Overlap integral of the electric field distribution

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shdotcom shdotcom 2017-5-19

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评论： Suresh Chejarla 2023-5-25

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.

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shdotcom shdotcom 2017-5-20

You are right, I have edited the code.

Suresh Chejarla 2023-5-25

Hello,

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

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Answer 1

Torsten 2017-5-19

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编辑：Torsten 2017-5-19

在 MATLAB Online 中打开

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.

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shdotcom shdotcom 2017-5-20

在 MATLAB Online 中打开

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 2017-5-22

在 MATLAB Online 中打开

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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