%% ----------------------------------------------------------------
%% ZZelastic.tex
%% ---------------------------------------------------------------- 
\chapter{Elasto-Mechanical Coupling for tuneable Liquid Crystal Metamaterials} \label{Chapter:ZZelastic}

The current effort in the field is being focused on implementing the idea of active and tuneable metamaterials (MMs), a generation of artificial photonic media with dynamically controlled optical properties. The latter should enable to dramatically expand the range of the potential applications of the MMs making them the fundamental base of future photonic devices \cite{zheludev2012metamaterials}.

In this chapter, a new generation of non-linear, dynamically tuneable artificial material systems is demonstrated. It belongs to a class of optical metamaterial hybrids that exploit elastic coupling of liquid crystals (the hybrids’ functional component) with the mechanically re-configurable fabric of the metamaterial host. Thus, the concept of non-linear tuneable metamaterials is taken to the next level by adopting the best of the indirect and direct control methods and eliminating their shortfalls with a single hybrid approach.

Following on the earlier work on hybrid LC-metamaterial, where the elastic forces on anisotropic media such as LCs was used to prevent the detrimental effect of stiction, the results of this experimental study discussed here focuses mainly on exploring if LCs could restore mechanical actuators damaged due to stiction.

\section{Hybrid  approach  to  controlling  metamaterials:  exploiting  elasto-mechanical  coupling}

Developing artificial photonic media with dynamically controlled optical properties has become one of the key stages in the metamaterial research, as it should enable the creation of smaller and more efficient photonic structures and devices, dramatically expanding the range of metamaterial applications \cite{zheludev2012metamaterials,shadrivov2015nonlinear}. The dynamic control of a metamaterial can be implemented using generally two approaches – the direct approach, by physically modifying (though often irreversibly) the fabric of the metamaterial through either mechanical deformations \cite{pryce2010highly,lapine2011metamaterials} or the use of MEMS/NEMS (micro/nano-electromechanical systems) -based actuators \cite{tao2009reconfigurable,ou2011reconfigurable}; and the indirect approach, by altering optical properties of the metamaterial’s host matrix or substrate/superstrate, which features naturally available functional materials (e.g. non-linear, phase change or gain). Among functional materials liquid crystals (LCs) possess arguably the largest broadband optical non-linearity and externally controlled birefringence, which has made LCs one of the first and most popular ingredients exploited by indirectly-tuneable metamaterial designs \cite{zhao2007electrically,evans2007electrically,khoo2014nonlinear,shadrivov2015nonlinear,pryce2010highly}. In particular, earlier work in the group demonstrated efficient spectral tuning of LC-MM system in the optical part of the spectrum, which was achieved by reorienting LC molecules in a specially designed nano-structured hybrid using in-plane electric field \cite{buchnev2015electrically}. 

In all reported designs of tuneable LC-MMs the role of the liquid crystals has so far been limited to acting as a macroscopic dielectric environment with controlled optical anisotropy. Although changes of the refractive index attainable in liquid crystals are hysteresis-free and large, the extent of spectral tunability demonstrated in LC-MM hybrids is still too modest for most of practical applications. For example, the maximum value of the birefringence of E7 $(\Delta n_{max} = 0.225)$ would correspond to a spectral shift of less than $15\%$. 

At the micro and nano scale, devices experience a range of effects that are not seen in larger components. One of these that can be very problematic for mechanically switching metamaterials is stiction. This occurs when a mechanical actuator comes into contact with another surface and becomes stuck as the adhesive forces, such as capillary, Van de Waals and electrostatic forces, exceed the restoring force of the actuator. This becomes more problematic as the size of the device decreases due to the restoring force, related to the volume, becoming weaker compared to the adhesive forces, related to the surface area. For functional devices that rely on mechanical switching, a method to mitigate or even control stiction would be extremely useful. Furthermore, in reality, the tuning range is reduced by at least a factor of two due to the presence of a supporting dielectric substrate, which prohibits the complete immersion of metamaterial framework into the bulk of LC. Moreover, the efficiency of tuning may be lowered even further as a result of strong anchoring of LC-molecules to the surface of the metamaterial; it renders few tens of nanometers of LC adjacent to the surface as inactive (which is particularly detrimental for nano-structured metamaterials designed to operate in the near-IR and visible spectral domains).

LCs are optimum materials to overcome these limitations and take full advantage of the available LC control mechanisms, involving temperature, light, electric and magnetic fields, and exploiting the elastic properties of liquid crystals. In the new section, it is shown how LCs, when coupled to the fabric of a re-configurable photonic metamaterial, can efficiently modify the character of its nanoscopic mechanical actuators, which then transform elastic distortions of LC into changes of the metamaterial optical properties. Furthermore, strong surface anchoring of LC-molecules turns here into an advantage: it ensures robust elasto-mechanical coupling between the metamaterial framework and LC, whilst eliminating the major shortfall of mechanically re-configurable systems, namely their susceptibility to electrostatic/capillary stiction resulting in permanent structural damage \cite{spearing2000materials,romig2003materials}.

