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Abstract
Exploiting of nonlinearity has opened doors into undiscovered areas to achieve multiplexed performances in recent years. Although efforts have been made to obtain diverse nonlinear architectures at visible frequencies, the room is still free for incorporating non-linearity into the design of microwave metasurfaces. In this paper, a passive dual-band power intensity-dependent metasurface is presented, which is composed of two different linear and nonlinear meta-atoms accommodating a capacitor and a PIN-diode, respectively. The proposed digital metasurface has three operational states: 1) it acts as a normal reflector at low power intensities while providing a dual-band nonlinear response upon illuminating by high-power incidences where 2) it perfectly absorbs the radiations at f1=6.7 GHz and 3) re-distributes the scattered beams by arranging the meta-atoms with a certain coding pattern at f2=9.4 GHz. The performance of the designed coding elements has been characterized by using the scattering parameters captured in the full-wave simulations and the nonlinear analysis performed in ADS software where the accurate model of diodes is involved. The emergence of microwave self-biased metasurfaces with smart re-actions against incident waves with different power levels reveals great opportunities for designing smart windows, smart camouflage coating surfaces, and so on.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Metasurfaces as the reduced dimensional version of 3D metamaterials can provide the same electromagnetic (EM) functionalities as many bulky components carry out, while they benefit from extraordinary features of being ultra-thin, easy to build, and easy to integrate. These unique properties have received broad interest in the engineering, physics, and optics communities, leading to extensive theoretical and experimental investigations. Since their creature, a wide variety of intriguing potential applications has been reported for metasurfaces from microwave to visible spectra. The field of metasurface has witnessed rapid growth and found a special place in obtaining negative refraction [1], polarizers [2], absorbers [3–5], anomalous reflectors [6], engineered antennas [7–9], beam scanning [10,11], invisibility cloak [12], dispersion management [13], and advanced analog computing [14–16]. With the advent of generalized Snell’s laws of reflection and refraction [17,18], the demands for any types of controllable metasurfaces have been gradually increased for which phase change materials, graphene [19–21], vanadium dioxide [22–24] and semiconductors [25,26] are known as reliable solutions. In recent years, a copious number of studies has incorporated nonlinearity into the metasurface design, yielding different functionalities such as frequency multiplexing [27], harmonic generation [28], and so forth. In the microwave regime, several proposals have elaborately explored power-dependent metasurfaces by embedding PIN-diodes into the building unit cells. PIN-diodes, while the power intensity is more than a specified threshold, are in On-state, acting as a small resistor; conversely, when the power intensity is less than that threshold, the diode operates in Off-state, acting as a small capacitor. In 2013 [29,30], through the use of diodes integrated into the metasurface, the Sievenpiper’s group introduced the concept of circuit-based nonlinear absorbers that absorb high power surface currents but not small signals. However, the proposed structure acts only upon exciting by high power surface waves propagating on the nonlinear metasurfaces. In 2017, Zhao et al. [31] designed a frequency selective surface to provide a passband for low-power microwave signals and a stopband for high-power microwave signals. Nevertheless, the presented architecture can manipulate only the spectral (not spatial) properties of the high power incident signals. Digital metasurfaces are aimed at engineering the scattered waves in a simpler manner than the conventional routes in which only two distinct coding elements with opposite reflection phases (e.g., 0$^\circ$ and 180$^\circ$) as the 0 and 1 digital bits form the device [32–36]. Through organizing the coding particles over a 2D plane based on a pre-determined coding pattern, such architectures can serve to realize diverse scattering functionalities. The coding strategy greatly facilitates the optimization procedures since the phase responses are elaborately quantized to a limited number of digital states, thereby noticeably alleviating the parameter search space. More recently, Z. Luo et al. [37] proposed an intensity-dependent nonlinear metasurface whose functionality is determined by the power intensity of the incident wave. However, besides resorting to an auxiliary active biasing circuit, the operating band of the digital metasurface was restricted to a single narrow frequency region. In this paper, a self-biased dual-band coding metasurface is proposed, comprising of linear and nonlinear power-multiplexed I-shape meta-atoms. At low power intensities, the designed metasurface functions linearly and the coding statuses of all digital particles are the same, resulting in a broadband EM mirror. At high power intensities, the nonlinear property of some meta-atoms makes the device as a bi-spectral nonlinear coding metasurface with two separate camouflage functionalities. In the lower band (C-band), the nonlinear coding metasurface perfectly absorbs more than 99 $\%$ of the incident wave power while in the upper band (X-band), a disordered distribution of anti-phase linear and nonlinear particles, as the 0 and 1 digital bits, is formed which dramatically reduces the specular reflection by generating multiple randomly-oriented scattered beams. Indeed, the operational status of the self-biased tri-state (EM mirror, absorber, and diffuser) digital metasurface is solely dictated by the power intensity of the incident wave. Hence, our design is fully passive that means it does not require any additional active biasing network. The numerical simulations verify the performance of the proposed bi-functional nonlinear coding metasurface.
