What happens if electric field is not perpendicular to the magnetic field? [duplicate]

What happens if the electric field is not perpendicular to the magnetic field for an electromagnetic wave? What could be the possible consequences if such a case was found? Are there examples or demonstrations where the two fields are not perpendicular?

• Are you talking about electromagnetic waves? Electric fields and magnetic fields needn't be perpendicular. – Yashas Feb 13 '17 at 13:12
• Yes, electromagnetic waves. – salvo9415 Feb 13 '17 at 17:42
• Just put a plane wave in which they are perpendicular in a background electric or magnetic field and then the total field won't be perpendicular everywhere. – octonion Feb 13 '17 at 19:20

The only actual constraints, in a vacuum, are the Maxwell equations $\nabla \times\mathbf E = -\frac{\partial\mathbf B}{\partial t}$ and $\nabla \times\mathbf B = \mu_0\varepsilon_0 \frac{\partial\mathbf E}{\partial t}$ (plus, obviously, the two divergence laws). Everything else is secondary.