LC-MM structures discussed here, with elastic forces preventing stiction, are directly relevant to NEMS (nano-electro-mechanical systems), which are integrated miniature devices that combine electrical and mechanical components at the nanoscale. They have demonstrated great potential for a wide range of applications including nanoactuators and sensors \cite{ekinci2005nanoelectromechanical,im2007dielectric,naik2009towards}, electromagnetic detectors \cite{bagci2014optical,akram2010single,verhagen2012quantum}, optical switches and relays \cite{lee2004three,jang2008fabrication,loh2012nanoelectromechanical} and, recently, reconfigurable metamaterials and plasmonic devices \cite{ou2013electromechanically,yamaguchi2013electrically,thijssen2013plasmon,liu2013dynamic,yamaguchi2016electrically}. The reliability of NEMS (as well as MEMS) faces challenges related to issues such as “stiction”, undesired adhesion between the relevant surfaces of the mechanical components, which typically leads to their irreversible damage \cite{maboudian1997critical,yapu2003stiction}.

Stiction takes place when surface adhesion forces, such as capillary, Van der Waals, electrostatic forces or their combinations, are stronger than the mechanical restoring force from an actuator. The methods to prevent stiction have been developed and are typically applied at the device fabrication stage, for example, by changing the surface hydrophobicity or by eliminating liquid-vapor interfaces through supercritical fluid, freeze-drying, or dry release methods \cite{guckel1990application,maboudian1998surface,maboudian2002tribological}. However, such approaches sometimes fail, for example, due to changes in ambient conditions or during routine operation of the device when its mechanical components come into close contact with each other. Therefore, there are ongoing efforts to tackle such undesired effect, including surface treatment and coatings \cite{mastrangelo1997adhesion,de2001tribology,maboudian2000self}, adapting the structure of designs of cantilevers and/or contact electrodes \cite{mercado2004mechanics,lee2013sub}. Stiction, while posing a significant issue in microscale electromechanical systems (MEMS) \cite{maboudian1998surface}, creates more major problems for the reliability of NEMS, with their larger surface-to-volume ratio. Furthermore, the stiction-preventive methods developed earlier and proven effective for MEMS \cite{de2001tribology,ashurst2003vapor} are not easily applicable to NEMS, with the reduced size of these devices. Therefore, the alternative method proposed here, using LCs with their fluidity accompanied by strong elastic forces offers an attractive solution to stiction issues.

The structures were first exposed to an AC voltage to check for any short circuits without moving the nanobridges and then to a DC voltage. It is worth noting that DC driven LC devices can suffer from long term stability issues. Charge carriers and ions can be generated with longer exposure to DC voltage and they can accumulate close to the conducting surfaces and electrodes, effectively screening the applied electric field. Such negative effects can be limited if LCs with low ionic content are used and the structures are refreshed with the application of AC voltage. This particular aspect was not studied in detail as part of this thesis, but it would offer an interesting extension to the work presented here.

\section{Background to experimental LC - Metasurfaces}

From the previous work carried out in the group by Buchnev et al. \cite{buchnev2015electrically}, where the already tested zigzag metamaterial design used in the past to implement active control via volume and in-plane switching of liquid crystals, a new metasurface was designed and fabricated \cite{stictioncontrol}. The changes from the previous metasurface can be seen in Figure \ref{Figure:Old2New} below. Joining the project \cite{stictioncontrol} in its final stages, I assisted with final tests, additional analysis and discussions. The methodology and the experiments carried out in \cite{stictioncontrol} are presented here in detail as they were followed for the fabrication and the experiments discussed in this chapter.

The zigzag geometry had each metamolecule consisting of a single chevron shape. This shape was chosen following earlier work in the microwave regime, where wave like structures were fabricated and showed distinct resonances. For the optical and near-infrared regime, the nanoscale fabrication is more challenging and sharper, rather than curved endings of the structures, are more feasible to achieve. In the first work on such “sharp” zigzag structures \cite{buchnev2015electrically} it was successfully shown that they act efficiently not only as an alignment layer, as electrodes, but also a polariser in MM-LC cells. Therefore, the zigzag pattern was retained for the further studies. 

\begin{figure}[!htb]
  \centering
  \includegraphics[width=14.5cm]{Figures/C2/old_to_new_zigzag.PNG}
  \caption{Comparison between the metasurface \cite{buchnev2015electrically}, (a), and the metasurface used to investigate stiction effects \cite{stictioncontrol}.}
  \label{Figure:Old2New}
\end{figure}

