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Abstract
Magnetic near-field control has attracted extensive attention and have a wide range of applications in filters, sensors, and energy-transfer devices. Coding metamaterial has the convenience of miniaturization and integration, which not only provides a bridge between physics and information science, but also exploits a whole new perspective for magnetic near-field control. In this work, we theoretically propose and experimentally verify that the coding metasurface can realize the reconfigurable magnetic near-field distributions. By adjusting the digital voltage signals which drive the resonant units of metasurface, capacitance of the resonator can be dynamically controlled, thus the dynamic modulation of magnetic near-field distribution can be achieved. Specially, this magnetic near-field control can be explained with the help of coupled mode theory and coherent superposition method. Moreover, simulated annealing algorithm is employed to determine working frequency of the whole modulation system, which can avoid time-consuming frequency scanning process. The experimental results are in good agreement with the calculated results. This work reveals the significant potential of coding metasurface for the experimental study of the magnetic near-field control and promotes the use of metasurface for numerous integrated functional devices.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Near-field electromagnetic modulation in low-frequency bands attracts much attention from researchers in recent years [1]. Metamaterial, a kind of artificial microstructure with specific properties, such as negative permeability or permittivity [2–7], is one of the most effective methods to achieve magnetic near-field modulation. For the purpose of modulation, a large number of meta units can be organized in the form of periodic planar array, which is called metasurface [8–9]. Metasurface not only has many far-field electromagnetic applications, such as frequency selection [10], narrowband perfectly absorbing [11], wavefront shaping [12–15] and so on, but also shows its capability for near-field controlling in terahertz and RF bands [16–26]. The development of metamaterials science gives birth to tunable metamaterial [27–34], based on which, a branch called ‘coding metamaterial’ is proposed [35–37]. Coding metamaterial is a combination of conventional metamaterial and digital electronic device, which improves flexibility of metamaterial and exploits a new research field [38–45]. It has several discrete working states which can be switched by external digital voltage signal. Compared with conventional metamaterial, coding metamaterial has several advantages. Firstly, coding metamaterial can achieve dynamic electromagnetic modulation, which makes a significant improvement on flexibility. Secondly, it has a convenience of integrating with digital control elements, such as field programmable gate array (FPGA). Last but the most important, coding metamaterial provides a bridge between physics and information science. The electromagnetic modulation effect can be studied from the scope of cryptography, data storage or computing science, which opens a wide research realm and has a great significance on artificial intelligence algorithms and machine learning [46–48]. Concept of coding metamaterial is firstly proposed around 2014 [36]. And soon after that Cui et al. achieved direction modulation for far-field electromagnetic wave with coding metamaterial which works around gigahertz [37]. By combining coding metasurface and artificial intelligence algorithms together, Li et al. made several achievements on far-field electromagnetic waves manipulation, such as holography in gigahertz [49]. Inspired by these achievements, research on coding metamaterials keeps growing [50].
Different from the previous coding metasurfaces, the distance between the resonators is small and the near-field coupling cannot be ignored in this work. In addition, previous researches on coding metasurfaces mainly focus on far-field transmission properties, such as selective reflection [37] and holography [49], while this work focuses on the control of magnetic near-field distribution in MHz band. With the aid of coupled mode theory and coherent superposition method, we can realize the reconfigurable magnetic near-field distributions in this compact coding metasurface. By loading digital voltage signal on a photo-relay, natural resonance frequency of coding meta unit can be switched between 3.4 MHz (‘0’ state) and 3.1 MHz (‘1’ state). With coding metamaterial of this type, we form a coding metasurface consisting of 16 units to achieve magnetic distribution modulation. Moreover, simulated annealing algorithm is employed to determine working frequency of the whole modulation system, which can avoid time-consuming frequency scanning process. Especially, the optical devices working at THz or even PHz frequencies are miniaturized because of the wavelength is small [51,52]. However, the case will be changed at low-frequency regimes. The corresponding wavelength of MHz band is very long, and the corresponding device size is very large, so miniaturization is very necessary. Coding metasufaces designed in this work have the convenience of miniaturization and integration. Recently, with the great development of near-field technology, a very important issue—magnetic shielding has attracted people’s attention. As a kind of traditional magnetic shielding material, ferrite will significantly increase the mass and volume of the device. The magnetic near-field control of metasurface provides a new way to realize the efficient magnetic shielding [24]. In addition, the regulation of magnetic near-field distribution is also proposed to be used in cloaking [53], wireless power transfer (WPT) [54–57] and wireless sensing [58]. Although this paper mainly considers the current wireless applications and designs the working frequency range to MHz regime, the relevant structure designs and results can be easily extended to higher frequency bands, such as GHz band.
