1. Introduction

Low-intensity RF energy harvesting has become a field of interest due to the need to acquire power in situations where the use of wires and/or batteries is impractical, such as in the cases of expansive sensor networks and structural health monitoring [1,2]. The recent proliferation of RF signals due to cell phones, Wi-Fi networks, and GPS has produced readily available ambient power sources (although of low power density) for scavenging energy [2–4]. Historically there has been difficulty with creating small energy harvesting antennas at RF frequencies that efficiently collect energy [5]. There is further difficulty with efficient AC to DC rectification in cases of low input power [4,6]. In this paper we demonstrate the potential of metamaterial-based energy harvesting antennas to address both of these issues [7,8]. Electromagnetic (EM) metamaterials [9–13] are man-made, typically periodically-arranged, metallic resonant structures that behave as homogeneous media with effective electric permittivity ($\epsilon $) and effective magnetic permeability ($\mu $). With appropriately engineered $\epsilon $ and $\mu $ values, metamaterials have realized unprecedented EM properties that do not exist in nature, such as a negative refractive index [14], diffraction-unlimited optical imaging [15,16], EM invisibility cloaking [17,18], and perfect absorption [19–21]. Metamaterials provided flexibility to design electrically small and low profile antennas [7,8]. The capability of manipulating $\epsilon $ and $\mu $ further provides the convenience to match input/output impedance of antennas to that of the surrounding environment. An antenna constructed out of an appropriately designed metamaterial that incorporates a means of rectification can operate as an efficient energy harvesting system that can be used to convert power captured from RF sources to useful DC power. Recent works have shown that metamaterials can create electrically small rectifying antennas (rectenna) with high RF-DC conversion efficiency [22,23] and improve the efficiency for wireless energy transfer [24] and harvesting [25]. In these works, a single element of an S-shaped resonator [23] or a one-dimensional array of split-ring resonators (SRR) with embedded Schottky diodes [22,25] were used as the rectennas, which reached ∼85% and ∼35% RF-DC conversion efficiency at 1.5754 GHz and 900 MHz, respectively. However, the intensities of incident RF waves in these experiments (∼$1.6\textrm{mW}/\textrm{c}{\textrm{m}^2}$) [22] ((∼$75{\mathrm{\mu} \mathrm{W}}/\textrm{c}{\textrm{m}^2}$)) are much stronger than ambient RF energy level (<$5\; {\mathrm{\mu} \mathrm{W}}/\textrm{c}{\textrm{m}^2}$) [4]. As the intensity decreases, the efficiency of rectennas decreases rapidly to nearly zero when the induced voltage falls below the turn-on threshold of the Schottky diodes. Therefore, harvesting RF signals with ambient levels of intensity [4,26–28], which are usually found in the ISM band (particularly those from 800 MHz to 6 GHz) from sources such as GSM cellphone and 3G. remains extremely challenging. The rectification efficiency achieved is typically below 3% for intensity on the order of 0.5${\mathrm{\mu} \mathrm{W}}/\textrm{c}{\textrm{m}^2}$ [3]. The metamaterial perfect absorber (MPA) [19,29–33], a recent development of metamaterials, can potentially resolve this challenge due to it remarkable features of perfect absorption of EM waves and strong field enhancement. The MPA has been exploited in a wide range of applications including EM wave absorption [19,34], spectral [32] and spatial [33] modulation of light, selective thermal emission [35] and detection [36], infrared photo detection [37,38], and refractive index sensing [39,40]. The MPA typically consists of three layers: a metallic resonator (e.g., cross-type resonator [20,35] or split-ring resonator [19]) and a highly reflective layer (e.g. metallic film [35] or metallic mesh grid [19]), separated by a subwavelength-thick dielectric film (spacer). Our recent works [40–42] have shown that the MPA works as a Fabry-Perot type meta-cavity bounded between the “quasi-open” boundary of the resonator and the closed boundary of the reflector. The cavity resonance modes exhibit a much higher Q-factor than the resonators [19,20,35] and thereby can significantly enhance the local electric fields to overcome the turn-on voltage barrier. Additionally, the MPA helps to convert RF waves more efficiently to DC power by perfectly capturing and storing the RF wave energy inside the meta-cavity. In this work, we demonstrated that using an MPA-based rectenna, the conversion efficiency is significantly improved, especially at very low intensity.

