# A typical optimization process consists of three components: mod

A typical optimization process consists of three components: model, optimizer and simulator (see Figure 1). The representation of the physical problem is done by using mathematical equations which can be converted into a numerical model. The formulation of a simple optimization problem can be done in many ways .Figure 1.A simple optimization process.For instance, the most popular way to do the formulation is to write a nonlinear optimization problem as:minimizefi(x),(i=1,2,��,M),(1)subject to the constraints:hj(x),(j=1,2,��,J),(2)gk(x),<0(k=1,2,��,K),(3)where fi, hj and gk are nonlinear functions. Here the design vector x = (x1, x2, ��) can be continuous, discrete or mixed in n-dimension . The function fi is called objective function (cost function). Here when M is 1, it is a single objective function.

But when M > 1, the optimization is multi objective . It is possible to combine different objectives into a single objective and in some cases it is a useful approach. It can be noted that the problem we formulated here is a minimization prob
The flexibility in the geometry of metamaterials has enabled the tailoring of interactions between resonances in such structures, leading to exciting research possibilities such as negative index response , enhanced transmission  and electromagnetic cloaking . In symmetric structures, super radiant or bright modes couple to the incident field, producing broad and lossy resonances. With the introduction of asymmetry in the metamolecule geometry, trapped or ��dark�� modes can be excited [4,5].

These dark mode resonances weakly couple to the free space [6,7] and therefore present high values of the quality factor Q. A Fano type resonance can result from the interference of bright and dark modes resulting in an asymmetric spectral profile [8,9]. Fano resonances caused by symmetry breaking have been reported in different structures such as double rod antenna with reduced symmetry [10�C13], split rings [14,15], ring/disk systems , just to list a few. As far as double rod metamolecules (dimers) are concerned, there are a number of different ways to excite a quadrupolar dark plasmon mode: vertically stacking rod pairs displaced along their axis , introducing an additional orthogonal wire Dacomitinib displaced from the symmetry centre , using oblique illumination of the symmetric dimer metasurface , introducing difference between rod lengths .

For planar metamaterials (metasurfaces) high quality resonances are challenging because of the reduced resonating volume. Nevertheless, Fano-resonant planar metallic nanostructures have the ability to strongly concentrate the electromagnetic field in small regions and increase the interaction with matter, making them promising components for the development of chemical and biological sensors [11,17,18].