2. Design of coding metamaterial
The magnetic coding meta unit in this paper is designed for RF band, so the general design is based on double-side square spiral structure. Figure 1(a) shows general design of coding meta unit. The main structure is metallic spiral coil locating on two sides of dielectric substrate. The spiral coil has a square shape and several turns for a compact size. Coil structure provides distributed inductance necessary for LC resonance. Between two ends of spiral coil, there are two lumped capacitors and one photo-relay. The photo-relay is driven by digital voltage signal loading between two input pins, and it can control validity of lumped capacitor 2. All these elements and spiral coil construct a resonant circuit, as shown in Fig. 1(b). By electromagnetic induction, the alternative magnetic field produces an induced electromotive force in spiral coil, and then generates a LC resonance. When driving signal remains at low level, lumped capacitor 2 is invalid, inductance coil and lumped capacitor 1 make up oscillation circuit. When driving signal is set to high level, lumped capacitor 2 is enabled, two lumped capacitors are combined together to participate in oscillation processing, and equivalent capacitance is sum of two capacitors. These two states have different resonance frequencies. In other words, for one fixed frequency, meta units in these two different states correspond to two currents which differs in amplitude or phase. Therefore, it causes different magnetic responses, and finally leads to different near-field modulation effects.
Fig. 1. Details of the circuit-based resonance unit of the coding metasurface. (a) Schematic of the reconfigurable resonance unit. (b) The effective circuit model of the reconfigurable resonance unit.
The detailed design of metamaterial structure is the iteration of parameters adjustment and performance measurement. For a specific meta unit design, its performance parameters can be obtained by simulation or experiment. By comparing measured performance parameters with the design target, we can make an adjustment to the former designed structure. This iteration may happen multiple times until the design meets the demands. In current research, there are two sets of parameters to describe properties of single meta unit. One set is based on coupled mode theory, which contains two parameters, resonance frequency and loss rate. Parameters extraction can use the setting of effective permeability measurement, which has been introduced in Ref. [3]. The effective permeability of metamaterial follows a Lorentz response as:
where ${\omega _0}$ is the resonance frequency of metamaterial unit, $\gamma$ is loss factor, $\Gamma $ is fill factor of a single cell and ${\omega _p}$ is magnetic plasma frequency. From frequency-permeability curve, resonance frequency ${\omega _0}$ can be identified easily, and loss rate can be measured from the full width at half maximum (FWHM) of imaginary part of effective permeability. Relation between loss rate and the FEHM is:Another set of performance parameter is based on Kirchhoff's equation, which includes inductance L, capacitor C and resistance R. These parameters can be directly measured from the real metamaterial unit by experiment, or obtained from simulation. In the following section, we will show that the circuit parameters are equivalent to parameters based on coupled mode theory.
Different from conventional meta unit, coding meta unit contains a photo-relay, which has an influence on performance of metamaterial. In real cases, photo-relay always has on-resistance Ron in its conducting state (‘1’ state), and it will weaken resonance in meta unit. Consideration this resistance, relationship curve between frequency and resonance current in two different states can be calculated out. Some typical results are shown in Fig. 2. On the one hand, it can be seen that coding meta unit in ‘1’ state has a lower resonance peak than that in ‘0’ state, which means a decrease of Q-factor. This effect is reflected as a decrease of effective permeability in effective medium theory, or a decline in magnetic field modulation capability. So, small on-resistance is quite meaningful for type selection of photo-relay. On the other hand, for a specific on-resistance of photo-relay, a smaller C2 can weaken the decrease of Q-factor in ‘1’ state. Figures 2(c) and 2(d) show the situations with different ${C_2}$ and a fixed Ron. It can be found that resonance inhibiting effect caused by photo-relay can be weakened by smaller C2, making two states refer to similar resonance current curves. So, a small C2 is also benefit to performance of coding meta unit.
