# Transmissive Polarizer Metasurfaces: From Microwave to Optical Regimes
## 3 History and Modeling of MSs
Therefore, to consider this, let us consider a case of patches (capacitive array) whose impedance is presented by \(\mathbf{Z_{p}}=\frac{1}{\mu\
u c}\). The wave penetrating from patches passes through the substrate and is reflected by the ground plate. The substrate acts as a small transmission line of thickness 'd' and wave impedance \(\eta_{2}\), whose impedance is \(\mathbf{Z_{d}}=\mathbf{j\omega L}\). Thus, the surface impedance of this MS turns out to be Zd \(\mid\mid\) Zp. Hence, this sheet can be characterized by an impedance of homogeneous MS. Here, 'd' behaves as an effective magnetic response which induces magnetic surface currents [39]. This concept is extended in Section 6.1, where it presents the concept of polarization conversion, though in transmission mode, where the ground plate will not be present to allow transmission. Frequency-selective filtering is a widely used operation in the microwave and optical regions of communication systems. FSS is used in this regard due to its very good transmission characteristics. They have a wide range of applications, such as splitters, duplexers, and radomes. They can achieve bandpass and bandstop properties depending upon the size, type, and shape of patches and substrate material. A detailed description of the calculations of FSS behavior can be found in [40; 41]. Nonetheless, FSS requires the unit cell to be at least half a wavelength, although it may operate at multi-resonances as well. However, if inclusion dimensions are changed to the subwavelength scale in such a way that inclusions still have resonant behavior, MSs can replace FSS [42]. It has several advantages, such as miniaturization, and lower sensitivity to the plane wave's angle of incidence. Another major attraction is for limited space, where more units fit the area [43], which is very useful for applications that have limited space, e.g., radomes. Complex shaped frequency-selective MSs can be designed for required applications by using independent inductive and capacitive elements, e.g., refs. [44; 45] used this concept by introducing lumped on-chip elements realizable in the microwave region. Another approach is to use patches for neighboring capacitive and inductive cells [46]. It is important to mention that, at these resonances, the structure provides very high electric polarizability. For the multiband operation of such frequency-selective MSs, one possible way is to use two complementary structures with the same periodicity on each side of the MS so that two parallel resonances can exist [47]. Another approach is to use the same geometry and shape different sizes according to the required multiple frequencies both present on a unit cell [45]. This concept can be applied to multiband polarization converters as well. Having discussed simpler cases of achieving transmission curves/reflection curves, we move to the requirement of different phase responses or, in other terms, phase control of microwave and optical waves. To have such a response, one needs to have a magnetic response in addition to the electric response. In this case, when an incident wave strikes MS from one side, the structure can be designed for desired operations, such as phase-shifting and optical activity.