As Figure \ref{Figure:Old2New} shows, the metasurface, while retaining the shape, was modified slightly and consisted of fully suspended on dielectric nano-bridges.  This new metasurface was designed to deform when a voltage was applied to the electrodes. The wires were arranged in pairs instead of the alternating electrode pattern used before, such that odd and even pairs were electrically disconnected from the opposite sides of the gold frame. Straight sections were added on to the ends of each wire to increase its flexibility and those straight extensions on each side of the nano-bridges ensured uniform displacement of the zigzag sections in the plane of the structure. The bridges were cut in a $50nm$ thick low-stress SiN membrane using focused ion beam. In more detail, the metasurface was fabricated by milling, with a focused ion-beam, a $50nm$ thick gold film, which had been sputtered beforehand on a $50nm$ thick silicon nitride membrane. The milling completely removed parts of the membrane in the gaps between zigzag nano-wires, yielding a wire grid that was fully suspended on silicon nitride bridges and could mechanically flex in the plane of the structure. The metamaterial structure was configured to operate in the near-IR, exhibiting a plasmonic resonance as a peak in the transmission spectrum at around $0.8 \mu m$.
 
The nano-wires were grouped in pairs with the odd and even pairs being connected to the electric potentials of opposite signs, so that the resulting electrostatic attraction/repulsion between the neighbouring wires would trigger their lateral displacement. That allowed us to apply a potential difference between the pairs, making sure that electrostatic forces acting on each and every nano-wire were not balanced. The resulting combination of repulsion and attraction triggered lateral displacements of the supporting nano-bridges. Hence, when a voltage was applied the wires were attracted together in pairs due to the electrostatic attraction and repulsion between them. In this way, a metamaterial could be made re-configurable.

%The design of a mechanically reconfigurable metasurface was based on a double-periodic array of electrically connected V-shaped plasmonic nanoresonators forming a continuous “zigzag” wire pattern (Figure \ref{Figure:Old2New}). The Metasurface, fabricated by Dr O. Buchnev, was produced by milling, with a focused ion beam, a $60 nm$ thick gold film that had been sputtered beforehand on a $50 nm$ thick ultra-low-stress silicon nitride membrane (Norcada). The resulting gold wires had a width of approximately $160 nm$ and were separated by $100 nm$ wide gaps. The unit cell of the zigzag pattern was rectangular with a size of $340 \times 490 nm$, which rendered our planar metamaterial as nondiffracting in the visible and near-IR, at wavelengths larger than $0.5 \mu m$. The milling also completely removed parts of the membrane in the gaps between the nanowires, thus yielding a gold zigzag grid fully suspended on silicon nitride nanobridges. Overall, the metamaterial structure was configured to operate in the near-IR, exhibiting a plasmonic resonance as a peak in the transmission spectrum at around $0.8 \mu m$.

The metamaterial structure was infiltrated with a nematic liquid crystal 5CB (Merck) applied to the surface of the sample using a drop-casting method. The choice of 5CB (versus other nematic LCs) was done for the convenience of working with this LC, which has the lowest clearing temperature among widely available nematic liquid crystals ($35 ^\circ C$), relatively low viscosity, and weak optical anisotropy ($n_o = 1.520$, $n_e =1.681$, $n_{iso} = 1.574$ at $\lambda = 1 \mu m$).

For the purpose of optical measurements, the drop was squeezed by a glass cover slide, yielding a thin, optically uniform LC layer. The glass slide was coated with a $20nm$ thick film of non-rubbed polyimide, which ensured both parallel alignment and weak anchoring of LC molecules at its surface. As observed in earlier work \cite{buchnev2013electro}, a zigzag patterned metamaterial can act as a polariser, an electrode and as an alignment layer. For the devices studied in this thesis, planar alignment of the LC on the metamaterial bridges was also observed so there was no need to rub the polyimide layer to ensure planar orientation. As a benefit, the weak anchoring from the non-rubbed polyimide provides extra freedom of orientation for the LC well above the metamaterial structure.

The thickness of the LC layer was set to $2 \mu m$ by using dielectric spacers placed between the glass cover and gold film. To promote the infiltration of the LC into the metasurface, the temperature of the sample was maintained above the clearing point of 5CB for about 10 minutes.

The optical response of the metamaterial sample was characterised in transmission at normal incidence using linearly polarized light. The polarisation was set either parallel or perpendicular to the wires of zigzag nano-grid. Transmission spectra were collected in the range $0.7 - 1.9 \mu m$ with a spectral resolution of $0.1 \mu m$ using a microphotospectrometer.  