Fig. 2. Frequency response of two state coding meta unit with different ${C_2}$ and ${R_{on}}$ (a) ${C_2}$=33pF, ${R_{on}}$=4.7$\Omega $ (b) ${C_2}$=22pF,${R_{on}}$=4.7$\Omega $ (c) ${C_2}$=33pF, ${R_{on}}$=20$\Omega $ (d) ${C_2}$=22pF, ${R_{on}}$=20$\Omega $. Each data is calculated under the condition that ${R_d}$=5$\Omega $.
The final detail structure design for coding metamaterial unit is shown as Fig. 3. The size of substrate plate is $50.8\;{\rm{mm}} \times 50.8\;{\rm{mm}} \times 1\;{\rm{mm}}$, Material of substrate is FR4 with a dielectric constant of 4.2. The dielectric loss tangent (tan δ) of the FR4 substrate is about 0.02. Metallic spiral coil locates on both sides of substrate plate. Each side contains seven turns with a via hole connected to each other. The width of spiral line is 10 mil (0.254 mm) and gap between lines is 10 mil (0.254 mm). The edge of the outmost turn is 1800mil (45.72 mm) in length, and it has a progressive decrease from outer to inner. Metallic spiral coil is made of copper with a thickness of 0.035 mm. The type of photo-relay is TPL3130 (Toshiba Corp.) which has an on-resistance of 4.7 Ω in its conducting state. Values of two lumped capacitors, ${C_1}$ and ${C_2}$, are 100 pF and 22 pF respectively.
Fig. 3. Detailed design of coding metamaterial. (a) Designment in Protel DXP. (b) Photo of the meta unit. Simulated (c) and measured(d) effective permeability in two states.
Properties of this designed metamaterial unit are acquired by simulation and experiment. According to CST simulation result, the resonance frequency is 3.36 MHz and 3.08 MHz. Metallic spiral coil has a total inductance of 20.694 μH, and it also produces a parasitic capacitance of 8.952 pF and resistance of 4.9 Ω. Figure 3(c) is the effective permeability curve of designed coding metamaterial unit acquired by simulation. The corresponding measured results are shown in Fig. 3(d). The effective permeability is obtained by a referenced time domain measurement. The reference electromotive force $emf{(t)_r} ={-} A{\mu _0}d{H_z}/dt$ is measured directly by a pair of coils without the metasurface. And the metasurface with the same area as the coils is placed between the transmitting and the receiving coils to obtain the electromotive force $emf{(t)_s} ={-} A{\mu _r}{\mu _0}d{H_z}/dt$. Then, the complex frequency dependent permeability is ${\tilde{\mu }_r}(\omega ) = {\{{\hat{F}(emf{{(t)}_s})/\hat{F}(emf{{(t)}_r})} } \}$ [59]. The measured results are meet well with the simulated results.
3. Method for magnet distribution modulation by metasurface
In this work, coding meta units are placed into 2-D planar array and locked by mechanical structure. A driving circuit is designed to provide bias voltage for photo-relay to switch working states of each unit. Therefore, the whole coding metasurface becomes reprogrammable.
Different from resonance behavior of single meta unit in free space, resonance of each unit in metasurface is affected by two following functions: electromagnetic induction from outer alternative magnetic field and near-field coupling between nearby meta units. Near-field coupling has a complicated influence on resonance behavior of the whole metasurface. For the coding metasurface in this paper, its working frequency is around megahertz and each meta unit works in the realm of deep subwavelength. Some coupling elimination methods, such as half-wavelength supercell [49], don't work well. So, coupling between nearby meta units should be fully considered, which can be a main feature to distinguish near-field modulation from far field interference.
3.1 Coupled mode theory applying in coding metasurface
Interaction between metasurface and alternative magnetic field is essentially a problem about coupled resonators, which can be well solved by coupled mode theory. Resonance of each meta unit can be viewed as a mode. Then coupling effect between resonances of two meta units is coupling between different modes. By coupled mode equations, resonance intensity of each meta unit can be solved under certain excitation conditions.
