Anapole-enabled RFID security against far-field attacks

2.1 Optimization with Mie theory

High-index dielectric resonators support a variety of electromagnetic modes, which are governed by structure’s geometry and a real part of the refractive index of constitutive materials. Adjustment of those parameters allows designing combinations of several interfering multipoles, e.g. [48, 49]. Furthermore, mixing high-quality ceramics powders enables considering refractive index as an additional engineering parameter, ranging from moderately low to extremely high values, approaching hundreds [50]. The later property allows achieving significant size reduction of a resonator.

Electromagnetic properties of structures with spherical symmetries can be assessed semi-analytically with the aid of Mie theory, which is beneficial for performing computationally efficient parametric studies over a large search space. A core–shell geometry was chosen as a starting point for optimization with the goal of obtaining a pair of anapole states. Those should be located close to each other in a parametric map. In this case an efficient modulation scheme to switch between them can be made possible. Once two anapole states, corresponding to zeroing of the scattering efficiency are obtained, a control element, capable of switching between those two, will be developed. This switching is essential for the RFID operation.

The initial structure, which consists of a concentric sphere, shell (with a different refractive index), and an air interlayer between them, has five degrees of freedom (radiuses and refractive indices of the materials). Those are sufficient for controlling the hierarchy of resonant multipoles. Scattering efficiency is given by [51]:

where k is a wavenumber outside the structure, r is outer radius of the shell, and a _n and b _n are Mie coefficients associated with electric and magnetic multipoles, respectively. In this case, spherical harmonics are taken as the expansion basis. Mutual orthogonality of the basis functions allows associating each spherical harmonic with an independent scattering channel. In particular, complex-plane poles of the scattering Mie coefficients correspond to the eigenmodes of the resonator. Nulls of the coefficients, lying on the real axis, correspond to anapoles – zero energy flow into a single scattering channel or, in other words, a vanishing partial cross-section. This definition will be used hereinafter. Hence, the anapole is not an eigenstate of a system, as it corresponds to the null but not to the pole of the scattering coefficient. Furthermore, anapole’s existence can be considered only in conjugation with the incident field.

While the anapole state is an effect of vanishing scattering into a single scattering channel, it is frequently associated with an emergence of toroidal moments, destructively interfering with other multipoles [52], [53], [54], [55]. However, as it was recently shown, the toroidal moments are not additional missing basis functions in the multipolar expansion, but they appear as higher-order corrections to approximate expressions for multipole moments, derived within to long-wavelength limit [29, 30].

To find the anapole state in our spherical core–shell geometry, a color map presenting Q _sca as a function of core refractive index and operational frequency is plotted in Figure 1. The upper bound on the size of the structure was chosen to be 3 cm to keep the tag’s footprint reasonable. The radius of the core is chosen to be 8 mm, the thicknesses of the intermediate air layer and shell are 1.5 mm and 5.5 mm, respectively. In practice, air gap can be filled with any RF-transparent material, e.g. polystyrene. After a set of preliminary assessments and considerations of experimentally available refractive indexes, the shell parameter was fixed to n _shell = 29. The core index was varied in the range n _core = 26–32. The imaginary part of refractive index was taken to be κ = 0.01, which complies with experimental data [50]. The relevant regions are highlighted with a black (first anapole state) and red (second anapole state) dashed circle. Two anapole states were found within the RFID frequency band (954–956 MHz) at n _core = 27.5 and n _core = 31, which will correspond to state 1 and state 2 of a modulation scheme (Figure 1). One of the design aims is to reduce the footprint of the tag, elevating the refractive indices (permittivity up to 1000 is possible, based on available ceramic powders) of constitutive components. An excessive size reduction, on the other hand, leads to the bandwidth degradation. In this case, at least a single the RFID communication channel should be supported.

Figure 1:

Scattering efficiency of the model.

(a) Core–shell geometry (b) color map (logarithmic scale) of scattering efficiency as a function of the cores’ refractive index and the operational frequency. The inner sphere’s radius is 8 mm, and thickness of the air interlayer and shell are 1.5 mm and 5.5 mm, respectively. Shell’s refractive index is n _shell = 29.

It is worth noting that modulating the refractive index is not practical, nevertheless it allows capturing the main physical principle and provides guidelines for further numerical optimization with an IC. This will be done hereafter.

