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\chapter{Introduction} \label{Chapter:Introduction}

\section{Motivation and aims}

Metamaterials are nano-patterned artificial media that can exhibit properties beyond those seen in natural materials. Their resonant response is mostly determined by the geometry and design of the core unit and the base material, thus can be induced by particular incident wavelengths. However, a number of practical applications require metamaterials that are capable of operating across a wider range of wavelengths. Creating metamaterial devices that are capable of tuning their operating wavelength is therefore of great interest. The patterned format of metamaterials has been shown to be well suited to consider hybrid systems, namely integrating metamaterials with soft matter or seminconductors to achieve adaptive response. 

The aim of the experimental projects carried out for this thesis was to explore nanoscale, planar metamaterials for visible and near-infrared light manipulation, investigating the robustness of their fabrication on the nanoscale for tuneable metamaterial technologies. The projects undertaken included designing, fabricating and characterising metamaterials, applying external electric fields and LCs to achieve functional metamaterial systems.

Three different, experimental projects were pursued for this thesis and their main findings are captured in the following chapters: Chapter 2 on mechanical metasurfaces, actuated with voltage and hybridised with LCs; Chapter 3 on zigzag metasurfaces and their sensitivity to the spatial coherence of incident light and finally Chapter 4 on optical activity with metasurfaces. Each chapter is accompanied by a brief introduction to the project-specific concepts. This chapter focuses on the introduction to the main concepts of metamaterials, metasurfaces and a brief overview of LCs.

\section{Artificial photonic materials (metamaterials)}

Introducing the general concept of metamaterials is often done through the context of other, well known, and often, man-made material systems, namely photonic crystals \cite{zhou2019photonic}. The simplest example of a photonic crystal -- a 1D photonic crystal -- is a dielectric mirror, which is a stack of thin dielectric slabs. Its optical response results from Bragg diffraction and interference of light at the resulting interfaces and therefore it requires structuring on the scale of the order of one wavelength \cite{belyakov1992diffraction}, as shown on Figure \ref{Figure:MM_Vs}. There different versions of photonic crystals, including those in 2D and 3D, which are obtained by structuring in 2 or 3 mutually orthogonal directions.

The condition that applies in such structures, namely their periodicity (a) being larger than wavelength ($\lambda$), photonic crystals cannot be described as an effective media.  While examples shown on Figure \ref{Figure:MM_Vs} demonstrate artificial photonic crystals, such structures also exist in nature, for instance, in the form of opals and beautifully coloured butterfly wings.

\begin{figure}[!htb]
  \centering
  \includegraphics[width=14.5cm]{Figures/C1/PhotonicVsMeta.png}
  \caption{Examples of (a) traditional photonic structures exhibiting standard diffraction and interference versus (b) controlling light at sub-wavelength scale with metamaterials.}   % ** [3]
  \label{Figure:MM_Vs}
\end{figure}

Metamaterials, on the other hand, are artificial by definition, as they are designed to interact with light in ways no natural materials can. More specifically, metamaterials are metal or dielectric composites that are structured on essentially sub-wavelength scale. They do not diffract, thus appearing homogeneous to the incident wave.

The exotic and often dramatic physics demonstrated by the metamaterial crystals is underpinned by resonant electromagnetic scattering of their unit cells, the so-called metamolecules, which can be made resonant in either one, two or three mutually orthogonal directions (Figure \ref{Figure:MM_Vs}).

\section{Metamaterials: basic principles and applications}

Metamaterials are a class of nano-structured artificial media that have properties beyond those normally found in nature. For optical metamaterials these properties are achieved by creating materials which are periodically structured on the nanoscale, designed to interact with light in novel ways. The unit cells of these structures, called the metamolecules, are arrayed to form large active regions. Effects such as negative refractive indices \cite{shelby2001experimental}, invisibility cloaks \cite{ergin2010three} and hyperlenses \cite{lee2007development} can be observed by utilising different designs for the metamolecules. Negative refraction, for example, is essential for the development of the hyperlenses, a key component of optical imaging systems that can beat the famous diffraction limit. 