According to coupled mode theory, resonance of some single unit in metasurface can be written as:
In this equation, subscript i and j refer to meta unit’s index. ${|{{{\tilde{a}}_i}} |^2}$ denotes the energy stored in different resonators [60,61]. ${\omega _0}$ is the natural resonant frequency of unit, which is determined by its induction and capacitance. ${\gamma _i}$ is decay rate. κ is coupling coefficient between two units. ${\tilde{F}_i}$ is driving term which refers to induced electromotive force by the outer magnetic field.
When metasurface interacts with a stable alternative magnetic field, induced electromotive force oscillates with time in the harmonic form with its amplitude remaining constant. Because of this electromotive force and the damping effect by loss, resonance of each meta unit will also reach stable state after a period of time. Therefore, it can be concluded that resonance intensity varies with time as a factor of ${e^{ - i\omega t}}$, and its differential operation is:
After substituting the Eq. (4) into Eq. (3), all time factor ${e^{ - i\omega t}}$ can be canceled:
Equation (5) can be applied for all meta units, and they are combined into matrix form as:
The coefficient matrix on the left side of equals sign has a size of $n \times n$, and n is the number of coding meta units in metasurface.
In this matrix, diagonal element relates to the total impedance in independent resonance situation, and off-diagonal elements refer to coupling effect between two meta units. For coding metasurface, natural resonance frequency is directly controlled by outer digital signal loading on photo-relay. So, for each coding meta unit:
Coupling coefficient of two meta units depends on their relative location and coupling structure. For the coding meta unit proposed in this paper, capacitance required for LC resonance is provided by lumped element, which will not generate electric field in surrounding space. So, coupling between two meta units is mainly the magnetic coupling caused by metallic spiral structure. Switching of working states doesn't lead to any change in spiral structure, which means coupling structure remains stable. Therefore, in coding metasurface, coupling coefficient of any two units only relates to their relative locations, but has nothing to do with their specific states.
Coupling coefficient can be measured by frequency difference between symmetric mode and anti-symmetric mode (frequency splitting effect). Both simulation and experiment prove that coupling coefficient between two units decreases rapidly with the increase of their distance. Based on this feature, Eq. (6) can be simplified. Only coupling coefficient of nearby units should be taken into consideration. For any two units which are not nearby each other, coupling effect can be ignored.
In metasurface structure, coupling effect between nearby meta units is reflected as mutual inductance in circuit theory, and coupled resonance mode of each unit manifests as LC resonance. This suggests that coupled resonance behavior of the whole metasurface also can be described by circuit theory. In the following, we will demonstrate equivalence of coupled mode theory and Kirchhoff’s law. According to Kirchhoff’s second law, for LC circuit of some single meta unit in metasurface, there has following equation:
The resonance frequency ${\omega _{0i}}$ is determined by ${\omega _{0i}} = 1/\sqrt {L{C_i}}$. Then Eq. (8) can be transformed into:
For megahertz metamaterial unit, magnetic modulation capability is mainly validated when working frequency is close to resonance frequency. For this point, there has an approximate relationship that:
Applying this approximation to Eq. (9), it can be transformed into:
In addition, parameters in coupled mode equation have following relations with circuit parameters:
Combining Eqs. (11) to (15) together, we can obtain coupled mode equation as Eq. (5). Thus, both coupled mode theory and circuit theory can describe coupled resonance of the whole metasurface, and they have an equivalence.
3.2 Sub-field superposition
For magnetic metasurface, its near-field modulation effect is derived from coherent superposition of sub-fields which are generated by all meta units. The sub-field of each meta unit is determined by its detailed spiral structure and resonance intensity. Geometry of metallic spiral structure determines the spatial distribution pattern of sub-field. And resonance intensity decides the overall strength of sub-field. It should be noted that relative phase relation between resonance currents of each two meta units has a direct impact on coherent superposition process. Result of superposition is the total magnetic field generated by the whole metasurface structure. Combining this total field and background field together, the final magnetic near-field modulation effect can be obtained.
