Electromagnetic fields produced by sources on a spherical wavefront

Transient solutions of the inhomogeneous Maxwell equations are obtained. The specific current source belongs to the spherical surface expanding with the velocity of light. Representations of the electromagnetic field components in the spherical coordinates in terms of the Fourier series are found. The obtained solutions are correct near the wavefront. The general expressions are applied to a description of electromagnetic waves produced by different sources and to a discussion of formation of directional waves and the family of relatively undistorted waves.