2. Coding meta-atom design
2.1 Principle mechanism
The coding metasurface of Fig. 1(b) is deliberately built by two different groups of linear and nonlinear meta-atoms. The overall geometry of the designed coding meta-atoms is depicted in Fig. 1(a), consisting of three separate layers: 1) the I-shape metallic part as the top layer, 2) the Rogers RT5880 substrate with the thickness of $h$=1 mm as the middle layer, and 3) a copper ($\sigma =5.96 \times 10^7$ S/m) ground plane as the bottom layer avoiding the energy transmission across the frequency band of study. The I-shape metallic part is loaded by a 0.25 pF lumped capacitor (Murata-GJM1555C1HR20WB01D) in the linear cells and a Macom MA4L401-134 PIN-diode in the nonlinear cells. The PIN-diode can be circuitally modeled as $R$=1.2 $\Omega$ in the ON state while it can be represented by C=0.2 pF in the OFF mode. The common structural parameters in the linear and nonlinear particles are $l$=6 mm, $p$=11 mm, and $t$=1 mm. However, $w_{lin}$=3.2 mm, $s_{lin}$=0.4 mm $g_{lin}$=3.88 mm, and $d_{lin}$=1.47 mm while $w_{nonlin}$=2 mm, $s_{nonlin}$=3.8 mm, $g_{nonlin}$=3 mm, and $d_{nonlin}$=1.31 mm for linear and nonlinear groups of meta-atoms, respectively. The purpose of our design is that: Upon illuminating by low-power radiations, the two groups of meta-atoms reflect the incident wave with identical reflection phase and amplitude. However, when exciting by high-power threats, the functionality of the nonlinear elements is changed, resulting in a dual-band metasurface. At the lower frequency band, the metasurface traps and absorbs the power carried by the incident wave. At the upper frequency band, the linear and nonlinear elements mimic the digital states of 0 and 1, realizing a specific coding pattern over the surface (see Fig. 1(b)). The principle mechanism of the nonlinear group of coding particles is based on changing the value of the equivalent lumped elements upon increasing the power level of the incident wave. Obviously, the voltage levels induced on both ends of the embedded diode strongly depend on the local field intensities stimulated by different incident power levels. If the peak of induced voltage is not enough to turn the diode ON, it can be approximately modeled as a small capacitance (OFF state). In contrast, at the condition of high power illumination, such AC voltage can bias the diode mounted in the gap so that it can be approximately represented by a small resistance (ON state).
Fig. 1. (a) The designed meta-atom of the proposed structure. The metasurface includes capactior in its linear cells and PIN-diode in its nonlinear cells. (b) A schematic model of the smart reflective metasurface. The designed metasurface acts as an EM mirror upon illuminating by low-power radiations. While the intensity is increased, the nonlinearity plays the dominant role, and the metasurface turns into a bi-spectral low-scattering surface exposing microwave absorption at ($f_1$) and scattering diffusion at ($f_2$).
In semiconductor physics, the average time for recombination of minority carriers during ON-to-OFF switching is typically on the order of a few microseconds or nanoseconds. Meanwhile, the time it takes that the majority carriers recombine during OFF-to-ON switching depends upon the resistivity and permittivity of the semiconductors and is typically on the order of a few picoseconds. Consequently, during the time variations of the AC illuminating signal (let us consider the frequency range of simulations between 5 to 10 GHz corresponding to the time periodicity range of T=100 ps to 200 ps), the OFF-to-ON switching is successfully performed once the induced voltage exceeds the threshold voltage but the PIN-diode does not have enough time to be OFF during the half-cycle of negative bias due to the small outgoing rate in ON-to-OFF switching. Indeed, a certain charge will be accumulated in the intrinsic layer, and the diode will work stably in the ON-state. More detailed information can be found in [38].
