Electromagnetic Funnel: Reflectionless Transmission and Guiding of Waves through Subwavelength Apertures

Confining and controlling electromagnetic energy typically involves a highly resonant phenomenon, especially when subwavelength confinement is desired. Here, we present a class of nonresonant, self-dual planar metastructures capable of protected energy transmission from one side to the other, through arbitrarily narrow apertures. It is shown that the transmission is in the form of matched propagating modes and is independent of the thickness and specific composition of the surface. We analytically prove that the self-dual condition is sufficient to guarantee 100% transmission that is robust to the presence of discontinuities along the propagation path. The results are confirmed numerically through study of various scenarios. The operation is broadband and subject only to the bandwidth of the constituent materials. The polarization of the internal field can also be independently controlled with respect to the incident one. Our structures are promising for applications in sensing, particle trapping, near-field imaging, and wide scan antenna arrays.

Figure 1

Self-dual periodic slabs. (a) Conceptual representation of the unit cell of a self-dual slab, infinitely extended in the $x$ and $y$ directions with period $L$. Green and blue represent regions with electrically polarizable ($ϵ={ϵ}_0{ϵ}_r$, $\mu ={\mu }_0$) and magnetically polarizable ($ϵ={ϵ}_0$, $\mu ={\mu }_0{\mu }_r$) materials, assuming ${ϵ}_r={\mu }_r$. Each unit cell is invariant under a 90° rotation around the $z$ axis and swapping electric and magnetic materials. For simplicity, the case of only two materials in shown here. A horizontal $z$ cross-section cut of the geometry along the gray surface is shown in panel (b). Cross section of the slab may arbitrarily vary between layers in terms of both shape and material properties, as long as the self-dual condition in Eq. (1) is satisfied (see examples in Ref. [41]). (c) Illustrations of three problems used in our proof: problem $a$, the original cross section; problem $b$, the dual of “problem $a$” constructed by changing the properties of constitutive materials and fields, according to duality theorem [42]; and problem $c$, 90° rotation of “problem $b$“(clockwise rotation is shown; the counterclockwise rotation follows similar formulation).

Figure 2

Matching and polarization conversion in a generic self-dual periodic slab. (a) Unit cell of a generic self-dual slab with period of $L=0.4{\lambda }_0$ in both the $x$ and $y$ directions. Green and blue represent regions with perfect electric conductor and perfect magnetic conductor boundaries, respectively. For simplicity, the slab is invariant along the $z$ direction between the interfaces at $z_1=-t/2$ and $z_2=t/2$, where $t=0.4{\lambda }_0$. More general cases including $z$-variant structures are studied in Ref. [41]. (b) Snapshot in time of the electric field distribution when the slab in panel (a) with $t=0.4{\lambda }_0$ is illuminated with a plane wave propagating along the negative $z$ direction. In each case, the component of the electric field parallel to the incident electric field is shown. Fields are normalized to the amplitude of the incident wave [color bar shown in panel (d)] and both cases are fully matched. (c) Reflected and transmitted powers from the slab shown in panel (a) (solid lines) vs its PEC counterpart, which is not self-dual (dashed lines) when illuminated with a $\widehat{\mathbf{x}}$-polarized plane wave propagating along the negative $z$ direction. (d) Snapshot in time of the $x$ component (left) and $y$ component (right) of the electric field, when the slab is illuminated with ${\mathbf{E}}_i=E_i\widehat{\mathbf{x}}$ and $t=0.362{\lambda }_0$. At this specific thickness, the transmitted wave experiences 90° polarization rotation, while matching is maintained.

Figure 3

Electromagnetic funnel: Reflectionless transmission of energy through deeply subwavelength apertures. (a) A horizontal cut of the unit cell of the self-dual periodic slab designed to transmit the EM energy through narrow air apertures (white). The period of the surface is $L=0.4{\lambda }_0$ in both the $x$ and $y$ directions with $r=0.02{\lambda }_0$, $g=0.01{\lambda }_0$. Green and blue represent regions with PEC and PMC boundaries and the structure is invariant along the $z$ direction between $z_1=-t/2$ and $z_2=t/2$, where $t=0.7{\lambda }_0$. (b) Snapshot in time of the $x$ component of the electric field distribution when the structure is illuminated with an $\widehat{\mathbf{x}}$-polarized plane wave propagating along the negative $z$ direction. Amplitude of the field is normalized to the incident wave. (c) Total field enhancement inside the narrow apertures. Polarization of the field in the center aperture is shown in the inset. Depending on the arrangement of PEC and PMC segments in the unit cell, each aperture supports a TEM-like mode with 45° tilted polarization. Because of illumination with an $\widehat{\mathbf{x}}$-polarized electric field, power is divided evenly among all apertures. (d) Normalized power flowing along the negative $z$ direction as a function of $x$ plotted at $y=z=0$ (center of the object). Blue and red lines correspond to illumination with $\widehat{\mathbf{x}}$-polarized and $-\widehat{\mathbf{x}}+\widehat{\mathbf{y}}$-polarized waves. In the latter case, only half of the apertures carry energy and therefore the local power is doubled relative to the former case. The gray regions indicate the position of apertures (air). (e) Normalized amplitude and phase of the electric field along the propagation path in the middle of one aperture. Structure is illuminated with an $\widehat{\mathbf{x}}$-polarized plane wave. Amplitude of the wave is approximately constant along the propagation path (except for short transition ranges at the beginning and end interfaces of the aperture with free space), and the phase remains virtually linear. Effective wave number of the wave is equal to that of free space, corresponding to the TEM-like nature of the wave inside aperture.