Based on former description about magnetic field modulation, for sub-fields of all meta units, the coherent superposition can be expressed as:
In practical application scenarios, such as WPT transmitting system, magnetic near-field modulation mainly focuses on normal magnetic distribution on some certain plane which locates above and parallel to metasurface. At present, it is a fundamental challenge for traditional materials to manipulate electromagnetic waves on the subwavelength scale. Generally, in order to realize the wireless charging of the load whose position is not fixed, it is necessary to design the transmitting coil with special geometry, so that the magnetic field excited by it is nearly uniform in the charging plane [62]. However, this is accompanied by unnecessary energy waste in the unloaded area. With the help of the flexible magnetic field control realized by the coding metasurfaces, this problem can be solved well. Here, according to the area and geometry of the load, we can flexibly control the corresponding intensity of the near magnetic field distribution. We are looking forward to utilizing the controlled magnetic field concentration of coding metasurfaces in the future to realize the efficient WPT devices. According to coherent superposition as Eq. (16), normal magnetic flux density distribution in some target plane above metasurface can be expressed as:
With Eq. (17), given the resonance intensity of each metamaterial element, the normal distribution of the target region can be derived, and the modulation effect of the magnetic distribution can be predicted.
3.3 Determination of coding states and working frequency
Near-field coupling between each two nearby units in coding metasurface mentioned in this paper follows weak coupling condition. Because of this, although near-field coupling has an influence on modulated distribution, locations of ‘enhanced’ and ‘reduced’ areas generally correspond to code figure of units. Here, ‘enhanced’ and ‘reduced’ areas refer to the relatively strong and weak areas in the magnetic field distribution. When the working frequency is close to the resonance frequency of the resonator, the large current in the metal spiral structure will produce a strong magnetic near-field in the surrounding space, and then the normal magnetic field intensity in the target plane is enhanced; on the contrary, when the working frequency deviates from the resonant frequency of the resonator, the current in the metal spiral structure is small, which leads to the reduced normal magnetic field in the target plane. Therefore, for coding metasurface in this paper, we simply use ‘direct coding strategy’. Binarization is applied on objective magnetic distribution to distinguish enhanced area from reduced area. Then coding meta units which locate below enhanced area are set to same working state. By setting a proper working frequency, the units below enhanced areas are in strong resonance, while resonances of the other units are weak. Here, ‘strong’ and ‘weak’ resonances directly correspond to the above ‘enhance’ and ‘reduced’ areas, respectively. Phase difference between strong and weak resonances should approach 180 degree, which is benefit to destructive interference and contributes to magnetic field elimination in reduced area. With all these functions, objective magnetic distribution can be achieved by coherent superposition of sub-fields from all units.
Near-field coupling between nearby units in coding metasurface changes the frequency characteristic of each unit, making it different from what it is in independent resonance condition. This point makes it necessary to reconsider working frequency to achieve desired modulation effect. The simplest method for this work is frequency scanning in concerned band. By coupled mode theory and coherent superposition principle, magnetic distribution modulated by some certain coded metasurface can be calculated at each sampling frequency. Based on cross-correlation value between each sampling distribution and objective distribution, an optimal solution can be selected for working frequency in the specific coding condition. Frequency scanning method works well when coding metasurface consists of limited number of meta units. However, when coding metasurface contains large number of units, or when the number of sampling frequencies is large, frequency scanning will become time-consuming.