2.2 Multipole engineering of modulation

Design of the core–shell structure, supporting two regimes of vanishing scattering cross-sections in the RFID frequency range (EPC Gen2, 860–960 MHz), was demonstrated in the previous section. This phenomenon was attributed to the emergence of anapole states, which will be proven now. For this purpose we provide a multipole expansion of the scattering cross-section (SCS) in Cartesian coordinates, using the analytical expression [56]:

where E ₀ is the amplitude of the incident plane wave, ϵ 0 is the vacuum permittivity, and c is the speed of light in the free space. Indices α , β run over the Cartesian coordinates x, y, z. Electric and magnetic dipole moments p α and m α , as well as electric and magnetic quadrupole moments Q α β e and Q α β m are obtained with exact expressions introduced in Ref. [57]:

where ω is a frequency, J is the induced electric current density, r is the radius vector and j _n ( n = 0,1,2,3 ) are the spherical Bessel functions. Note, that Eq. (1) uses spherical harmonics basis, while Eq. (2) makes the expansion in Cartesian system. However physical meaning of multipole moments is independent from their basis as for any physical quantity. Calculation of the moments is done with COMSOL Multiphysics^®. In particular, we solve scattering problem numerically, obtain the current density and then substitute it to Eqs. (3)–(6).

The corresponding spectra of the SCSs in the range of 948–958 MHz are shown in Figure 2. The geometry is taken from the previous section. The total SCS is governed by the non-resonant residual magnetic dipole, while electric dipole scattering channel vanishes if two special frequencies are considered – 955.1 MHz for n core = 27.5 [Figure 2(a)] and 956.4 MHz for n core = 31 [Figure 2(b)]. These dips in the spectra are the anapole states, which were identified by observing Figure 1(b). Those specific frequencies can be further tuned by varying the geometry and swept over the entire RFID frequency band. In addition, here we will demonstrate that toroidal moments are only quasi-static corrections in the frame of the long-wavelength approximation, and can be avoided by using the exact expressions. For this purpose, partial SCS is calculated as a coherent sum of the approximated electric dipole moment p α app and toroidal dipole moment T α , obtained via the conventional expressions [55]:

Figure 2:

Multipole expansion of the scattering cross-section (SCS is in logarithmic scale) of the core–shell particle with the refractive index of the core (a) n _core = 27.5 and (b) n _core = 31. The expansion is done up to the quadrupole order, such that C _full is the sum of the calculated partial cross-sections. C _p+T is the contribution of the toroidal dipole moment and the electric dipole moment in the long-wavelength approximation. Black dashed curve C _p+T overlaps with the red curve, corresponding to the partial SCS of fully-retarded electric dipole moment C _ed. Insets demonstrate C _p and C _T corresponding to contributions of p ^app and T, respectively. Vertical black dashed lines correspond to the SCS minima at (a) 955.1 MHz and (b) 956.4 MHz.

The results of the calculations are also shown in Figure 2 by dashed black lines. As it was expected, C p + T and C e d completely overlaps indicating that the toroidal dipole moment is needed only to correct an approximated value of the electric dipole moment. Here, p α app is calculated via Taylor expansion of currents in the source region [58], while Eq. (3) for p α is an exact expression obtained without any approximations. In addition, insets in Figure 2 demonstrate values of C _p and C _T , which are partial SCSs calculated via Eq. (4) for p ^app and T, respectively. Each of them do not vanish in the region of interest; however their interference results in a dip, reducing the partial CSC by two orders of magnitude.

3.1 Design of the structure

While the theoretical model with fast Mie theory-based optimization allows assessing a range of relevant parameters, an outlook to a practical implementation suggests employing an IC for the switching. In this case, closed-form Mie solutions do not exist. Hereinafter, we will consider a short dipole with a switch, plugged in a gap [Figure 3(a)].

Figure 3:

Schematics of an RFID tag.

(a) A core–shell ceramic structure and dipole with an RFID chip, soldered within a gap. (b) The principle of operation – destructive interference between electric dipolar resonances in the shell and in the core. The impedance, soldered within a gap of a thin wire, controls the dipolar resonance of the core, switching between two anapole states of the structure.

A full-wave numerical simulation in CST MICROWAVE STUDIO, frequency-domain solver, was used for designing the structure. We optimize the switching between two anapole of the core–shell, which was analyzed in the previous section. In the theoretical model, we vary the core’s refractive index to null the scattering into dipolar channel. However, this approach cannot be implemented in practice. To shift ED resonance of the core with an IC, we introduce a metal wire, passing through the center of the structure (Figure 3). This strategy was chosen since the ED of the core has a maximum electric field at the center and as the result, might have a sufficient coupling with the ED of the metal wire. Thus, modulating the impedance of the wire (open and short circuit in the middle gap), we change its coupling with the core and control the resonance of the latter.

The design, shown in Figure 3(a), consists of a shell tuned to ED (see Figure 3(b)) and a core, functionalized with a small dipole + IC (see Figure 3(b)). The previously discussed geometry was used as an initial starting point for the optimization. Changes, introduced by inserting the wire within the shell were compensated by varying parameters around their initial values. After a set of optimizations, the parameters are: the core’s radius r _core = 8 mm and inner and outer radiuses of the shell r _{inner shell} = 9.5 mm and r _{outer shell} = 15 mm (there is a 1.5-mm-wide air layer between the core and the shell). The real and imaginary part of refractive indices of shell and core was taken from the theoretical model. A cylindrical hole with a radius of 0.5 mm was made through the core to host the copper wire (electric conductivity σ = 5.8 × 10⁷ S/m). Plane wave excited the structure in a way that the electric field vector was directed along copper wire.

