Launching and controlling Gaussian beams from point sources via planar transformation media
Based on operations prescribed under the paradigm of Complex Transformation Optics (CTO) [1- 4], it was recently shown in [5] that a complex source point (CSP) can be mimicked by a paritytime transformation media. Such coordinate transformation has a mirror symmetry and results a balanced loss/gain metamaterial slab. A point source placed at the center of such slab produces a Gaussian beam propagating away from the slab surface. Here, we extend the CTO analysis to non-symmetric complex coordinate transformations and show that by using simply a (homogeneous) doubly anisotropic gain-media metamaterial slab, one can still mimic a CSP and produce Gaussian beam. Notably, a Gaussian beam can be produced in this case by point sources placed outside the slab as well. By making use of the extra degrees of freedom provided by CTO, the near-zero requirement on the real part of the resulting constitutive parameters can be relaxed to facilitate potential realization. In addition, exploitation of both real and imaginary parts of the CTO design yield direct control of the Gaussian beam properties such as peak amplitude and waist (focus) location.