Nonreciprocity has been investigated historically starting from Faraday rotation [1] which was discovered in 1845. In modern research and industrial applications, there are numerous phenomena and devices that are significant because of their nonreciprocal properties such as circulators, isolators, and duplexers. A traditional way of providing nonreciprocity is to use a magnetic bias which aligns the spin of magneto-optical or ferrite materials, resulting in a large difference in wave propagation behavior depending on the direction of propagation. However, these conventional ferrite-based solutions [2,3], are bulky and heavy. Non-magnetic-based nonreciprocal devices, antennas, or surfaces can play an important role in applications for both microwave and optical frequencies due to the increasing demand for compact, lightweight systems [4–6]. One recent work used a moving fluid to create a circulator for acoustic waves [7]. Recent research has also demonstrated several other approaches to break time reversal symmetry using time-varying media [8–10]. Other works have involved modulating the substrate to vary its effective index, which could be applied in nonreciprocal leaky wave metasurface antennas and isolators, etc. [11–13]. The spatio-temporal modulation method has also been explored to provide unidirectional transmission [14–17]. Another new approach is to apply switches to transmission lines and manipulate the waveforms that control the sequences of the switches [18,19]. However, there is less work carried out for applications of nonreciprocal surface wave absorbers. Absorbers targeting normal incidence are widely studied; however, surface wave absorbers are also important but less investigated. These are particularly important for absorbing transverse magnetic (TM) waves on metal structures, which may be excited by leakage from openings or seams between discontinuous metallic structures. Metasurface absorbers [20–22] are widely studied and applied in both free-space wave and surface wave absorption due to their low profile, subwavelength thickness, and simplicity. Recent studies have brought active electronics, including diodes, varactors, and transistors to metasurface absorbers, enabling attractive properties such as power dependency, waveform dependency, switchability and self-tuning capabilities [23–27]. However, all of these absorbers are still reciprocal. In this Letter, we introduce a nonreciprocal surface wave absorber based on propagating control signals applied to a switchable metasurface.

Nonreciprocal surface wave absorbers can provide unidirectional communication or surface waveguiding, while simultaneously absorbing waves that are propagating in the opposite direction. One important application of a nonreciprocal surface wave absorber is that the received energy from an aggressor can be absorbedwithout scattering/reflection, while the forward wave transmission is maintained. In other words, these devices could be used to avoid interference to sensitive electronics or devices from other high-power transmitters, unwanted reflections, or other jamming signals. The high impedance surface (HIS) [28,29] is a good candidate for surface wave absorbers because it supports no modes within its bandgap and, thus, stops surface waves from propagating. By simply placing resistors at the gap between neighboring unit cells, energy can be also dissipated as ohmic loss.

Here, in order to achieve a nonreciprocal surface wave absorber, we propose an HIS structure that is modulated by a traveling wave, so that the symmetry of the surface is broken without the use of magnetic materials, as indicated in Fig. 1. Spatiotemporal modulation method allows the surface a have nonreciprocal behavior without bringing in bulky ferrites or magnets. An ideal switch is placed between the top patch and the via to the ground plane, allowing the metasurface to be configured in two possible states. When the switch is in the ON state (connecting the top patch to the ground), the surface forms an HIS which has a bandgap between the first TM and TE modes that prevents surface waves from propagating. When the switches are in the OFF state (creating an open circuit between the top patch and the ground), the bandgap close, and TM waves can propagate along the surface at over a broad range of frequencies. The absorption rates for the two different switch states are simulated and shown in Fig. 2. Figure 2(a) gives the full wave simulation model in Ansys HFSS with periodic boundaries on the two lateral sides [25] and 10 kΩ resistors between the gaps of the patches. The absorption rate is calculated as

 

Fig. 1. Principle of the time-modulated, nonreciprocal metasurface surface wave absorber. An ideal switch is placed at the via of the HIS, connecting or isolating the via and the top metallic patch. When the vias are modulated from left to right using a traveling wave signal, surface waves can propagate unimpeded from left to right but are absorbed when propagating from right to left.