%As the voltage was increased, the potential of each wire could be seen in the SEM image as a change in the brightness. The wires remained in place until the voltage reached the critical value of $2.7V$, when they quickly snapped together in pairs. Once the wires were touching the voltage was decreased but they remained coupled in pairs due to the adhesive forces between the wires being greater than the restoring force from the deformation. This effect as described before is called stiction. SEM images of the structures as the voltage was increased are shown in Figure \ref{Figure:DryCoupling}(a)-(c).




\begin{figure}[!htb]
  \centering
  \includegraphics[width=14.5cm]{Figures/C2/DryStickandSEM.PNG}
  \caption{(a)-(c) SEM images of the nanowire metasurface captured as voltage was increased. Scale bars corresponds to $200 nm$.
  (d) Transmission spectra of the metasurface as voltage was increased.
  (e) Plot of transmission at $0.9 \mu m$ as voltage was increased and then decreased.}
  \label{Figure:DryCoupling}
\end{figure}

%To appreciate the role of elastic response of nematic liquid crystals in preventing sticking, the first stage of experimental work focused on capturing the images of metamaterial and its spectra, when electrically switched, as shown on Figure 4**.

The failure of the reconfigurable metamaterial due to stiction was first observed directly under a scanning electron microscope. As the voltage was increased, the potential of each wire could be seen in the SEM image as a change in the brightness. The wires remained in place until the voltage reached the critical value of $2.7V$, when they quickly snapped together in pairs. Once the wires were touching the voltage was decreased, but they remained coupled in pairs due to the adhesive forces between the wires being greater than the restoring force for the deformation. This effect, as described before, is called stiction. The SEM images of this process are shown in Figure \ref{Figure:DryCoupling}. 

The same experiment was conducted with a new sample while the spectral response of the metasurface was observed with a microphotospectrometer. The transmission of the sample was seen to remain stable with the increasing voltage until, as expected from the previous experiment, it sharply reduced at $2.7V$. Above this voltage the transmission spectra showed no changes. The spectra are shown plotted in Figure \ref{Figure:DryCoupling}(d). To make this easier to view the transmission value at the peak of each spectrum was plotted against the applied voltage. This is shown in Figure \ref{Figure:DryCoupling}(e). We can see the sharp fall in the transmission value as the wires couple together and that as the voltage was ramped back down the transmission remained at its final value. This showed we could verify optically when stiction had taken place.

A new set of samples was then fabricated and infiltrated with 5CB, a liquid crystal. The sample was observed under the microphotospectrometer as before. Due to the presence of the LC, the transmission resonance of the sample was red-shifted by approximately $200nm$ and the voltage required to actuate the sample was increased from $2.7V$ to $6V$. This is because of the increased electrical permittivity from the LC. First the sample was observed with the LC in its disordered isotropic phase. This was done by heating the sample above the clearing point of 5CB, $35 ^\circ C$, using a heated stage for the microscope. Figure \ref{Figure:LCcoupling}(a) and (b) show the response as the voltage was applied. A similar response to that seen with the dry sample was observed with the transmission at the peak of the resonance sharply falling around $6V$. Above this the transmission spectrum remained the same and as the voltage was ramped down the sample remained in this final state. This showed that the bridges had become stuck due to stiction. 

%Figure ** 6 shows a typical, **(reference) switching behaviour of the metasurface driven only by mechanical deformations of its zigzag wire grid. Here, at temperatures above $35 ^\circ C$ the role of long-range elastic forces of LC was suppressed and 5CB behaved as an ordinary isotropic liquid. With the potential difference ramping from $0V$ to $6.5 V$ for the first time the metamaterial transmission was seen to decrease slowly with a pronounced change observed only at around $5.8 V$. Increasing bias voltage past $6.5 V$, as well as ramping it down to $0 V$ (and up again) did not produce any changes, which signified damage of the re-configurable structure due to electrostatic stiction. By switching the phase of 5CB between nematic and isotropic it was possible to toggle at will between the reversible and irreversible regimes of metamaterial operation.

\begin{figure}[!htb]
  \centering
  \includegraphics[width=14.5cm]{Figures/C2/isoVSnemStiction.PNG}
  \caption{(a) Transmission spectra with isotropic LC as voltage increased. (b) Transmission at $1.2 \mu m$ as voltage was ramped up and down with isotropic LC. (c) Transmission spectra with nematic LC as voltage increased. (d) Transmission at $1.2 \mu m$ as voltage was ramped up and down with nematic LC.}
  \label{Figure:LCcoupling}
\end{figure}

The difference between isotropic and nematic LC effect could be understood through an increase in the restoring force acting on the nanowires, such additional originating from the elastic bend and splay deformation of the LC in the area between and directly above the oppositely charged wires \cite{stictioncontrol}. The force acting on the wires is much stronger in the nematic than in the isotropic phase. This is because the force results from the local distortions of the LC interacting with the large scale nematic order present in the bulk of the LC. This force is not confined to the case where the wires are closest together, but during their entire range of motion, acting to cushion their movement. 

