An electromagnetic wave is a signal that goes in all directions. The wave will move uniformly through its medium if the medium is uniform. A plane wave is the concept of think an electromagnetic wave only flows in one direction.

The principal plane in wave propagation is the E-plane and the H-plane of an

antenna. The E-plane consists of the electric field vector, and by convention,

it's the direction in which the wave is said to be 'polarized'. The H-plane consists

of magnetic field vector of the wave. The electric field vector and the magnetic

field vector are perpendicular to each other, and the direction in which the wave

propagates (moves) is perpendicular to both of them.

The wavelength gets longer.

An electromagnetic wave is properly called a Transverse Electro Magnetic wave, or TEM wave. It consists of an alternating magnetic wave at right angles to an alternating electric wave, with both fields being at right angles to the direction of propagation.

The plane of the electric field is defined as the plane of polarization.

It depends on the hamiltonian but it would be of the form of a regular plane wave.