An Optimization of Impedance-Modulated Passive and Lossless Metasurfaces for Expansion of a Gaussian Beam

We study a reflectionless transformation of an incident Gaussian beam in which the transmitted beam increases its waist. A 2D problem is solved analytically and numerically. The incident beam is diffracted on a synthesized spatially-modulated omega-bianisotropic meta-surface. The electric impedance, magnetic admittance, and magnetoelectric coupling coefficient were obtained using numerical optimization based on analytical formulas assuming evanescent surface waves propagating over the metasurface. In two examples with different output beam widths, the optimization results were verified by full-wave simulations with a transmission efficiency of over 90% for a triple-impedance-layer representation of the structure. The proposed approach could be used efficiently to provide any other output beam profile if it satisfies the local power conservation principle.