The wavelength of peak transmission for the case of a sample with the isotropic LC shifted to a lower wavelength and the peak became less pronounced as the applied voltage was increased. The exact mechanism behind these trends is still not fully understood. There are many different contributions stemming both from the material properties of the LC as well as from the structure of the flexible nanobridges changing as they become coupled. Additionally the LC can become locally aligned due to the applied electric field while remaining disordered away from the metasurface. To investigate these factors and to fully understand the interplay between them would require a complex simulation model to be created which is outside the scope of this project.

While the application of LCs showed that stiction could be avoided, the aim of the further study pursued for this thesis was whether the application of LCs after stiction took place could reverse the damage and free up the nanobridges.

\section{Experiments on zigzag metasurfaces for preventing irreversible damage}

This previous study led to the question and idea whether LCs in nematic phase could be used to repair damaged nanobridges by separating them after stiction had occurred or whether prior infiltration was required for the observed effect. This required tests on multiple, pristine metasurface samples to check the repeatability and universality of the stiction effect. 

The fabrication process of metasurfaces for this thesis followed the procedure pursued for \cite{stictioncontrol}. With the assistance of Dr Buchnev, six new metasurfaces were produced. The fabrication is a very delicate process hence the need to fabricate multiple metasurfaces, with the aim of selecting those of the best quality. They were fabricated together on the same, large substrate and after inspection, only two were selected for further study. These 2 samples were electrically isolated by cutting wide strips in the gold with the FIB. There were 4 external connections onto the membrane allowing each sample to be investigated individually.

These two samples were then observed with the microphotospectrometer as voltage was applied with the aim of more detailed characterisation of the spectral response when the stiction effect occurs. The results of this were not as expected so the samples were viewed with the SEM to inspect for any problems. This showed that both samples had sustained major damage, most likely from electrical short circuits where some gold had not been fully removed. This led to excess heating of the nanobridges resulting in large deformations and some gold being vaporised. SEM images of other samples with similar damage are shown in Figure \ref{Figure:MEMSXXX}.

\begin{figure}[!htb]
  \centering
  \includegraphics[width=14.5cm]{Figures/C2/Mems_damaged.png}
  \caption{SEM images of two samples after damage from electrical problems. Scale bars, shown at the bottom of the SEM images, are $10 \mu m$}
  \label{Figure:MEMSXXX}
\end{figure}

2 new samples were fabricated on the same membrane. These were the same design but with slightly reduced overall size to ease the fabrication process. A zoomed out SEM image of the membrane is shown in Figure \ref{Figure:MEMSWhole}. The tracks cut in the gold can be seen with the 2 old damaged samples in the center and the other rejected samples. To connect the new samples to milled track in the gold must be bridged. This was done by depositing a small track of platinum using a gas injection system.

\begin{figure}[!htb]
  \centering
  \includegraphics[width=12cm]{Figures/C2/mems whole thing.jpg}
  \caption{Zoomed out SEM image of the samples.}
  \label{Figure:MEMSWhole}
\end{figure}


\subsection{Spectra response of metasurfaces with applied voltage}

Our two new metasurfaces were then observed with a microphotospectrometer, using the same method as in \cite{stictioncontrol}. The aim was to investigate how the spectra are affected by the, effectively, changing structure and pattern of the metasurface. 

In order to capture in more detail, the relevant differences in the spectra, the whole spectrum was collected from $400nm$ to $2000nm$, although for the wavelengths below $600nm$, the spectra are dominated by the absorption of gold. As shown in the following figures, the spectra are rather complex for such zigzag membranes, with the actual resonances being quite broad and does not consist of a single, resonance peak. Indeed, with incoherent illumination from the spectrometer, the broad resonance peak appears to be split, with a dip in the middle. The investigation of this feature was pursued in a separate project and is covered in Chapter 3. Here, for the purpose of the analysis of the change in spectra/resonance due to applied voltage, the comparison between transmission at different voltages was carried out for a wavelength at which the changes in transmission were the largest.