Successes in achieving negative permeability and permittivity are paving the way to new phenomena including negative refraction which offers exciting applications in energy harvesting, sensors and image processing \cite{tong2018functional}. In particular, the opportunity to realise negative-index materials led to a rapid growth of a dedicated branch of metamaterials research. One of the first demonstrations was based on integrating arrays of conducting wires with arrays of split-ring resonators, exploiting the overlap between their frequency bands of negative permittivity and permeability. In this early work, the possibility for creating a perfect lens was also demonstrated \cite{Pendry2000}. Furthermore, particularly captivating was the demonstration of negative refraction at the optical communication wavelength of 1.5 $\mu$m using an array of pairs of parallel gold pillars, thus demonstrating the capability to fabricate metamaterials on the nanoscale \cite{shalaev2005negative} to manipulate light.

The design and engineering of metamaterials for particular response and wavelength relies on the consideration of their basic unit, which are called metamolecules, organised in a periodic arrangement in three dimensions and exhibiting a resonant response \cite{smith2010metamaterials}, acting as antennas. When an electro-magnetic field is incident, oscillating currents are generated in the individual metamolecules and electro-magnetic waves are re-radiated, combining to form the transmitted and the reflected, secondary waves.

%As long as the features of the metamolecules are much smaller than the wavelength of light interacting with them, the metamaterial will behave like a homogeneous medium. 

\begin{figure}[!htb]
  \centering
  \includegraphics[width=6cm]{Figures/C1/Metasurface design examples.png}
  \caption{Typical examples of metamaterial designs.} % ** [3]
  \label{Figure:MS_design_examples}
\end{figure}

The metamolecule patterns are typically metallic and fixed onto an insulating substrate. The resonances, $\lambda_0$, where strong scattering occurs, of such metamolecule antennas are determined by their sizes and design, and the materials used. By choosing appropriate pattern, the resonances can be tailored to a particular wavelength of interest.  However, the limit on the metamolecule size means that for visible and infrared wavelengths, the fabrication challenges to produce precise patterns are more significant than, for example, the metamolecules for THz. Figure \ref{Figure:MS_design_examples} presents some examples of metamaterial designs.

As summarised in \cite{kasap2017springer}, for metamolecules driven by the external electro-magnetic field, their resonant frequency depends on the inductance L and capacitance C of the pattern:

\begin{equation}
    \omega_0 = 2 \pi f_0 = \frac{1}{\sqrt{LCs}}
\end{equation}

The configuration of metamolecules-antennas, effectively operate as, a type of transmission line with resonant standing waves of conduction currents excited along the length of the structure. 

\begin{figure}[!htb]
  \centering
  \includegraphics[width=12cm]{Figures/C1/Resonant modes split ring.png}
  \caption{Resonant modes of metamolecules as standing waves.} % ** [3]
  \label{Figure:SRR_resonate}
\end{figure}

The full analysis of the resonant mechanism is complex, but with some approximations, the resonance wavelengths of metamaterials can be understood through a mass-spring model. In the simplest case, the resonance wavelength of the metamolecule, treated as an antenna, is proportional to the effective path of an electron, which in conductors is typically proportional to the size of the antenna. This direct relationship between the resonant wavelength and the size of the unit element is behind the need to match the structure of the metamaterial to the scale of the wavelength of incident light, hence the nanoscale patterning requirement for a response at visible wavelengths \cite{Min:15}.

Following Lewin's theory \cite{Lewin1947TheEC}, it can be shown that the resonant wavelength is also dependent on the dielectric permittivity, thus the resonance can be tuned either by the choice of materials or the dimensions and geometry of the core unit \cite{Wang17}. The representation as standing waves shown in Figure \ref{Figure:SRR_resonate} provides a useful approximation and visualisation of resonances, with:

\begin{equation}
    \lambda_0 \approx \sqrt{\epsilon} \frac{2 l_e}{m}
\end{equation}

where $l_e$ is the total electrical length of the metallic design forming the metamolecule, $\epsilon$ is the relative permittivity of the dielectric medium that the pattern is embedded in, such as dielectric substrate, for example, and m is a positive integer. 

