Workshop: Fully-polarimetric phased array far field modeling

In this tutorial, the methods used in industry by the instructor to model phased arrays, with all the effects of polarization in the far field, will be taught. Maxwell´s equations and their time-harmonic general solutions in the far field will be reviewed. First cut and general element patterns with arbitrary polarization will be discussed and developed, together with the very useful Ludwig-3 polarization basis. As the array elements need to be translated and rotated into their desired positions and orientations, the effect of translations and rotations on far field patterns is discussed, with an introduction to rotation matrices. The general formula for the far field electric field of a general 3D phased array with arbitrary elements is developed. Examples with identical elements in the same orientation in either an arbitrary 3D array, or the more common rectangular planar array are discussed, together with the associated array factors. Conformal arrays are briefly discussed in the context of specification of their orientation. Basic elements of beamsteering and beamforming are discussed at the end. The course will be taught at a level that may be followed by those with a background in basic electromagnetics and linear algebra.