Figures \ref{Figure:S3dry} and \ref{Figure:S3dryzoom} presents the spectra collected for Sample 3, for voltages increasing from $0V$, through $2V$, then $3V$ and back to $0V$.

\begin{figure}[!htb]
  \centering
  \includegraphics[width=14cm]{Figures/C2/Dry_coupling_Sample 3.png}
  \caption{Transmission spectra of Sample 3 metasurface measured at increasing voltage starting from $0V$ to $3.4V$ and then back to $0V$.}
  \label{Figure:S3dry}
\end{figure}

\begin{figure}[!htb]
  \centering
  \includegraphics[width=14cm]{Figures/C2/Dry_coupling_Sample 3 zoom.png}
  \caption{Zoomed in transmission spectra of Sample 3 metasurface measured at increasing voltage starting from $0V$ to $3.4V$ and then back to $0V$.}
  \label{Figure:S3dryzoom}
\end{figure}



As shown in Figure \ref{Figure:S3dryzoom}, the spectra for the initial $0V$ and $2V$ are closely overlapping, with little difference between them, indicating that up to $2V$, the nanobridges are only slightly deformed from their initial state. There is evidence of stronger deformation at $3V$ and then again at $3.4V$, suggesting that mechanical reconfiguration becomes noticeable around that voltage. Finally, reducing voltage to $0V$ makes no obvious difference to the spectra – they remain approximately the same as for $3.4V$, thus confirming the results from the SEM images, that the nanobridges experienced stiction at $3.4V$ and remained attached to each other even if the voltages is switched off.

Figure \ref{Figure:S4dry} shows an example of the same measurement for Sample 4, where a larger range of deformation was observed for voltages from $0V$ to $3.9V$ and then back to $0V$.

\begin{figure}[!htb]
  \centering
  \includegraphics[width=14cm]{Figures/C2/Dry_coupling_Sample 4 zoom.png}
  \caption{Transmission spectra of Sample 4 metasurface measured at increasing voltage starting from $0V$ to $3.9V$ and then back to $0V$.}
  \label{Figure:S4dry}
\end{figure}

The comparison between spectra of the two samples provided some important insight, confirming the need to test multiple samples.

In Sample 3 spectra at $0V$ before and after the voltage was applied were noticeably distinct. The spectra Sample 4 for such case showed a somewhat different trend. While the metasurface does not recover completely to the initial state, the blue and black curves (at $0V$ before and after higher voltage was applied) overlap more closely than in the first sample. Furthermore, the trend in the changes in transmission with applied voltage, increasing to $3.9V$, while evident does not follow the same route as in Sample 3 nor does it follow what was observed in \cite{stictioncontrol}.  

%{\color{cyan}{**Plot additional figure with selected region from 550 to 800 nm - Highlight spectral changes in Figures 2.7 and 2.8**}}


\subsection{SEM images of fabricated metasurfaces actuated with electric field}

Following the measurements using the microphotospectrometer the metasurfaces were viewed again under the SEM to verify that a change had occurred. All of the wires had coupled together on sample 4 but 2 pairs of wires remained unstuck on sample 3. Figure \ref{Figure:SEMappliedV} shows sample 3 with $3V$ applied. The electrical potential can be seen on the wires as a change in brightness. 

\begin{figure}[!htb]
  \centering
  \includegraphics[width=14cm]{Figures/C2/sample3 3V.jpg}
  \caption{Sample 3 with $3V$ applied. Most bridges are coupled except the bottom pair and a pair in the center. Scale bar, shown at the bottom right of the SEM image, is $5 \mu m$.}
  \label{Figure:SEMappliedV}
\end{figure}

As seen in Figure \ref{Figure:SEMappliedV}, most of the nanobridges are in direct contact. The voltage was increased in steps to $3.7 V$ and then switched off. Figure \ref{Figure:SEMcoupling} shows SEM images of one of the unstuck pairs as the voltage was varied. The zigzags can be seen to couple together at $3.7V$ and remain stuck once the voltage was reduced to $0V$.

\begin{figure}[!htb]
  \centering
  \includegraphics[width=12cm]{Figures/C2/SEMstick.PNG}
  \caption{Zoomed in image of a pair of nanobridges as voltage was applied and then removed.} 
  \label{Figure:SEMcoupling}
\end{figure}

This experiment on the pristine metasurface shows that the nanobridges that bore the wires connected to opposite potentials, started to move only at around $3V$ and come into physical contact with each other immediately.  When the bias voltage was withdrawn the nano-brides remained stuck, held together by Van der Waals forces and dielectric charging. That process permanently transforms the pattern of the metamaterial from a single to a, effectively, double-wire zigzag grid {\color{blue}{as shown on Figure \ref{Figure:DryCoupling}c}}, which was also detected optically as an irreversible change in the transmission spectrum of pristine metamaterial samples. Hence, in comparison with \cite{stictioncontrol} and between two samples (3 and 4), it can be concluded that in spite of fabrication aiming to produce exactly the same samples, their response to applied voltage – for example – the voltage that stiction occurs can vary from $2.7V$ to $3.4V$, for example, and the spectral response of such dynamic system is complex and not exactly overlapping for different samples with the same applied voltage.

