Giant Faraday rotation in a hybrid graphene-split ring resonators metasurface with magneto-electric tunability

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. 1 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

Facile Handling of 3D Two‐Photon Polymerized Microstructures by Ultra‐Conformable Freestanding Polymeric Membranes

Micro-nano-fabrication on objects with complex surfaces is essential for the development of technologies in the growing fields of flexible electronics and photonics. Various strategies are devised to extend the fabrication from conventional planar substrates to curved ones, however, significant challenges still exist, especially in the framework of 3D printing and additive manufacturing. In this study, a novel technique is presented to realize 3D micro-structures on arbitrary complex surfaces providing an extreme level of conformability. This method relies on the fabrication of micro-structures via two-photon polymerization on polymeric nano-membranes that can be efficiently transferred to a specific target. Ultra-thin polymeric films are exploited as the support to suspend and transfer the printed micro-structures on the predefined surface. The nanofilm can finally be easily removed, apart from the region underneath the printed elements where it serves as a few tens of nanometers adhesive. The repeatability and feasibility of the proposed process are investigated and shown to provide large flexibility of choice on the printed structures, materials used, transfer procedures, and targeted substrate geometries. By integration with standard fabrication processes, the described technique offers a great potential for the development of next-generation multidimensional/multi-material micro-nano-technologies

Optomechanical response with nanometer resolution in the self-mixing signal of a terahertz quantum cascade laser

Owing to their intrinsic stability against optical feedback (OF), quantum cascade lasers (QCLs) represent a uniquely versatile source to further improve self-mixing interferometry at mid-infrared and terahertz (THz) frequencies. Here, we show the feasibility of detecting with nanometer precision, the deeply subwavelength ($\lt \lambda /6000$<λ/6000) mechanical vibrations of a suspended ${{\rm Si}_3}{{\rm N}_4}$Si3N4 membrane used as the external element of a THz QCL feedback interferometer. Besides representing an extension of the applicability of vibrometric characterization at THz frequencies, our system can be exploited for the realization of optomechanical applications, such as dynamical switching between different OF regimes and a still-lacking THz master-slave configuration

Microcavity resonators and schemes for dynamical control of terahertz quantum cascade lasers

Terahertz radiation is the object of a wide range of technological efforts, in fields as diverse as solid-state fundamental physics, biomedicine and astrophysics. Terahertz light is particularly suitable for sensing, imaging, spectroscopy and communication. In order to unlock the full potential of these applications on a large scale, compact and versatile terahertz sources are needed. A promising candidate is the quantum cascade laser, a compact laser device based on electrically injected semiconductor heterostructures. Quantum cascade lasers operating in the terahertz have already shown high emitted powers and spectral coverage throughout the 1-5 THz range with single mode and broadband devices. However, the research community strives to achieve the performances necessary for the large-scale exploitation of quantum cascade lasers in terahertz technology. Here, we investigated the possibility to add novel functionalities to terahertz quantum cascade lasers allowing to dynamically control their operation and enlarge their versatility. One part of the work is dedicated to the photonic engineering of their cavity. We first considered a particular microcavity resonator consisting of two coupled whispering gallery resonators, which shows low-threshold, high efficiency, vertical collimated single mode emission in continuous wave operation. We thus developed this microresonator design allowing the tuning of the laser emission by exploiting different integrated effects. Directly embedding a suspended mechanical resonator, the proposed microcavity concept presents an optomechanical interaction between the confined electromagnetic field and the resonator mechanical motion, which can affect the laser emission frequency. In an optimized design, where self-oscillation in the system is possible, the device can show a dynamical frequency sweep at the mechanical resonance frequency. A second functionality originates from the engineering of the device injection architecture. In a slightly modi- fied version of the same microcavity, a large continuous frequency tuning and an unconventional far-field modification from radial to vertical emission can be obtained by spatially controlling the pumping strength within the device. The system operation for both microcavity designs is shown through finite-element simulations, the corresponding fabrication is described and a preliminary characterization is performed. Exploiting a different concept for the terahertz quantum cascade laser cavity, relying on line defects in a photonic crystal structure, several devices are designed by simulation, fabricated and characterized to finally show features such as in plane directional emission and mode selectivity. Slow-light effects were shown to produce laser current thresh- old reduction with respect to a reference Fabry-Pérot laser with the same active region. Thanks the defect-line ability to waveguide light in the structure, an example of an active platform integrating multiple line-defects to provide single mode emission in different directions is experimentally shown as proof-of-concept of the potential of the line-defect architecture. Finally, we investigated the modification of quantum cascade laser parameters, such as the emission frequency and laser voltage, in a self-mixing configuration where the intracavity electromagnetic field interferes with the emitted light, reinjected as optical feedback inside the laser cavity, after reflecting on an external element. Specifically, the external element was a mechanical resonator constituted by a suspended silicon-nitride membrane. An optomechanical response with nanometer resolution to membrane mechanical vibrations was observed in the self-mixing signal. The proposed laser feedback interferometry can be viewed as a starting point for more complex schemes for the dynamical control of terahertz quantum cascade laser operation. A promising perspective is represented by the realization of a self-mixing configuration at terahertz frequencies where different lasers could be coupled through the motion of a mechanical resonator driven by radiation pressure