2. Sample preparation

Our MPA-based rectenna consists of a $4 \times 4$ array of double-gap SRRs (Fig. 1(a)) and a copper ground plane (not shown in Fig. 1) with the same size, separated by a distance, s. The sample is fabricated on a copper-coated FR4 circuit board (with dielectric constant ${\epsilon _{FR4}} = 4.34$) by using lithography followed by chemical etching. The geometric parameters are given as follows, d = 30 mm, a = 40 mm, g = 1mm, w = 1mm, t = 0.8128 mm (thickness of FR4 substrate) and t_m = 0.0178 mm (thickness of copper). A Schottky diode (Skyworks SMS-7630-079LF) was soldered across one gap of each SRR, serving the purpose of creating DC voltage by rectifying resonant current excited by the incident RF wave. Each row of SRRs are connected via copper strips along x-direction, forming a series connection of four effective “batteries”. Four rows of SRRs are connected through two thicker strips at the left and right ends, forming a parallel connection along y-direction. The polarities of the diodes alternate in adjacent rows and columns as shown in Fig. 1(b), for creating correct polarities of effective “batteries” in series and parallel connections. The alternating arrangement of diodes also helps to harvest both the forward and backward currents induced by the positive and negative half cycles of the incident RF wave, respectively. With this arrangement, the actual unit cells of the array consist of four SRRs as shown in Fig. 1(b). We carry out 3D full-wave simulations to solve Maxwell’s equations and obtain numerical solutions by Computer Simulation Technology (CST) Microwave Studio that uses a finite integration technology [43]. In our simulation, an effective circuit model (Fig. 1(c)) for the Schottky diode was used [44], where the values of junction capacitance, $C = 0.14\; pF$, and series resistance, ${R_1} = 20.0\; \mathrm{\Omega }$, I₀ = $5 \times {10^{ - 6}}\; A$, and R₂ = 5000 Ω were obtained from the datasheet. The incident wave is perpendicular to the plane of the rectenna and polarized in the x-direction. Figure 1(d) shows the current distribution at the perfect absorption frequency (0.90 GHz), the same frequency where we observe the optimal RF-DC conversion efficiency. We find the current in the array of SRRs approximately forms circular current patterns in each unit cell (Fig. 1(b)) as indicated by the red arrows in Fig. 1(d).

 

Fig. 1. Rectenna sample design. (a) The SRR array with diodes embedded in the gaps. (b) The unit cell. (c) Effective circuit model for the Schottky diode. (d) The surface current modes activated at the resonance frequency (0.90 GHz) are shown on the sample.

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3. Measurement method

A signal generator (Agilent N5181AEP) produces a sinusoidal RF signal and sweeps both frequency and output power with frequencies ranging from 0.7-2.0 GHz. The signal is sent to an amplifier (Mini-circuit ZHL-30W-252+) which increases the signal strength by about 45 dB (depending on the frequency). A small fraction of the amplified signal is extracted with a coupler, and then measured with a signal analyzer (Agilent N9020A) to determine the strength of the amplified signal. The amplified signal is transmitted by an SAS-570 horn antenna at normal incidence to the rectenna sample, which is located about 380 cm away from the transmitting antenna. A metal ground plane is placed behind the sample with the purpose of creating a Fabry-Perot cavity to increase the amount of captured RF radiation. The experiment takes place within an anechoic chamber to isolate the rectenna sample from multi-path interference and outside signals. The rectenna sample is connected to a decade resistor box set at 1k$\mathrm{\Omega }$, which is used as a proxy for a device that DC power will be delivered to. All instruments are controlled by a LabVIEW program and the measurement is automated by sweeping both the power and frequency of an incident RF wave.

