%% ----------------------------------------------------------------
%% MOKE.tex
%% ----------------------------------------------------------------
\chapter{Specular optical activity with metasurfaces} \label{Chapter:MOKE}

Specular optical activity effect manifests itself as rotation of light polarisation upon reflection from chiral materials and diffusive scattering from chiral liquids. It is an extremely weak phenomenon which has been rarely studied and reported in literature or, indeed, used in practical applications. One exception was the strong specular optical activity observed at microwave frequencies for oblique incidence of an incident beam on a reflective planar metamaterial \cite{plum2016specular}. However, the demonstration of the effect in the visible domain has remained difficult to achieve mainly due to the challenging nanoscale fabrication.

%In this chapter, first experimental demonstration of specular optical activity at visible wavelengths is shown and discussed. It is shown that specular optical activity can be enhanced using a ? **

The results show a strong effect from a single reflection from our nano-structured non-magnetic metal films, so called metasurfaces, where it mimics longitudinal magneto-optical Kerr effect. While the magneto-optic Kerr effect is a well-known phenomenon of rotating light polarisation on reflection and is commonly used to characterise magnetic materials, the new, subtle effect explored here investigates the contribution to polarisation rotation from nanostructured metallic films that are not magnetic themselves.

\section{Optical activity}

{\color{blue}{***Comment about optical activity from materials such as CLCs ***}}

There are many examples of materials which have the ability to rotate the polarisation of light. This effect is called optical activity and is usually observed from the transmission of linearly polarised light through structurally chiral materials, such as quartz crystals or solutions of chiral molecules such as sugars. {\color{blue}{Optical activity is also present in some liquid crystals, mainly in cholesteric liquid crystals that form a helical order with their molecules. Their spiralling structure is present with the average direction of the molecules twisting around an axis perpendicular to the long molecular axis. Incident, linearly polarised light is rotated by such helix and if its pitch is comparable to the wavelength, then reflected light of a single wavelength can be observed. The cholesteric pitch, and thus the wavelength of the reflected light can be changed with temperature, where the pitch decreases for increasing temperature. Temperature was therefore used from early on to tune the response of chiral systems and they found applications in thermometers, guest-host colour displays and lasers \cite{sym6020444}.}}

%Such optically active materials are typically chiral and linearly polarised light incident on them, while remaining linearly polarised, experienced polarisation rotation.

Chirality can be expressed as asymmetry between the refractive indices for right and left-hand circular polarised light ($\Delta n$), so the light polarisation undergoes optical rotation by an angle determined by

\begin{equation}
    \Delta \phi = \frac{\pi L \Delta n}{\lambda} 
\end{equation}

where L is the thickness of the medium and $\lambda$ is the wavelength of incident light \cite{pedrotti2017introduction}.

If in a medium the absorption coefficients for the right and left-hand circular polarisations are different, the effect called circular dichroism \cite{kauranen2008polarization}, optical activity also takes place.

Manipulation of light polarisation in bulk metamaterials has been extensively explored over the past several years \cite{kasap2017springer}. For example, photonic metamaterials were fabricated, consisting of a lattice of submicron gold helices, which acted as a broadband circular polariser \cite{gansel2009gold}.  Other metamaterial designs of chiral metamolecules included sets of two identical, twisted planar metallic coils, crosses and rosettes \cite{svirko2001layered}. 

Exploring metasurfaces for optical activity offers a clear advantage in terms of more straightforward fabrication. Indeed, such planar metamaterials, when homogeneously patterned, act on light polarisation \cite{hao2007manipulating}, but their effect is not confined to its rotation and more complex polarisation patterns can emerge. The underlying mechanisms \cite{maradudin2011structured} are not just stemming from the asymmetry of refractive indices or absorption and the medium chirality in its structure is no longer required to observe asymmetric light transmission. 

While polarisation rotation is often described considering transmission through an optically active medium (as in Equation 4.1), for planar metamaterials, the rotation is due to reflection from the surface. Upon reflection from a chiral material the polarisation of light will be rotated by a much smaller amount when compared to transmission through the material \cite{silverman1992multiple}. This is due to the light only interacting with a few atomic layers at the surface, in contrast to propagating through the bulk of the material.