The above analysis applies mainly to IR and longer wavelengths, where metals are good conductors. In the visible regime, the resonances of metamolecules are explained through plasmons. 

The design of metamaterials is not the only important parameter. The electromagnetic properties of the metamaterials can then be described by effective parameters for the permittivity, $\epsilon$, and permeability, $\mu$, caLCsulated by averaging the local electromagnetic fields \cite{smith2006homogenization,liu2007description}. Most natural materials have a magnetic permeability and electric permittivity greater than 0. By engineering the design of the metamaterial, values for $\epsilon$ and $\mu$ beyond these limits can be achieved. This can lead to novel optical properties, for example if a metamaterial is created with both $\epsilon$ and $\mu$ being negative, a so-called left-handed material, it will support backward propagating waves \cite{veselago1968electrodynamics}. If $\epsilon$ and $\mu$ are equal then the metamaterial will be perfectly impedance matched with free space resulting in zero reflection at the free space and metamaterial boundary \cite{smith2010metamaterials}.

Most metamaterials only show their designed function for a narrow wavelength band. This leads to difficulties when utilising them as many applications require them to function for a range of wavelengths. Designing devices with the ability to tune their operating wavelength is therefore of great interest. Methods to achieve this include mechanically switching the geometry of the metamolecules \cite{zhu2011switchable}, taking advantage of phase changes in materials \cite{dicken2009frequency,kyoung2011active}, and utilising LCs \cite{buchnev2015electrically} which we will explore further in this project.

Over the past decade this concept of artificially engineered media, namely metamaterials, has revolutionised the field of optics, pushed the boundaries of microfabrication, and stimulated the development of novel characterisation techniques \cite{ozbay2008magical,soukoulis2011past}. Recent demonstrations of anomalous reflection and refraction of light by metasurfaces opened another exciting chapter in optical engineering \cite{zhao2012large}.  They can display novel effects or can be used to mimic bulk optical components such as lenses.

\section{Metasurfaces}

The focus of metamaterial research has shifted towards planar metamaterials, or the so-called metasurfaces.  While metamaterials and metasurfaces are, in principle, two types of materials they are often used interchangeably, as will be used in this thesis. They are a class of low-dimensional (planar) metamaterials or in other words, 2D metamaterials and are typically formed by optically thin metal films periodically patterned on a sub-wavelength scale. Due to their planar nature they can take advantage of currently available fabrication techniques meaning they are less expensive and simpler to make when compared to bulk metamaterials which require complex multilayer technologies in terms of three-dimensional fabrication techniques. 

In spite of their small thickness, metasurfaces interact strongly with light, which they can transmit, absorb or reflect without diffraction, effectively operating as optical media of zero dimension along the direction of light propagation. That sets planar metamaterials aside from resonant gratings of various kinds, photonic crystal slabs \cite{ozbay2008magical,soukoulis2011past} and perforated metal films exhibiting extraordinary optical transmission \cite{genet2007light}.

Metamaterials are fully compatible with the existing fabrication processes adopted by CMOS technology, and offer unmatched flexibility in the design and control of light propagation, exhibiting exotic electromagnetic phenomena and replacing conventional bulk optical components. In particular, metasurfaces have already enabled spectral \cite{munk2005frequency,vardaxoglou1997frequency} and directional \cite{fedotov2015wavevector} filtering, asymmetric transmission \cite{genet2007light,munk2005frequency}, polarisation control and analysis \cite{menzel2010asymmetric,hao2007manipulating}, absorption enhancement \cite{pors2015plasmonic,engheta2002thin}, imaging \cite{landy2008perfect,aieta2012aberration} and sensing \cite{ishii2013holey,zhao2012large} as well as being fully compatible with the existing fabrication processes adopted by CMOS technology.