2.2 Frequency-domain analysis
The overall EM functionality of the proposed metasurface is determined by the reflection phase/amplitude spectra as well as the spatial distribution of the occupying elements over the surface. When a y-polarized plane wave excites each particle, the complex reflection coefficient of the nonlinear meta-atoms can be tuned by the voltages induced across the PIN-diode. In this section, we intend to characterize the linear and nonlinear meta-atoms in the frequency domain for both low- and high-power radiations by using the commercial program, CST Microwave Studio (MWS). Periodic boundary conditions are applied to the x- and y-directions, while Floquet ports are assigned along the z-direction to form a transversely-infinite array from the meta-atoms of Fig. 1(a). The polarization of the incident EM field is set to be parallel with the middle metallic lines of the I-shape coding elements. As previously mentioned, the linear and nonlinear groups of particles embed a capacitor and a PIN-diode, respectively. The EM-circuit co-simulation approach is utilized in this paper to involve the simulation of two types of problems: 3D EM full-wave simulation and circuit analysis. The procedure of simulation can be summarized as follow: Firstly, in the full-wave simulations, the capacitor and diode are replaced with a discrete port, making the structure as a two-port network: the Floquet port and the port replaced with the lumped elements. The scattering parameters are obtained at this stage. Secondly, after incorporating the 2-port S-parameters of linear and nonlinear meta-atoms into the circuit simulation, the 2-port system is terminated by a capacitor for the linear cell and the approximated model of the PIN-diode in the ON and OFF states for the nonlinear cell. The standard EM/circuit co-simulation then solves the full problem to extract the reflection spectrum of the whole structure.
Figure 2 illustrates the flow-chart of the simulation procedure. The reflection coefficients of the linear and nonlinear meta-atoms are also plotted in Figs. 3(a)–(f) for the low- (OFF state) and high-power (ON state) input signals. The results are separately given for the lower and upper frequency bands. The first deduction is that upon illuminating by low-power signals, both linear and nonlinear coding particles mimic the "0" digital state with high reflectivity (more than 0.85) across 4 GHz to 14 GHz (see Figs. 3(a), 3(b)). In this case, the structure plays the role of an EM mirror. In contrast, when the nonlinear particles are exposed to high-power plane waves, a bi-spectral EM response is observable. At $f$=6.7 GHz, the array of nonlinear meta-atoms plays the role of a perfect absorber with more than 99.9$\%$ efficiency (see Figs. 3(c), 3(d)). Therefore, the metasurface can serve well as an energy harvesting platform in this frequency band. In the vicinity of $f$=9.4 GHz, however, the coding status of the nonlinear meta-atom is changed to "1", because of showing a 180$^\circ$ phase difference with respect to the linear particles (see Figs. 3(e), 3(f)). Furthermore, the binary phase response required for constructing the coding metasurface is acquired at the upper frequency band. In this regime, the reflectivity of both linear and nonlinear coding particles is high enough to manipulate the scattered waves with high efficiency (see Figs. 3(a), 3(c), 3(e)). In summary, the intensity-dependent reflection properties of the nonlinear I-shape inclusions would bring up tri-state functional modes: 1) EM mirror, 2) energy harvester, and 3) coding metasurface within a shared aperture.
Fig. 3. The comparison of the (a), (c) , (e) amplitude and (b), (d), (f) phase of the reflection coefficients for the linear and nonlinear cells when the PIN-diode is (a) (b) OFF and (c), (d), (e), (f) ON.
