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I'm reading about optical waveguide analysis, and often come across the terms "transverse electric mode" vs. "transverse magnetic mode". As I unerstand, it means that the electric/magnetic field has only transversal component.

But how could it have longitudinal component? Aren't the electric and magnetic fields always perpendicular to the direction of propagation?

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"Aren't the electric and magnetic fields always perpendicular to the direction of propagation?" In free space, yes. However, waveguides can support waves with longitudinal field components. I seem to recall that most texts do an example of one of those, but it has been a long time... – dmckee May 1 '13 at 15:49
    
Electrostatic waves have $\mathbf{k} \ \times \ \mathbf{E}$ = 0, but then again, I think they can only exist in a medium, not a vacuum. Hmm... – honeste_vivere Oct 3 '14 at 18:07

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