A universal electromagnetic energy conversion adapter based on a metamaterial absorber

On the heels of metamaterial absorbers (MAs) which produce near perfect electromagnetic (EM) absorption and emission, we propose a universal electromagnetic energy conversion adapter (UEECA) based on MA. By choosing the appropriate energy converting sensors, the UEECA is able to achieve near 100% signal transfer ratio between EM energy and various forms of energy such as thermal, DC electric, or higher harmonic EM energy. The inherited subwavelength dimension and the EM field intensity enhancement can further empower UEECA in many critical applications such as energy harvesting, photoconductive antennas, and nonlinear optics. The principle of UEECA is understood with a transmission line model, which further provides a design strategy that can incorporate a variety of energy conversion devices. The concept is experimentally validated at a microwave frequency with a signal transfer ratio of 96% by choosing an RF diode as the energy converting sensor.

part of incident energy that is usefully converted, can be incorporated into the system. The developed TL model leads to a clear structural design strategy for achieving near 100% signal transfer ratio. The concept of UEECA along with the design strategy is confirmed by an experimental demonstration of converting incident EM wave into DC voltage choosing RF diodes as the energy converting sensor.

Model Discussion
The main component of the MA is a periodically distributed metal front structure represented by the yellow dipoles in Fig. 1 (a). Besides the front structure, a separation layer supporting the front structure and a metal back layer is also crucial for constructing a functional MA unit cell as shown in Fig. 1 (b). For a resonant antenna with periodically distributed front structure ( Fig. 1 (c)), the components used to model the antenna are the effective capacitance C A , inductance L A , thermal dissipation load Z T A and radiation load in both front and back directions Z Rad A+ [15][16][17][18] . They are respectively determined by the power stored in the electric fieldW e , stored in the magnetic field W m , dissipated by thermal loss P T and radiated to infinite space in the front and back direction of the front structure P Rad + (The derivation can be found in the supplementary material). A conceptual electromagnetic energy converting sensor modeled by a load with impedance Z L is attached on the front structure of every unit cell. This front structure can be characterized using classical antenna theory and treating metal as a non-perfect electric conductor. It is worthy to point out that the loss of metallic material cannot be ignored at optical frequencies, and another component TL Metal should be added between the shorted line and the component TL S . In this way, the phase shift and attenuation in the metallic material can be taken into consideration. According to the model in Fig. 1 (c), the maximum signal transfer ratio between the incident wave and the sensor is limited to ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Z rad Aw Z rad Az zZ rad A{ À Á q (Z rad Aw is the larger value between Z rad Az and Z rad A{ ). Previous studies suggest that the addition of the metal back plate does not produce serious distortion to the EM field distribution in the front structure, therefore adding the metal back layer will not sig-nificantly change the effective RLC components 19 . As a result, the TL model of the MA can be reconstructed as shown in Fig. 1 (d). The permittivity e d , permeability m d , and thickness h d of the separation layer are effectively described by the components of TL S . In the case where the separation layer is composed of multiple dielectric layers, a group of series-connected TL S components should be used in the TL model corresponding to each dielectric layer. According to the model in Fig. 1 (d), the perfect absorption and the maximum transmission between the incident wave and the energy converting sensor can be simultaneously achieved only when: antenna with complex frequency response, the definition of X A can be found in the supplementary material) and Z A L~Z L zZ T A . For physically meaningful solutions, the condition of Re Z A L Â Ã vZ rad Az has to be satisfied. By solving Eq. (1), one is able to obtain the smallest separation layer thickness and the corresponding angular frequency, respectively: where c is the speed of light in vacuum. These two equations indicate that for the resonant front structure with arbitrary shape, the full absorption can always be achieved by intentionally choosing the thickness of the separation layer. When an antenna with complex frequency response is considered, Z LC 5 X A , the optimized h d can be still achieved by solving Eq. (1). In the meantime, the transmission between the incident wave (emitted wave for the emission process) and the sensor, which is the signal transfer ratio, is optimized to be: For the ideal situation in which the thermal loss can be ignored (Z T A ?0), 100% of the signal transfer ratio can be achieved. In practice, Z T A is directly related to the dissipation property of the materials as well as the EM field distribution, as indicated by Eq. S6 in the supplementary material. In this case, the largest signal transfer ratio of the device is determined by Eq. (4).
A simple physics picture of the optimum signal transfer ratio can be offered by the interference theory 20 , in which perfect absorption arises from the destructive interference between the direct reflection from the front structure and the multi-reflections inside the separation layer. An appropriate thickness of the separation layer as indicated in Eq. (2) is critical in producing perfect absorption because the destructive interference is mainly controlled by the phase shift inside the separation layer. What makes UEECA distinct from the conventional MA is how the trapped energy is converted. Instead of being dissipated largely in the separation layer 11 as in a conventional MA design, the existence of the load in a UEECA offers another path from which the transfer ratio efficiency can be determined by Eq. (4).