\section{Polarisation control with metasurfaces}

Giant specular optical activity from a single reflection off a metasurface has been demonstrated in the microwave region of the spectrum \cite{plum2016specular,plum2009metamaterials,plum2008optical}. The concept exploited an array of oriented, achiral metamolecules in combination with particular direction of propagation of incident light, such as oblique incidence.
%**[3]**

The effect was demonstrated on metasurfaces with arrays of asymmetric, split-ring metamolecules, which was an example of a unit without two-fold rotational symmetry, that together with together with oblique incidence of an illuminating beam forms a chiral system. 

\begin{figure}[!htb]
  \centering
  \includegraphics[width=12cm]{Figures/C4/MOKE_MW_theory_pic.jpg}
  \caption{(a) - Metamolecule with fictitious magnetic currents and resultant fictitious electric and magnetic dipoles. (b) - Interaction at normal incidence \cite{plum2016specular}.}
  \label{Figure:MW_vector_pic}
\end{figure}

Figure \ref{Figure:MW_vector_pic} presents a metasurface consisting of an array of double split circular slits \cite{plum2016specular}. At the metamolecule level the optical activity is due to simultaneously excited electric and magnetic dipoles in the structure, just as with conventional optical activity. These dipoles are the result of fictitious magnetic currents oscillating along the length of the slits. The fictitious currents oscillate with a phase difference dependant on the frequency of incident radiation and can oscillate in two modes, symmetric and anti-symmetric. The symmetric mode where they oscillate together results in a fictitious magnetic dipole in the plane of the surface while the anti-symmetric mode results in a fictitious electric dipole normal to the surface. This is shown in Figure \ref{Figure:MW_vector_pic}(a). When both dipoles radiate differently polarised fields in the direction of the reflected wave certain effects can be observed. At normal incidence, shown in Figure \ref{Figure:MW_vector_pic}(b), only the magnetic dipole can contribute to the reflected wave so there is no effect. Whereas at non-normal incidence, shown in Figure \ref{Figure:MW_vector_pic}(c), both dipoles contribute leading to the polarisation state of the reflected radiation being altered, except when the plane of incidence is parallel to the plane of symmetry of the structures. Therefore, at other than normal incident angles, both dipoles can contribute which leads to the polarisation state being altered. The change is due to the circular dichroism and circular birefringence exhibited by the metasurface. In general, the contribution from each of these effects varies with the frequency of the incident radiation. 

In summary, optical activity occurs when both dipoles radiate differently polarised fields in the direction of the reflected wave

Exploring this effect with the microwaves Plum at al. \cite{plum2016specular}, constructed a sample consisting of $1mm$ wide slits cut into a $1mm$ thick aluminium plate. Each metamolecule comprised of a $15 \times 15mm^2$ unit cell with a $1mm$ wide circular slit, of $6mm$ radius, split at two positions, leaving two arcs: one subtending an angle of $140 ^\circ$ and the other $160 ^\circ$.

\begin{figure}[!htb]
  \centering
  \includegraphics[width=6cm]{Figures/C4/MW_MS_design.png}
  \caption{Design of a metasurface for observing optical activity at microwave frequencies \cite{plum2016specular}.}
  \label{Figure:MW_design}
\end{figure}

The change to the polarisation state is caused by the circular dichroism and circular birefringence of the surface. Circular dichroism is the difference in reflectivity between left and right circularly polarised radiation whereas circular birefringence is the difference in the phases of the reflected components. 

Characterising specular activity, the metasurface involved considering the linearly polarised, reflected light as a combination of left- and right-hand polarised light. Following the analysis outlined in \cite{plum2016specular}, in the first step, the electric field of the reflected light $E^r$:

\begin{equation}
    E_i^r = r_{ij} E_j^{inc}
\end{equation}

is related to the incident light $E^{inc}$ through right-handed (RCP, $i=+$) and left-handed (LCP, $i=-$) circularly polarised light components. The reflection coefficient is defined as:

\begin{equation}
    R_{ij} = |r_{ij}|^2
\end{equation}

Specular circular dichroism, which can be also described as circular differential reflectance $\Delta R$ is defined as the difference between the reflection coefficients between incident RCP and LCP waves. Given that on reflection from a homogenous surface, the handedness of circularly polarised waves is reversed, specular circular dichroism can thus be calculated from:

\begin{equation}
    \Delta R = R_{-+} - R_{+-}
\end{equation}

Next, angle of rotation $\Delta \theta$ experienced by an incident linearly polarised wave upon reflection, the  specular circular birefringence effect, can be defined as:

\begin{equation}
    \Delta \theta = \frac{1}{2}\left( arg(r_{-+}) - arg(r_{+-})\right)
\end{equation}

\begin{figure}[!htb]
  \centering
  \includegraphics[width=10cm]{Figures/C4/MW_graphs.png}
  \caption{Reflection spectra for left and right polarisations \cite{plum2016specular}.}
  \label{Figure:MW_graphs}
\end{figure}

Figure \ref{Figure:MW_graphs} presents the main experimental results on specular reflection spectra of a metasurface for an angle of incidence of $30 ^\circ$. This particular metasurface has a resonance at approximately  $9.4 GHz$. As Figure \ref{Figure:MW_graphs}(a) shows, reflection coefficients are different for RCP and LCP components, thus from these results the presence, as well as the magnitude, of specular circular dichroism can be extracted. The phases are also different and hence specular circular birefringence was also detected.

The most interesting is the narrow band around $9.4GHz$, at a $30 ^\circ$ incidence angle, this double split ring metasurface exhibited a large circular birefringence, but no circular dichroism meaning the surface acts as a pure polarisation rotator. Using this metasurface, Plum et al. \cite{plum2016specular} demonstrated a $17 ^\circ$ polarisation rotation from a single refection at $9.4GHz$. 

\section{Designs of achiral Metasurface for Optical Activity upon Reflection}

For this thesis, in order to explore this effect at optical wavelengths new metasurfaces were explored. This involved the fabrication of such nano-structured metal surfaces featuring a specially design resonant achiral nano-pattern. The metamolecules of this metasurface consist of a pair of slits of different length residing in a square $250 \times 250nm$ unit cell, a simplified design for the ease of fabrication. Samples with various sizes of slits (ranging from $50nm$ to $200nm$) were fabricated. Reference samples with single slits and double slits of equal length were also fabricated. The metal for the samples was changed from aluminium, used in the microwave regime, to gold to take advantage of its plasmonic properties. The slits were milled, using a focused ion beam, into an $80nm$ thick gold film that had been deposited on a fused quartz substrate. Each sample consisted of $80 \times 80$ metamolecules resulting in a $20 \times 20 \mu m$ active region.

The schematic design for the new metasurface is shown in Figure 4.4 with typical dimensions indicated.

\begin{figure}[!htb]
  \centering
  \includegraphics[width=13cm]{Figures/C4/Asym designs.jpg}
  \caption{Design of the metasurface for optical activity at optical wavelengths.}
  \label{Figure:asymdesign}
\end{figure}

Figures \ref{Figure:asymdesign} and \ref{Figure:MOKESEM} show that an individual metamolecule consists of a pair of slits, each of different length. Two main metasurfaces designs were therefore considered, both achiral and with the same sub-wavelength period. One had an asymmetric design with two slits of different length per unit cell and the second, reference metasurface had a symmetric design featuring a single slit per unit cell.
%The small and large slits are $50nm$ and $150nm$ respectively. The slits were milled into an $80nm$ thick gold film, sputtered onto a fused quartz substrate, using a focused ion beam. 
Samples consisting of single and double slits of the same length were fabricated to act as a reference.

\begin{figure}[!htb]
  \centering
  \includegraphics[width=14.5cm]{Figures/C4/MokeSEM.png}
  \caption{SEM image of symmetric and asymmetric designs. {\color{blue}{The scale bars are indicated at the bottom of each panel, namely 1 $\mu$m for the a) panel on the left and 3 $\mu$m for the b) panel on the right}}}
  \label{Figure:MOKESEM}
\end{figure}

%Figure \ref{MOKESEM}(b) presents another example of images of nanoslits samples, showing a general view of the samples (Figure 4.6a), asymmetric design (Figure 4.6b) as well as a symmetric double slit design (Figure 4.6c).


