• Faraday rotation
• graphene
• metasurface
• SRRs

Light propagation is usually reciprocal. A beam of light, which changed its polarization state after passing through a medium, retrieves the original one when it performs the same path in the opposite direction. However, a static magnetic field along the propagation direction breaks the time- reversal symmetry in the presence of magneto-optical materials: forward and backward propagation of a linearly polarized electromagnetic wave now doubles the phase retardation between the two circular components of the traveling wave, with the final effect of a net rotation of the plane of polarization. The amplitude of the rotation angle is linearly proportional to the external magnetic field B, to the traveled geometric distance and to the Verdet constant of the medium. This purely non-reciprocal phenomenon is called Faraday effect and it constitutes the subject of my thesis work.
The Faraday effect has its most important application in optical isolators. These are crucial de- vices in optical systems. Due to their ability to allow the transmission of light in only one direction, they are used to shield laser cavities against back reflected light, as well to limit the detrimental effect of back propagating spontaneous emission. Faraday isolators are typically bulky due to the weak Faraday effect of available magneto-optical materials. The very quick growing research for more compact integrated optics demands thin-film Faraday rotators and the enhancement of the Faraday effect. Furthermore, a very important open challenge is the realization of isolators in the in technologically developing terahertz (THz) range. This achievement is made difficult by the presence of intrinsic losses in current non-reciprocal materials at THz frequencies.
One of the most promising candidates for a compact isolator in this electromagnetic range is constituted by graphene. Besides its well-known unusual electronic and photonic properties, graphene represents an intrinsically excellent magneto-optical material. Only recently, a Faraday rotation of about 6 degrees in a single sheet of graphene has been observed at fields of only a few Tesla. Using constructive Fabry-Perot interference in the substrate supporting graphene, an even bigger Faraday angle of 9 degrees together with better transmittance is achieved. In both these two cases the doping level of graphene and applied magnetic field put the system in the classical regime. The separation between the Landau Levels in graphene at the Fermi energy (EF) is much smaller than EF itself. In this limit, Dirac quasiparticles are in fact expected to exhibit the classical cyclotron resonance and they can be well described by the Drude-Lorentz model.
Our purpose is to find a particular configuration able to enhance the Faraday rotation of graphene. Metamaterials, which represent an efficient way to design and tailor existing materials towards nat- urally unavailable properties and enhanced optical processes, are a possible solution to achieve this goal. In this direction, we propose a metasurface of sub-wavelength metallic resonators to enhance the Faraday rotation of graphene. The choice of a metasurface stems from the desire to preserve the compactness provided by the natural bi-dimensionality of graphene. The chosen optical resonators are split ring resonators (SRRs), one of the most common resonators used at THz frequencies.
In the thesis, I show by simulations that a resonant planar array of SRRs placed in close proximity to the graphene layer can highly confine and amplify the electromagnetic fields of the incoming wave. The frequency matching of the resonant Faraday rotation of graphene with the resonance of the dispersive susceptibility of the overall metasurface puts the system in a non-perturbative regime in which the Faraday effect is strongly amplified. The Faraday angle is observed to reach values above 0.3 rad (18 degrees) with a transmittance of more than 0.3. Using a classical approach, this enhancement can be qualitatively explained by an increase of the effective length of the system or a decrease of the phase velocity of the incoming light in correspondence of the resonators.
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The work is divided in three fundamental parts. First, a simulation study has been performed to investigate the magneto-optical properties of graphene and to individuate a particular design of the SRRs metasurface with an appropriate substrate to reach the highest possible performance. The following step was the fabrication of the hybrid graphene-SRRs metasurface. It consisted in the electron beam lithography of the metasurface upon a copolymer substrate, the thermal evapo- ration of gold constituting the SRRs, the sputtering of an oxide (SiO2) layer and finally the growth (CVD on Cu) and transfer of graphene above the structure. In this way, four samples with different dimensions of the unit cell of the SRRs array were fabricated in order to show the amplification of the Faraday effect over a wide portion of the THz spectral range.
In parallel with the fabrication process, the spectrometric measurements (without external magnetic field) of the samples have been performed using the Fourier transform infrared (FTIR) spectroscopic technique. The spectra of the samples are obtained at different stages of the fabrication process; after the fabrication of the metallic surface on the substrate, after the sputtering of the SiO2 and at the end of the graphene transfer.
For future perspectives, the use of materials that highly increase the mobility of graphene and the confinement of the electromagnetic field, for example by packaging graphene inside thin boron nitride membranes, has been observed by simulation to greatly improve the performance of this system.
Moreover, the presence of the oxide layer and the metallic metasurface arranged in a connected fashion offers the possibility to create a back gate voltage to vary the Fermi energy, which has seen to be a fundamental parameter for the amplification of the Faraday effect. Thus, by changing simultaneously the applied electric voltage and the external magnetic field, the electromagnetic behaviour of the hybrid metasurface can be tuned to reach the best working point.
The use of the gate voltage can also allow to explore the quantum regime (limit of low doping) of graphene. The effects on the quantum Faraday effect caused by the interaction of the metallic metasurface with graphene could get the Faraday rotation to anomalously large values.