Results
To validate the concept of a UEECA, an MA array consisting of 12 3 12 unit cells has been constructed and characterized. An RF diode (Avago HSMS-286B), serving as the energy converting sensor, is attached on each unit cell as shown in Fig. 2(a). The MA is essentially constructed of 4 layers ( Fig. 2 (b)): a copper (5.8 3 10 7 S/m in conductivity) front structure (17 mm in thickness) fabricated using standard photolithography techniques; a Rogers 5880LZ first separation layer (0.79 mm in thickness); an air second separation layer (0.80 mm in thickness); and a copper back layer (17 mm in thickness). The real part and loss tangent of the permittivity of the Rogers 5880LZ are 1.96 and 0.002, respectively. The simulated reflected and transferred (to RF diode) signal ratios using HFSS are shown in Fig. 2  (d), where both near zero reflection (225 dB) and peak transfer (20.30 dB or 97%) occur at about 6.7 GHz. The corresponding experimental data are shown in Fig. 2 (e). The minimum reflection of 217 dB and the peak transfer of 20.38 dB or 96% appear at about 6.9 GHz, which agrees well with the simulation results.

Discussion
The electric current distribution on the metal structure at the full absorption frequency is shown in Fig. 3 (a), which is similar to the current distribution of a dipole antenna 21 . The largest current flow is located at the center where the sensor is placed. The streamline of the Poynting vector of the incident EM wave is shown in Fig. 3 (b)-(d) in both perspective and side views. It is clear that most of the incident EM energy is focused, confined and transferred into the lumped port which represents the energy-converting sensor.
With a given energy converting sensor, the maximum signal transfer ratio is determined by the thermal loss component Z T A in Eq. (4), which comes from both the non-zero permittivity loss tangent of the first separation layer and the finite conductivity of the metal. A comparison among the transferred energy, ohmic loss energy and dielectric loss energy of UEECA in Fig. 2 (b) was shown in Fig. 2 (f). All three curves peak at a frequency of 6.7 GHz, where ohmic loss and dielectric loss consume 2% and 4% of the incident energy, respectively. To illustrate how the optimum signal transfer ratio varies with the loss tangent of the separation layer, a series of simulations using different material as the separation layer have been carried out. A UEECA using FR-4 (with e r 5 4.4 2 j0.088) has also been constructed and tested. Fig. 2 (g) shows the maximum signal transfer ratio as a function of the loss tangent of different materials for both simulation and experimental results (blue). The maximum signal transfer ratio approaches 100% when perfect electric conductor (PEC) is used and the loss tangent of the separation layer material is below 10 23 . To explore the potential of energy transfer ability of UEECA, it is shown in Fig. S1 that a signal transfer ratio of 0.99998 can be achieved in a simulation using UEECA with lossless materials.
While this experimental demonstration does not include the EM wave polarization and incident angle dependence, the solutions to these problems have already been provided. Absorbing an arbitrary polarization can be accomplished by adopting a 90u rotation symmetrical front structure 22 . For incident angle dependence, the MA maintains near 100% absorption for a TE mode with incident angle between 280u to 80u and above 89% absorption for a TM mode with incident angles smaller than 50u 9 . Therefore, the proposed UEECA is capable of maintaining high signal transfer ratio with different EM wave polarizations and very wide incident angles.
A significant feature of the UEECA is that it can be incorporated with a variety of energy converting sensors. Their different characteristic impedances can be easily accommodated by choosing the appropriate separation layer thickness using Eq. (2). The amount of the incident energy that transfers to the sensor can be maximized and quantitatively calculated using Eq. (4). The schematics of energy conversion process using UEECA can be seen in Fig. 4. The incident EM wave is maximally transferred to different energy converting sensors indicated by Z L in the TL model of the MA.
