## Metasurface It has long been our dream to fabricate certain structure and gain such structure induced properties. This could provide us the ability to tune material properties with unparalleled freedom and accurately control the material behaviors. By cleverly selecting the boundary conditions of how the wave propagate in the space, we could actually reach this target. However, metamaterials in three dimensions could extremely difficult to fabricate considering the fabrication accuracy (defects would cause huge losses) and scalability. One alternative solution, photonic crystals, would be discussed in [[Metamaterial (optical) and photonic crystals]]. The fabrication of 2D structure could be easier, and governing by the same idea, similar structures, or meta-atoms, could be engineered to shape how light is transmitted. >[!Note] >The idea is just the Huygens's principles, that evert point on a wavefront can be seen as a secondary source from which emanate a spherical wave, and the new wavefront is defined by the surface tangent to the secondary wavelets. >By engineering the constitutive met-atoms as the secondary source, the phase front of transmitted light could be shaped. This idea is similar to the [Fresnel lens](https://en.wikipedia.org/wiki/Fresnel_lens). ### Design approaches #### Dielectric phase shifter By controlling the geometries (like the cross-section diameter for cylinders) of high-refractive index meta-atoms, the phase accumulation could be achieved. The accumulated phase could be $0-2\pi$. (intuitively, smaller volume, smaller effective refractive index, therefore less phase accumulated) The problem is, high aspect ratio is require to cover the $2\pi$ range, this brings extra difficulty to fabrication. ![[Drawing 2024-08-08 21.18.47.excalidraw.svg]] #### Resonant tuning (metallic nanostructure phase shifter) Using metallic nanostructures and forming localized surface plasmons could also control the phase. For example, changing the length of the golden nanorods to adjust phase. This approach can be imagined as forming harmonic oscillator whose amplitude and phase change across the resonance. The limit for metallic nanostructure is that only $0-\pi$ phase range could be achieved. It is also possible to extend this method to dielectric nano-resonators, similar to what we had in [[Mode engineering]] by detuning electric and magnetic dipoles. This could extend the phase range to $2\pi$. #### Geometrical phase By adjusting the polarization and relative phase, the geometrical phase could control the phase of transmitted light also. This approach is similar to controlling the orientations of sub-wavelength polarizer (could be some grating-like structure). In actual design, this geometrical phase approach is combined with other phase shifter to achieve higher accumulated phase shift. ### Problem, applications and beyond Besides those common issue like fabrication difficulties and scalability, chromaticity is a big issue in metasurfaces. It has two origins: - For design with resonator (resonant tuning, like using metallic or dielectric structures), a high chromaticity is the result of the strong dispersion of the resonant mode (wavelength dependence). - For phase shifter, material dispersion also leads to significant chromaticity. Adding a compensation phase shift could solve this problem in defined working range, but this typically requires modifying the meta-atoms and could make the designing and fabrication process even more difficult.