4. Results

Figure 2(a) shows the absorption cross-section area, $\sigma = {P_a}/I$, where ${P_a}$ and I are the power absorbed by the rectenna and the intensity of the incident wave, respectively. The electric field of the incident wave in the simulation is set as 15 V/m, which corresponds to the intensity of a wave of 30$\; \mu $W/cm². The absorption cross-sections for both the SRR array (without a ground plane) and the MPA predict a peak energy harvesting frequency around 0.90 GHz. Adding the ground plane causes the peak to become much narrower, but much larger, indicating a significant increase in Q-factor. As seen in Fig. 2(b), the power delivered to the load is primarily from DC, while power from AC signals is much smaller, suggesting good rectification efficiency. When the ground plane is incorporated, the DC power is much higher. The maximum effective area of the sample can be estimated by calculating its directivity in CST Microwave Studio and then applying the equation ${A_{eff,\max }} = {{{\lambda ^2}D} / {4\pi }}$. The directivity in transmitting mode is calculated by exciting a model of the sample with discrete ports and using broadband far-field monitors.

 

Fig. 2. Absorption cross-section, effective area, and RF-DC conversion efficiency. (a) Simulated rectenna absorption cross-section area with (blue) and without (red) the ground plane. (b) Simulated power delivered to the load from a Gaussian pulse. (c) The effective area of the rectenna calculated from simulated directivity. (d) Measured RF-DC harvesting efficiency using the effective area in (c).

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According to the reciprocity theorem, the directivity will be the same for the receiving mode. We determined an appropriate model for the sample by first noting that the electrical current within each cluster of four cells follows a loop-like pattern (Fig. 1(d)). This suggests that the sample can be approximated as an array of 4 loops corresponding to the geometry of the sample. Current-source discrete ports are used and excited simultaneously to mimic the response that would occur for a plane wave incident on the sample. The directivity is calculated both with and without the ground plane. PEC is used for all metal components and the substrate is lossless FR4 to thereby eliminate any losses and obtain maximum effective area. Once the effective area is obtained, efficiency is calculated as $\eta = \frac{{{A_{eff,DC}}}}{{{A_{eff,\max }}}} \times 100\%$, where ${A_{eff,DC}} = \frac{{{P_{Load,DC}}}}{I}\,$, P_Load,DC is the DC-power delivered to the load, and I is the intensity of the incident wave. The effective area, ${A_{eff,\; max}}$, for the MPA shows a peak value of 683 cm² at 0.83GHz, which is significantly larger than both ${A_{eff,\; max}}$=239 cm² for the SRRs at the same frequency and the physical area ${A_{phy}} = $297 cm². Using the effective area shown in Fig. 2(c), we measured the rectification efficiency for intensities of 2.6 μm/cm² and 65 μm/cm² as shown in Fig. 2(d). The efficiencies for both SRRs and the MPA reach peak values at 0.90 GHz as predicted. The efficiency for the MPA is comparable to the SRRs at 2.6 μm/cm², however, it is lower for 65 μm/cm². This result may be deceiving since the actual DC power delivered to the load, ${P_L} = \eta I{A_{eff,\; max}}$, for the MPA is much larger due to a larger effective area. To make fair comparisons between the SRR array and the MPA, in the following discussion, we use the physical area to calculate the effective efficiency, i.e. $\eta = {P_{Load,DC}}/({I \cdot {A_{phy}}} )\; $. In addition, efficiencies calculated from the physical area can provide simplicity and accuracy to predict the actual power delivered to the load, because most of the previous works only use very rough estimations [22,23,45] (e.g. a short dipole model) to obtain the effective area of a rectenna consisting of an array of elements.

To investigate the highest possible efficiency, we first measured the sample for relatively high intensities of incident RF waves as shown in Fig. 3. The intensity range, 2.6 μm/cm² to 65 μm/cm², is well above what would typically be expected to be available from ambient RF signals and thus would only be found within close proximity (<25m) to a strong RF source such as a cell phone tower or right next to a weak RF source. For the cases of with or without the ground plane, the maximum energy harvesting efficiency both occurs at 0.90 GHz, which is comparable to the frequency predicted by the absorption cross-section. Without the ground plane, the SRR array reaches the highest efficiency of ∼60% at 0.90 GHz when the intensity of the incident RF wave reaches 65 μm/cm². When the ground plane is placed at the optimum distance ($s = \; $4 cm), the energy harvesting efficiency improves considerably (compare Fig. 3(a) and 3(b) with 3(d) and 3(e), and reaches the highest efficiency of ∼140%. The efficiency above 100% indicates that the ground plane has caused the effective area of the rectenna to become significantly larger than its physical area as shown in Fig. 2(c). As shown in Fig. 3(c) and 3(f), the efficiency of the sample generally increases with incident intensity. However, the efficiency saturates when the intensity reaches above ∼10 μW/cm². This is because the resistance of Schottky diodes rapidly decreases to nearly zero when the induced voltage overwhelms the turn-on threshold. Therefore, the overall ohmic resistance of the rectenna, ${R_{ohm}}$, is dominated by the losses of the SRR array and the FR4 substrates, which have no power dependence. As a result, the efficiency, which can be written as $\eta = \frac{{{R_{rad}}}}{{{R_{ohm}} + {R_{rad}}}}$ with ${R_{rad}}$ being the radiation resistance, does not change with the intensity. Figure 3(a) and 3(d) also show that the peak efficiencies do not shift in frequency as the incident power increases, showing good stability with frequency.