Now, we want to elucidate the physical mechanism of absorption and 180$^\circ$ phase difference for the lower and upper frequency bands of the nonlinear meta-atom at the ON operational mode, respectively. As depicted in Fig. 4(a), the PIN-diode treats as a small resistance allowing us to describe the nonlinear meta-atom as an equivalent series RLC circuit placed at the input terminal of a short-circuited transmission line representing the substrate and ground plane. The capacitance represents the gap between the horizontal strips while the inductance is due to the induced currents flowing on the vertical strip. Both of them have an effective role in providing the impedance matching. According to the resistive nature of the nonlinear meta-atom at the ON-state, a great portion of the incident power can be ensnared and absorbed whenever the impedance matching condition is satisfied. Based on the effective medium theory [39], the normalized impedance value (z) of the nonlinear meta-atom at the ON-state can be computed from its reflection coefficient [40]:
Here, $R_{NL}^{ON}$ denotes the reflection coefficient of the nonlinear meta-atom when the PIN-diode is ON. The normalized impedance is plotted in Fig. 4(b), wherein the blue and red lines stand for the real and imaginary parts of the normalized impedance, respectively. As noticed, upon illuminating by high-power radiations, the nonlinear meta-atom resonates in the vicinity of 6.7 GHz where the real part of the normalized impedance matches the free-space value, Re(z)=1, and the imaginary part of the normalized impedance approaches to zero at the same time, Im(z)=0. To gain further insight into the physics behind absorption, the spectrum of the induced current is monitored in Fig. 4(c) for both OFF and ON operational modes of the PIN-diode. At the OFF-state (low power level), the PIN-diode is open and no current can pass through it. At the ON-state (high power level), however, the current induced on the PIN-diode reaches its maximum and the power is mostly dissipated by the internal resistance of the PIN-diode. As evidence, the power-loss distribution of the meta-atom at 6.7 GHz concentrates around the PIN-diode (see Fig. 4(d)). Evidently, due to utilizing a low-loss dielectric, the substrate does not contribute to the incident wave absorption. The origin of the 180$^\circ$ phase difference between the linear and nonlinear units can be explained by writing the phase cancellation condition $R_{NL}^{ON}=-{{R}_{L}}$ [41]:Fig. 4. (a) The approximated models for the linear and nonlinear meta-atoms. (b) Normalized input impedance of the nonlinear cell when the PIN-diode is ON. (c) The spectrum of the induced surface currents on the PIN-diode for high and low power levels. (d) The surface power loss density of the nonlinear meta-atom at 6.7 GHz, when the PIN-diode is ON.
Fig. 5. (a) The Harmonic Balance analysis of the nonlinear cell. (b) The time domain response pertaining to the voltage signals induced one the PIN-diode at high and low power intensities.
2.3 Time-domain analysis
The nonlinearity also manifests itself to the time-domain response of the nonlinear group of meta-atoms whereby we can obtain the threshold power of OFF-to-ON switching. In this section, a Macom MA4L401-134 PIN-diode with low parasitic capacitance, short switching time, and small ON-state resistance has been chosen for our demonstrations. Using the same simulation setup in ADS software and upon exciting by different power levels, a probe captures the voltage wave-form at the place of PIN-diode. The frequency of simulation is chosen as 6.7 GHz and the results are shown in Fig. 5(b). When the small-signal impinges on the coding element, the voltage waveform of the PIN-diode behaves as a complete sinusoidal wave, indicating that such low-power signal cannot excite and so change the operational status of the PIN-diode diodes. However, shinning the coding element with large-signal inputs (more than +4 dBm at the meta-atom level) makes the voltage wave-forms of the PIN-diode distorted, demonstrating that the PIN-diode toggles (becomes ON) and the I-shape meta-atom reaches its nonlinear working region. As expected, since the forward voltage of the employed PIN-diode is reported as 0.75 V, the positive half-cycle voltage is successfully truncated at the level of 0.75 V when the diode is triggered by high-power illuminations (with the threshold power of +4 dBm at the meta-atom level). Assume that the whole metasurface is occupied with 256 unit cells. In this case, the power impinging on the metasurface should exceed +28 dBm (=4+10$\times$log(256)) to turn all PIN-diodes of the nonlinear cells ON at the macroscopic level. In the previous metasurface demonstrations with non-linear elements [26,37] , the designs were accompanied by an auxiliary DC biasing network (active circuit), which controls the state of the contributing diodes. In fact, the ON or OFF state of the diode is determined by the DC controlling signals generated by an additional biasing network. Instead, the proposed device in this paper does not require any additional biasing system, as the state of the embedded diodes is directly dictated by the AC incident electromagnetic wave. Indeed, at the condition of high power, such AC voltage can bias the diode mounted in the gap. This feature allows us to call our structure as a passive self-biased design. Again, we should emphasize that since the speed of the electrons/holes injected to the P- and N-type junctions in the positive cycle is much more than that of the outgoing electrons/holes during the negative period, the working mode of the PIN-diode is not altered by time variations of the AC input signal unless the input power varies [43].
