The recent concept of metasurfaces is a powerful tool to shape waves by governing precisely the phase response of each constituting element through its resonance properties. While most efforts are devoted to realize reconfigurable metasurfaces that allow such complete phase control, for many applications a binary one is sufficient. Here, we propose and demonstrate through experiments and simulations a binary state tunable phase reflector based on the concept of hybridized resonators as unit cell for a possible metasurface. The concept presents the great advantages to be very general, scalable to all frequency domains and above all very robust to fluctuations induced by the tunable mechanism, as we prove it at microwave frequencies using electronically tunable patch reflectors.
© 2014 Optical Society of America
Controlling the propagation of wave is a long standing concern. For centuries scientists have been using lenses made out of bulky materials with a given refractive index to bend and focus the waves following the Snell laws. More recently there have been a lot of interests in devising ways to control waves in reflection or in transmission using surfaces made out of unit cells or pixels whose transmittance or impedance can be modified. This offers drastic advantages over bulky dielectric components. Indeed, these surfaces can be very thin as compared to dielectric lenses, which is of great interest especially at low frequencies. But the main advantage of these flat devices lies in the fact that their pixels can be designed to be electronically tunable, hence transforming this surface into a tunable component that allows shaping waves dynamically in unprecedented ways.
A first example can be found in optics with the concept of spatial light modulators (SLMs) [1–4] that are surfaces made out of small tunable pixels (mirrors, liquid crystals) for which the phase of the transmitted or reflected wave can be independently tuned to achieve beam shaping. A similar concept exists in the microwave domain with active antenna arrays or passive reflectarrays [5–7] made out of electronically tunable λ0/2 reflectors that are currently used to create pre-designed radiation fields, to focus or to implement beam steering and scanning. The recent development of metasurfaces [8–11], made out of small resonators, takes the wave control a step further while decreasing the size of the elementary pixels down to deeply subwavelength scales thus increasing the controllable degrees of freedom (sub-diffraction control, or multiple bands and polarizations).
May it be for SLMs, reflectarrays, or metasurfaces, the practical implementation of applications requires cheap, low loss, low consumption, versatile and easy to fabricate tunable resonators/reflectors. However, in order to get the best control over the wave propagation, the pixels (reflectors, resonators…) are often and ideally designed to provide a tunable continuous 2π phase shift, which can lead to complicated designs and tunable mechanisms, especially in the case of reflectarrays electronically tunable pixels. To overcome this complexity issue that impacts both the design and the control of the pixels, digital phase shifters  may be used at low frequencies to discretize the phase shifts. For many applications, including wavefront shaping in complex media or Fresnel zone plate focusing for instance , a simple binary phase reflector (0 or π) can perform very well while being much simpler to design and control. This approach follows the current trend that tends to simplify as much as possible (namely with binary elements) the devices or bulky materials to control the propagation of waves . May it be for fully or discretized phase controlled pixels, the tunability most often requires a tunable mechanism that brings along uncertainties and fluctuations (impedances, voltage …) that naturally impinges on the phase response leading to less efficient control.
In this context, we propose here a new design of two states electronically tunable phase pixel based on the hybridization of two resonant elements , one being a static reflector (called “main reflector”) which is resonant at the operating frequency f0, and the second one being a tunable element (named “parasitic resonator”). First we expose the very general concept of how hybridized resonances based unit cells can provide a robust π-phase shift of the reflected field at f0. We then focus on a specific design of unit cell (a patch reflector) that operates at microwave frequencies and whose tunable mechanism uses electronic components. We show, both numerically and experimentally, that it not only addresses the previously cited requirements (low cost, low loss and easy to fabricate), but it also presents other notable advantages, the main one being that it is independent of the tunable mechanism at the operating frequency f0. It is moreover single layered and does not need high power components since the operating mode does not appeal for the electronic circuit which can be of great interest for many microwave applications. The proven concept of hybridized resonances to provide a binary phase shift is very general, can be realized using many types of resonators and should be scalable to higher frequencies (THz, optics) provided that adequate resonators/reflectors (metallic nanoparticles…) and tunable mechanism are implemented.
Our binary phase pixel is based on the very general concept of hybridized coupled resonant elements whose resonant frequencies can be tuned by adjusting the coupling strength κ. The idea is to design a system that can be either resonant or not resonant at a given operating frequency f0. In the first case, the resonant behavior of the system provides a π phase shift of the reflected wave while in the second case, the system is transparent to the incident wave, and that is, there is no phase shift.
