Conformal metamaterial absorber for curved surface

: In this paper, three different unit cells are designed on the basis split-ring-cross resonators, and each unit cell has an absorption rate greater than 90% at incident angles of 0°, 30°, and 45°, respectively. They are non-periodically placed in three different zones on the curved surface. Therefore, the proposed conformal metamaterial absorber can achieve a high absorption rate. The performance of the proposed absorber is compared with that of a metallic curved surface and a conformal metamaterial absorber with the same unit cells.

most widely known metamaterial-based absorber is the Salisbury absorber [2].While this absorber is only a quarter-wavelength thick, its thickness increases at low frequencies.Metamaterial absorbers comprising plasmonic nanostructures provide high absorption values over a wide range of frequencies [3,4].However, they have complex nanofabrication requirements, which may limit practical device applications.Metamaterial absorbers can also be realized using a periodic array of a split ring resonator (SRR) [5][6][7][8][9][10][11][12][13][14].SRR-based absorbers use a resonant-type structure, which consists of a periodic unit cell array of metal patches and a substrate with a lossy interface.Since it is designed by metallic SRR patterns, it provides easy fabrication and a high absorption rate at the resonant frequency in spite of the thinnest structure.However, the previously reported metamaterial absorbers have planar structures.These absorbers exhibit a high absorption rate only at normal incidence because they are designed for normal incidence.When a metamaterial absorber is built on a curved surface, only the unit cell at the center of the absorber is normal incidence, whereas the other unit cells on the areas of the absorber are oblique incidence.The absorption rate of the metamaterial absorber drops drastically when an EM wave is incident obliquely onto the absorber [5][6][7], because the condition for zero reflection coefficient at oblique incidence differs from that at normal incidence.Recently, it has been followed by some work to improve the angular and polarization performance [8][9][10][11][12].
This letter proposes a new conformal metamaterial absorber suitable for a curved surface.At normal incidence on the curved surface, different areas experience different incident angles.Normal incidence occurs at the center of the absorber, whereas oblique incidence occurs at the other areas of the absorber.Therefore, we have designed three different unit cells, which are optimized at 0°, 30°, and 45° incident angles, respectively.
For achieving a high absorption rate, the three types of unit cells are distributed on a curved surface.The proposed concept is demonstrated by EM simulation and experiments.The RCS reduction with nonuniform unit cells is compared with that of the conventional planar metamaterial absorber with uniform unit cells.

Conformal absorber design
A metamaterial absorber can be realized by eliminating the reflected wave, and the transmitted wave can be absorbed through the conductive and dielectric losses.Zero reflection can be achieved by artificially manipulating ε and μ of the metamaterial because the reflection condition is determined by the permittivity (ε) and permeability (μ) of the medium.
In this work, we used effective medium theory in [15] which provides good physical insight into the nature of the electromagnetic response of a composite although they may not provide sufficient information to obtain a solution from Maxwell's equations.In addition, if the metamaterial substrate is very thin (kd ≈0), the reflection coefficient at normal incidence is approximated to ( ) ( ) where Γ 1 , k M , d, η M and η 0 are the first reflection, the wavenumber of the metamaterial, the thickness of the substrate, the intrinsic impedances of the metamaterial and free space, respectively.Therefore, the reflection coefficient at the normal incidence is zero when η M is the same as η 0 .In contrast, the reflection coefficient at the oblique incidence of the TE mode is expressed as obliq , where θ i and θ t are the incident angle and transmitted angle, respectively [16].From Snell's law and Eq. ( 2), the zero reflection condition at the TE oblique incidence is expressed as sin 0 where ε M and μ M are the permittivity and permeability of the metamaterial, respectively.In this letter, X crit is defined as a criterion for zero reflection at oblique incidence.Although the reflection coefficients for the TE and TM modes are different, only the TE mode is considered in this work.The TE mode implies perpendicular incidence, whereas the TM mode implies parallel incidence.A metamaterial absorber can be realized by a periodic structure of electric LC resonators (ELCs) similar to split-ring resonators (SRRs) [3,4].It is designed to have high absorptivity only at normal incidence.Therefore, when the metamaterial is applied on a flat surface, each unit cell is designed to satisfy Eq. (1).However, when the metamaterial is applied on a curved surface, the incident angles on all the unit cells are different, as illustrated in Fig. 1.Although the center of the curved surface experiences normal incidence, the other areas of the curved surface experience oblique incidence.Therefore, when a curved metamaterial absorber is designed with uniform unit cells, the zero reflection condition is violated because the conditions for the normal and oblique incidences are different, as observed from Eqs. ( 1) and (3).In this work, we propose a novel approach to achieve a high absorption rate for the curved surface.Instead of uniform unit cells, three different unit cells are designed and placed on three zones (zones A, B, and C) on the curved surface, as shown in Fig. 1.The unit cells A, B, and C are designed to satisfy Eq. ( 3) at incident angles of 45°, 30°, and 0°, respectively, in the TE mode; therefore, the unit cells have a high absorption rate at these incident angles.When the conformal absorber consists of 41 unit cells, unit cell A is distributed on zone A, as shown in Fig. 1(a), which ranges from the 1st column to the 6th column and from the 36th column to the 41st column.Unit cell B is distributed on zone B, as shown in Fig. 1(a), which ranges from the 7th column to the 15th column and from the 27th column to the 35th column.Unit cell C is distributed on zone C, as shown in Fig. 1(a), which ranges from the 16th column to the 26th column.Using Eqs. ( 1)-( 3), the unit cells A, B, and C are designed on the basis of split-ring-cross resonators, as shown in Fig. 1(b).The ELC resonance can be generated from the inductance of the crossed plate as well as the gap capacitance between the circle rings.There is no transmitted wave because the bottom of the substrate is completely made of metal.Unit cell C is designed to satisfy Eq. ( 1) because it is realized for normal incidence.Unit cells A and B are designed to have a permittivity and a permeability at θ i = 45° and 30°, respectively, as shown in Eq. ( 3).ANSYS HFSS is used as the EM simulation tool for the design and simulation of the unit cells.The geometrical dimensions of each unit cell are determined with the optimization in ANSYS HFSS where the goal is set by the condition of X crit in Eq. ( 3).The final dimensions are indicated at each unit cell in Fig. 1(b).Figure 2 shows the simulated reflection coefficients of the proposed absorber.As expected, each unit cell shows more than 90% maximum absorption rate at 10.85 GHz.