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Fig. 2. Full wave simulation model and absorption rate of metasurfaces with and without vias. (a) Full wave simulation model with a perfect electric conducting (PEC) boundary on the top and bottom and a perfect magnetic conducting (PMC) boundary at the two sides. The unit cells of the metasurfaces are with width $ w = {18}\;{\rm mm}$, gap size $ g = {2}\;{\rm mm}$, substrate (Rogers Duroid 5880) thickness $ t = {3.175}\;{\rm mm}$, and gap resistance $R = {10}\;{\rm k}\Omega $. (b) Simulated absorption rate versus frequency with and without vias. (c) Dispersion diagram of the periodic surface with via switches ON and OFF. Surface waves at frequencies within the bandgap cannot propagate with the vias present, but a broadband TM mode is supported when the vias are absent.

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Fig. 3. Spatiotemporal modulation of the HIS presented in dispersion diagram. (a) Dispersion diagram of the first three space harmonics ($ n = 0$, $ \pm 1 $), in which $ k $ is the surface wave vector and $ p $ is the periodicity of the spatial modulation. (b) Time modulation to the dispersion curves in the $ y $ axis. A TM mode is supported for forward propagation but forbidden from backward propagation, resulting in a nonreciprocal surface wave structure.

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The symmetry of response of the surface to transmitting surface waves can be broken by introducing time and spatial modulation. For the proposed surface above, when the switches turned ON and OFF in a sequence following a traveling wave, the property of the surface from one side to the other differs, demonstrating nonreciprocal behavior. When the surface wave propagation follows the direction of the modulation direction, the travelling wave barely detects the vias along the traveling path. In other words, the surface appears nearly as isolated periodic patches without vias, as a structure that supports surface wave propagation. On the other hand, when waves propagate in the opposite direction relative to the modulation direction, the surface is equivalent to the HIS with the majority of the vias present, which stops surface waves from propagating and absorbs the surface waves through ohmic losses in the gap resistors.

By adding the spatio-temporal modulation to the surface, a set of additional modes is created in the system. The important property of such modes is their unidirectional momentum, which is imposed by the spatio-temporal modulation. We call them modulation modes in this Letter, and they are associated with different mixtures of patches with and without vias, with different time modulation speeds. If the excitation wave is in the same direction as the surface modulation, some of these modulation modes are populated and carry energy along the surface. For the opposite direction, such mode population does not occur. In such a case, the excitation wave experiences a series of stationary absorbing resonators along its path, assuming we operate in the surface impedance bandgap. Figure 3(a) shows the spatial modulation of the HIS, determined by the number of vias on and off per period, with $ + {1}$ and $ - {1}$ spatial harmonics. When a temporal modulation is applied to the surface, the modulated dispersion curves are shifted up/down along the y axis, as shown in Fig. 3(b). For the propagation in the forward directions (defined as the same direction as the traveling modulation direction), the positive harmonics of the dispersion diagram are shifted up, while the negative harmonics are shifted down, in contrast to the negative direction propagations [15]. Rigorous analysis of the system dynamics goes beyond the scope of this Letter. However, we verify the concept with an EM-circuit co-simulation example. The same full wave simulation model is adopted and shown in Fig. 4(a). Lumped ports are designed between the top patch and the via vertically for each element to control the via connecting or isolating with the top patch from the ground. Additionally, there are lumped ports assigned at the gaps between the neighboring patches for assigning gap resistors. Wave ports are assigned at the left (forward incidence) and right side (backward incidence) with the characteristic impedance determined by the ratio of the height and the width of the transverse electromagnetic (TEM) waveguide. The periodicity of the unit cells $ p $ is 20 mm, the patch width $ w $ is 18 mm, the gap size $ g $ is 2 mm, and the substrate (Roger Duroid 5870) thickness $ t $ is 3.175 mm. The extracted S-matrix from a wide band (DC to 12 GHz) full wave simulation is plugged into a circuit simulator to perform transient simulation shown in Fig. 4(a). The S-matrix is composed of two ports at the top on the left and right indicating transmitting and receiving ports with characteristic impedance the same with the TEM waveguide. The gap ports are assigned resistors with resistance $ R = {10}\;{\rm k}\Omega $, while the via ports are assigned to ideal switches which control the vias to be conducted to the ground (switches on) or not (switches off), reconfiguring the surface to be an HIS or isolated periodic patches. A traveling square wave, which can modulate the switch to be on and off following a sequence, is transmitted through a 50Ω impedance-controlled transmission line from the left to the right. Here we are using a square wave for the modulation because the surface unit cells have two discrete states (via connected or not), which can be reached with high and low states of the square wave respectively. The modulation is in a traveling wave manner from the WP1 direction towards the WP2 direction. For forward (left to right)/backward transmission (right to left), WP1/WP2 is assigned a source, while WP2/WP1 is assigned to be a receiving port. By sweeping all interested frequencies in the transient simulation, the incident, transmitted, and reflected power of the source is obtained; thus, the absorption rate is calculated from Eq. (1).