To that aim, we take as unit cell a system made out of two individual monomers: one static reflector (referred to as the main reflector), whose frequency is fixed to the operating frequency and one tunable parasitic resonator (referred to as the parasitic resonator) whose frequency can be wisely adjusted by a given tunable mechanism. We work with two limit behaviors as displayed in Fig. 1.In the first case (Fig. 1(a)), the resonance frequency of the parasitic resonator is different enough from the resonance frequency of the main reflector, so that the two resonant elements do not couple (κ~0). The eigenfrequencies of the entire system remain the same as the resonant frequencies of the monomers. At the operating frequency (red dotted line in Fig. 1), the system is then resonant. We call this state the π-state. In the second case however (Fig. 1(b)), we set the resonance frequency of the parasitic resonator to match that of the static reflector (κ>0). In that case, the monomers hybridize to create a dimer whose eigenfrequencies are respectively under and above the initial resonance frequency of the monomers and can be referred to as bounding and anti-bounding states.
This can be seen as a consequence of the level repulsion that occurs when two coupled resonant elements have the same resonance frequency, as it is the case for atoms in solid state physics  for instance. The frequency splitting depends on the strength of the coupling κ that is driven, in our case, by the detuning of the monomers. In the so called 0-state, the dimer has no resonance at f0, that is, the reflected wave displays no phase shift. This design presents many advantages. One can first remark that at the operating frequency f0, the pixel is never affected by the resonance of the parasitic reflector. If only this element sees the tunable mechanism, it makes it very robust to any fluctuations or uncertainties that can be brought along. Moreover, we can emphasize that this concept is very general and can be applied to any frequency range if adequate monomers are to be used as reflectors.
For a practical implementation of this kind of binary tunable pixel, we choose to work at microwave frequencies with reflectarray unit cells that are well-known: planar patch reflectors, whose resonances are set by their dimensions. One rectangular patch reflector is set to be the main reflector resonant at f0 while the parasitic resonator is a parasitic strip of tunable length, leading to a tunable resonance. Both main and parasitic elements are put close to each other to ensure a non-zero near field coupling κ. The schematic design is displayed in Fig. 2(b).
To first validate the concept of hybridized monomers using our static and parasitic elements, we check the effect of the tunable resonance frequency of the parasitic strip on the eigenfrequencies of the whole system. To do so, we simulate an infinite array of our microwave unit cell using CST Microwave Studio. Both monomers sit on a perfect ground plane (Copper thickness 30 µm) and are separated from it by a substrate that models the NELTEC one used in experiments (tangent loss δ = 3.10−3, permittivity ε = 3.4, height h = 1.5 mm). At this point, we want to stress that the ground plane insures the π phase shift at the resonance of the main reflector and a reflection coefficient close to unity (limited by the losses in the substrate). Perfect electric conductor (PEC) boundaries are used in the direction perpendicular to the main reflector’s polarization while perfect magnetic conductor (PMC) boundaries are used along its polarization (Fig. 2(a)). A vertically polarized plane wave is sent on the whole unit cell (10x10 cm2), two wavelengths away from the pixel. We monitor the simulated S11, that is, the reflection coefficient of an infinite array of pixels (namely the reflectarray or metasurface). To probe the hybridization property, we look at the S11 when varying the length of the parasitic strip through its upper part of length L (see Fig. 2(b)). This results in the tuning of the parasitic strips resonance frequency. The two eigenfrequencies of the whole pixel (main reflector + parasitic strip) are displayed on the map in Fig. 2(c) as a function of the frequency and L. We clearly see that for L close to zero, the system presents a single resonance around 2.43 GHz, which is the frequency of the static patch f0 while the frequency ftun of the tunable parasitic strip is much higher and out of the monitored frequency range.
