  We introduce the idea of discontinuous electric and magnetic fields at a
boundary to design and shape wavefronts in an arbitrary manner. To create this
discontinuity in the field we use electric and magnetic currents which act like
a Huygens source to radiate the desired wavefront. These currents can be
synthesized either by an array of electric and magnetic dipoles or by a
combined impedance and admittance surface. A dipole array is an active
implementation to impose discontinuous fields while the impedance/admittance
surface acts as a passive one. We then expand on our previous work showing how
electric and magnetic dipole arrays can be used to cloak an object
demonstrating two novel cloaking schemes. We also show how to arbitrarily
refract a beam using a set of impedance and admittance surfaces. Refraction
using the idea of discontinuous fields is shown to be a more general case of
refraction using phase discontinuities.
