Holographic metasurfaces applied to generation of non-diffracting beams

Abstract

In this work, we present the computational realization of holographic metasurfaces to generation of the non-diffracting waves. These holographic metasurfaces (HMS) are simulated by modeling a periodic lattice of metallic patches on dielectric substrates with sub-wavelength dimensions, where each one of those unit cells alter the phase of the incoming wave. We use the surface impedance (Z) to control the phase of the electromagnetic wave through the metasurface in each unit cell. The sub-wavelength dimensions guarantees that the effective medium theory is fulfilled. The metasurfaces are designed by the holographic technique and the computer-generated holograms (CGHs) of non-diffracting waves are generated and reproduced using such HMS in the microwave regime. The results is according to the theoretically predicted by non-diffracting wave theory. These results are important given the possibilities of applications of these types of electromagnetic waves in several areas of telecommunications and bioengineering. arXiv:1908.09624v1 [physics.class-ph]

Possibilities to generation of optical non-diffracting beams by holographic metasurfaces using surface impedance

“…where X and M would be adjustment values for making Z to be inside the interval previously calculated for surface impedance [Z min , Z max ], making the calculations, we found: X = Z min and M is the maximum integer value satisfying: M ≤ (Z max − Z min )/2π [44].…”

“…For reconstructing the radiation wave, we use the surface wave to excite the interference pattern: (ψ * surf ψ rad )ψ surf = ψ rad |ψ surf | 2 . Thus, to realize the radiation pattern, we need a distribution for a surface impedance on the metasurface, the theoretical equation for the surface impedance is given by the interference of ψ surf and ψ rad [25,44]…”

“…The impedance surface (Z) is defined as the ratio between the component of electric field parallel to a current along the surface and the current per unit length of surface: E t = Z(x t )J. For the case of a metasurface, we should average that equation over the unit cell, the result for the TM modes (transverse magnetic waves) is given by [25,44]:…”

“…In this way, we design the holographic metasurface (HMS) consisting on a set of unit cells, each one of them formed by a metallic patch on a dielectric substrate, both elements have square shape being the side of metallic patch always less than the side of substrate, thus, a gap (g) is formed in each unit cell (see Figure 1) [44]. We can choose a determinate numbers of gaps for making the simulations, usually nine or ten values equally spaced are chosen, from a g min till g max .…”

“…Every pixel of the computer-generated hologram has a gray level between 0 (black) and 255 (white), we associate each one of these values to a value of phase between 0 and 2π for obtaining a matrix of phase (Φ) for the selected CGH. Thus, according to the expression 13, we have [44]:…”