1. Introduction

The appearance of metamaterial sun on the horizon of electromagnetic field results to/into absorbing most researchers to them (directing most researches into them). Although these structures were used a long time ago, it did not take a long time from when the metamaterial was introduced. Ref. [1] reviews a brief history about metamaterial structures over time. The importance of metamaterials is hidden behind (due to) their behaviors. The ability to control the refractive index, in other words constitutive parameters, of metamaterials leads into their interest behaviors [1, 2]. These structures help engineers to design new devices and improve the performance of available systems. Some of them are THz detectors, new substrate, modulator, THz switches, cloaking, bolometers, and angular-independent surfaces [2].

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

square root function. Typically, the choice of the sign of a square root is made unambiguous by ensuring positive power flow in the direction of propagation [2]. In some situations, local

In contrast, there are some metasurface studies that have modeled the film as a single-layer metamaterial. In this way, a metasurface is replaced with a boundary plane with surface

As mentioned above, a metasurface is a periodic structure that is comprised from distributing a lot of micro-scatterers on a plane (Figure 2a). Therefore, for extracting the behavior of structure, it is sufficient to consider a period of structure with suitable boundary conditions [6]. Figure 2b shows these boundary conditions. These are two perfect electric conductors and two perfect magnetic conductors. On the other hand, these boundary conditions form/constitute a TEM waveguide, and the metasurface element in the middle is a transverse discontinuity in the waveguide. The element divides the inner medium of the waveguide into two media,

Now, this model must be analyzed by a numerical technique such as mode matching, FDTD, or so on [7–12]. Generally, the element (partially) blocks the way of incident power (Pincident). It causes some of the incident power passes through discontinuity toward load (Ptransmitted), and the remaining power reflects back to the source (Preflected). In mathematical form (Eq. 1)

According to mode-matching method, the reflected and transmitted waves are expanded in terms of different modes supported by TEM waveguide (Eqs. 2–4) [7]. These modes are men-

!<sup>i</sup> <sup>¼</sup> ^ayA00, H!<sup>i</sup> ¼ �^ax

Figure 2. Front view of a metasurface structure (a) a TEM waveguide with a metasurface element in the middle (b) and

Pincident ¼ Preflected þ Ptransmitted (1)

Investigation into the Behavior of Metasurface by Modal Analysis

http://dx.doi.org/10.5772/intechopen.80584

5

(2)

A<sup>00</sup> η0

susceptibilities. It is called the Generalized Sheet Transition Condition (GSTC) [2, 4, 5].

effects near the boundaries of the sample must also be taken into account.

3. Analysis of a periodic structure with modal analysis

E

incident, reflected, and transmitted waves in the TEM waveguide from side view (c) [7].

medium I and medium II (Figure 2c).

tioned in Eqs. 2–5:

Figure 1. A metamaterial structure consisted of micro-scatterers in a regular array (reproduced from [1]).

Generally, a metamaterial is a periodic structure that is made from arranging a lot of the same micro-scatterers in a regular lattice/network (Figure 1) [1, 2]. A metamaterial layer is created when micro-scatterers are distributed in a plane. The difference between metamaterials and other periodic structures is mentioned in [2].

Impinging a wave into the metamaterial structure induces currents and charges on the metamaterial elements. In other words, the existence of metamaterial elements reinforces the structure in the (electric and magnetic) polarization. There are different methods developed to determine this polarization. In the following, we discuss about these methods. Then the structure is modeled and analyzed by modal analysis to calculate the S parameters of structure. These parameters show the general behavior of structure.
