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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

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