Periodic Reporting for period 4 - QUANTUMMETALINK (Quantum Metamaterials: A Theoretical and Computational Approach Towards Seamlessly Integrated Hybrid Classical/Quantum Nano-structures) Reporting period: 2019-12-01 to 2021-01-31 Summary of the context and overall objectives of the project The overarching aim of this project is to initiate and advance an integrated theoretical and computational research programme in an emerging area of metamaterials research, namely Quantum Metamaterials. Thus, it is commonly believed that one of the most noteworthy developments witnessed in the last decade in physical sciences and engineering is the emergence of metamaterials. Unlike ordinary materials, which are assembled at the atomic level, metamaterials are composite materials built up from artificially engineered meta-atoms and meta-molecules. The fundamental idea in this area of research is that remarkable physical properties beyond those available in naturally occurring materials can be achieved by designing the meta-constituents of the metamaterial and structuring it at a scale comparable or smaller than the optical wavelength. In this context, a new paradigm in metamaterials research emerges when the building blocks of metamaterials are quantum resonators, e.g. quantum dots (QDs), QD molecules, graphene disks coupled to interacting QDs, quantum nanowires, and quantum rings, case in which the macroscopic properties of quantum metamaterials are determined by the quantum properties of their basic constituents. We have organised this research programme along three broad, synergistically integrated themes. The first will focus on the development of a general theory of the effective, macroscopic properties of quantum metamaterials. The key challenge is to build a theoretical framework in which the macroscopic properties of quantum metamaterials are derived directly from those of their quantum building blocks. The second theme will be geared towards developing a set of numerical methods and software tools for ab initio simulations of fundamental physical properties quantum metamaterials. The foundational work pertaining to the first two themes will enable us to pursue the main objective of the third theme, which is the exploration of new science and novel applications of quantum metamaterials. Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far Following the general proposed methodology, the research activities pertaining to the project have been devoted to three main research themes, which closely overlap with the three thrusts of the research project: i) studied theoretically and computationally classical and quantum properties of metamaterials; ii) developed computational tools for modelling classical and quantum physical properties of metamaterials; and iii) investigated potential applications of quantum metamaterials. As the work on the project will be advancing, these research directions will converge towards a unified description of physical properties of quantum metamaterials. In what follows, we summarize the work done along these three main research directions. i) Theoretical and computational study of quantum properties of metamaterials: a) developed a numerical method based on the rigorous coupled-wave analysis to model linear and nonlinear optical properties of periodically structured 2D materials, such as graphene and transition metal dichalcogenide (TMDC) materials; b) developed a homogenization method to calculate linear and nonlinear optical constants of graphene metamaterials. A paper on this topic is under preparation; c) developed an FDTD-type numerical method that incorporates optical nonlinearities of graphene and TMDC materials; d) explored physical mechanisms to enhance the nonlinear optical response of graphene nanostructures, namely by employing specially engineered nanostructure that possess double plasmon resonances; e) studied the optical properties of metallo-dielectric superlattices containing graphene, as well as light propagation in such photonic structures; f) performed numerical simulations related to second-harmonic generation in metallo-dielectric nanostructures containing nonlinear 2D materials, aiming to compute linear and nonlinear optical constants of these metamaterials; g) developed a theoretical approach to calculate the effective Raman susceptibility of a silicon-based metasurface made of photonic crystal cavities; h) developed a theoretical approach to study the optical properties of quantum waveguides consisting of coupled silicon-based photonic crystal cavities; i) analyzed theoretically and computationally the quantum properties of single graphene nanoflakes and dimers made of graphene nanoflakes; j) computed quantum mechanically the polarizability and hyperpolarizabilities of graphene nanoflakes and dimers made of graphene nanoflakes; k) investigated computationally quantum plasmon based sensors; l) studied topological properties of metamaterial superlattices with changing sign of the average permittivity; m) investigated theoretically and computationally the linear and nonlinear mixing of spin and orbital angular momenta in plasmonic and dielectric chiral nanostructures. ii) Computational tools for modelling physical properties of quantum metamaterials: a) implemented the method discussed at item i-a in a code and tested it for specific photonic nanostructures of interest; b) implemented the homogenization method discussed at item i-b in a code and tested it for specific nanostructures of interest and for different angles of incidence, wave polarization and physical parameters of graphene; c) implemented the method discussed at item i-c in a code and tested it for second- and third-order optical nonlinearities; d) developed a Python code for calculation of optical response of graphene nanoflakes within the tight-binding approximation; e) developed a GS-FDTD computer code that incorporates optical nonlinearities and used the code to investigate linear and nonlinear optical properties of graphene metasurfaces.iii) Potential applications of quantum metamaterials: a) studied linear and nonlinear optical properties of passive and active graphene-based polarizers; b) investigated light transport in a generic quantum waveguide, namely an array of coupled silicon-based photonic crystal cavities; c) studied optical properties of metamaterials-like plasmonic Bragg fibers with negative average permittivity; d) performed a rigorous theoretical analysis of a surface-plasmon nanolaser containing a monolayer MoS2 as gain medium; e) developed a theory of quantum plasmon tunnelling between graphene nanoflakes via molecular bridges and its implications to molecular sensors.The scientific outcomes of this work were reported in about 50 journal articles, 70 conference peer-reviewed papers, and 20 seminar, colloquium and workshop talks. Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far) We have made significant progress in all three main research areas of the project. On the theory side, we have developed a theoretical framework for describing the effective linear and nonlinear optical coefficients of metamaterials and the computational approaches to validate this theoretical framework. In addition, we have performed in-depth studies of the quantum physical properties of graphene nanoflakes with size of up to a few nanometers and the interaction between such quantum nanostructures. Regarding the work on numerical methods and their software implementation, we have developed a numerical approach based on the rigorous coupled-wave analysis method for modelling the linear and nonlinear optical response of photonic structures containing 2D materials, such as graphene and transition metal dichalcogenide materials. This numerical method has been implemented in a software package, which is perhaps the first computational tool specially tailored for optical 2D materials. In addition, we have augmented an in-house developed software implementing the finite-difference time-domain method with key features that make it suitable to model quadratic and cubic optical nonlinearities (the main types of nonlinearities encountered in nonlinear optics), thus greatly enhancing its capabilities. Finally, the theoretical and computational tools developed as part of this project have been used to investigate a series of photonic nanodevices, such as graphene based diffraction gratings and graphene quantum plasmon based sensors. quantummetalinklogo.png