 

Fig. 4. EM-circuit co-simulation. (a) The solved EM model of the surface is plugged into the circuit simulator, with its lumped port connected with absorbing resistors at the gap and switches at the vias, with its two ports connected with wave ports to feed input waves. (b) Absorption rate of forward and backward incidence in transient simulation is extracted with via switches modulated in a travelling manner at the speed of light with period 1.2 ns, 1/3 duty cycle.

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There are several parameters of the square wave for this traveling modulation that can be optimized for this nonreciprocal surface wave absorber, including the modulation wave’s phase velocity, period, and duty cycle, targeting maximizing the difference between the forward absorption and backward absorption rate. The phase velocity of the modulation wave is the same as the first TM mode surface wave phase velocity, which can be extracted from the dispersion curve from the eigenmode simulation of the periodic patches without vias (almost equal to the speed of light), to ensure the maximum transmission of the power from the left to the right along the spatial modulation direction. The period and duty cycles of the square waves are swept and optimized to give the largest difference in absorption rate from opposite incident directions. As mentioned above, the periodicity of the modulation determines the range of upshift and downshift of the dispersion curve, while the duty cycle of the modulating square wave determines the modulation depth. One extreme case is to set the duty cycle to be 0, which disconnects all vias, maximizing the transmission rate. The other extreme case is to set the duty cycle to be 1, which connects all vias, forming an HIS and maximizing the absorption rate. For the proposed nonreciprocal metasurface surface wave absorber, the period of the square wave is optimized to be 1.2 ns, and the duty cycle is 1/3 accordingly. The absorption rates from forward (left) and backward (right) incidence, shown in Figs. 4(a) and 4(b). are simulated and plotted in Fig. 4(c). At 2.55 GHz, the peak absorption rate from backward incidence is 86% with a forward incidence to be 28%. The limited bandwidth is due to the inherent property of the HIS and can be improved to some extent by using wider bandwidth structures. Figure 3 shows the spectral content of the excitation, forward, and backward outputs of the system. It is evident that additional modulation modes are excited in the forward direction, causing energy transfer along the surface before absorption. The backward output, however, does not include any additional modes.

In summary, we have proposed an HIS based a time-modulated metasurface-based surface wave absorber. By using a traveling square wave to modulate the vias of the HIS structure, the absorber shows nonreciprocal properties in terms of incidence direction. At targeted frequencies, when the incident wave travels against the direction of the modulation, the majority of the power is absorbed, whereas transmission is obtained when the incident wave is along the direction of the modulation signal. This can potentially be used for future systems that may require unidirectional propagation for control of surface wave propagation, such as for protection from unwanted interference.