\section{Experiments with optically active metasurface system}

{\color{blue}{**NanoMOKE3 details and design, Background field, Why use NanoMOKE3? **Advantages and disadvantages***}}

\medskip

{\color{blue}{The metasurfaces were investigated using a magneto-optical Kerr effect microscope, the NanoMOKE3 from Durham Magneto Optics Ltd. It provides the ability to view samples simultaneously in reflection mode and polarisation rotation mode (Kerr signal). The core principles behind the NanoMOKE3 measurement and imaging techniques were developed in 2003, to provide high sensitivity measurements of nanostructures and capture maps of magnetic domains on the surface of samples \cite{Allwood_2003}. The instrument is a very powerful tool, but its main purpose is the investigation of magnetic materials and as it is an all-in-one system, is not particularly flexible. For example, it is not possible to freely adjust the angle of incidence which would be an interesting parameter to explore for the different slit designs considered in this work. Nevertheless, the ease of access to this instrument and the nature of the project pursued as part of this thesis, namely providing an initial proof of concept, justified the use of the NanoMOKE3.}}

\begin{figure}[!htb]
  \centering
  \includegraphics[width=10cm]{Figures/C4/NanoMOKE_setup.jpg}
  \caption{{\color{blue}{Schematic diagram of MOKE instrument with the main  optical components indicated: neutral density filter (ND),  beam expander (BE), polariser (Pol), beam splitter (BS), lens (L), quarter-wave plate $\lambda$ /4; variable neutral density filter (VarND), photodiode detector (PD1, PD2) to collect the Kerr and reference signals, respectively (from \cite{Allwood_2003})}}} 
  \label{Figure:NanoMOKE_setup}
\end{figure}


{\color{blue}{Figure \ref{Figure:NanoMOKE_setup} presents a schematic diagram of the design and the main optical components. 
A linearly polarised beam is reflected off the sample and in the case of a passive surface, the reflected light remains polarised in the same plane as the incident beam. If optical activity is present, the light becomes elliptically polarised and with its major axis rotated from its initial incident polarisation direction. This is usually expressed as the rotation of the major axis with respect to the plane of polarisation of the incident light beam and the ellipticity factor, so called Kerr rotation and Kerr ellipticity, respectively \cite{Lin_2012}.

On reflection from the sample, the light passes through the quarter-wave plate and then the analyser, namely a Glan–Taylor polarising analyser, which directs the transmitted and reflected beams to be detected by the photodiodes. The main role of this combination of quarter-waveplate and analyser, both being adjustable, is to calibrate the system. For example, through the rotation of the quarter-waveplate and adjusting the position of the analyser, its fast axis can be set to match the polarisation of the reflected beam and thus null the effect of rotation of that axis. The settings of the polarisers/analyser and the waveplate are important for the correct offsetting of any depolarisation, non-Kerr rotation or ellipticity that contribute to the signal \cite{Allwood_2003}.
A background field can come from the variation of the incidence angles of the light beam reflecting from the surface of the sample and its micro or nanostructure. The inclusion of the neutral density filters also allows for setting the intensities of the Kerr and reference signal to be comparable for the ease of analysing the results. 

The main goal of this experimental study, however, was not the precise determination of the rotation of polarisation, but exploring if the effect can be detected from the asymmetric slits and if so, to provide initial data on the size and the geometry of the samples that yield the strongest effect.}} 
{\color{blue}{In the results presented here, the Kerr microscope measured polarisation rotation of linearly polarised light, at the wavelength of $660 nm$, reflected off the samples at $30 ^\circ$ from the normal to their surface, forming the Kerr signal. Both reflection and Kerr rotation modes were collected.}}

Figure \ref{Figure:nanoMOKE} presents a photograph of the NanoMOKE3 set up and the arrangement for the incident and the reflected beam.

\begin{figure}[!htb]
  \centering
  \includegraphics[width=14.5cm]{Figures/C4/NanoMOKE pics.png}
  \caption{Pictures of the NanoMOKE3 microscope used.}
  \label{Figure:nanoMOKE}
\end{figure}

The geometry of the incident and the reflected beams are illustrated on Figure \ref{Figure:MOKEangle}, indicating linearly polarised $660nm$ light incident on the sample and then collected for analysis.