To overcome this shortcoming, simulated annealing algorithm can be employed to improve the calculation process [63]. The essence of simulated annealing algorithm is solution optimization by iteration and comparison. By the introduction of uncertainty, the algorithm acquires the capability to jump from local optimization solution and converge to global optimum. Searching optimal working frequency by simulated annealing algorithm can use following steps. First, in concerned frequency band, a frequency is randomly chosen as an initial frequency. At this initial frequency, magnetic distribution modulated by coding metasurface can be calculated, and the cross-correlation between this calculated distribution and objective distribution can be acquired as ${\Delta _1}$. Second, a new frequency is randomly picked in neighborhood of initial frequency, and the corresponding cross-correlation value is ${\Delta _2}$. There are two possible results for comparison between ${\Delta _1}$ and ${\Delta _2}$. If ${\Delta _2}$ is greater than ${\Delta _1}$, the new frequency will be accepted as current frequency to replace the initial frequency. If ${\Delta _2}$ is less than ${\Delta _1}$, it will also get a chance P to perform the above replacement. The probability P is:
where S is probability coefficient, T is the ‘annealing temperature’ which decreases with the number of iterations increasing. By repeating all these procedures above, an optimal working frequency for the metasurface can be finally obtained. With the help of simulated annealing algorithm, calculating time can be significantly reduced, which is meaningful for dynamism of magnetic modulation by coding metasurface.With working frequency determined by simulated annealing algorithm or frequency scanning, direct coding strategy can fulfill desired modulation effect in most cases. However, in some particular situations, code figure of meta units may not be similar to modulated magnetic distribution. For these situations, coding states of the whole metasurface can be adjusted to provide some other options, which generate their modulated distributions with working frequencies determined. By comparing all these modulated distributions, the optimal one can be selected to determine the coding states and working frequency of the whole metasurfaces.
4. Experiments
In this section, we use coding metasurface to achieve magnetic near-field distribution modulation in target plane. Coding meta units are organized into different planar structures ($1 \times 2$, $2 \times 2$ and $4 \times 4$). In all experiments below, all coding meta units are in the same type as designment in Sec. 2, and parameters used in numerical calculation also follow the former measured result.
Framework of modulation system is shown as Fig. 4. Magnetic field is generated from transmitting coil, which is driven by harmonic voltage signal from waveform generator (Agilent 33600A). Modulated by metasurface structure, the magnetic field will form some certain normal distribution (z-component) in the target plane located above the metasurface. The distance between the transmitting coil and the metasurface is 10 cm. According to Biot-Savart law, the magnetic near-field generated by the transmitting coil in the sample plane is approximately uniform. A small coil is used as a probe to measure z-component of the magnetic flux density. The near-field magnetic probe is a home-made loop antenna, whose radius is 0.5 cm. Induced electromotive force excited by alternative magnetic field can be read through oscilloscope (Keysight DSOS054A), and its amplitude can show the magnetic flux density in the normal direction. In particular, the transmitting coil and probe should work in non-resonant state to reduce the interference to coding metasurface. The reconfigurable magnetic field in this paper is normalized to the distribution without metasurface structure.
4.1 Two units
One simplest model for coding metasurface is the metasurface which only contains two coding metamaterial units. Two coding metamaterial units are placed side-by-side in modulation system and target plane is 50 mm above the two-unit metasurface. According to theory in Sec. 3, modulation effect of this model can be predicted. Working frequency of this system is set at 3.18 MHz, and coupling coefficient for this distance condition is $\kappa /\omega ={-} 0.02472$. Coupled mode equations for this model can be written as:
According to knowledge on permutation and combination, and considering the symmetry of structure, this two-unit coding metasurface has three possible working states: ‘00’, ‘11’ and ‘10’. Resonance intensities ${a_1}$ and ${a_2}$ for these three states can be worked out by coupled mode equations. Calculated response spectra of the two-unit system, which contains the spectra of the ‘00’, ‘11’, ‘10’ states, individual ‘0’, ‘1’ states are shown in Fig. 5.
Fig. 5. Calculated response spectra of the two-unit system, which contains the spectra of the ‘00’, ‘11’, ‘10’ states, individual ‘0’, ‘1’ states. The target frequency 3.18 MHz is marked by the dashed line.
Then, with the pattern function of coding meta unit, normal magnetic distribution in the target plane for these three states can be obtained by superposition process, which are shown in Fig. 6. The red and blue lines represent the magnetic field amplitudes of the individual left and right resonators, respectively. And the black line denotes the magnetic field amplitude of the composite structure with two resonators
Fig. 6. Calculation results for magnetic distribution modulated by two meta units in three situations. (a), (b), (d), (e), (g), (h) The magnet field distributions on the working plate. (c), (f), (i) Field amplitude along the symmetry axis. The blue and red are for the unit in left and right correspondingly and black is total field according to superposition. (a)-(c) Field modulation effect for code ‘11’ situation, in which both units are in un-excited state. (d)-(f) Similar to (a)-(c), but for code ‘00’, both units are in excited state. (g)-(i) Similar to (a)-(c), but for code ‘01’, two meta units work in different states and total field concentrate to one side.
