A practical question of basic EM: E-field H-field

Hi,

(For example if I use HFSS): After simulation, I obtain

rE_Phi (real+imag) and rE_Theta (real+imag).

(they are Electric field in the far field).

How do I convert them to rH_Phi and rH_Theta ?
Can I convert each complex values to Mag+Angle, then add 90 to the angle ?

Thank you so much.

You will need to compute H from E using Maxwell's equations. The curl equation is

Δ×E=-jωμH

Assuming your far-field is of a plane wave form

E = E0 * exp(-i*k*z)

then your H-field will be

H = (Ex*ay - Ey*ax)/η

Here ax and ay are unit vectors in the x and y directions. η is the impedance of the far-field medium, and Ex and Ey are components of the electric field. Assuming this wave was travelling in the z-direction, the E field has only has x and y components.

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Another approach is to simply realize the magnitude of the H field can be computed from the magnitude of the E field through the impedance of the far field medium.

|H| = |E|/η

The direction of the vector of H can be found through the Poynting vector. This says E and H are normal to each other and the direction of the field is propagating (P). They form a "right handed" system.

E×H=P

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I should mention the phase of E and H are the same.

Hope this helps!!
-Tip