## 2 Metamaterial Sensor for eNDE and Theory
### Plates from FRPC Composite Materials  
The study involved quasi-isotropic FRPC plates produced by Tencate [35] (Almelo, The Netherlands), having 150 \(\times\) 100 \(\times\) 4.2 mm\({}^{3}\), containing 12 layers of 5 harness satin (5 HS) carbon fibers woven with balanced woven fabric [81] (Figure 3c). The matrix is made of PPS, a thermoplastic polymer consisting of aromatic rings linked with sulfide moieties. It is resistant to chemical and thermal attack, and the amount of gas released due to matrix ignition is low. The carbon fibers are T300 JB type (TORAYCA, Santa Ana, CA, USA); their volume ratio is 0.5 \(\pm\) 0.03 and the density is 1460 kg/m\({}^{3}\). Carbon fiber woven embedded into PPS offers strength of composite to impact. The FRPC has the transverse electric conductivity between 10 S/m and 100 S/m and longitudinal conductivity ranging between 5 \(\times\) 10\({}^{3}\) S/m and 5 \(\times\) 10\({}^{4}\) S/m and is paramagnetic, allowing eNDE. The samples were impacted with an energy of 8 J [59], in order to induce delaminations. The impacts are induced with FRACTOVIS PLUS 9350 CEAST (Instron, Nordwood, MA, USA), which allows the modification of impact energies as well as the temperature during impact. The conditions of the impact are designed according to ASTM D7136 [82] at a temperature of 20 \({}^{\circ}\)C. Under impact, the FRPCs suffer delamination, usually accompanied by a dent, deviation, and/or breaking of the carbon fibers. In all cases, a reduction in the space between fibers in the thickness direction appears and this causes an increase in fiber contact, leading to a decrease of electrical resistance in the thickness direction and modifying the local electrical conductivity both in the plane of the fibers and perpendicularly on fibers [83]. The energy absorbed by the composite serves as the plastic deformation of the composite in the contact zone, being dissipated through internal friction between the matrix's molecules, carbon fibers, and matrix-carbon fibers, as well as at the creation of delaminations. Typical records of force _vs._ time during impact can give information about the FRPC status (delaminated or not) [84]. The generation and detection of evanescent waves from slits/fibers has been made using a sensor with MM lens and the equipment presented in Figure 4. The rectangular frame used for the generation of the TM\({}_{x}\) polarized EM field has 35 \(\times\) 70 mm dimensions, from a 1 mm diameter Cu wire. This represents the excitation part of the transducer. The lens is constructed from two CSRs with the large bases being placed face to face. The insulated conductor is a copper foil with 18 \(\upmu\)m thickness laminated adhesiveless with a polyimide foil (LONGLITE(tm200, produced by Rogers Corporation (Connecticut, CT, USA)), in order to reduce the losses at high frequencies, with 12 \(\upmu\)m thickness (Figure 2b). Each CSR has 1.25 turns, 20 mm diameter large base, 3.2 mm diameter small base, aperture angle of 20\({}^{\circ}\), and 50 mm height. The reception coil with 1 mm diameter and one turn from 0.1 mm diameter Cu wire was placed in the focal plane of the lens. A grounded screen made from the same insulated conductor as the CSR, having a circular aperture with diameter \(d=100\)\(\upmu\)m, is placed in front of the lens (Figure 2a). The distance between screen aperture and the surface to be examined has been maintained at 20 \(\pm\) 1 \(\upmu\)m.  
The EM sensor with MM lens, presented above, is connected to a Network/Spectrum/Impedance Analyzer type 4395A Agilent USA Analyzer (Agilent Technologies, Santa Clara, CA, USA). During the measurements, the transducer was maintained in fixed position and samples were displaced with a XY displacement system, type Newmark--Newmark Systems Inc. (Santa Margarita, CA, USA) that ensures the raster scanning in plane with \(\pm 10\)\(\upmu\)m precision and rotation with \(\pm 2^{\sigma}\).