From the normal magnetic distributions in three coding states shown in Fig. 6, several following features can be observed: (1) In the target plane, normal magnetic flux density in some certain area is mainly determined by resonance intensity of the unit which locates right below. When the unit is in strong resonance state, normal magnetic flux density in directly above area will be likely stronger, and vice versa. (2) As the sub-field of one unit can spread to large area in target plane, resonance intensity of the unit has a certain influence on magnetic field in adjacent area. Phase relation between two sub-fields plays an important role in their interference, determining constructive or destructive result. (3) State changing in one unit may cause resonance intensity changing in the other unit. This near-field coupling will change the frequency characteristic of resonance, making it different from that in independent working condition.
Experimental measured modulated distribution by two-unit coding metasurface are shown in Fig. 7, and they are in good agreement with the calculation results. By setting different 2-bit code strings on two-unit coding metasurface, normal magnetic distribution in target plane can be switched accordingly. Besides, experimental results also show some features on interaction between resonances of two units, reflecting the near-field coupling effect.
Fig. 7. Experimentally measured magnet distribution modulation effect by 2 meta units. Two meta units are coded by (a) ‘11’, (b) ‘00’, (c) ‘01’. (d) Magnet distribution along long symmetry axis of 2 units are extracted and they fit calculations result generally. Frequency of background magnet field is 3.18 MHz.
4.2 Four units
Four coding meta units form a $2 \times 2$ array tightly to construct a 4-unit coding metasurface. This metasurface is placed in modulation system and target plane is 50 mm above the metasurface. Working frequency of the system is 3.21 MHz. Coupled mode equations for this 4-unit coding metasurface can be written as:
Considering symmetry of the metasurface structure, there are 8 possible coding states in total. Here, ‘0110’ state is taken as an example. By couple mode equations and superposition process, the numerical result for normal magnetic distribution in target plane is shown as Figs. 7(a) and 7(b). Magnetic field is concentrated above the coding meta units which are working in ‘0’ states, and magnetic field above the other two units is suppressed. Because of destructive interference, magnetic field in suppressed area can be reduced to very low level. Contrast ratio of total distribution can be more than 10, which is hardly achieved by simply removing the meta unit in suppressed area. Experimental result for 4-unit coding metasurface in ‘0110’ state is shown as Figs. 7(c) and 7(d). and it fits the numerical result at frequency of 3.19MHz.
Fig. 8. Numeric calculations and experimental result of modulation effect of 4 units array coded by ‘0101’. (a) and (b) are magnet distribution modulation effect at 3.21 MHz, in this frequency area above ‘1’ unit is cut down effectively. (c) and (d) are experimental magnet distributions which is achieved by experiment at 3.19 MHz.
4.3 Sixteen units
To realize magnetic modulation by $4 \times 4$ coding metasurface, we design a type of assembled metasurface structure, as shown in Fig. 9. The whole structure is composed of one baseboard and 16 coding meta units. Each meta unit is embedded in a certain location on baseboard to form a 2-D planar array. For convenience of assembling, a 5-mm gap is reserved between every two nearby units. Every meta unit is connected to baseboard by two metal leads. These two leads can import digital voltage signal into meta unit to drive switching element, and they also have a function of mechanically fastened structure. Besides, 6-mm-diameter holes are made on baseboard for Teflon fastener. Driving circuit is distributed on baseboard so that working states of all meta units can be controlled manually by mechanical switches. In another design, a 16-bit port is also reserved for controlling metasurface by external device, such as FPGA.
Fig. 9. Structure of 16-unit coding metasurface. (a) and (b) are schematic drawing of metasurface. (c) is picture of real structure.
The assembled metasurface structure is placed in magnetic near-field modulation system and the target plane is set 25 mm above the metasurface. In the experiment, the size of the transmitting coils used is close to that of the different planar structures. When the power of the transmitting coil fixed, the energy density of the magnetic near-field generated by the large-scale transmitting coil on the planar structure is smaller than that of the small-scale transmitting coil. Therefore, in order to ensure that the probed signal on the target plane is close, the distance between the target plane and the 4×4 metasurface is smaller than that of the 1×2 and 2×2 metasurfaces. For 4×4 coding metasurface, each working state corresponds to a string of 16-bit binary code, and there ${2^{16}} = 65536$ possible working states in total. Here, we take three states (code= ‘1111100110011111’, ‘0000011001100000’ and ‘0011001111001100’) as examples to show the modulation performance.
