Shaping Electromagnetic Waves with Flexible and Continuous Control of the Beam Directions Using Holography and Convolution Theorem

In this article, several versatile electromagnetic (EM) waves are presented with predefined shapes and directions based on the holography and convolution theorem. Inspiring the holography theory, a reflective interferogram is characterized by interfering the near field distributions of the object and reference waves. In this regard, the interference pattern on the hologram could be viewed as the inverse Fourier transform of the object and reference waves. Therefore, the capability of steering the EM shaped beam is realized using the convolution theorem (as an interesting property of the Fourier transform), which makes a link between the hologram impedance-pattern and far-field pattern domains. The main advantage of incorporating the holography concept and convolution theorem is realizing arbitrary shaped-beam EM waves with the possibility of flexible manipulation of the beam directions without employing any optimization algorithm and mathematical computation. It is demonstrated that the method could implement a combination of simple beams (such as collimated beams) and complex beams (such as cosecant squared, flat top, isoflux beams, etc.) with each beam possessing arbitrary direction by the same design topology. To experimentally verify the concept, a prototype of the hologram with three separate beams including two tilted cosecant squared shaped beam and one broadside pencil beam is fabricated and measured. The measured results show a significant agreement between theoretical findings.