\begin{figure}[!htb]
  \centering
  \includegraphics[width=14.5cm]{Figures/C4/incident_angle_MOKE.png}
  \caption{Diagrams showing the angle of incidence (a) and the angle of the plane of incidence with respect to the samples (b). {\color{blue}{The size of each unit, a set of two asymmetric slits, is 250 nm.}}}.
  \label{Figure:MOKEangle}
\end{figure}

A series of images were collected and analysed. An example of a raw imaged collected is shown on Figure \ref{Figure:MOKEsoft}. As shown, the microscope can image the surface in reflection and polarisation rotation modes. Images were taken at regular intervals as the samples were rotated through $360 ^\circ$ and then data was then extracted from these images.

\begin{figure}[!htb]
  \centering
  \includegraphics[width=8cm]{Figures/C4/MOKEsoft.png}
  \caption{Example of reflection image output. \color{blue}{The colour bar represents the percentage of reflection. The line at the bottom is the scale bar indicating the size of the area probed.}}
  \label{Figure:MOKEsoft}
\end{figure}


\section{Main experimental results specular optical activity}

The experiments were carried out on several sets of samples, with slits of different dimensions and design as shown on SEM images in the previous section. Multiple measurements were taken to detect and confirm the effect as well as check the repeatability. This section presents the main results with the measurements taken shortly after fabrication and they demonstrate the strength of the effect, while the following section includes examples of supplementary measurements.  

Multiple experiments were carried out with a NanoMOKE3 microscope at Dr Gavin Stenning’s, Materials Characterisation Lab at the Rutherford Appleton Laboratories. Another set of experiments undertaken for this thesis was carried out at the University of Cambridge using the same NanoMOKE instrument, which additionally included an extra magnifying optics. 

Each sample was mounted on a holder, as shown in Figure \ref{Figure:nanoMOKE} that allowed it to be rotated while keeping the same incidence angle. During imaging the sample were rotated in their plane to extract the contribution of the metamaterial anisotropy to the Kerr signal. Therefore, the samples were rotated with respect to the plane of incidence keeping the incidence angle constant. Reflectance and Kerr rotation images were taken for each angle. From these images the Kerr signal from the sample could be determined. 

\begin{figure}[!htb]
  \centering
  \includegraphics[width=13cm]{Figures/C4/Ref designs.jpg}
  \caption{Design of the reference metasurfaces.}
  \label{Figure:REFdesign}
\end{figure}

\begin{figure}[!htb]
  \centering
  \includegraphics[width=14cm]{Figures/C4/KerrSigSym.png}
 \caption{Measured Kerr signal against angle between the plane of incidence and the sample slits for single slit (SS) and double slit (DS) samples.}
\label{Figure:KerrSigSym}
\end{figure}

First set of data, shown on Figure {\ref{Figure:KerrSigSym}} presents results collected for the reference samples with either single slits (SS) or with different sizes of double slits (DS) – all symmetric samples. As expected from the experiments, and the analysis, in the microwave regime, standard sine-like signal was detected, without any additional prominent features. The origin of the difference in their amplitudes and in the smoothness of the curves is likely to originate from the experimental procedure and the precision of mounting the sample exactly in the middle of the holder to ensure precise rotation. This was difficult to achieve, given some degree of undesired movement of the holder while rotating. Such technical issues are most likely responsible for the differences in those symmetric curves, especially for the $100 nm$ double slits results.

{\color{blue}{*** Why DS100 flipped - Explanation added ***}}  

{\color{blue}{As can be observed on figure \ref{Figure:KerrSigSym}, the reference curve for the $100 nm$ DS case is $180 ^\circ$ out of phase with the other metasurfaces. This is likely due to an experimental error that was not realised during the measurement, stemming from the calibration of the machine. This reference plot was nevertheless included to show its regular and smooth shape, as expected}} 

The symmetric samples were then replaced by three different asymmetric samples ones and the results are presented on Figure \ref{Figure:KerrAsym}.

\begin{figure}[!htb]
  \centering
  \includegraphics[width=14cm]{Figures/C4/KerrAsym1.png}
  \caption{Measured Kerr signal against angle between the plane of incidence and the sample slits asymmetric samples.}
  \label{Figure:KerrAsym}
\end{figure}