Metasurfaces offer unmatched flexibility in the design and control of light propagation \cite{zhao2012large,yu2014flat,wang1993theory,zhou2014progress,huang2008nanohole,aieta2012aberration} and demonstrating novel electromagnetic phenomena \cite{zhao2012large,schwanecke2008nanostructured,menzel2010asymmetric,plum2016specular}. Because of the sub-wavelength patterning they do not diffract, being effectively media of zero-dimension in the direction of light propagation.

\begin{figure}[!htb]
  \centering
  \includegraphics[width=12cm]{Figures/C1/Metasurface SEM examples.png}
  \caption{Different patterns of planar metamaterials (metasurfaces).} % ** [3]
  \label{Figure:MS_SEM_examples}
\end{figure}

The planar format of metasurfaces offers the benefit of their resonant response in terms of transmission, reflection or absorption for a relatively narrow range of frequencies, thus they can be regarded as an example of frequency selective surfaces, the concept developed the RF and microwave ranges \cite{munk2005frequency}.

The concept of frequency selective metasurfaces has been exploited in this thesis in all three projects. In general, such metasurfaces consist of a two-dimensional lattice of metamolecules with periodicity lower than the incident wavelength. Metamolecules are typically metallic wires or slits of a particular design and dimensions, designed to have a resonance for a particular band of incident wavelengths and transparent beyond that range \cite{kasap2017springer}. Figure \ref{Figure:SRR_Bab} illustrates the main concepts behind such metasurfaces. 

As shown on Figure \ref{Figure:SRR_Bab}(a) and (c), the metasurfaces can be formed by shaping metallic wires (so called positive metasurfaces) as well as through a complementary design of slits cut in the metal film. Such perforated apertures (negative metasurfaces). Their transmission and reflection spectra are complementary, following the Babinet principle, as shown in Figure \ref{Figure:SRR_Bab}(b) and (d) \cite{kasap2017springer}. 

Similarly to the case of bulk metamaterials, the geometry of the shape determines the resonance frequencies. Furthermore, as such metasurfaces are also typically embedded in a thin, dielectric substrate, dielectric permittivity of such supporting medium also influences the resonant wavelengths. 

For estimating the frequency selective metasurfaces, the expression for metamaterials (Equation 1.2) can be adapted to provide \cite{kasap2017springer}:   

\begin{equation}
    \lambda_0 \approx \sqrt{\frac{\epsilon + 1}{2}} \frac{2 l_e}{m}
\end{equation}

where $l_e$ is the total electrical length of the shape of a metamolecule, pattern that forms the metamolecule, $\epsilon$ is the relative permittivity of the dielectric medium surrounding the metamolecules;  $m$ is a positive integer. 

The difference between two expressions, (1.2) and (1.3), for metamaterials and metasurfaces, respectively, originates from different conditions in terms of surrounding media. In particular:

\begin{equation}
    \sqrt{\epsilon} \rightarrow \sqrt{\frac{\epsilon + 1}{2}}
\end{equation}

The replacement of factors indicated in (1.3) stems from having two different media surrounding metasurfaces: the supporting dielectric and air on the other side. 
Following the treatment developed earlier for conducting wires embedded in to dielectric media, the effective permittivity is the average of dielectric substrate and of air. Such effective permittivity, namely $\sqrt{\epsilon}$, can be understood as the overall permittivity of a homogeneous medium that represents the layer of air and the dielectric regions of the wire, thus the field of the resulting electromagnetic wave will be partly in the dielectric and partly in air.
The right-hand side of expression (1.3) therefore represents such effective permittivity of the conducting-dielectric system, estimated as an average between the permittivities of the dielectric and air as shown in \cite{munk2005frequency}.

\begin{figure}[!htb]
  \centering
  \includegraphics[width=12cm]{Figures/C1/SRR_mirror.png}
  \caption{Principle of operation of frequency selective metasurfaces consisting of array of split-ring resonator metamolecules. (a) array of split-ring wires b) spectra of transmission (solid line) and reflection (dashed line) for wires c) array of split-ring slits cut in thin metal d) spectra of transmission (solid line) and reflection (dashed line) for split-ring slits \cite{kasap2017springer}.}
  \label{Figure:SRR_Bab}
\end{figure}

Such analysis of resonant frequencies, with their transmission and reflection bandwidths for positive and negative metasurfaces only applies to thin samples \cite{munk2005frequency}, where the total thickness, $d$:

\begin{equation}
    d << \lambda_0
\end{equation}

The designs of metamolecules could be made more complex and this created a rich field of metasurfaces of different designs, with either narrow or more broad transmission/reflection properties, in line with the needs of particular applications, as summarised earlier in this section.

