What is the actual definition of the TM mode?

[dayan83]

What is the actual definition of the TM mode? A typical definition that I've come across is that there is no Magnetic field component in the direction of wave propagation. As it is an EM wave, according to that definition the Magnetic field should be in the plane normal to the direction of propagation.

Recently I saw in some books, it states that if a TM wave is traveling in x direction, the magnetic field component should be y direction (i.e Hy is the only nonzero component, with Hx=0 & Hz = 0). (The other only nonzero components being Ex & Ez). Is it always the case for TM waves? Or is this for some special condition?

 

[jasonRF]

What is the actual definition of the TM mode? A typical definition that I've come across is that there is no Magnetic field component in the direction of wave propagation. As it is an EM wave, according to that definition the Magnetic field should be in the plane normal to the direction of propagation.

A standard electromagnetic wave is often labeled TEM (transverse electric and magnetic), since there are no components of the wave field in the direction of propagation. In free space all electromagnetic waves are TEM.

However, if you launch an electromagnetic wave inside a metal pipe (aka waveguide) it turns out that a TEM wave cannot propagate, but modes that have either electric or magnetic fields in the direction of propagation do propagate. Just as you stated, TM modes have no magnetic field parallel to the direction of propagation. Another kind of mode, called TE, has no electric field parallel to the direction of propagation.

Recently I saw in some books, it states that if a TM wave is traveling in x direction, the magnetic field component should be y direction (i.e Hy is the only nonzero component, with Hx=0 & Hz = 0). (The other only nonzero components being Ex & Ez). Is it always the case for TM waves? Or is this for some special condition?

That is a special case.

 

[Born2bwire]

TE and TM are just a generic way of describing an electromagnetic mode. In most electromagnetic problems, you can decompose an arbitrary EM wave into two components, TE and TM, with respect to an arbitrary direction. This can make things much easier to solve, like if you have a 2D scattering problem. With a 2D problem, one axis is assumed to be invariant and this is the axis that we refer to for the TE and TM. If we have a waveguide, the direction of guided propagation is the axis referred to for the TE and TM modes. And so on.