It is also helpful to compare on the same graph the Kerr signal detected for an asymmetric sample with respect to the signal for a symmetric sample. Figure \ref{Figure:CLEOMOKE} presents the two signals, with the region where the optical activity was detected indicated by a dashed, light red line.

\begin{figure}[!htb]
  \centering
  \includegraphics[width=14cm]{Figures/C4/cleoMOKE.png}
  \caption{Measured Kerr signal compared between active and reference samples.}
  \label{Figure:CLEOMOKE}
\end{figure}

%Figure 5.3 shows Kerr signal measured for different orientations of metasurfaces with respect to the plane of incidence, thus demonstrating how Kerr signal varies with the rotated angle.

As shown on the figure, the reference sample shows a sinusoidal like dependence, whereas the asymmetric double slit sample shows more features, indicating potential optical activity. This typical sinusoidal variation of the Kerr signal for the symmetric metasurface originates from its inherent structural anisotropy of the design. The same response was observed for all of the single and double slit reference samples as well as the asymmetric samples which are not resonant with the wavelength of the laser. This background effect only varied in amplitude for the different samples.

This is sinusoidal variation is also seen for all the asymmetric slits, as shown on Figure \ref{Figure:KerrAsym}, but it is accompanied by additional features, which can be regarded as modulation from the polarisation rotation. Importantly this modulation reverses when the sample is rotated through $180 ^\circ$, which is characteristic of the specular activity effect, which was the aim of this experiment. 

The behaviour of the asymmetric metasurface is more complex, with two pronounced asymmetric features in the Kerr signal (amplitude $~1 ^\circ$) located at $90 ^\circ$ and $270 ^\circ$ superimposed on the sinusoidal profile, which correspond to optical activity of opposite signs. They correspond to specular optical activity exhibited by the sample when the plane of incidence becomes parallel to the slits, with the strength of the effect of around $1 ^\circ$.

The results obtained for the three sizes of the asymmetric slits show that the specular optical activity was the strongest for the design that had the largest difference between the two slits forming a metamolecule, namely $50/150nm$ (red curve on Figure \ref{Figure:KerrAsym} and blue curve on Figure \ref{Figure:CLEOMOKE}). For the two other asymmetric in size slits, the effect was not as strong. For these two other slits, with $50/100 nm$ and $50/120 nm$, some indication of specular optical cavity could be detected inspecting the asymmetry of the signal – the difference in the slope of the leading and the trailing edge of the sine-like curve (green and blue curve in Figure \ref{Figure:KerrAsym}). Such asymmetry in the signal was not observed for the symmetric slits. The effect was expected to be the strongest for the largest difference in the two slit sizes, such as $50/150 nm$, as indeed observed.  

\section{Robustness and long-term stability of symmetric and asymmetric slit metasurfaces}

This section provides a more detailed account of the experimental work carried out, with the aim of confirming repeatability and robustness of the observed effect. The limited access to the NanoMOKE instruments as well as unavoidable delays, including those caused by maintenance and repairs, meant that the measurements presented here were collected over three years. Due to this, in some cases the samples were tested soon after their fabrication and then re-tested several months later. 
{\color{blue}{Care was taken to store the nanostructured gold samples in a suitable environment but despite this, possible deterioration of their quality and thus performance was expected.}}

New sets of samples were also fabricated, and given the challenging nanofabrication requirements, their quality was not always sufficient to use in experiments or detect such subtle effect as specular optical activity. The following figures capture the results from each round of experiments. 

Two sets of samples were initially fabricated and called Set 2 containing asymmetric samples was assessed via SEM as having good quality. Previously Figure \ref{Figure:asymdesign} showed the design of the three asymmetric slits. Set 2 results were included in the previous section already, but shown here for completeness and comparison. As described before, they had the structures milled from gold mounted on a fused quartz substrate. The unit cell was $250 \times 250nm$ unit and the total area was $20 \times 20 \mu m$.

