1.给参数赋值,再解六元一次方程组,分别画出ratio与其中两个解C11、C12的图像,以及表达式g2=2*C12^2/C11^4的图像。
clc
close all
clear all
syms C11 C12 C20 C21 C30 C31
g = 2*pi*4;
Omega1 = 2*pi*1.3;
Omega2 = 2*pi*1.5;
gamma31 = 2*pi*3;
gamma21 = 2*pi*0.3;
k = 2*pi*4;
E = 2*pi*0.01;
delta2=2*pi*0;
fi=pi*0;
ratio = -50:0.001:50; %横坐标从-50到50取1000个点
for ii=1:length(ratio)
delta1(ii) =2*pi*ratio(ii);
deltam(ii) = delta1(ii);
ff1 = E*C11+Omega1*C20; %六个方程组
ff2 = E+(deltam(ii)-1i*k)*C11+E*sqrt(2)*C12+Omega1*C21+g*C30;
ff3 = sqrt(2)*E*C11+(deltam(ii)-1i*k)*C12+sqrt(2)*g*C21;
ff4 = C11*Omega1+E*C20+(deltam(ii)+delta1(ii)-1i*k-1i*gamma21)*C21+Omega2*C31;
ff5 = C11*g+Omega2*C20*exp(-1i*fi)+(delta1(ii)+delta2-1i*gamma31)*C30+E*C31;
ff6 = sqrt(2)*g*C12+Omega2*C21*exp(-1i*fi)+E*C30+(deltam(ii)-1i*k+delta1(ii)+delta2-1i*gamma31)*C31;
[C11,C12,C20,C21,C30,C31] = solve(ff1,ff2,ff3,ff4,ff5,ff6); %解方程
C11 = vpa(C11,4); %得到方程的解C11
C12 = vpa(C12,4); %得到方程的解C12
CC11(ii,:) = double(C11);
CC12(ii,:) = double(C12);
g2(ii) = 2*(abs(CC11(ii,:)))^2/(abs(CC12(ii,:)))^4; %表达式g2=2*|C12|^2/|C11|^4
end
plot(ratio,CC11,'r',ratio,CC12,'b',ratio,g2,'g') %画出ratio与C11和C12以及g2的函数图像