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90                                                                 Chapter 2

        at some  fixed frequency  should look like shown in Figure 2.7.4. Evidently, similar low
        frequency loss splash takes place for   () too.  Accordingly, the ferrites have two operating
                                        −
        regions of small energy dissipation: the first bellow resonance and the second above. Although
        there is no clear defining low-frequency limit, typically it lies between 100 MHz and 500 MHz
        depending on ferrite type. Above the resonance operation region can be expended up to 100
        GHz and higher.

        2.8  METAMATERIALS
                                  18
        2.8.1   Introduction
        In general, any material can be assigned to the class of “metamaterial” if it is fabricated such
        way that its electromagnetic properties (  or   , or both) depend on density, structure, and
                                               
                                          
                                                            lattice of such  artificial  tiny
                                                            inclusions  as  metal  or
                   SNG Material   Dielectric Material       dielectric spheres, cylinders,
                                                            or printed  metal strips of
                                                            different shapes embedded in
                     Plasmas       Dielectrics              a host dielectric material with
                                                            low dielectric permittivity.
                    DNG Material   SNG Materials            When the size of lattice cell
                                                            with  multiple inclusions is
                                                            much   shorter  than  the
                 Metamaterials      Ferrites                electromagnetic wavelength,
                                                            the external electromagnetic
                   Figure 2.8.1 Material classification     fields can be considered
                                                            constant across several cells.
        Based on such wide-ranging definition,  we can consider as  metamaterials  the artificial
        dielectrics described in Section 2.2.7 (see Figure 2.2.10) and most of the magnetic materials in
        this chapter. Following the common classification, we denote the metamaterials as more narrow
        class of unconventional mediums qualified as Single-NeGative (SNG) or Double-NeGative
        (DNG). In the SNG  materials, only permittivity or permeability (  or  ) can achieve the
                                                                     
                                                                
        negativity at some frequencies, while DNG means that both of them negative simultaneously.
        The diagram in Figure 2.8.1 illustrated such permittivity-permeability classification. According
        to the  American Physical Society, the metamaterials are considered one of the three  most
        important discoveries of the decade in the field of physics.

        Why is the metamaterial so exciting? It is well-known that the speed of light c in a vacuum is
        one the universal physical constant related to two SI derived units   and   (see Table 1.5)
                                                                
                                                                      0
        giving us  = 1 �    . From above discussion surrounding the interaction electromagnetic
                     ⁄
                          0
        fields and materials follows that the polarization effects changes the dielectric and magnetic
        material properties as    →      and  →   . Therefore, the speed of light in  material
                                  
                            
                                         0
                                              0 
        deviates accordingly
                                        1         
                                                          =  =  =
                                    �      0    √     

        18  Greek prefix “meta” means “beyond” (imagination?).
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