Commercial RFID ICs typically have complex impedances in modulation states and may vary from vendor to vendor. Here we will use a pair of our custom-designed impedances to control the structure. Metal wire shifts the resonances of the initial structure to higher frequencies. To compensate for the shift, we added a lumped coil with L = 47 nH. This state will correspond to State 2. State 1 corresponds to L = 111 nH. Thus, modulating the impedance of the dipole (inductance) we switch between two anapole states (see Figure 4). As it was mentioned previously, the structure in State 1 has two nearby anapoles. IC shifts the higher frequency state to the spectral location of the first one. As the result, the tag remains in the anapole state for both of the impedance nominals, ensuring the far-field leakage suppression. The inserts in Figure 4 show absolute values of electric field amplitudes in two anapole states and verify that the high-frequency anapole was shifted from 972 MHz to 955 MHz by changing the IC inductance.

Figure 4:

Scattering efficiencies of the structure for (a) “state 1” – L = 111 nH and (b) “state 2” – L = 47 nH. Inserts – absolute values of electrical field amplitude in anapole states.

3.2 Tag’s security assessment

To verify the proposed hardware security scheme, our design will be assessed versus a standard commercial realization and a pair of special short-range tags. Both near- and far-field readout performances will be estimated. Six-element linearly polarized Yagi-Uda was designed to operate at 900–990 MHz and was used to interrogate the tags [Figure 5(a)]. Antenna’s gain is 11.5 dBi. Near-field distance was chosen to be 3 cm, while far-field scenario is 1 m. Complex reflection coefficients (S₁₁ parameters) were calculated. Modulation efficiency (absolute value of a difference between S₁₁ parameters of two states (|S⁽¹⁾ ₁₁–S⁽²⁾ ₁₁|)) plays a significant role in tag’s operation. Our anapole tag can be further optimized by considering this criterion – the modulation efficiency should be maximized at the near-field and suppressed at the far-field. For this purpose, we kept L = 47 nH (State 2) constant, while varying the inductance at State 1 from 60 nH to 120 nH. Figure 5(b) shows the near- and far-field modulation efficiencies as the function of the inductance. It can be seen that nearly maximal contrast at the near-field and the dip for the far-field case is obtained for L = 111 nH, exactly as it was designed to support the switchable anapole state. While the anapole design was made for a plane wave incidence, considering a practical interrogating antenna might introduce variations. Figure 5(b) shows the modulation efficiency as a function of frequency. Here, L = 111 nH in State 1 was kept constant. A minor shift of the operational frequency can be observed. Under those optimal conditions, 34 dB difference in the modulation efficiency at near- and far-fields can be observed.

Figure 5:

Tag’s security assessment in near- and far- fields.

(a) Near- and far-field interrogation schemes. (b) Near- and far-field modulation efficiencies, as the function of the lumped element induction in state 1. (c) Near- and far-field modulation efficiencies, as the function of the operation frequency. L = 111 nH in state 1 is kept constant.

In order to assess the far-field security, granted by the anapole design, commercial ALN-9654-FWRW tag and near-field tags (GEE-UT-J41 Impinj J41 UHF tag, J51 Impinj Monza5 tag) were used for a reference. Table 1 summarizes the results and shows a minor advantage of the anapole tag in near-field interrogation along with more than an order two of magnitude suppression of the far-field leakage compared to the standard dipole tag and an order of magnitude compared to the short-range desighns. In other words, the anapole tag grants an ordinary short-range operation, while the far-field attack is significantly suppressed. To attack the anapole tag with the same success, as it is possible with a commercial tag, 100 times increase of the reader’s radiated power is needed. Introducing an IC with a low activation threshold, as it is done in GEE-UT-J41 Impinj J41 and J51 Impinj Monza5 tags [59], can improve the security furthermore. Our tag can be further improved by suppressing the residual magnetic dipole moment, as it can be seen from Figure 2.

Table 1:

Modulation depth |S⁽¹⁾ ₁₁–S⁽²⁾ ₁₁|, comparison between different tags.

	Anapole RFID tag	ALN-9654-FWRW tag	GEE-UT-J41 Impinj J41 UHF tag	J51 Impinj Monza5 tag
Near-field (0.03 m)	5 × 10−3	2.5 × 10−3	2.2 × 10−4	2.5 × 10−4
Far field (1 m)	5.5 × 10−6	4 × 10−4	1.8 × 10−5	2.2 × 10−5