FIG. 4: Band-width, Δ ω , of the negative magnetic perme- ability regime vs the inverse unit cell size, 1 /a$_{k}$ , for fish- net (black circles), wide-slab-pairs (red squares), narrow-slab- pairs (green diamonds) and slabs&wires (blue triangles). The band-width is normalized by the minimum frequency (lower limit) of the negative permeability regime, ω min . a$_{k}$ is the lattice constant along propagation direction. 0.1 1 10 1/ a$_{k}$  [ m$^{-1}$] 0 0.1 0.2 0.3 0.4 0.5 0.6 min fishnet slabs-wide slabs-narrow slabs&wires for the four structures of Fig. 1 as the structures are scaled down from mm to nm scale; in Fig. 3 we show the real and imaginary part of the magnetic permeability as a function of frequency, for wide-slab-pairs (structure of Fig. 1(b)) of various length scales. As can be seen in Fig. 2, in slab-pair systems we observe the same behavior as the one reported earlier for SRR structures $^{30,35}$: while in larger length-scales the magnetic resonance frequency scales inversely propor- tional to the structure linear size, at frequencies in the near infrared (IR) towards optical regime this linear scal- ing breaks down, and the magnetic resonance frequency saturates to a constant value. This saturation value is dif- ferent for the different designs employed, with larger the one of the fishnet structure. Note that in the slabs&wires case (structure of Fig. 1(c)) the presence of wires does not affect the magnetic resonance frequency of the slabs, while in the fishnet structure the presence of wires leads to higher saturation value for the magnetic resonance fre- quency. This behavior of the fishnet design will be dis- cussed and explained in Section IV. It is important to mention here that the saturation values for the magnetic resonance frequency of the slab- pair-systems are in all cases larger than the saturation values obtained for SRRs of a single gap 39 (like, e.g., U- shaped SRRs; single-gap SRRs are the only SRR-based system that has been fabricated in the nm scale), indi- cating once more the suitability of the slab-pair-based systems for the achievement of optical magnetic meta- materials. is ultimately killed in the nm scale structures. Among our four structures the wide-slab-pair one is characterized by the larger band-width. Finally, it is worth-noticing the reduced band-width of the fishnet design, compared to the band-width of the slab-pair-only structure. This bandwidth behavior will be discussed in the next section. Since a main issue for the achievement of high fre- quency metamaterials of satisfactory performance is the losses, due to the increased resistive losses in the metal- lic components going to the optical regime, we performed a detailed analysis of the losses in high frequency meta- materials, trying to estimate which aspects of the high frequency metamaterial response are mainly affected by the resistive losses, and, consequently, to seek ways to minimize the influence of those losses, using proper de- sign modifications. As a first step we calculate the losses as a function of frequency for various length scales of our systems. In Fig. 5 we present these losses for the wide-slab-pair system of Fig. 1(b). The losses, A , have been calculated through the relation A $^{= 1}$− $^{R}$−T , where R and T are the reflec- tion and transmission coefficient, respectively, through one unit cell of the structure along propagation direc- tion. As is expected, the losses show a dramatic increase by going to smaller length scales and higher frequencies. This increase seems to have an exponential dependence on the magnetic resonance frequency. From Figs 2-5, one can see clearly the decreased per- formance of our structures going to nm scale, inhibiting their ability to give high quality optical left-handed meta- materials. An interesting question arising here is the role of the resistive losses on this decreased performance. To examine this role, we repeated the above shown calcu- lations using for the metal a 2 π × 1000 times reduced collision frequency compared to that of aluminum, i.e. One quantity which is of great interest in left-handed materials and it is strongly affected by the weakening of the permeability resonance is the width of the negative permeability regime, which roughly corresponds with the operational band width of a LHM. In Fig. 4 we present the relative band-width (i.e. band-width divided by the lower frequency of the negative permeability band) for the four structures shown in Fig. 1. As can be seen in Fig. 4, the operational band-width, which in larger scales is almost independent of the length scale, in smaller scales it is strongly reduced, ultimately going to zero for all designs. This shows that the negative permeability Concerning the permeability results shown in Fig. 3, we observe that, just like the SRRs $^{30,35}$, as the length scale of the structure becomes smaller the permeability resonance becomes weaker, ceasing ultimately to reach negative values. This weakening is revealed in both the real and imaginary part of the permeability resonance, and it will be analyzed in more detail and quantified in the following paragraphs. (Note that the “truncation” of the resonances of Fig. 3, which is observed in the larger scale structures, is a result of the larger influence of the periodicity in these length scales $^{40}$. In smaller scales this influence becomes smaller, due to the deeper sub-wavelength scale of the corresponding structures and the weaker resonant response, which results to smaller ef- fective index and thus larger wavelength inside the struc- tures.)