Modelling the expected response typically involves COMSOL simulations and its libraries provide suitable underpinning code. They are based on consideration interaction between the incident electro-magnetic wave and using Maxwell equations to derive an appropriate version of wave equation. For metamaterials, in general, the unit cells (metamolecules) are much smaller than the incident wavelength, hence the whole material could be assumed as being homogenous \cite{tong2018functional}. Hence, the effective permittivity and effective permeability can be expressed as $\epsilon_{ff} = \epsilon_0 \epsilon_r$ and $\mu_{ff} = \mu_0 \mu_r$ with $\epsilon_{ff}$ and $\mu_{ff}$ being averaged over each metamolectules and do not depend on the wave vector, $k$ or their values in the adjacent units, thus neglecting spatial dispersion. 

Maxwell equations for metamaterials can be expressed \cite{menzel2010asymmetric}: %**

\begin{align}
    \nabla \times \mathbf{E} = - \mu_0 \mu_r \frac{\delta \mathbf{H}}{\delta t} \qquad \qquad \nabla \times \mathbf{H} = \epsilon_0 \epsilon_r \frac{\delta \mathbf{E}}{\delta t}
\end{align}

Taking the curl of both the left and the right sides and applying Ampère’s Law, leads to the following wave equation for metamaterials \cite{wartak2011introduction}:

\begin{equation}
    \nabla^2 \mathbf{E} = - \epsilon_0 \mu_0 \epsilon_r \mu_r \frac{\delta^2 \mathbf{E}}{\delta t^2}
\end{equation}

If losses are negligible and $\epsilon_r$ and $\mu_r$ are considered as real, then the wave equation remains the same when both $\epsilon_r$ and $\mu_r$ are negative.

Exploring different options for $\epsilon_r$ and $\mu_r$ leads to some interesting effects, as discussed in \cite{tong2018functional,wartak2011introduction}. For example, when both $\epsilon_r$ and $\mu_r$ are smaller than zero, the direction of the refracted beam is on the same side of the normal as the incident beam, thus the metamaterial is regarded as having an effective negative refractive index. 
Hence, if both the effective relative electric permittivity $\epsilon_r$ and magnetic permeability $\mu_r$ magnetic permeability are negative, the value that can be associated with the effective medium’s refractive index is: 

\begin{equation}
n_{eff} = - \sqrt{{\epsilon_r{{}} \mu_r}}
\end{equation}

Having an effective refractive index of a medium that is negative when both the real parts of the permittivity and permeability are negative is a general result, and can apply to different materials. However, careful consideration is needed in the case of materials where either the permittivity or the permeability is active. The rich opportunities to design new metamaterials led to the modelling of several exotic phenomena, initially for the microwave regime, including the impact of having asymmetric designs \cite{kasap2017springer} and such robust modelling was essential to guide the experimental work carried out.

\bigskip

Given the constraints on the size of metamolecules, the fabrication of metamaterials is particularly challenging for the optical regime, as will be discussed in detail in the following chapters. However, in general, while technical challenges meant that high precision and a cleanroom environment was required for optical and near-infrared metamaterials, the flexibility and almost unrivaled prospect to manipulate local electric and magnetic properties led to the development of underpinning fabrication methodologies and the sharp increase in the demonstration of nanostructures with distinctive electromagnetic response to incident light. The other approach to address this challenge was to reduce the complexity related to bulk, three dimensional metamaterials by constraining them to thin planar surfaces, called metasurfaces. The fabrication approach also benefits from the experience and recipes from well known technologies such as computer chip, phase-array antennas and diffractive optics. Optically thin layers, structured on the sub-wavelength scale not only can influence polarisation or phase of light, but they can also be chosen from a wide range of materials with attractive electronic and optical properties, such as graphene, semiconductors or plasmonic metals. Therefore, the benefits and the exciting opportunities to explore new fascinating phenomena with prospects for further miniaturisation and high performance optical components mean that the effort devoted to fabrication methods has been paying off \cite{Urbas2016} 


