对于沿着z轴传播的单色平面波,其表达式可写为
选择横平面上的某一点,假设该点上的相位保持恒定,即常数,则有
根据以上关系,等式两边对时间求导,即可得
则,得到相速度表达式为
其表示具有恒定相位的表面(点)在介质中运动的速度。
Matlab可视化代码如下:
clear all
N_max = 101; % number of points for plot
t = linspace(0,30d-15,N_max); % creation of theta arguments
%
c = 3d14; % velocity of light in microns/s
n = 3.4; % refractive index
v_p = c/n; % phase velocity
lambda = 1.0; % microns
k = 2*pi/lambda;
frequency = v_p/lambda;
z = 0.6; % distance in microns
omega = 2*pi*frequency;
A = sin(k*z - omega*t);
plot(t,A,'LineWidth',1.5)
xlabel('Time','FontSize',14);
ylabel('Amplitude','FontSize',14);
set(gca,'FontSize',14); % size of tick marks on both axes
axis([0 30d-15 -1.5 2])
text(17d-15, 1.3, 'z(t)','Fontsize',16)
line([1.53d-14,2d-14],[1,1],'LineWidth',3.0) % drawing arrow
line([1.9d-14,2d-14],[1.1,1],'LineWidth',3.0)
line([1.9d-14,2d-14],[0.9,1],'LineWidth',3.0)
pause
close all
以上,希望对大家有所帮助!