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Power Passing through a Monitor at an Angle

    • Sabrina Corsetti

      Hello! This seems like a silly problem to be having, but I've been trying numerous methods to solve it, to no avail.

      The trouble is, I have an FDTD simulation of a grating. The grating creates scattering in all dimensions - up, down, left, and right, with some transmission and reflection.

      To measure the power scattered in each direction, I have 6 monitors (top, bottom, left, right, etc.) enclosing the entire simulation region. So, in theory, the sum of the power through the 6 monitors should be 100% of the source power. 

      The trouble is that, depending on the method I use to calculate the power through each of the monitors, this sum comes out to well over 100%. 

      For example, suppose I find the power in the "upwards" monitor using the integral of the electric field intensity, e.g.:

      • E2_UP = getelectric("UP",2);
      • E2_UP_int = integrate(E2_UP,[1,3],x_UP,z_UP);
      • Power_UP = c*n*eps0/2*E2_UP_int;

      • P_Source = sourcepower(getdata('source_WGmode','f'),2);

      If I then take Power_UP/P_Source, that quotient alone turns out to be about 1.56. So just one monitor seems to be recording more than 100% of the source power. 

      The total power does come out to 100% when I take "transmission" through each of the monitors, from getresult. However, since "transmission" integrates only normal to the surface, it seems like power is lost in the calculation, due to the grating emission propagating at 45 degrees. This is confirmed by integrating power in a spot in the far-field over the grating, using the electric field amplitude method above. The fractional power in that spot comes out to be larger than the "transmission" value for the entire upwards monitor.

      In short - is there something conceptual I'm missing here, regarding how to integrate power? Essentially, I don't see how taking  c*n*eps0/2*E2_UP_int could ever give a value larger than the source power, unless I'm misunderstanding how the source power is normalized?

      Any feedback on this issue would be appreciated. Thank you!

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