Although, optical changes due to complete structural switching in a reconfigurable metamaterial can in principle be extremely large, it is of no use if the switching happens once and cannot be reversed. Thus, highlighting once again that stiction is a major reliability issue in many micro and nano-electro-mechanical systems, and it so far has severely limited the application of mechanical tuning in metamaterials.

While applying voltages and measuring spectra, the resistance between nanobridges was also monitored, providing additional data on when the bridges get attached and their resistance changes. 

After testing the metasurface samples and leading to stiction, in the next part of this project LCs were applied to their surface to explore if the nanobridges could be repaired using the elastic forces of the LC.


\subsection{Spectra of zigzag nanowire membrane with liquid crystals and applied voltage}

%The experimental study described in the previous section highlights the need for hybrid metasurface solutions, with materials such as liquid crystals, to prevent the undesired stiction effect.

Sample 3 and Sample 4 were then hybridised with the liquid crystal 5CB following the procedure described earlier. A drop of LC was deposited on a glass substrate, covered with polyimide, a typical alignment layer used in LC cells to ensure uniform arrangement of LCs. The glass substrate was placed on a hot plate, kept there for approximately 15 minutes and thus warmed up to the temperature of $65 ^\circ C$, to induce a phase transition in the LC to the isotropic phase. Subsequently, the substrate was then put together with a metasurface membrane. {\color{blue}{Figure \ref{Figure:S3BA} shows the changes in transmission spectra of sample 3 with the addition of 5CB.}}

{\color{blue}{Spectroscopic results provided most useful insight into the response of the bridges with and without LCs. Ideally, capturing images of the membranes containing organic layers would have been very helpful, but given the nanoscale of the zigzag features, optical microscopy would be of limited value. SEM images, of sufficient resolution and contrast, were not possible to obtain due to technical challenges in capturing images of systems with an organic overlayer.}} 



\begin{figure}[!htb]
  \centering
  \includegraphics[width=14cm]{Figures/C2/S3BA_mod.png}
  \includegraphics[width=14cm]{Figures/C2/S3BB_mod.png}
  \caption{Transmission spectra of sample 3 before and after 5CB added for polarisation parallel (a) and perpendicular (b) to the nanowires.}
  \label{Figure:S3BA}
\end{figure}

\begin{figure}[!htb]
  \centering
  \includegraphics[width=14.5cm]{Figures/C2/S4BAa.png}
  \includegraphics[width=14.5cm]{Figures/C2/S4BAb.png}
  \caption{Transmission spectra of sample 4 before and after 5CB added for polarisation parallel (a) and perpendicular (b) to the nanowires.}
  \label{Figure:S4BA}
\end{figure}

{\color{blue}{Figure \ref{Figure:S4BA} shows the changes in transmission spectra of sample 4 with the addition of 5CB.}}


5CB remained as a LC of choice. Although there are other liquid crystals that have higher elastic constants \cite{brouckaert2022nanoparticle}, so in principle other LCs could provide a stronger restoring force. 5CB elastic constants are $K_1 = 6 pN$ and $K_3 = 9 pN$ while another, easily available liquid crystal, E7, has $K_1 = 10.7 pN$ and $K_3 = 16.2 pN$. However, E7 has relatively high phase transition temperature, $58 ^\circ C$, so realising isotropic-nematic transition as shown in \cite{stictioncontrol} for 5CB (with its nematic to isotropic phase transition temperature of $35.2 ^\circ C$) would be more difficult to realise. Furthermore, another important parameter for infiltrating small gaps between nanobridges is viscosity. 5CB has rotational viscosity of approximately $92.5 m.Pa.s$, while E7 has viscosity approximately 2.5 times higher, namely $232.6 m.Pa.s$ \cite{cui1999temperature}.  Thus, 5CB is more suited as a tool to detach stuck nanobridges. The viscosity of 5CB decreases to approximately $20 m.Pa.s$ in the isotropic phase, hence the LC was heated to reach this phase, thus promoting more strongly the infiltration of the gaps between the nanobridges. The elastic constants are also reduced in the isotropic phase, all approaching $2pN$. Hence, the effect observed in Figure \ref{Figure:LCcoupling}, where voltage was ramped up and down with LC being in the isotropic phase and this state, there was a hysteresis in transmission, indicating that the nanobridges remained stuck. The small elastic forces of 5CB in the isotropic phase were not able to prevent stiction, but when cooled to the nematic phase, at room temperature, the bridges were unstuck.