ftun logically decreases while increasing L until it gets closer to f0, leading to a finite coupling κ. That comes out as a modification of the eigenfrequencies of the system with one frequency under and one above f0. The optimum coupling, which provides the strongest splitting, occurs for Lopt ~ 7 mm. As L is further increased, we get the two non-hybridized monomer resonances again. This can be again physically interpreted as an anti-crossing splitting of coupled resonators or level repulsion analogous to two atoms systems. Now that we have an efficient hybridization of our main reflector and parasitic resonator, we understand that for two well-chosen values of length L (let say L ~ 0 and Lopt = 7 mm), we can get the two limit behaviors described in the Concept section. We display in Fig. 2(d) the corresponding S11 coefficients: in the first case (L ~ 0), the so-called π-state, we have a resonance at f0 = 2.43 GHz while in the second case (L = Lopt), the so-called 0-state, the eigenfrequencies respectively under and above f0 are f- = 2.337 GHz and f+ = 2.524 GHz with no overlapping at f0. This proves that a binary tunable pixel working at f0 can be efficiently implemented by using a main reflector and well-designed binary tunable resonator.
4. Experimental results
The general idea to implement the binary response of the parasitic reflector is to design a reflector whose frequency can be binary modulated only. In our microwave design for instance, the length L of parasitic strip can be binary modulated to couple or not to the static main reflector. To do so, we start with the design of the strip presented in Fig. 2(b), in which we add a p-i-n diode that cuts the length in two as displayed in Figs. 3(a) and 3(b). When the diode is forward biased, the whole length sets the resonance of the parasitic strip so that it matches the one of the main reflector f0 (0-state). On the other hand, when the diode is reverse biased, only the lower part of parasitic strip resonates at a frequency much higher than f0, preventing the two elements from coupling (π-state). We fabricate this binary tunable pixel by classical etching of a copper layer (35µm) on low loss substrate (NELTEC NH9338ST) following the dimensions of Fig. 3(b). Additionally to the p-i-n diode (Infineon BAR 63-02V) we solder two 18 nH choke inductors (TE Connectivity 36401J18NGTDF) in order to decouple the radio-frequency signal from the DC bias and avoid parasitic effects. A resistor R is used to decrease the bias current to fit the diode's operating current and lower the overall electrical consumption. The reflection properties of the reflector are measured in a 1 meter long metallic single mode waveguide (ATM 430-120A-1m-2-2, 1.7-2.6 GHz); see Fig. 3(c).
We plot in Fig. 4 the resonance properties of the system in both states in amplitude and phase. We observe as expected that in the π-state (0V bias = reverse biased diode), one resonance (f0 = 2.466 GHz) occurs while in the 0-state (5V bias = forward biased diode) we see the hybridization splitting (f- = 2.396 GHz and f+ = 2.524 GHz). Those frequencies are slightly different from the simulation since the experimental geometrical parameters do not exactly match the simulated ones. The phase properties of the reflection show that at the operating frequency f0, the phase shift reaches 180° as expected for an efficient binary tunable pixel used in reflection. In the π-state, the resonance at the operating frequency suffers from 3 dB losses which are comparable to simulations, and relatively usual for reflectors printed on a substrate. The latter are intrinsic losses due to the high resonance field in the substrate that may alter at some point the feasibility of some antenna applications, even though the phase response remains good. Those losses may be decreased by carefully optimizing the design of the unit cell and choosing a different substrate.
5. Bandwidth and angular response of the unit cell
One important aspect to take into account when designing a phase shifter for metasurfaces or reflectarrays is the bandwidth on which the device provides an effective response. In our case, we can note that the bandwidth is first limited by the fact that the unit cell absorbs almost completely the incoming waves at the resonances f+ and f- of the 0-state (around 20 dB losses, see Fig. 4). That approximately limits our bandwidth to slightly more than 100 MHz (Δf = f+- f-). Moreover, since the main characteristic of the cell is to provide a π phase shift at the working frequency, the parameter of interest to define an efficiency bandwidth is the phase difference of the reflected waves between the 0-state and the π-state. In Fig. 5(a), we see that this experimental phase difference is around 180° at f0 and remains in a +/− 50° interval within the 100 MHz bandwidth, which is enough to reverse the sign of the incoming waves though it is not extremely precise. It means that in the case of applications in or through complex media such as multiple scattering ones or reverberating ones, a bandwidth of 100 MHz may be used. This has been verified in another study which is out of the scope of this paper . For free space application however, we may consider that the cell is efficient if the phase difference at f0 remains within the interval 180°+/−10° (see inset of Fig. 5(b)). The bandwidth would then be considerably decreased to 7 MHz.
