Take a rect 2D silicon waveguide that propagates in x for example. I suppose we can use sqrt(ewfd.Poavx^2+ewfd.Poavy^2+ewfd.Poavz^2) as the poynting vector, right? But what is it really?
How does comsol calculate the power average over time?
Can we get to the same results somehow by using E and H fields?
The time averaged poynting vector is defined as
P = 1/2 * (E x H*)
You can take the cross product of E and H and you should get:
2*Px = Ey * Hz - Ez * Hy
2*Py = Ex * Hz - Ez * Hx
2*Pz = Ex * Hy - Hy * Hz
If your waveguide is propagating in the x-direction you would want to use the formula for Px. Depending on your mode (TE or TM) only Ey or Ez will exist. For TM-modes for examples only Ez will exist (electric field in the plane, if you are looking at your silicon waveguide from the top down in the 2D simulation) so you are left with:
Px = - 1/2 * (Ez * Hy*)
As a COMSOL expression, this would be:
-0.5 * ewfd.Ez * conj(ewfd.Hy)
which, if you plot it, should be identical to
ewfd.Poavx
I hope this is of help.
The time averaged poynting vector is defined as
P = 1/2 * (E x H*)
You can take the cross product of E and H and you should get:
2*Px = Ey * Hz - Ez * Hy
2*Py = Ex * Hz - Ez * Hx
2*Pz = Ex * Hy - Hy * Hz
If your waveguide is propagating in the x-direction you would want to use the formula for Px. Depending on your mode (TE or TM) only Ey or Ez will exist. For TM-modes for examples only Ez will exist (electric field in the plane, if you are looking at your silicon waveguide from the top down in the 2D simulation) so you are left with:
Px = - 1/2 * (Ez * Hy*)
As a COMSOL expression, this would be:
-0.5 * ewfd.Ez * conj(ewfd.Hy)
which, if you plot it, should be identical to
ewfd.Poavx
I hope this is of help.
Thanks for taking your time for answering this Jens Høvik
I actually did help a lot. It's much simpler than I originally thought. Thanks
I was testing for the other components as well and found slightly different component indexes from the cross product. Minor things though.
2*Px = Ey * Hz - Ez * Hy
2*Py = Ez * Hx - Ex * Hz
2*Pz = Ex * Hy - Hy * Hx
So:
ewfd.Poavx = -0.5 * ewfd.Ez * conj(ewfd.Hy)
ewfd.Poavy = 0.5 * ewfd.Ez * conj(ewfd.Hx)
ewfd.Poavz = 0.5 * ewfd.Ex * conj(ewfd.Hy)
You could have found that in the Variables tab in Equation View subnode of Wave Equation node in your EM physics. For future questions regarding equations of COMSOL you should follow this route first, it is extremely useful (to enable Equation View, in the top panel of Model Builder click the eye icon and choose Equation View).
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