Figure 10 shows numerical (3.163 MHz) and experimental (3.180 MHz) modulated distributions of normal magnetic flux density in three coding states. For different planar structures (1×2, 2×2 and 4×4), the working frequency of system is discrepant. The frequency deviation mainly due to the coupling effect between resonators. Although the working frequency of the controlled magnetic near-field distribution is between 3.4 MHz (‘0’ state) and 3.1 MHz (‘1’ state), the actual working frequency will be determined by the coupling between the resonators. For state ‘1111100110011111’, magnetic field is concentrated in center area while field in surrounding area is reduced, which can be marked as distribution of ‘concentration’. For state ‘0000011001100000’, magnetic field in center area is eliminated and part of magnetic field is redistributed to surrounding area, marked as distribution of ‘isolation’. For state ‘0011001111001100’, magnetic field in two diagonal areas is enhanced. In the other two diagonal areas, magnetic field is reduced. This can be marked as ‘diagonalization’.
Fig. 10. Modulated magnetic distribution achieved with 16-unit coding metasurface (a)-(c) Centralization formation ‘1111100110011111’ (d)-(f) Dispersing formation ‘0000011001100000’ (g)-(i) Diagonalization formation ‘0011001111001100’.
From experimental results, it can be concluded that strength of magnetic field in certain location has much interrelation with state of the unit in corresponding location. Except this general relationship, magnetic distributions in these three states also show some unusual features. For example, in distribution of ‘concentration’, magnetic field in four corners is stronger than other surrounding area, appearing as minor peaks. In distribution of ‘diagonalization’, magnetic field in each quarter area is not uniform. According to the study on coupled mode theory, these features are due to near-field coupling effect which is significant in deep sub-wavelength condition. Coding meta units in same state may be affected by different coupling conditions, thus changing the frequency characteristic of resonance and causing non-uniformity mentioned above. The deviation between numerical and experimental results in Figs. 8 and 10 mainly come from the errors of sample construction and experimental measurement.
5. Conclusion
This paper proposes a design of coding meta unit which works around 3 MHz and constructs coding metasurface structure consisting of up to 16 coding units. By adjusting the digital voltage signals which drive meta units in metasurface, working mode of the whole metasurface can be dynamically controlled, and dynamic modulation of magnetic field in near-field realm can be achieved. Configurability of coding meta unit comes from controlment of lumped capacitor by photo-relay. When digital signal changes working state of photo-relay, resonant capacitance of meta unit also changes, thus causing a change of natural frequency and leading a different modulation behavior in specific fixed frequency condition. Mechanism of magnetic modulation by metasurface is explained by coupled mode theory and near-field superposition principle. Simulated annealing algorithm is employed to pick the optimal working frequency to improve modulation effect. Using the algorithm can avoid time-consuming frequency scanning process, and it is quite meaningful on dynamism. Results of numeric calculations based on these theories fit the experimental results well.
Coding metasurface proposed in this paper provides an effective modulation technique for magnetic near-field distribution modulation around megahertz. Its multifunction and dynamicity are of much value for many industrial techniques, such as WPT. Distributions of ‘concentration’, ‘isolation’ and ‘diagonalization’ achieved in this paper may have much importance on rapid-charging, foreign object tolerance and multi-terminal charging in WPT system. And coding metasurface can also provide reliable solutions for magnetic near-field modulation in other applications.
Funding
Opening Project of Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology; Shanghai Super Postdoctoral Incentive Program; China Postdoctoral Science Foundation (2019M661605, 2019TQ0232); National Natural Science Foundation of China (11604136, 11674247, 11775159, 11935010, 11974261, 12004284, 61621001, 91850206); Science and Technology Commission of Shanghai Municipality (18JC1410900, 18ZR1442900); National Key Research and Development Program of China (2016YFA0301101).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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