## Bachelor thesis:

Thesis can be assigned in the framework of the following areas. The specific topic can be identified and even proposed by the student during a meeting in office hours.

Three-phase systems

Electric motors

Inductive charging

Metasurfaces

Dielectric optical accelerators

## Master thesis:

**Title:** **Inverse Design of Dielectric Optical Accelerators**

**Aims:** Linear Accelerators (LINACs) are widely used in medicine for diagnostic imaging, cancer treatment, sterilization of equipment, irradiation of blood products, and other applications. In this framework, the increasing demand for portable healthcare products pushes for the conception of compact LINACs capable of guaranteeing higher particle energy. Nevertheless, in conventional metallic structures accelerating gradients are limited by material breakdown, power losses in metals, high cost and maximum power of RF generators. Instead, hollow-core dielectric accelerating structures (HODACs) are characterized by larger breakdown threshold and smaller absorption, thus overcoming the main drawbacks of conventional LINACs. Furthermore, HODACs can potentially work at MHz repetition rates, without resorting to expensive superconductive technologies. Last, but not least, in a guiding structure the interaction length can be maximized with respect to side-pumped gratings.

In this activity a novel HODAC will be designed by using numerical simulations. First, the most suitable geometry will be chosen among different configurations proposed in the literature (see e.g. woodpile structures, photonic crystal slabs, slot waveguides, metasurfaces). Then, inverse design techniques will be applied to the coupled electromagnetic and particle acceleration problems in order to identify an optimal set of geometrical parameters with respect to figures of merit such as characteristic impedance and energy gain.

**Title: ****Second Harmonic Generation in Degenerate Band Edge Optical Resonators**

**Aims: **A novel optical structure that may be beneficial to obtain strong second harmonic generation using the concept of slow light at the fundamental resonance and the second harmonic will be investigated. The structure of interest is based on coupled resonators optical waveguides (CROWs), which can exhibit high order exceptional points of degeneracy through the fine tuning of the CROW parameters. Here focus will be put on the degenerate band edge (DBE), which is a fourth order degeneracy that occurs due to the coalescence of four Floquet-Bloch eigenwaves in CROWs, without the presence of gain and loss. The DBE in the proposed unconventional periodic CROW occurs at the edge of the Brillouin zone. The unconventional scaling of the quality factor (Q factor) of the DBE CROW that is proportional to L^{5}, where L is the length of the CROW, has the potential for boosting efficiency of the Second Harmonic Generation (SHG) process. In particular, in this activity scaling of SHG with respect to the length L will be determined by reformulating an analytical procedure already reported in the literature for the case of conventional doubly-resonant gratings.

**Title: ****Spontaneous Parametric Down Conversion in a Doubly Resonant 1D Photonic Crystal**

**Aims: **Photon pairs, which are useful in metrology, communication, and computation, can be generated via Spontaneous Parametric Down Conversion (SPDC) in second-order nonlinear media. In a simple and intuitive picture, SPDC can be viewed as the spontaneous fission of an input photon into two daughter photons, in accordance with the laws of energy and momentum conservation. One of the simplest systems in which the dielectric function is modulated on a scale comparable with the wavelength of interest is the one-dimensional photonic crystal (1D PC). This system has been studied extensively for the enhancement of second-harmonic generation (SHG), in which multiple configurations can be explored with the fundamental, second harmonic, or both fields resonant at a photonic band-edge. These structures are also a natural playground to understand the generation and control of non-classical light via SPDC.

In such a structure SHG scales as L^{8}, where L is the length of the 1D PC, whereas an unusual L^{5} scaling law for SPDC was numerically predicted. In this framework, we will study scaling of SPDC with respect to the length of the 1D PC by reformulating an analytical procedure already reported in the literature for the case of SHG in conventional doubly-resonant gratings. The analytical treament will aim at clarifying the conditions for obtaining different SPDC scaling laws as a function of the PC properties.