Characteristic mode theory is presented as a method of calculating the characteristic currents, the equivalent magnetic current, the radiation patterns, and the field everywhere (especially in the aperture region) of an infinitely long, thin, perfectly conducting cylinder with an infinitely long slot illuminated by a uniform transverse magnetic (TM) plane wave to the slot. The characteristic modes obtained are the solution of an eigenvalue equation representing the continuity of the tangential component of the magnetic field in the slot.