Extra solutions using fimplicit
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Question has three parts
1) For a slab waveguide, I have been trying to obtain Dispersion plot like this:
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/253136/image.png)
2) So, I wrote a code using fimplicit and some well-chosen parameters:
function main
fimplicit (@(x,y)f(x,y),[0 10])
end
function fun = f(x,y)
nc=1.45; %cladding
nf=1.5;
ns=1.4; %substrate
h=5; %width of waveguide
beta=sqrt(x^2*nf^2-y.^2);
gammas=sqrt(beta.^2-x^2*ns^2);
gammac=sqrt(beta.^2-x^2*nc^2);
z=sin(h*y);
%TE mode
fun=z-cos(h*y)*(gammac+gammas)./(y-gammas.*gammac./y);
%TM mode
%b=(nf^2*gammas/ns^2+nf^2*gammac/nc^2)./(kappa-gammas.*gammac./kappa*nf^4/nc^2/ns^2);
%fun = ((3*I2).^(n/2)).* (an1 + an2 + an3) - (2*(189.32)^8);
end
It produced:
![mat.png](https://www.mathworks.com/matlabcentral/answers/uploaded_files/253145/mat.png)
3) Now to verify the correctness of this plot, I took an example from a book for x=
according to which (
,0.55), (
,1.2),(
,1.65),(
,2.15)should be data points in dispersion curve. In plot above, corresponding to x=
, there are 5 values with the zig-zag line being unwanted one, why is this zig-zag spoiling the diagram ?
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/253138/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/253138/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/253138/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/253138/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/253138/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/253138/image.png)
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