An electromagnetic beam that is not the solution to the paraxial wave equation but is the solution to Maxwell's equation is simulated directly by the finite-difference time-domain method. Electrical and magnetic field components of the beam are presented graphically. Then the diffraction of the electromagnetic beam pulse by an aperture in a conducting screen is analyzed. The fraction of the beam power through the aperture is defined and calculated. The fields in the time domain near the aperture, which show the diffraction by the aperture, are presented graphically.