中文摘要：

光在具有负等效折射率的二维光子晶体中传输时会产生反常Doppler现象,为了分析光在该反常效应中传输时的相位变化,首先用时域有限差分（FDTD）法仿真了光经过静止光子晶体时的负折射现象,然后对光子晶体中沿光传输方向的Bloch波做快速傅里叶（FFT）处理.对滤波后的频谱,用iFFT反演出各平面波分量,并通过分析各平面波分量的相位演变,分离出与负折射产生有关的后退波分量.然后,将实验中的连续运动过程分解为各静止瞬间,分析了各相邻时刻探测面上信号光和参考光的相位变化,此处两束光的相位变化差随时间的变化量就是差频.静态FDTD方法仿真计算得到的差频与理论值的误差约为20％,能较好解释反常Doppler效应发生过程中光的相位变化.本文的研究揭示了反常Doppler效应发生时光子晶体中起作用的分量的相位变化,也为研究光在运动介质中的传输特性提供了新的思路.

英文摘要：

The inverse Doppler effect in two dimensional photonic crystal with negative index was proved.In order to analysis the phase evolution of light propagated through this effect,the negative refraction was simulated in static photonic crystal by the Finite Difference Time Domain （FDTD）method.Subsequently,the Bloch wave along the propagating direction was analyzed based on the Fast Fourier Transform （FFT） method.Then,the components were retrieved by iFFT method from the filtered spectrum.The phase evolution of each component was analyzed for the extraction of the backward wave component related to the negative refraction.Furthermore,the phase evolution of signal beam and reference beam on the detecting surface was deduced by dividing the continuous movement of the platform into a series of static moment,where the variation of phase difference with time is the beat frequency.These values obtained with this method are closed to the theoretical values,with an error of 20％,which can explain the phase evolution of light in the inverse Doppler effect.The result reveals the phase evolution of the backward wave in photonic crystal,and provides a new way in dealing with the case of light passing through moving objects.