《非线性光纤光学》第四章第4题,我的解答

题目:画出KDP晶体的角度调谐曲线

mmexport1637455043064.jpg

(1)

前辈有题解了咱这里就偷个懒咯~

第一问题解.jpg

代码也很简单,把公式抄一抄带一带就好了,注意的话,书上的每个常数都别简化估算,全部写进代码里,不然算不出精确结果哒。

lamda = 347.2;
lamda_p = lamda*1e-3;
lamda_s = 2*lamda_p;
lamda_i = 2*lamda_p;
no_2w_squ = 2.259276 + 0.78056/(77.26408*lamda_p*lamda_p-1) + (0.032513*lamda_p*lamda_p)/(0.0025*lamda_p*lamda_p-1);
no_w_squ = 2.259276 + 0.78056/(77.26408*lamda_i*lamda_i-1) + (0.032513*lamda_i*lamda_i)/(0.0025*lamda_i*lamda_i-1);
ne_2w_squ = 2.132668 + 0.703319/(81.42631*lamda_p*lamda_p-1) + (0.00807*lamda_p*lamda_p)/(0.0025*lamda_p*lamda_p-1);
ne_w_squ = 2.132668 + 0.703319/(81.42631*lamda_i*lamda_i-1) + (0.00807*lamda_i*lamda_i)/(0.0025*lamda_i*lamda_i-1);
inside = (ne_2w_squ./no_w_squ )*(no_2w_squ - no_w_squ )/(no_2w_squ - ne_2w_squ  );
theta = asin(sqrt(inside))*180/pi;

(2)

很合理的,把第一问由特殊到一般推广一下。从300 nm到500 nm取一些波长,再把公式改写成矩阵乘法的形式,做图即可

lamda = linspace(300,500,301);
lamda_p = lamda*1e-3;
lamda_s = 2*lamda_p;
lamda_i = 2*lamda_p;
no_2w_squ = 2.259276 + 0.78056./(77.26408*lamda_p.*lamda_p-1) + (0.032513*lamda_p.*lamda_p)./(0.0025*lamda_p.*lamda_p-1);
no_w_squ = 2.259276 + 0.78056./(77.26408*lamda_i.*lamda_i-1) + (0.032513*lamda_i.*lamda_i)./(0.0025*lamda_i.*lamda_i-1);
ne_2w_squ = 2.132668 + 0.703319./(81.42631*lamda_p.*lamda_p-1) + (0.00807*lamda_p.*lamda_p)./(0.0025*lamda_p.*lamda_p-1);
ne_w_squ = 2.132668 + 0.703319./(81.42631*lamda_i.*lamda_i-1) + (0.00807*lamda_i.*lamda_i)./(0.0025*lamda_i.*lamda_i-1);
inside = (ne_2w_squ./no_w_squ ).*(no_2w_squ - no_w_squ )./(no_2w_squ - ne_2w_squ  );
theta = asin(sqrt(inside))*180/pi;
d_theta = abs(50.5480 - theta);
plot(lamda,d_theta);
xlabel("lamda")
ylabel("角度变化")

做图的结果

程序结果.jpg

由图观察波长范围大致在306 nm 到 443 nm,因此可以有λs和λi的调谐范围是612 ~ 886 nm