EEE 17 Negative in

EEE17

Negative Refraction in Metamaterials

Cheng Zixiang Raffles Institution Lian Kay Sean Temasek JC

NRP Supervisor: Prof. Luo Yu NTU

EEE 17 Negative Refraction in Metamaterials Research Plan

Artificially engineered metamaterials have unique properties that cannot be obtained with natural materials. Negative Index Metamaterials or NIMs, as they are commonly known, have a negative , thus rays are refracted on the same side of the normal on entering the material. Our project focuses on two ways of achieving NIMs. One would be constructing metamaterials created with a periodic array of subwavelength unit cells, the other would be creating a hyperbolic by alternating layers of mediums of different refractive index. The aim of our project is to investigate the materials that can be used to construct the hyperbolic and dielectric method of realising negative refraction and the efficacy of the material used. Both approaches achieved negative refraction in the mid infra-red frequency. The simulation would be done with COMSOL software.

EEE 17 Negative Refraction in Metamaterials Abstract

A metamaterial is a material engineered to have a property not found in nature. Metamaterials usually gain their properties from structure rather than composition, offering a great freedom in material design. Recently, well designed metamaterials have received much interest because their atypical interaction with electromagnetic waves that can be used for subwavelength imaging and designing cloaking devices. In my project, that property is to be able to realise negative refraction in certain frequencies of the electromagnetic spectrum. The metamaterial concept was proposed in 1999 by John Pendry, who detailed in a paper in 2000 applying the concept of negative refraction to create a lens that can focus light onto a sub-wavelength area. There are currently two main ways of achieving negative refraction which we would study. The first is by is the dielectric metamaterial created with a periodic array of subwavelength unit cells. The second is by using hyperbolic materials which are layers of materials with large difference of refractive index layered over each other with a sub-wavelength thickness. Of the two, hyperbolic materials are more established and understood, however it has its limitations. Most of them exhibit their negative refractive property in the microwave spectrum. However, the method of using dielectric materials to construct unit cells is more customisable and can be engineered to exhibit negative refraction in the visible light zone (wavelength of 700 to 800 nanometers).

EEE 17 Negative Refraction in Metamaterials Report For negative refractive index to be achieved, it requires and permeability coefficients to be simultaneously negative. This can be achieved over a small range of frequency through having resonance at that particular frequency.

Key variables: Permittivity (휖) describes the manner in which the material interacts with electric fields of incident light. Permeability (휇) describes the manner in which the material interacts with magnetic fields of incident electromagnetic radiation.

Refractive index (n) = √휖 √휇 where 휖 and 휇 are both complex numbers. In order for n to be negative, epsilon and miu both have to be negative, where θ is between 90 to 270 degrees. Materials such as compounds of silicon as well as silver metal inherently have negative permittivity. Light is unable to pass through these materials in the natural environment. However, in the subwavelength construction of cells with these materials, light is forced to refract. Because 휖 and 휇 are constructed to be negative, negative refraction occurs. In this project, we are using CST as well as COMSOL (formerly under MATLAB), to do simulations and determine which material can create the biggest negative refraction. Our main assumptions are the conditions in which our investigation of negative refraction takes place. We assume that the size of the structure is smaller than the wavelength of incidence (subwavelength). The experiment is conducted in a vacuum. The inner permittivity and permeability of structure of silicon carbide is homogeneous. A key limitation of this study is that simulators are used to calculate the magnetic and electric response and we are unable to test if the actual structure would give the same results as engineering such structures are costly. Furthermore, the simulations use tetrahedrals to approximate the results which may be unable to see the actual materials electromagnetic response. First method: For the dielectric method of achieving this phenomenon, permittivity coefficients are controlled by the type of material. Metal achieves resonance at the microwave-infrared frequency range which allows it to achieve a high negative dielectric constant. The method of using Nano-cylinders is able to cause permeability to achieve resonance around the same frequency range. For our project we have used Silicon Carbide in cylinders of diameter 1.5um due to its strength and electromagnetic properties. The sub-light-wavelength cylinder displays a negative refractive in index behavior in the infrared frequency. EEE 17 Negative Refraction in Metamaterials

This simulation using Comsol Multiphysics has confirmed the occurrence of the phenomenon at wavelength 9.71 x10-6m (colour indicating difference in wavelength, red for upper limit and blue for lower limit).

Second method: The hyperbolic metamaterial uses the big change in refractive index between layers of material to create the negative refraction phenomenon. In our simulation, we used a single layer of hypothetical metallic material and vacuum. The purpose of this method is to demonstrate a way to model a metamaterial domain with bulk negative permittivity and permeability. EEE 17 Negative Refraction in Metamaterials

Since the model space is infinite and invariant along the interface, it is possible to model a finite-sized unit cell around the interface, and use Floquet-periodic boundary conditions. The incident wave is modeled using a Port boundary condition, which both launches the incident wave and absorbs the reflected wave. Two different ways are demonstrated for modeling boundary to the infinite metamaterial domain. In the first case, a Port boundary condition is used. This boundary condition requires computing the wavevector in the metamaterial, and manually adjusting the propagation constant at the boundary to account for the negative index. In the other case, a Perfectly Matched Layer (PML) is used to truncate the domain. The PML acts as an absorbing medium for all energy incident upon it, but must also be adjusted to account for the negative index. It is simpler to use, but increases the model size. The transition between the two materials requires some special care. The natural boundary condition between domains of different material properties does not account for the change in direction of the flux. An additional degree of freedom has to be added to the model. This can be done by using the Transition Boundary Condition (TBC), which allows for a change in flux across the boundary. The TBC takes as input the material properties on one side of the domain, it does not matter which side. The thickness of the TBC should be approximately 1/1000 of the wavelength. If it is too small, it can introduce numerical difficulties. If it is too big, it alters the results significantly. The TBC only needs to be used in this way if the effective refractive index is similar in magnitude, but opposite in sign.

EEE 17 Negative Refraction in Metamaterials

Conclusion & further extension: Hyperbolic and dielectric methods used above are able to create materials that display left-handed properties in a small frequency range. Applications such as electromagnetic cloaking are unachievable yet with these methods as successful cloaking requires the material to show left handed characteristics at a larger frequency spectrum. Layering multiple layers to cloak for different frequencies is unrealistic and would reduce each layers efficacy in achieving resonance at that particular frequency. From an engineering perspective, silicon may be the easiest semiconductor to work with, and it produces an observable negative refraction. It may be useful to experiment with other methods such as doping ions into polymers, such as using protonated poly(benzimidazole) whose resonant frequencies can be controlled by concentration of ions. More research can be done into other possible materials that can be utilized, possibly one that can produce negative permittivity and permeability simultaneously over a wider frequency range for the unique properties of NIMs to be more significant.