Apart from different shapes of metamolecules, there are also different options in the choice of supporting dielectric media, an example of such investigation with different media will be discussed in the next chapter, where LCs, instead of air, were surrounding a metasurface from one side. This project was among the recent effort of the world’s leading metamaterial labs on implementing the idea of tuneable and active metamaterials, a generation of artificial photonic media with dynamically controlled optical properties. The latter is perceived as the next important stage in the development of the metamaterials, which should dramatically expand the range of their potential applications. One of the first proposals towards this goal was to combine metamaterials with nematic LCs. 

\section{Liquid crystals for tuneable metamaterials}

LCs are molecules which exhibit phases of matter in between the basic solid and liquid phases \cite{collings1997introduction}. These phases have some degree of orientational order and in some cases a degree of positional order, but are also able to flow like liquids. The different phases exhibited depend on the molecular structure, with some only having a single LC phase and others having multiple phases depending on their temperature. In the simplest case, called the nematic phase, the molecules tend to point in one direction even if they are flowing. The result of this preferred orientation is that nematic LCs can be described as anisotropic fluids, characterised by optical and dielectric anisotropy. Another more complex phase of LCs is the smectic phase, where the molecules are pointing in the same direction but are also organised in layers showing some long range positional order. 

\begin{figure}[!htb]
  \centering
  \includegraphics[width=10cm]{Figures/C1/LCphases.png}
  \caption{The phases of a nematic LC as temperature is increased.}
  \label{Figure:LCphases}
\end{figure}

The transition between the solid, LC and isotropic liquid phases is achieved through increasing the temperature, which reduces the degree of order. The materials exhibiting LC phases start with a high degree of order at low temperature when they are solid and then with increased temperature turn into LC phases. First, for LCs that show this phase, there will be a more ordered smectic phase and then the less ordered nematic phase as the temperature increases. Finally, at the so called clearing temperature, the material will turn into an isotropic liquid. This change of order and of material parameters that is induced and controlled by temperature adds to the versatility of LCs, explored both for research and practical applications.

In this work, only nematic LCs were considered, thus the discussion of LCs material parameters and their influence on metallic structures will only consider this phase. Therefore, when LCs will be mentioned, this means nematic LCs.

There are several nematic LCs that exhibit high optical birefringence in the visible range. Those with high birefringence, such as 5CB which will be discussed in the next chapter, retain sizeable birefringence even in the terahertz range, namely $0.14$ around $2 THz$ \cite{Vieweg:10}. LCs are easily controlled by temperature, light, electric and magnetic fields. They have also arguably the largest and most broad-band optical nonlinearity. They share properties with both liquids and crystalline solids, appearing to move like a liquid but show an ordered nature like that found in crystals upon closer investigation. The structure of these ordered phases depends on the type of LCs and on external properties such as temperature and external fields \cite{collings1997introduction}. One of the simplest and most useful of these is the nematic phase where the molecules behave like rods with no positional order but with the molecular rods all pointing in the same direction described by a vector called the director. Light passing through such anisotropic materials experiences a different refractive index depending on its polarisation and propagation direction. There are two possibilities, $n_o$ and $n_e$. If the direction of propagation is the same as the director then no is experienced by all polarisations of the light. If the light propagates perpendicular to the director then light with polarisation parallel to the director will experience $n_e$ while the light with polarisation orthogonal will experience $n_o$. The director can be influenced by external forces such as magnetic and electric fields. This effect is utilised in LCs displays to vary the intensity of transmitted light. One example of this is the twisted nematic cell in which the LCs is sandwiched between two glass planes each coated with an aligning layer with a transparent electrode underneath. This set up is shown in Figure \ref{Figure:LCs_cell}.

