Real Sources in Complex Spaces

We utilize complex transformation optics (CTO) to mimic complex source point (CSP) fields. It is shown that the CSP fields can be exactly reproduced via planar metamaterial slabs associated with the proper complex coordinate transformations. CTO extends the real-valued coordinate transformations to complex-valued coordinate transformations. Of conventional TO, one can also control the amplitude of the fields in addition to their phase paths. In the present paper, we demonstrate that CSP fields can be produced through appropriate material tensors prescribed by the corresponding complex coordinate transformations.