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I have three questions about electromagnetic waves and was wondering whether anybody here could comment on these things:

Wikipedia says that there are no longitudinal EM waves, although TM and TE waves exist. How can I see that an EM wave can never be purely longitudinal?

Does it always hold that the E-field is perpendicular to the B-Field in an EM wave?

Wave packets have a group velocity that can be different from the phase velocity. Is it correct that due to $\omega= vk$, the phase and group velocity for a plane wave are always the same?

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  • $\begingroup$ The dispersion $\omega(k)=v(k)k$ is independent of the type of wave but depends on the boundary conditions you impose. In materials or wave guides, it can be non-linear leading to different group and phase velocities. In free space, however, where the dispersion is linear, group and phase velocity are the same. $\endgroup$
    – Jonas Greitemann
    Commented Jun 16, 2014 at 14:11
  • $\begingroup$ As for the first two questions: are you familiar with the differential formulation of Maxwell's equations? $\endgroup$
    – Jonas Greitemann
    Commented Jun 16, 2014 at 14:12

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  1. The properties of EM wave do depend a lot on the material where it exists. In common material like air it indeed only admits transverse waves. Longitudinal waves can appear in more complex materials, such as plasmas.

  2. The answer is the same as for question #1. What you read in wikipedia is concerning usual isotropic and homogeneous materials.

  3. The linear relation you mentioned is called dispersion relation, which is very important for waveguiding structures. By different designs the dispersion relation could be much more sophisticated than the simple linear form. Particular features of dispersion relation could have implications, such as slow light, for interesting applications.

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