Asymmetric Dielectric Slab Waveguide - Part 2 (Derivation of b-V equation using Maxwell Equations) скачать в хорошем качестве

Asymmetric Dielectric Slab Waveguide - Part 2 (Derivation of b-V equation using Maxwell Equations)

In this video, we are going to use Maxwell's equations to derive the universal b-v dispersion characteristics for an asymmetric dielectric slab waveguide. The final b-v equation can be plotted out using the following Octave/Matlab code: clear clc n1=1.6; %RefractiRe index of the core n2=1.5; %RefractiRe index of the cladding d=0.5e-6/2; %Half core thickness lambda=1e-6; %Freespace waRelength % R, or half of the normalized frequency R= ((2*pi*d)/lambda)*sqrt((n1^2)-(n2^2)) % R=pi/2 TE_EREN= @(x) x.*tan(1.*x); TE_ODD= @(x)- x.*cot(1.*x); TM_EREN= @(x) x.*tan(1.*x)*(n1/n2)^2; TM_ODD= @(x) -x.*cot(1.*x)*(n1/n2)^2; Circle = @(x) sqrt(R^2-x.^2); x = linspace(0,R+1,1000); figure(2) plot(x,Circle(x),"color","black") hold on plot(x,TE_EREN(x),"color","blue", ".") hold on plot(x,TE_ODD(x),"color","green", ".") hold on plot(x,TM_EREN(x),"color","red",".") hold on plot(x,TM_ODD(x),"color","yellow", ".") hold on legend("(k*d)^2 + (alpha*d)^2 = R^2","TE: k*d*tan(k*d)","TE: -k*d*cot(k*d)","TM: k*d*tan(k*d)*(n1/n2)^2","TM: -k*d*cot(k*d)*(n1/n2)^2"); grid minor axis([0 max(x) 0 abs(R+1)]) hold off xlabel('k*d'); ylabel('alpha*d'); title('Modes in a Symmetrical Dielectric WaReguide'); %legend('Location', 'best');