3 being proportional to the square of the velocity (and thus of the frequency, just like the magnetic energy), is added to the magnetic energy of the structures and in small length-scales it dominates the magnetic metamaterials response. The consideration of this kinetic energy is done here through an equivalent “kinetic” inductance 30,36 (or electrons’ inductance), added to the magnetic field induc- tance in an effective resistor-inductor-capacitor (RLC) description of the artificial magnetic structures. Specifically, the paper is organized as follows: In Sec- tion II we present the “high frequency” response of our structures, as revealed by numerical simulations concern- ing the magnetic resonance frequency, the form of the magnetic permeability resonance and the losses. The wave propagation characteristics in those structures are analyzed and explained in Section III, using an effective RLC description of the structures and taking into ac- count the dispersive behavior of the metals through the kinetic metal inductance. Based on the results and anal- ysis of Sections II and III, in Section IV we present basic optimization rules for the achievement of high frequency magnetic metamaterials and left-handed materials with improved performance. There we discuss also the fishnet design, which has been proven up to now the optimum design for achievement of optical negative index materi- als. Finally, in Section V we show that the simple RLC circuit model does not only have qualitative power, but it can be used also to give quantitative results if plugged with accurate relations for the capacitance and the in- ductance of the system. In this section we present calculation results concern- ing the scaling of the magnetic resonance frequency and the magnetic permeability of the structures shown in Fig. 1. The geometrical parameters used in the simulations are those mentioned in Fig. 1; for the permittivity of the metal the Drude dispersion model has been employed, i.e. ε = ε$_{0}$ [ ε (0) − ω 2 $_{p}$/ ( ω 2 + iωγ$_{m}$ )], with the parameters of the aluminum (plasma frequency ω$_{p}$ = 22 . 43 × 10 15 sec − $^{1}$, collision frequency γ$_{m}$ = 12 . $^{18}$× 10 13 sec − $^{1}$), and ε (0) = 1. Using Drude dispersion model one takes auto- matically into account the mass and any kinetic energy of the current-carrying electrons inside the metal (the contribution of the bound electrons is also taken into ac- count, through the constant ε $^{(0)}$). The calculations presented here have been per- formed using the Finite Integration Technique, employed through the MicroWave Studio (MWS) commercial soft- ware. Using MWS, the transmission and reflection from a monolayer of the structure have been obtained; these data have been used for the determination of the effective permittivity and permeability of the structures, through a standard retrieval procedure based on a homogeneous effective medium approach $^{37,38}$. In Fig. 2 we present the magnetic resonance frequency FIG. 3: Frequency dependence of the real (top panel) and the imaginary (bottom panel) part of the magnetic perme- ability of the wide slab-pair system for various length scales. The legends indicate the lattice constant along propagation direction for each specific system. FIG. 2: Scaling of the magnetic resonance frequency with the linear size of the unit cell along propagation direction ( a k ) for the four designs of Fig. 1: Fishnet (black circles), wide-slabs (red squares), narrow-slabs (green diamonds), slabs&wires (blue triangles). The solid symbols indicate the existence of negative permittivity values, while the open symbols indicate that the permeability resonance is weak and unable to reach negative values for the Re( µ ). II. NUMERICAL SIMULATIONS 0 10 20 30 40 50 60 70 1/ a$_{k}$ [ m$^{-1}$] 200 400 600 800 Frequency[THz] fishnet slabs-wide slabs-narrow slabs&wires Magnetic resonance frequency 100 200 300 400 500 600 700 Frequency [THz] -2 0 2 4 6 8 Re( ) 160nm 106.6nm 80nm 64nm 40nm 32nm 24nm 16nm 100 200 300 400 500 600 700 Frequency [THz] 0 2 4 6 8 10 Im( )