Overlap integral of the electric field distribution

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.

[David Goodmanson]

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.

[shdotcom shdotcom]

You are right, I have edited the code.

[Suresh Chejarla]

Hello,

Can you please provide the reference for the OI expression which you have put here ?

Answer 1

[Torsten]

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.

[shdotcom shdotcom]

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]

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.