3. Results and discussion
As depicted in Fig. 6, the proposed architecture is composed of linear and nonlinear I-shape meta-atoms whose spatial distribution over the surface constructs a tri-state intensity-dependent bi-spectral metasurface. In order to suppress the corner-related coupling effects, 4 $\times$ 4 linear I-shape meta-atoms are integrated into a lattice. The same scheme is realized for nonlinear lattices. The linear and nonlinear lattices are marked by red and blue colors where different arrangements of nonlinearity would lead to various EM functionalities at the upper-frequency band. The nonlinearity distribution can be arbitrary. The tri-state metasurfaces with different arrangements of nonlinearity have been built in CST MWS to be numerically simulated. The intensity-dependent metasurfaces are all composed of 6$\times$6 lattices, each of which is occupied by 4$\times$4 I-shape meta-atoms. The overall dimensions of the metasurface are 264 mm$\times$264 mm. The 2D and 3D scattering patterns in each case are demonstrated in Figs. 7 and 8. Under low-power normal plane waves, all lattices behave linearly in identical coding statuses, and the metasurface act as an EM mirror regardless of the operating frequency. Therefore, the far-field patterns at 6.7 GHz and 9.3 GHz have single scattered beam pointing at the broadside direction (Figs. 8(a), 8(c)). When the metasurface is excited by high-power illuminations, the EM response of nonlinear lattices alters while that of the linear group is kept unchanged. In this case and at the lower frequency band, the nonlinear group of the I-shape meta-atoms traps and dissipates the input signals with more than 99 $\%$ absorption rate while the linear group reflects the input signals with more than 0.86 magnitude. Although the overall response of the metasurface, as the superposition of these distinct responses, is dependent on the nonlinearity distribution over the surface, the far-field patterns of different arrangements show a radar cross section (RCS) reduction of at least 10 dB at the lower frequency band. The corresponding results are given in (Fig. 8(b)) where a remarkable RCS reduction is obtained in comparison to a metallic reference plane of the same size. The absorption result for the random arrangement of elements is given here. At the upper frequency band, the linear and nonlinear lattices treat as the "0" and "1" binary elements with a 180$^\circ$ phase difference, forming a digital metasurface. In such a situation, the nonlinearity distribution becomes very important since different coding sequences of 0 and 1 lattices would lead to diverse types of scattering patterns. Assuming that the reflection phase distribution over the surface is denoted by $\phi _{mn}$, the scattering pattern of the coding metasurface can be expressed as:
Fig. 6. Different distributions of nonlinearity over the surface which result in various types of coding pattern seen by a high-power incidence at upper-frequency band.
Fig. 7. 2-D far-field results that show the performance of the metasurface upon illuminating by high-power incidences for (a) 000..0/11⋯1 coding sequence along the x-direction and (b) 01..0/10⋯1 coding sequence along both x- and y-directions.
Fig. 8. The 3D far-field patterns of the designed metasurface for (a), (c) low and (b), (d) high illumination powers at the (a), (b) lower and (c), (d) upper-frequency bands.
4. Conclusion
In summary, we proposed a tri-state bi-spectral power-dependent metasurface with an arbitrary distribution of nonlinearity over the surface. The designed metasurface is composed of two linear (capacitor-loaded) and nonlinear (diode-loaded) groups of I-shape meta-atoms. The EM functionality of the nonlinear group was solely determined by the power intensity of the incident fields without the need for any active biasing circuit. Being excited by low-power radiations, the whole metasurface played the role of an EM mirror while under high-power illuminations, it acted as an energy harvesting platform and an EM diffuser at the lower and upper frequency bands, respectively. It was shown that different distributions of nonlinearity over the surface would lead to diverse types of scattering patterns at the upper frequency band. The numerical simulations verified the tri-state performance of the proposed nonlinear metasurface.
Disclosures
The authors declare no conflicts of interest.
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