Symmetry enhanced non-reciprocal polarization rotation in a terahertz metal-graphene metasurface

In the present article we numerically investigated the magneto-optical behaviour of a sub-wavelength structure composed by a monolayer graphene and a metallic metasurface of optical resonators. Using this hybrid graphene-metal structure, a large increase of the non-reciprocal polarization rotation of graphene can be achieved over a broad range of terahertz frequencies. We demonstrate that the symmetry of the resonator geometry plays a key role for the performance of the system: in particular, increasing the symmetry of the resonator the non-reciprocal properties can be progressively enhanced. Moreover, the possibility to exploit the metallic metasurface as a voltage gate to vary the graphene Fermi energy allows the system working point to be tuned to the desired frequency range. Another peculiar result is the achievement of a structure able to operate both in transmission and reflection with almost the same performance, but in a di erent frequency range of operation. The described system is hence a sub-wavelength, tunable, multifunctional, e ective non-reciprocal element in the terahertz region

Highly conformable terahertz metasurface absorbers via two-photon polymerization on polymeric ultra-thin films

The continuously increasing interest in flexible and integrated photonics requires new strategies for device manufacturing on arbitrary complex surfaces and with smallest possible size, respectively. Terahertz (THz) technology can particularly benefit from this achievement to make compact systems for emission, detection and on-demand manipulation of THz radiation. Here, we present a novel fabrication method to realize conformable terahertz metasurfaces. The flexible and versatile character of polymeric nanomembranes is combined with direct laser writing via two-photon polymerization to develop free-standing ultra-thin quasi-perfect plasmonic absorbers with an unprecedentedly high level of conformability. Moreover, revealing new flexible dielectric materials presenting low absorption and permittivity in the THz range, this work paves the way for the realization of ultra-thin, conformable hybrid or all-dielectric devices to enhance and enlarge the application of THz technologies, and flexible photonics in general

Highly conformable terahertz metasurface absorbers via two-photon polymerization on polymeric ultra-thin films

The continuously increasing interest in flexible and integrated photonics requires new strategies for device manufacturing on arbitrary complex surfaces and with smallest possible size, respectively. Terahertz (THz) technology can particularly benefit from this achievement to make compact systems for emission, detection and on-demand manipulation of THz radiation. Here, we present a novel fabrication method to realize conformable terahertz metasurfaces. The flexible and versatile character of polymeric nanomembranes is combined with direct laser writing via two-photon polymerization to develop free-standing ultra-thin quasi-perfect plasmonic absorbers with an unprecedentedly high level of conformability. Moreover, revealing new flexible dielectric materials presenting low absorption and permittivity in the THz range, this work paves the way for the realization of ultra-thin, conformable hybrid or all-dielectric devices to enhance and enlarge the application of THz technologies, and flexible photonics in general