The proposed UEECA is feasible for wide applications by accordingly choosing the electromagnetic energy converting device or material as the conceptual sensor Z L . For example, the UEECA eliminates the necessity of an impedance matching circuit for the energy harvesting application. The optimized signal transfer ratio can be easily achieved by choosing the appropriate thickness of the separation layer as suggested by Eq. (3). As an important aspect of the energy harvesting, further design strategies for broadband absorption can be found in some recent publications [23][24][25] . The UEECA could also make a high impact in photoconductive antenna applications, where the energy conversion between DC and terahertz wave is desired. The UEECA could also be highly desirable in nonlinear optical devices. It advances the previously reported nanostructures 5,6 since the UEECA not only fully absorbs but also confines the incident wave in the region where largest field intensity is located 8 . Dramatic increases of the energy conversion ratio can be realized by integrating a material with nonlinear optical properties as the UEECA separation layer. For instance, LiNbO 3 can be selected for second harmonic generation applications.
In summary, by applying the classical antenna theory with infinite periodic boundary conditions, a conceptual energy converting sensor can be integrated into the TL model of a metamaterial absorber (MA). This integration leads to the concept of a universal electromagnetic energy conversion adapter (UEECA). The signal transfer ratio between the incident wave and the sensor can be maximized by simply choosing the optimal separation layer thickness. Using low loss separation material, a UEECA with 96% signal transfer ratio has been experimentally demonstrated.

Methods
Measurement setup. In the measurement, two horn antennas for emission and detection are connected to an Agilent 8722ES network analyzer and are positioned in front of a sample in the far field zone of the antennas. The reflection of the sample is calculated by R Sample 5 S Sample /S Metal , where S Sample and S Metal are the measured transmission between the two antennas when the MA sample and a thick metal plate are, respectively, placed at the same position in front of the antennas. The signal transfer ratio between the RF diode and the incident wave was determined by calculating ffiffiffiffiffiffiffiffiffiffiffiffi P m =P i p , where P i and P m are the incident power and the power detected by the RF diode, respectively. The incident power P i is determined by measuring the transmission between the emission and detection antennas by moving the detection antenna to the sample location. The RF diode detected power P m is calculated by V m /b, where V m is the output DC voltage from the parallel connected RF diode and b is the signal sensitivity of the RF diode. The DC voltage from the RF diodes is measured by a Keithley 2000 multimeter.
Simulation setup. The simulation of the UEECA is carried out by the commercial HFSS simulation software. Master and slave boundaries are applied on faces parallel to the EM wave propagation direction to mimic the periodically distribution of the units. Floquet excitation is used to simulate the incident wave. More than 20000 tetrahedrons in the final mesh process are used in the model. Since the impedance of the lumped port contains imaginary parts, the S-parameters were the ''generalized Sparameters'', which can be calculated by the equations 26 Where Z 01 and Z 02 are the impedances of port 1 and 2 respectively, R 01 and R 02 are the real part of Z 01 and Z 02 respectively. Z 11 , Z 12 , Z 21 and Z 22 are the Z matrix of the two port network which are given by the HFSS simulation.