Figure \ref{Figure:RalCamb} show the comparison of the Kerr signal dependence on rotation angle for measurements taken shortly after fabrication at RAL NanoMOKE3 (Figure \ref{Figure:RalCamb}(a)) and then after three months using Cambridge NanoMOKE3 instrument (Figure \ref{Figure:RalCamb}(b)). Only the most promising, $50/150 nm$ sample, was tested in that second instrument to investigate reliability.

\begin{figure}[!htb]
  \centering
  \includegraphics[width=12cm]{Figures/C4/CambA.jpg}
  \includegraphics[width=12cm]{Figures/C4/CambB.jpg}
  \caption{(a) Initial measurement with the setup at RAL, (b) Measurement three months later using the Cambridge setup. {\color{blue}{***Increased size***}}}
  \label{Figure:RalCamb}
\end{figure}

In spite of using two different instruments and the passage of time the presence of the additional features/modulation can be observed in both experiments, thus confirming repeatability. The use of additional optics to focus the signal, available with the Cambridge NanoMOKE3 was also tried in this measurement, but this additional element did not bring any significant improvements in the resolution achieved.  

For calibration and as an additional reference, a Kerr signal was collected for the incident light polarised along the perpendicular direction, namely s-polarisation on the $50/150 nm$ Set 2 slits. 

\begin{figure}[!htb]
  \centering
  \includegraphics[width=12cm]{Figures/C4/sPOL.png}
  \caption{Kerr signal as sample was rotated for incident s-polarisation.}
  \label{Figure:SPOL}
\end{figure}

No specular optical activity was expected and, indeed, none was observed, as shown on Figure \ref{Figure:SPOL}. This experiment was carried out after the measurement of Kerr signal for p-polarisation with the Cambridge NanoMOKE3 for the same set of $50/150 nm$ slits (Figure \ref{Figure:RalCamb}(b)). The signal in Figure \ref{Figure:SPOL} shows a regular sine-like dependence, similar to the traces measured for the symmetric cells. This experiment on polarisation dependence provided an additional argument on the specular optical activity being the source of the additional features as detected and shown in Figure \ref{Figure:RalCamb}.

Figure \ref{Figure:720k} shows the follow-on measurements on the same Set 2 taken 17 months after the original measurement of Kerr signal. The experiments were carried out with the RAL NanoMOKE3. The experiment conducted after 17 months also included the measurements for a larger range of angles, namely from $0 ^\circ$ to $720 ^\circ$. 

\begin{figure}[!htb]
  \centering
  \includegraphics[width=14cm]{Figures/C4/720Kerr.png}
  \caption{Kerr signal as sample was rotated.}
  \label{Figure:720k}
\end{figure}

Capturing the signal over this large range of angles means that the details of the additional features are less visible, even for the $50/150 nm$ sample (green curve), but nevertheless, their presence was detected, thus again, confirming the robustness of the samples.

In parallel with the investigation of the asymmetric slits, similar long term stability tests were carried out for the symmetric slits. Figure 5.8 presents the main design of the symmetric slits, called Set 3.

The symmetric samples were fabricated together with the asymmetric ones, again milling their nanostructure in gold, supported by a quartz substrate. The metamolecules had unit cells size of $250 \times 250nm$ and the total area was $20 \times 20 \mu m$. 

Figure \ref{Figure:720REF} shows the results of Kerr signal measured after 17 months. When compared to Figure \ref{Figure:KerrSigSym} in both cases featureless sine-like dependence with respect to the rotation angle was measured, as expected. 

\begin{figure}[!htb]
  \centering
  \includegraphics[width=14cm]{Figures/C4/720KerrRef.png}
  \caption{Kerr signal from reference samples as they were rotated.}
  \label{Figure:720REF}
\end{figure}

%For completeness, figure 6.0 presents a selection of images collected from Cambridge NanoMOKE3 measurements, taken three months after fabrication.

%**Kerr signal normalised pics**

In the next stage of the experimental work, new metasurfaces were fabricated to explore if the effect could be enhanced with improving further the quality and the precision of the slit shapes. The same design and size as the most promising sample explored before was fabricated. This challenging fabrication process produced one set that was deemed to have good quality, namely one set of symmetric $50/150 nm$ slits as well as $150 nm$ symmetric double slits, as seen from their SEM images, shown on Figure \ref{Figure:pairDES}.

\begin{figure}[!htb]
  \centering
  \includegraphics[width=12cm]{Figures/C4/Pair design.jpg}
  \caption{Active and reference sample pair SEM image. {\color{blue}{***Scale bars added***.}}}
  \label{Figure:pairDES}
\end{figure}

