The radiated fields can be found from distribution of the electric and magnetic currents by the use of dyadic Green’s functions that contain source and field coordinates. We sometimes refer to the Green’s functions as vector propagators or transfer functions between currents and fields. We calculate the fields from integrals over the source points of the dot (scalar) product between the dyadic and current densities. The dyadic Green’s function contains both near- and far-field terms and requires slightly different expressions for the electric and magnetic fields. The general propagator from electric and magnetic currents has separate terms for electric and magnetic currents, which when used with surface patch currents can be reduced to short subroutines or procedures easily programmed [1]:
 (1)
  (2)
These expressions integrate over the currents located at source points r for a dyadic Green’s function that changes at each field point r and source point r. Although these Green’s functions are valid at all field points in space both near and far field, they are singular at a source point. Only retaining terms with 1/R dependence for the far field greatly simplifies the expressions.
When fields are incident on a perfect electric conductor (PEC), the combination of incident and reflected tangential magnetic fields induces an electric current density on the surface. The fields inside the conductor are zero. We assume locally plane surfaces on patches and compute currents that satisfy the boundary condition. Given the local unit normal ˆn to the surface, the induced current density is given by
 (3)
The reflected magnetic field equals the incident magnetic field because the field reflects from the conductive surface. The sum of the tangential electric fields must be zero. Because the reflected wave changes direction, the vector (cross) product of the electric and magnetic fields must change direction. The reflected tangential electric field changes direction by 180â—¦, so the tangential magnetic field must not change direction because the Poynting vector changed its direction. Equation (3) is the magnetic field equation applied on a PEC. Equation (4) is the general magnetic field equation at a boundary.
 (4)Physical optics starts with a given current distribution that radiates, or the measured pattern of an antenna. When an object is placed in the radiated field, the method calculates induced current on the object to satisfy the internal field condition. For example, PEC or PMC have zero fields inside. When we use simple functions such as constant-current surface patches, the sum of the radiation from the incident wave and the scattered fields from induced surface currents produces only approximately zero fields inside. As the patch size decreases, the method converges to the correct solution. To obtain the radiated field everywhere, we sum the incident wave and scattered waves. The fields radiated by the induced currents produce the shadow caused by the object. With geometric optics techniques such as UTD, the object blocks the incident wave and we determine the fields in the shadow regions from separate diffraction waves. In physical optics the incident wave continues as though the object were not present. Only geometric optics techniques use blockage.
We can calculate the fields radiated from antennas in free space or measure them in an anechoic chamber that simulates free space, but we mount the antenna on finite ground planes, handsets, vehicles, over soil, and so on, when we use them. Physical optics is one method of accounting for the scattering. We show in later chapters that the mounting configuration can enhance the patterns. |