The same procedure was undertaken to test the samples as in \cite{stictioncontrol} and in the case of pristine samples, as shown in the previous section, except as mentioned earlier, the samples could not be observed using the SEM as having an organic layer of LCs on top, the image of the underlying structure could not be captured with a technique like SEM. The samples were therefore only tested using a microphotospectrometer as before. As in the previous study, due to the presence of the LC, the transmission resonance of the sample was red-shifted by approximately $200nm$, as 

%The LC influence, preventing sticking, is due to an increase in the restoring force acting on the nanowires. The additional force comes from the elastic bend and splay deformation of the LC in the area between and directly above the oppositely charged wires. 

As stated earlier, following the results shown in Figure \ref{Figure:LCcoupling}, the challenge was whether a metasurfaces, with stuck nanobridges, could be repaired by the subsequent application of liquid crystals. This was tested on Sample 3 and Sample 4, with stuck nanobridges and LCs applied to their surface after stiction occurred. The spectra were then collected to see if returning to $0V$, following application of voltages above $3V$, leads to close overlap with the spectrum recorded for a pristine sample (and accounting for a phase shift due to LC layer).

\newpage

\begin{figure}[!htb]
  \centering
  \includegraphics[width=14cm]{Figures/C2/LCramps_a.png} \\
  \includegraphics[width=14cm]{Figures/C2/LCramps_b.png} \\
  \caption{Transmission at $1 \mu m$ as the voltage is varied with 5CB for polarisation parallel to the nanowires. (a) Sample 3 and (b) Sample 4.}
  \label{Figure:LCramps}
\end{figure}


The preliminary results, shown in Figure \ref{Figure:LCramps} were promising. Both samples show similar paths as the voltage was varied. {\color{blue}{The relatively flat response in the level of transmission, measured at the resonant wavelength, from 0V up to approximately 5V indicates that the core membrane structure remained the same in that range. The transmission for neither of the samples returned to its starting point once the voltage (10V) was removed. It is hard to tell whether this change is from the increased mobility of the bridges, once released, or whether we are seeing changes due to the liquid crystal present. As the change is irreversible, one explanation could be the LC being worked into the metasurface and penetrating further as the voltage was cycled.}}

The differences in spectra of the pristine samples 3 and 4 as they were coupled, indicated their differences, stemming from their different stiffness and their varying dependence with increasing voltage. Therefore, it was decided that several additional samples, had to be fabricated in order to fully understand the effect. Unfortunately, in spite of successful fabrication of the previous samples, all the new metasurfaces kept failing due to persistent short circuit problems, with the issue persisting for months in spite of multiple attempts. One of possible reasons was a different supply of gold material (as the old source was no longer available) or contamination from the FIB. The attempts with fabrication were paused and the closure of cleanrooms due to Covid prevented any later experiments.

\newpage

\section{Conclusions}

The results shown in this chapter extended the earlier work aiming to implement tuneablity in metamaterials as well as offering an anti-stiction solution for NEMS/MEMS, multifunctional sensors and switches. Liquid crystals were chosen to achieve this functionality and given a wide range of the structural transitions exhibited by these materials at the nano-scale, smart and adaptable nano-systems and meta-devices could be envisaged.

As shown in the experimental section, the work carried out for this thesis, confirmed in new samples that LCs, when coupled to the fabric of a re-configurable photonic metamaterial, can efficiently modify the behaviour of nanoscopic mechanical actuators. 

SEM images and spectra were captured from two different nanobridge metasurface samples and their analysis showed that stiction observed in SEM images of the pristine samples can also be detected through the observed spectra. The optical spectra capture the changes in the structure of the nanobridges, where in places it changes from a single zigzag wire to a double zigzag, where the nanobridges end up attached to each other. The comparison of the two metasurface samples, although designed to be the same, revealed that while they both experienced stiction, the effect started at different voltages and the trends observed in their spectra with increasing voltage were also somewhat different. {\color{blue}{Further investigation could include measurements with AC voltage at different frequencies to explore the effect on the spectra and on the voltage when stiction occurs. In addition, different polarisation states of the incident light, such as circular for example, could be included, following the experiments presented here with linearly polarised light parallel or perpendicular to the zigzag nanowires.}}

{\color{blue}{*** Make better links between chapters - {\textit{Linking, short paragraphs added to all chapters ***}}}}

{\color{blue}{The results and analysis shown in this chapter demonstrate that nanostructured metasurfaces remain an attractive platform and test bed to explore both optical and mechanical effects, in spite of the challenging fabrication techniques required. Their structure is well suited to integrate organic materials, such as LCs, to investigate how the dielectric, optical and elastic properties of the organic layer can affect the response and the performance. This study of a suspended metasurface was followed by a related project which explored the optical characteristics of the zigzag metasurface geometry on a static glass substrate, in particular their response to light with different levels of coherence.}}