 

Fig. 3. Measured RF-DC conversion efficiency by physical area. Experimental measurements of energy harvesting efficiency as a function of frequency and intensity. (a)-(c) are measurements without the ground plane. (d) - (f) are measurements with the ground plane.

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5. Discussion

Our recent works have shown that MPAs can be understood as a Fabry-Perot type meta-cavity bounded between a resonator array and a metallic ground plane [40–42]. The meta-cavity usually has a thickness less than $\lambda /10$, much thinner than the $\lambda /2$ thickness of a typical Fabry-Perot cavity between two closed boundaries. In the following, we show that our MPA rectenna works as an electrically thin meta-cavity. As shown in Fig. 4, the efficiency exhibits several branches as the cavity length (the distance, s, between the SRR array and the ground plane) increases. Each branch corresponds to a resonance mode of the meta-cavity and follows a linear function as the wavelength increases. To understand this linearly scaling property, we draw white dash-lines and black solid-lines to show vacuum-filled Fabry-Perot cavities bounded between two “closed” boundaries ($s = m\lambda /2$) and between one “open” and one “closed” boundaries ($s = m\lambda /2 + \lambda /4$), respectively, where m is positive integers ($m > 0$) for the former and non-negative integers ($m \ge 0$) for the latter. Here we use “closed” and “open” to represent the boundary conditions of nodes (${E_t} = 0$, where ${E_t}$ is the tangential component of the electric field) and anti-nodes (${E_t}$ reaches maximum), respectively. The lowest resonance mode occurs below the first black line ($s = \lambda /4$), indicating a cavity mode bounded between a “quasi-open” boundary formed by the SRR array and a “closed” boundary formed by the ground plane. The maximum efficiency of this mode occurs at $\lambda = 34$ cm (frequency of 0.90 GHz) with the cavity length, $s = 4\; \textrm{cm} \approx \lambda /8.5$. This thin cavity length can be explained by the phase condition of the Fabry-Perot cavity, ${\phi _1} + {\phi _2} + 2ks = 2m\pi $, where ${\phi _1}$ and ${\phi _2}$ are the phase of refection at two boundaries, k is the wavenumber and s is the cavity length. For an ordinary Fabry-Perot cavity between two closed boundaries, ${\phi _1} = {\phi _2} = \pi $, so the cavity length is $s = m\lambda /2\; .$ For the MPA, at the resonance frequency of the cavity mode, the phase of reflection for the SRRs is given by ${\phi _1} = \pi - \mathrm{\Delta }$, where $\mathrm{\Delta }\sim 0$. So the cavity length can be calculated as $s = ({\lambda /4\; } )\cdot ({\mathrm{\Delta }/\pi } )\ll ({\lambda /4\; } )$ [41]. The thin cavity length greatly decreases the profile of RF energy harvesting devices and can be further decreased by filling the cavity with low-loss, high dielectric constant material. The thin cavity length allows small mode volume, which leads to a strong enhancement of the local field and therefore can activate the diode at low incident power density. The second and the third modes follow the black lines for $s = 3\lambda /4\,(m = 1)$ and $s = 5\lambda /4\,(m = 2)$, respectively, indicating higher-order modes of “quasi-open” cavities. The MPA plays triple role in improving the efficiency of RF energy harvesting. First, it enlarges the effective area by a factor of 2.86 compared with the SRR array (Fig. 2(c)), which greatly increases the amount of energy entering the rectenna. Second, it captures nearly 100% RF wave energy by eliminating reflection. The RF wave energy is then stored in the meta-cavity through cavity resonance modes, and the waves are reflected multiple times between the SRR array and the ground plane. Each time a wave is reflected by the SRRs, a certain amount of RF energy is converted to DC power delivered to the load through induced resonant current. Third, the meta-cavity exhibits a much higher Q-factor than plasmonic resonators [22,23] (e.g. SRRs), and thereby can significantly increase the induced voltage across the diodes and activate the diodes for low-intensity RF waves.

