In classical waveguide analysis (e.g. for optical fibers, as in the notes Modal analysis of step-index fibers, ECE 4006/5166 Guided Wave Optics, Robert R. McLeod, University of Colorado), one can find the various supported vector modes, which are typically defined as TE, TM, HE, EH groups etc
For any given mode, expressions for the mode field then exist: $E_r$, $E_\theta$, $E_z$, $H_r$, $H_\theta$, $H_z$ where $E$ is electric field, $H$ is magnetic field and we're in polar coordinates assuming a cylindrical waveguide.
Some of these field components are complex. Can anyone please explain the physical significance of the imaginary part please? I assume this is somehow related to phase?
Following on from this, what part of the field then defines the modal polarization. e.g. on p76 of the lecture notes cited above the field for TE01 is shown to exhibit a 'swirling pattern' as follows:
Is this related to the real part of the modal amplitudes? Or the magnitude (i.e. if we converted to cartesian coordinates, this would be found by adding the square of X and Y terms in quadrature?)