In order to get a complete characterization of our binary phase shifter, we simulate using CST Microwave studio its far field angular response at the operating frequency f0. To do so, we put a small dipole exciting port in the near field of the main reflector’s resonant edge and observe the radiated field. By virtue of spatial reciprocity, it is formally equivalent to measuring the angular response of the reflecting unit cell (with the exception that the latter would be squared). We display in Figs. 5(c) and 5(d) the angular response of the unit cell in its resonant π-state. The 3D radiation pattern (Fig. 5(c)) is logically coherent with the one of a rectangular patch since the parasitic resonator plays almost no role in this state. The radiation in the patch plane (xy plane) displayed in polar representation (Fig. 5(d)) shows the non-isotropic response of the binary phase reflector along the resonant (x-axis) and non-resonant (y-axis) polarization. We observe that the maximum of the directivity of the reflected waves is in the forward direction (ϕ = 0°) which is of interest for free space application such as beam steering with reflectarrays.
Our system presents many advantages, the main one being that the response is completely independent of the electronic components (here the tunable mechanism) at the operating frequency. It ensures that the phase shift at f0 remains 180° whatever the uncertainties are on the components impedances and on the ones due to soldering. Indeed, we have put all the electrical components on the parasitic reflector so that the resonance at f0, which is set only by the main one, cannot be perturbed. The binary tunable pixel is then very robust. This leads to another advantage: as the operating frequency does not see the electronics, the components can be low power and hence low cost whatever the power of the incident field. This also means that our design works with a very low electrical consumption and low losses which is an important feature if one is to consider practical implementations. The latter indeed depends on the value of the resistor R in the circuit that can be decreased down to a few tens of µW when setting R = 500 kΩ without altering the properties of the binary pixel. Moreover, our reflector is single sided hence leading to a very simple fabrication process. Finally, we emphasize that the concept of hybridized resonances based binary phase shifter is valid for higher frequency ranges as THz or optics, provided that one uses adequate resonators (nanoparticles…) and tunable mechanism such as photo-injected charge carriers in semiconductors or height of the substrate [18,19]. One has however to address the specific experimental issues of the investigated frequency domain, such as losses in metal in the visible range for instance. In that case, the only requirement is that whatever the tunable mechanism is, it should be placed on the parasitic resonator only.
In this paper, we exposed a new design of binary tunable reflector as a metasurface pixel to implement a π phase shift based on two strongly hybridized resonant elements which has not yet been proposed to our knowledge. The concept is very general and implies only two resonant elements, one static (main reflector) and one tunable (parasitic resonator), that can hybridize or not depending on the value of the resonance frequency of the parasitic resonator. By choosing wisely two states of the parasitic resonator, one can obtain a system that is either resonant at the operating frequency (the elements do not hybridize: the phase shift is then π in reflection) or non-resonant (the two elements hybridize: the phase shift is then 0 in reflection).
We first demonstrated the feasibility of the concept at microwave frequencies through CST simulations and then we proved an experimental implementation in the microwave domain using two common single layer reflectors that are a planar rectangular patch reflector and a parasitic strip. Contrarily to such existing devices, our system presents the main advantage to be independent of all electronic impedance uncertainties due to the components fabrication process or to the soldering thus providing a robust π phase shift at the working frequency. In our design, the tunability of the parasitic strip relies on a single p-i-n diode which makes it a very simple, cheap, and low consuming circuit to implement. Of course, a single diode design reduces the degrees of freedom of the phase shift since it is only binary. To overcome this limit, we can use several p-i-n diodes or even achieve analogic phase shifts using a varactor. In one case or the other however, it would be detrimental to either the simplicity of the circuit and cablings or to the intrinsic losses.
To conclude, the concept of hybridized resonant elements to provide a phase shifter in reflection presents many advantages that make it a promising alternative to existing devices in the telecommunication domain and find applications in radars, satellites, wireless communications and remote sensing systems. More generally, it can be used for any wave front control or more fundamental studies of complex, reverberating or highly scattering media .
N.K and M.D. acknowledge funding from French “Direction Générale de l’Armement” (DGA). This work is supported by LABEX WIFI (Laboratory of Excellence within the French Program “Investments for the Future”) under references ANR-10-LABX-24 and ANR-10-IDEX-0001-02 PSL*. G.L acknowledges funding from French Agence Nationale de Recherche under reference SPHOCYA.
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