Simulated and measured results
The prototype of the curved surface absorber is built on a 0.4-mm-thick FR4 board with a complex dielectric constant of 4.4-j0.088.As shown in Fig. 3, the proposed absorber consists of a 41 × 10 array of unit cells, and the overall size is 246 mm × 60 mm.In order to form a curved surface, the absorber is bent with a radius (R) of 15 cm.Unit cells A, B, and C are shown in the inset of Fig. 3.The bottom plate is completely copper-plated; therefore, no power is transmitted.For demonstrating the absorption rate of the proposed conformal absorber, a bistatic RCS is first simulated on the curved surface with R = 15 cm.As shown in Fig. 4, the RCSs of the perfect conductor (PEC), metamaterial absorber using uniform unit cells, and proposed absorber using three different unit cells are compared at 10.85 GHz.When compared with the PEC, the RCS of the proposed absorber is 11.4 dB lower at 0°.In addition, when compared with the metamaterial absorber using uniform unit cells C, the RCS of the proposed absorber using nonuniform unit cells is 4.6 dB lower at 0°.Although the RCS on a curved surface can be reduced by using the metamaterial absorber with uniform unit cells, it is successfully demonstrated that RCS can be further reduced by using the proposed metamaterial absorber with nonuniform unit cells.It is observed from Fig. 4 that the uniform unit cell has slightly better RCS reduction effect than the absorber with non-uniform unit cells for the angles from 30° to 50°.In this design, the unit cells are distributed and they have a high absorption rate at the incident angles of 0°, 30°, and 45°.Therefore, most EM energy is absorbed on the areas that experiences 0°, 30°, and 45° incidence, while the other areas partially reflect the incident EM energy.For the nonuniform unit cells, these areas reflect the incident EM energy toward 30° to 50°.This problem can be solved with more types of unit cells.The bistatic RCS is experimentally demonstrated by using two horn antennas and a network analyzer, as illustrated in Fig. 5.In order to transmit a plane wave toward the absorber, the distance between the horn antennas and the absorber is 1 m which satisfies the far-field condition.When the transmitting horn antenna is fixed, the other receiving horn antenna is rotated and measured S 21 .In order to measure only reflected wave from the absorber, the time gating function is used in the HP 8722D network analyzer.
Figure 6 shows the experimental reflection coefficients of the metal plate and the proposed absorber on the curved surface.As expected, the proposed conformal absorber shows high absorption rate and RCS reduction at 10.85 GHz.When compared with the metal plate, the RCS of the proposed absorber is reduced at the broadside by 11.4 dB.Although the proposed absorber is designed for TE-mode, it is expected to have a good absorption ratio for TM-mode as well due to polarization-insensitive unit cells.Figure 7 shows the measured reflection coefficients for both TE and TM modes at the normal incidence.In this case, a monostatic RCS measurement is performed with a single horn antenna.It is observed that the proposed curved absorber is successfully working for both TE and TM modes.In addition, the reflection coefficients at different angles of incidence are measured and plotted in Fig. 8.The reflection coefficient is less than 10 dB from 0° to 60° except for 20° and 40°, although the resonant frequency is changed.

Conclusion
This study proposes a novel metamaterial absorber for a curved surface.Three unit cells of 41 × 10 dimension, with absorption rates of over 90% at 0°, 30°, and 45° incident angles, are distributed in three different zones on the curved surface.The absorption capacity of the proposed structure is verified through EM simulation and measurement.The proposed conformal absorber on the curved surface with a 15-cm radius shows an 11.4-dB RCS reduction as compared with the metal plate at 10.85 GHz at TE mode incidence.Although the proposed absorber is designed for TE mode incidence, high absorptivity is also achieved for TM mode incidence.

Fig. 2 .
Fig. 2. Simulated reflection coefficients of unit cells A, B, and C.

Fig. 4 .
Fig. 4. Simulated bistatic RCSs of the PEC, conventional metamaterial absorber using uniform unit cells, and proposed metamaterial absorbers using three different nonuniform unit cells.

Fig. 6 .
Fig. 6.Measured and simulated reflection coefficients of the proposed conformal metamaterial absorber and the metal plate.

Fig. 7 .
Fig. 7. Measured reflection coefficients of the proposed conformal metamaterial absorber for TE and TM mode.

Fig. 8 .
Fig. 8. Measured reflection coefficients of the proposed conformal metamaterial absorber at different angles of incidence.