The fabrication of the samples took place 27 months after the initial fabrication. As seen from Figure \ref{Figure:pairDES}, the SEM images indicated good quality and correct size of the slits. Kerr signal experiments were then carried out using RAL NanoMOKE3, following the same procedure. Two sessions scheduled over a period of seven weeks produced the plots shown in Figures \ref{Figure:pairRESULTS}, each session consisting of at least two sets of measurements. Unfortunately, the signal detected from the asymmetric samples was dominated by sine-like dependence, similar to the symmetric samples, thus not showing any obvious features originating from the specular optical activity. 

\begin{figure}[!htb]
  \centering
  \includegraphics[width=12cm]{Figures/C4/pairRESULTS1.png}
  \includegraphics[width=12cm]{Figures/C4/pairRESULTS2.png}
  \caption{Kerr signal from 2 pairs of samples as they were rotated. {\color{blue}{***Made larger and colours fixed***}}}
  \label{Figure:pairRESULTS}
\end{figure}

The Kerr signal for the asymmetric slit sample, while not showing in such detail the additional features to the extent observed for the original Set 2, does not follow the regular, symmetric angle dependence as detected for the symmetric double slit sample. The leading and the trailing edge of the asymmetric slits Kerr signal are different, again indicating the influence of specular optical activity.

The repeated tests did not lead to resolving in more detail this difference between the two edges of the signal. It was also not possible to achieve a stronger indication of the specular optical activity effect. Inspecting the results from several experimental attempts confirmed that the precision of alignment was extremely crucial as well as the precise collimation of the beam. Instruments such as NanoMOKE3 are intended for testing other types of materials, such as larger samples ferromagnetics, so achieving precise alignment of the light source on a relatively, small sample proved very challenging as well as the position of the detector.

The incidence angle was also limited by the instruments constraints, with the option of just two incidence angles, namely $30 ^\circ$ and $45 ^\circ$.  Hence, it was not possible to optimise the incidence angle to achieve a stronger signal.

\section{Conclusions}

{\color{blue}{*** Add more detail - done ***}}

Specular optical activity is generally extremely weak, especially in the visible domain. This subtle effect was detected as the contribution to polarisation rotation coming from nanostructured metallic films that are not magnetic themselves and no magnetic field was present. Such specular optical activity in the visible part of the spectrum was shown as part of this thesis, for the first time to the best of our knowledge, present for a single reflection from nano-structured achiral metal surfaces.

%Here strong specular optical activity at the wavelength of $660nm$ achiral non-magnetic metasurfaces featuring nano-scale periodic slit patterns milled into a gold film. The effect measured was compared with the signal from reference, symmetric samples, where specular optical activity was not expected and, indeed, not detected.

The originally fabricated set of $50/150nm$ asymmetric samples produced the strongest evidence for specular optical activity, with the measurements being repeatable after three months. However, further tests revealed the issues with the long term stability of the samples as well as unknown contamination of the samples during nanofabrication which affected their performance.

{\color{blue}{This demonstration of principle could be followed by further experiments as well as simulations to extract more quantitative estimates on the magnitude of the optical activity observed as well as to potentially increase the effect. Further extension, in line with the other project carried out in this thesis, is to consider integrating the structure with liquid crystal chiral materials. However, as the results show here demonstrated, a detailed spectroscopy of nanostructured gold would be need to be captured to detect possible contamination or the use of different metals. Simulations will also aid further optimisation of the possible designs to optimise the strength of the specular optical activity. 

In addition, while the NanoMOKE instrument can provide very high resolution measurements, it is not particularly flexible in terms of changing the incidence angle. The incidence angle of 30$^o$ was attempted in this project, following the initial estimates as likely to yield the maximum effect, but exploring a wider range of incident angles and for all the sets of slits considered would provide a more comprehensive study of this phenomenon. Furthermore, the initial estimates also indicated that 50/120 nm slits would be the optimum design for maximising optical activity, while in fact 50/150 nm slits provided the strongest response. In order to carry out such investigations, own MOKE experimental set up would need to be designed and constructed rather to have the required flexibility in adjusting the measurement conditions.}} 