Calculation and application of dyadic Green's function

  • #1
Jeffrey Yang
39
0
Hello everyone:

I'm confusing with the construction and application of dyadic green's function. If we are in the ideal resonant system where only certain resonant mode is supported in this space (such as cavity), the Green's function can be constructed by the mode expansion that is:

Gij(r,r') = ff = fi(r)⋅fj(r')

In this formula, fi and fj are the normalized mode.(Here we consider electric field). Bold means vector.

For example, in a numerical simulation, we got the electric field E0(r), and then we normalized it to f(r) = E0(r)/A with normalization number A (which will be the square root of total energy of the system). Then, the dyadic Green's function will be constructed, such

Gxx(r,r') = fx(r)⋅fx(r') = E0x(r)⋅E0x(r')/A2

Now, if we want to calculate the field E(r), induced by a dipole P(r0). Then, the x component of the field will be:

Ex(r) = Gxx(r,r0)Px(r0) + Gxy(r,r0)Py(r0) + Gxz(r,r0)Pz(r0)
=(E0x(r)⋅E0x(r')⋅Px(r0) + E0x(r)⋅E0y(r')⋅Py(r0) + E0x(r)⋅E0z(r')⋅Pz(r0))/A2

These are my understanding, are they correct?

Thanks for your help
 

Answers and Replies

  • #2
18,823
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Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
 

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