\begin{figure}[!htb]
  \centering
  \includegraphics[width=14.5cm]{Figures/C1/TNLC.png}
  \caption{Twisted nematic LCs cell in ON state, left, and OFF state, right. P, G and E are the polarisers, glass and electrodes respectively.
}
\label{Figure:LCs_cell}
\end{figure}

The electrodes, typically made from Indium Tin Oxide, allow an electric field to be placed across the cell. The aligning layers consist of a rubbed polymer such as polyimide which causes the local LCs molecules to align with the rubbing direction. For a twisted cell the rubbing directions of the top and bottom aligning layer are perpendicular to each other causing the LCs molecules to form a helix like structure with a $90 ^\circ$ twist between the 2 layers. The last part of the device is a set of crossed polarisers on the outside of the glass planes which are aligned parallel to each of the alignment layers. Light passing through the device will be linearly polarised by the first polariser, then have its polarisation rotated by $90 ^\circ$ as it propagates through the LCs \cite{hecht2002optics}. The light can then pass through the second polariser without being absorbed leading to the ‘on’ state of the device. When an electric potential is placed across the cell the LCs molecules will align in the direction of the electric field, destroying the helix like structure. Now the polarisation of the light will not be rotated and the light will be absorbed by the second polariser creating the ’off’ state for the device.

There have been a number of works on LCs-loaded metamaterials since the emergence of the field. Early work included radio-frequency and microwave metamaterials controlled by electric and magnetic fields \cite{zhang2008magnetic,zhao2007electrically}, followed by Near-IR metamaterials controlled with temperature \cite{xiao2009tunable}, then by near-IR metamaterials controlled with light, namely UV light \cite{kang2010optical} and finally near-IR materials controlled by electric field \cite{minovich2012liquid,buchnev2013electro,buchnev2015electrically}.

It has been shown that metasurfaces can be used to replace many of the components of a LCs cell. Buchnev et al. \cite{buchnev2013electro,buchnev2015electrically} demonstrated this by fabricating a cell with one half consisting of the traditional assembly of a glass substrate, polariser, ITO electrode and polymer aligning layer, as shown in Figure \ref{Figure:LCs_cell}, and the other half consisting of a gold metasurface on a glass substrate. The metasurface was formed of zigzag shaped gold nanowires which effectively acted as the polariser, electrode and aligning layer for the cell.

Using LCs to tune the operating wavelength of negative permeability \cite{zhao2007electrically} and negative index \cite{zhang2011electrically} metamaterials has been experimentally shown in the microwave regime. Tuning at optical wavelengths has been demonstrated relying on the LCs phase change from nematic to isotropic as the temperature is increased \cite{xiao2009tunable}. This tuning will only allow two discrete values to be attained in contrast to electrical tuning which will allow for a near continuous range of values.

The ability of LCs for tuning metamaterial devices operating at optical and near-IR is impeded due to the surface anchoring of the LCs molecules \cite{khoo2014nonlinear,decker2013electro}. To efficiently tune such devices, the LCs must be able to switch in the vicinity of the metamaterial structure where the plasmonic fields are strongest. The surface anchoring of the molecules renders the region of the LCs in contact with the substrate inactive. One solution to this problem was demonstrated here, at the University of Southampton, by Buchnev et al. \cite{buchnev2015electrically}. A metasurface was fabricated from gold deposited on a SiN membrane using a focused ion beam. During the fabrication the focused ion beam cut through the supporting membrane as well as the gold leaving zigzag shaped gold nanowires suspended on SiN bridges. LCs added to this metasurface have no surface to anchor to and are therefore free to move in the plane of the metasurface when a voltage is applied between the wires of the device. This allowed the spectral tunability of the sample to approach the theoretically predicted limit of $9\%$.

All the methods summarised here, aiming to enhance functionality of metasurfaces, rely on strong optical birefringence from the LCs. Although changes of the refractive index attainable in LCs are hysteresis-free and large, the extent of tuneability achieved for metamaterials in this way proved relatively modest for widespread and practical applications. Therefore, in this thesis, the main focus will be on expanding the area of hybrid metamaterials and their functionality further, by engaging the elastic response of nematic LCs.