Three-Dimensional Electromagnetic Void Space

Electromagnetic void space is a medium, while geometrically occupying a finite volume of space, optically equivalent to an infinitesimal point, in which electromagnetic waves do not experience any phase accumulation. Here, we report the first realization of three-dimensional (3D) electromagnetic void space by an all-dielectric photonic crystal possessing vanishing permittivity and permeability simultaneously. The 3D electromagnetic void space offers distinctive functionalities inaccessible to its 2D or acoustic counterparts because of the fundamental changes in topology, which comes from the ascension of dimensionality as well as the transverse nature of electromagnetic waves. In particular, we demonstrate, both theoretically and experimentally, that the transmission through such a 3D void space is unaffected by its inner boundaries, but highly sensitive to the outer boundaries. This enables many applications such as the impurity “antidoping” effect, outer-boundary-controlled switching, and 3D perfect wave steering. Our work paves a road toward 3D exotic optics of an optically infinitesimal point.

Figure 1

Special characteristics of the 3D electromagnetic VS. (a) The expansion of an infinitesimal point of space into a cube of DZM. (b) The transmission through such a VS is unaffected by impurities that are completely embedded in DZM. The PEC walls (colored yellow) and PMC walls (colored blue) attaching the surfaces of DZM. The incident plane wave with $E_z$ polarization comes from positive $x$ direction. (c) The same as (b), but the PMC walls are replaced by PEC walls and the impurities are removed. (d) and (e) The same as (c) with different boundaries.

Figure 2

Realization of 3D electromagnetic DZM in a photonic crystal. (a) The unit cell of the 3D PC. The host medium (gray) is air. The dielectric meshes (red) are aluminum oxide blocks ($ϵ=9$) with side length $L\times L\times a$. (b) Band structure of the PC when $L=0.32a$, exhibiting a sixfold Dirac-like point (the black dot) at the $\mathrm{\Gamma }$ point. (c) The dispersion surfaces near the Dirac-like point in the $k_x\text{−}{k}_y$ plane. (d) Arrow maps of the electric field, exhibiting electric “dipolar $z$” states and the magnetic dipolar $z$ states. (e) The relative permittivity (black curve) and relative permeability (blue curve). The red dashed line corresponds to the frequency of Dirac-like point.

Figure 3

Demonstration of the antidoping effect. (a) Experimental setup. (b) Illustration of the metamaterial polarization converter in a TEM waveguide. TE wave with $E_z$ polarization comes from positive $x$ direction. (c) The region between metamaterial and waveguide in (b) is filled with our PC. (d) and (e) The simulated $E_z$ field in the dashed box in (b) and (c), respectively. (f) and (g) The simulated $E_y$ field in the dashed box in (b) and (c), respectively. (h) and (i) The experimental results of $E_y$ field in the dashed box in (b) and (c), respectively.

Figure 4

(a) and (b) Illustration of the boundary-controlled transmission switching effect with a PC composed of $10\times 10\times 10$ unit cells. The top and bottom surfaces of PC are covered by two PEC walls (yellow), the left and right surfaces in the $x\text{−}z$ plane can be switched between (a) PMC (blue) and (b) PEC. TE wave comes along the positive $x$ direction. (c) Simulated and (d) experimental electric field distributions in the region colored purple in (a). (e) Simulated and (f) experimental results in the region colored purple in (b).

Figure 5

Perfect 3D wave steering. (a) and (f) Illustrations of two wave-steering cases. PMC and PEC walls are indicated by blue and yellow. At $f_{\text{Dirac}}$, a TE incident beam comes along the positive $x$ direction. (b) Simulated and (c) Experimental results of electric field $E_z$ in the region marked by purple in (a). (d) and (e) The same as (b) and (c) but without the PC. (g) Simulated and (h) experimental results of electric field $E_x$ in the region marked by purple in (f). (i) and (j) The same as (g) and (h), but without the PC.