms.After frequency-to-time mapping,various waveforms(triangular,sawtooth,rectangular,trapezoidal,Gaussian,and parabolic waveforms)have been successfully created.Furthermore,both transform-limited pulse sources and temporally-gated incoherent sources can provide broadband spectrum for arbitrary waveform generation,corresponding to coherent and incoherent frequency-to-time mapping.Compared with coherent frequency-to-time mapping used in this manuscript,incoherent frequency-to-time mapping has a lower cost but requires averaging operation to improve the signal-to-noise ratio,hindering real-time measurement.This simple and flexible method of arbitrary waveform generation has a certain reference value for arbitrary waveform generation and application.