Hello, i am using the following paper to try and visualise the TM TE modes in the microstrip as shown in the photos bellow.
the mode is described by three digits.
the solution for TM001 is shown bellow.
In the X direction we have the electric field
i the Y direction we have the magnetic field
So we have E field Cosine pattern along Z with X polarity and H along the Z direction with Y polarity.
But i cant se how it works witht the formal definition of TM shownshown in the end.
our H field is at Y direction while its propogating in the Z-direction
there is a contradiction with the formal definition.
How the magnetic field is peralel to the direction of propogations?


Thanks.
page 16
http://www.acad-antenna.co.il/pics/ACAD/_thumbs/21_Microstrip_2.pdf

 

The thing about vector fields that often confuses people is the nature of the derivative of a vector. In a scalar field the derivative is an expression of the change in magnitude at every point in the field. In a vector field the derivative has two parts; one part describes the change in magnitude and the other part describes the change in direction. One of the consequences of Maxwell's Equations is that changing magnetic fields produce electric fields that are normal to (perpendicular to) the magnetic fields. Similarly, changing electric fields produce magnetic fields, that are you guessed it, normal to those electric fields.

Lastly, all the solutions for wave equations have a provision for both standing waves and traveling waves. The thing about traveling waves is that when they reach an impedance discontinuity something has to change. What changes is usually the magnitude and the direction. The direction change is because of a reflection and the magnitude change is because some of the energy in the incident wave passes through or is absorbed by the discontinuity.

Your solutions are standing waves because there is no explicit time dependence. They are only a function of the spatial coordinates.
The effect of the "walls" in your diagram, as I understand it is to confine energy of that type, either electric or magnetic to the inside of the box. However magnetic energy can be transmitted through the electric wall if it was moving in that direction. Likewise electric energy can penetrate the magnetic walls if it was moving in that direction.