## 2 Metamaterial Sensor for eNDE and Theory  
MMs, EM structures with distinguished properties, have started to be studied especially in the last few years. EM MMs belong to the class of artificially engineered materials, which can provide an engineered response to EM radiation, not available from naturally occurring materials. These are often defined as the structures of metallic and/or dielectric elements, periodically arranged in two or three dimensions [61]. The size of the structure is typically smaller than the free space wavelength of incoming EM waves. Nowadays, multitudes of MM structural elements type are known, conferring special EM properties. Depending on the frequency of the incident EM field, the type and geometrical shape of the MM may have a high relative magnetic permeability, either positive or negative [61]. Also, MM lenses allow the amplification of evanescent waves [62]. These properties strongly depend on the geometry of MM rather than their composition [63], and were experimentally demonstrated [64]. MMs have started to interest engineers and physicists due to their wide application in perfect lens [65], slow light [66], data storage [67], _etc._  
In order to find the effective permittivity and permeability of a slab of MM, the material has to be homogeneous. The permittivity and permeability can be found from the \(S\) parameters data. For a MM slab characterized by effective permittivity \(\varepsilon_{\mathrm{eff}}\) and effective magnetic permeability \(\mu_{\mathrm{eff}}\), the refractive index is:  
\[n=\sqrt{\varepsilon_{\mathrm{eff}}\mu_{\mathrm{eff}}} \tag{1}\]  
and the impedance is given by:  
\[Z=\sqrt{\frac{\mu_{\mathrm{eff}}}{\varepsilon_{\mathrm{eff}}}} \tag{2}\]  
The relationship between \(\varepsilon\) and \(\mu\) for a medium as well as the wave propagation through it can categorize the media into the following classes [68, 69]:  
1. Double positive medium (DSP) when \(\varepsilon>0\) and \(\mu>0\); Only propagating waves;* Single negative medium-electric negative (ENG), when \(\varepsilon<0\) and \(\mu>0\); only evanescent waves;
* Double negative medium (DNG) when \(\varepsilon<0\) and \(\mu<0\) ; propagating waves and evanescent waves;
* Single negative medium-magnetic negative (MNG), when \(\varepsilon>0\) and \(\mu<0\) ; only propagating waves. When the effective electrical permittivity \(\varepsilon_{\mathrm{eff}}\), and the effective magnetic permeability \(\mu_{\mathrm{eff}}\) of a MM slab are simultaneously \(-1\), the refractive index of the slab is \(n=-1\)[70]. Therefore, the surface impedance of such an MM is \(Z=1\), there is no mismatch and consequently no reflection at the slab-air interface [64]. This MM slab forms a perfect lens [62] and is not only focusing the EM field, but also focuses the evanescent waves [62]. Due to experimental difficulties in obtaining a perfect lens, the manipulation of the evanescent modes can be made with an EM sensor with MM lenses that have, at the operation frequency, either \(\varepsilon_{\mathrm{eff}}=-1\) when electric evanescent modes can be manipulated, or \(\mu_{\mathrm{eff}}=-1\) when the lens can focus magnetic evanescent modes [61]. Moreover, working at a frequency that ensures \(\mu_{\mathrm{eff}}=-1\) for the same lens, the magnetic evanescent modes can be manipulated [20, 71]. According to the above classes, as shown in Ref. [30], the electric evanescent modes can be manipulated with a sensor made from a special MM, named Conical Swiss Roll (CSR) [31], functioning in a frequency range that ensures the maximum \(\mu_{\mathrm{eff}}\)[60]; it did not accomplish the conditions imposed for a perfect lens but will lead to the substantial enhancement of spatial resolution. The spatial resolution of the system (the distance between two distinctively visible points) was verified according to [59] and the analysis of data obtained shows that the realization of MM lenses in the RF range is possible using the CSR, whose distortions are minimal and whose calculation is made based on Fourier optic principles.