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Overlap integral of the electric field distribution

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shdotcom shdotcom
shdotcom shdotcom on 19 May 2017
Commented: Torsten on 22 May 2017
Hi, I am trying to calculate overlap integral (OI) of electric field distribution, using Matlab, when run the following code:
xc = linspace(0,1,M);
yc = linspace(0,1,M);
A = E1 * E2;
B = (abs(trapz(xc,trapz(yc, abs(A))) ) ).^2;
C = trapz(xc,trapz(yc, abs(E1).^2)) * trapz(xc,trapz(yc, abs(E2).^2 ));
OI = B./C;
where E1 is the electric field distribution of the desired mode and E2 is polarized mode. Both E1 and E2 are matrices of size MxM.
but, I have got this error: Error using trapz (line 57) *LENGTH(X) must equal the length of Y in dim 1.

  2 Comments

David Goodmanson
David Goodmanson on 19 May 2017
Hi shdot, in the equation for B, I believe the 'abs' is in the wrong place. You should integrate first, take abs afterwards. Same in Torsten's code which he inherited and modified.

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Accepted Answer

Torsten
Torsten on 19 May 2017
Edited: Torsten on 19 May 2017
xc = linspace(0,1,M);
yc = linspace(0,1,M);
A = E1 .* E2;
B = (trapz(xc,trapz(yc, abs(A), 1)) ).^2;
C = trapz(xc,trapz(yc, abs(E1).^2, 1)) * trapz(xc,trapz(yc, abs(E2).^2, 1 ));
OI = B./C;
Best wishes
Torsten.

  2 Comments

shdotcom shdotcom
shdotcom shdotcom on 20 May 2017
I have edited the code based on @David Goodmanson's comments. Could you please explain to me why you used 1 instead on 2 in the trapz()
C = trapz(xc,trapz(yc, abs(E1).^2, 1)) * trapz(xc,trapz(yc, abs(E2).^2, 1 ));
Torsten
Torsten on 22 May 2017
So the code should read:
xc = linspace(0,1,M);
yc = linspace(0,1,M);
A = E1 .* E2;
B = (trapz(xc,trapz(yc, A, 1)) )^2;
C = trapz(xc,trapz(yc, abs(E1).^2, 1)) * trapz(xc,trapz(yc, abs(E2).^2, 1 ));
OI = B./C;
I used 1 instead of 2 in trapz() because you have to integrate each column of A if you integrate over y.
Best wishes
Torsten.

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