 

Fig. 4. Meta-cavity resonance modes. Measurement of the effect of the Fabry-Perot cavity length on energy harvesting efficiency at fixed power density (30 μW/cm²). White-dash lines indicate cavity lengths for three lowest orders vacuum-filled Fabry-Perot cavities bounded between two closed boundaries ($m = 1,2,3$) and black-solid lines show the cavity lengths for four lowest order cavities bounded between an open and a closed boundary ($m = 0,1,2,3$).

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Figures 5(a) and 5(b) show the energy harvesting efficiency measurements at intensities that are comparable to what can be found from ambient sources (up to 1.0 µW/cm²). The intensity levels presented were chosen to correspond to what can be found on the streets of urban environments [4,28] including GSM cellphone (<$1.930\; {\mathrm{\mu} \mathrm{W}}/\textrm{c}{\textrm{m}^2}$ at 900 MHz and $< 6.40\; {\mathrm{\mu} \mathrm{W}}/\textrm{c}{\textrm{m}^2}$ at 1800MHz) and 3G (<$2.4\; {\mathrm{\mu} \mathrm{W}}/\textrm{c}{\textrm{m}^2}$ at 2110 MHz). Now the efficiency is clearly much lower than it was for the high-power measurements. However, the presence of the ground plane increases the efficiency by a large factor (up to 16) in this case. A plot of the ratio of the efficiency with the ground plane to the efficiency without the ground plane, which will be referred to as the enhancement factor, is shown in Fig. 5(c). The presence of the ground plane produces the large enhancement factor at very low powers (about 0.01-1 µW/cm², which is at a typical ambient level). The SRR array gives about 1%, 2%, 5% and 15% efficiency for 0.01µW/cm², 0.03µW/cm², 0.06µW/cm² and 0.4µW/cm² respectively, while the MPA can boost the efficiency to ∼10%, ∼15% and 25% and 80%, respectively. We attribute the enhancement to the fact that the MPA significantly increases the induced voltage across the diodes due to the high Q-factor meta-cavity resonance as shown in Fig. 2(a), which makes it easier for the diode to activate (particularly at low power). As an example, to obtain 100$\; {\mathrm{\mu} \mathrm{W}}$ power, a typical threshold for low power electronic devices [28], our MPA requires an incident intensity of 0.4µW/cm², which can be found at ∼100 m distance from a GSM base station [28], or using a dedicated RF source.

 

Fig. 5. Efficiency at low intensity. Measurements corresponding to power densities that would be available at the specified distances from a 100 mW source possessing a transmitting antenna with a gain of 3/2. (a) No ground plane. (b) Ground plane present. Same legend as 5a. (c) Enhancement factor; defined as the ratio of power harvested with the ground plane to power harvested without the ground plane, measured at 0.90 GHz. The peak frequency is slightly different than before because of slight differences in the angle of incidence of the rectenna between measurements.

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6. Conclusion

Designing RF harvesting rectennas based on metamaterial perfect absorbers is a promising solution for collecting ambient RF energy in low power density environments because they are tunable, highly efficient, and electrically small. The perfect absorber design of the metamaterial rectenna dramatically improves the RF-DC conversion efficiency (especially for lower available power densities) by increasing the effective area of the antenna, eliminating the reflection due to impedance mismatching, and helping to overcome the high resistance below the turn-on threshold. The ultra-small thickness ($\lambda /8.5$), which can be further reduced by filling the cavity with a dielectric material, provides great flexibility for designing low-profile, portable wireless energy transferring devices (e.g. long-distance wireless charging).