# Plasmonic and Dielectric Metasurfaces: Design, Fabrication and Applications
## 1 Introduction  
A \"metamaterial\" is a man-made material whose properties can be attained by designing the unit structure, having been widely focused on for a dozen years since it was firstly reported by [PERSON] et al. in 2000 [PERSON] et al. (2000). The unit structure in metamaterial, called meta-atoms or meta-molecules, must be considerably smaller than the operating wavelength, and the distance between neighboring meta-atoms also has a subwavelength scale [PERSON] et al. (2000). This subwavelength scale inhomogeneity makes the whole metamaterial uniform on the macro of performance, and this phenomenon makes this artificial structure essentially a \"material\" rather than a device. Therefore, one can arbitrarily arrange the so-called meta-atoms into periodic arrays to build one-dimensional (1D) materials (chains), two-dimensional (2D) materials (metasurfaces) and three-dimensional (3D) materials (metamaterials),as shown in Figure 1[3]. For the metamaterial, one can even manipulate its macroscopical properties, such as permittivity \(\varepsilon\) and permeability \(\mu\). The research of metamaterials is essentially related to the exploitation of the electromagnetic parameter space for better control of electromagnetic waves, as depicted in Figure 1. Utilizing metamaterials, one can enter regions of the electromagnetic parameter space that are not observed in conventional material, but that are not forbidden by Maxwell's equations, such as the third quadrant of the parameter space (negative-index materials), zero-index materials and the space far away from the non-magnetic line [4; 5; 6; 7]. Taking advantage of these attractive features, as shown in Figure 1, metamaterials have been widely applied in optical negative index materials [8; 9; 10; 11; 12], nonlinear optics [13; 14; 15; 16], optical magnetism [17; 18; 19], super resolution [20; 21; 22; 23; 24; 25], giant artificial chirality [26; 27], electromagnetic cloaks [28; 29; 30; 31; 32], etc. Besides 3D materials, 2D metasurfaces are also widely focused on for their ability for flexible light manipulation (phase, amplitude, polarization) over subwavelength propagation distances [33; 34; 35; 36; 37]. Most of the metasurfaces can be divided into two categories by the material type of unit structure: plasmonic and dielectric, as displayed in Figure 2. For plasmonic metasurfaces, they are made on the basis of metallic meta-atoms whose optical responses are driven by the plasmon resonances supported by metallic particles. When a metallic particle is placed in an electric field, the conduction electrons escape from their equilibrium positions with respect to the core ions, resulting in a polarization of the particle and generating a depolarizing field. In a time-varying external field, this collective motion in the metallic particle can be seen as a Lorentzian oscillator whose characteristic peak in the displacement amplitude is around the resonance frequency and accompanied by a phase shift of \(\pi\) over the spectral width of the resonance [38; 39; 40; 41; 42; 43; 44; 45; 46]. For dielectric metasurfaces, the unit structure is constructed with high refractive index dielectric resonators, such as silicon, germanium or tellurium, which can support electric and magnetic dipole responses based on Mie resonances [47]. When a dielectric particle is illuminated by a light wave whose frequency is below or near the bandgap frequency of the material of particle, both the magnetic dipole (first Mie resonance) and electric dipole resonances (second Mie resonance) are excited. The magnetic and electric Mie resonance can then enhance the magnetic and electric field at the particle's center at optical frequencies, respectively, and this enhancement is related to the intrinsic properties of dielectric particles [48; 49; 50; 51; 52; 53; 54; 55; 56; 57; 58]. Therefore,  
Figure 1: Schematic illustration of meta-atom, 1D chain, 2D metasurface and 3D metamaterials.