在光波导理论中,求解波导色散曲线的常用数值方法之一是效折射率法,本文给出了有效折射率求解思路,并给出了具体的matlab程序,可供学习集成光学的学生参考使用。

clear V b;

end;

end;

axis([0, 5, 0, 1]);

xlabel('V');

ylabel('b');

gtext('E11');gtext('E12');gtext('E21');gtext('E22');

title('归一化色散曲线 a:d = 2:1');

zoom on;

yTE_DispesionFun.m函数文件：

function dTE = yTE_DispersionFun(NTEx, n)

lambda = 1.550e-6;

k0 = 2*pi/lambda;

[n1TE, n2TE, n4TE] = deal(1.5370, 1.5100, 1.4440);

dTE = 1e6*(n*pi + atan(sqrt((NTEx.^2 - n2TE^2)./(n1TE^2 - NTEx.^2))) + ...

atan(sqrt((NTEx.^2 - n4TE^2)./(n1TE^2 - NTEx.^2)))) ...

./(k0*sqrt(n1TE^2 - NTEx.^2));

yTM_DispesionFun.m函数文件：

function bTM= yTM_DispersionFun(NTMx, n)

lambda = 1.55e-6;

k0 = 2*pi/lambda;

[n1TM, n2TM, n4TM] = deal(1.5360, 1.5095, 1.4440);

bTM = 1e6*(n*pi + atan(sqrt((n1TM^2*(NTMx.^2 - n2TM^2))./(n2TM^2*(n1TM^2 - NTMx.^2)))) + ...

atan(sqrt((n1TM^2*(NTMx.^2 - n4TM^2))./(n4TM^2*(n1TM^2 - NTMx.^2)))))...

./(k0*sqrt(n1TM^2 - NTMx.^2));