Metasurfaces enable us to control the fundamental properties of light with unprecedented flexibility. However, most metasurfaces realized to date aim at modifying plane waves. While the manipulation of nonplanar wavefronts is encountered in a diverse number of applications, their control using metasurfaces is still in its infancy. Here we design a metareflector able to reflect a diverging Gaussian beam back onto itself with efficiency over 90% and focusing at an arbitrary distance. We outline a clear route towards the design of complex metareflectors that can find applications as diverse as optical tweezing, lasing, and quantum optics. IntroductionMetasurfaces are artificially engineered arrays of subwavelength-spaced optical scatterers patterned on a flat surface [1][2][3][4][5][6]. The basic concept was introduced long ago in millimeter and microwave technology to manipulate the wavefronts of light by spatially patterning an interface [7][8][9][10][11]. Through advances in nanofabrication, this concept has nowadays been extended to visible light, as nanopatterning tools allow us to induce local and abrupt phase changes to light at the subwavelength scale. The wavefronts of reflected and transmitted beams can be engineered nearly at will by adjusting material and geometrical parameters such as size, shape, separation, and orientation of the metasurface building blocks.The subwavelength separation of the metamaterial building blocks not only enables the control of the phase, amplitude, and polarization of light at high spatial resolution, but also avoids the formation of spurious diffraction orders, which appear in conventional diffractive optical systems such as gratings. In the past few years, metasurfaces have been used for applications such as cloaking [12][13][14][15], absorbing and antireflection coatings [16-18], high-resolution imaging [19,20], focusing [21-24], slow light [25], polarization control [26-28], energy harvesting [29], and tunable beam steering [30]. The versatility in their design together with their straightforward fabrication, which usually involves a single-step lithographic process, makes metasurfaces good candidates to realize multifunctional flat photonic devices [3,31,32].Despite large efforts, metasurfaces are most often designed to manipulate plane waves [33][34][35]. This is mainly because a plane wave is independent of the position of illumination on the metasurface, which significantly simplifies the computational complexity during the design stage as it allows for the use of periodic boundary conditions. Light beams with more complex wavefronts do not have this translation symmetry, and therefore require the simulation of full device structures of the order of tens of micrometers. This often leads to design problems that are computationally too expensive even for modern powerful computers. Nevertheless, the possibility of modifying beams with strongly shaped wavefronts rather than plane waves is of very high importance, in particular for reflectors, i.e., optical elements able t...

This paper focuses on quantifying the uncertainty in the specific absorption rate values of the brain induced by the uncertain positions of the electroencephalography electrodes placed on the patient’s scalp. To avoid running a large number of simulations, an artificial neural network architecture for uncertainty quantification involving high-dimensional data is proposed in this paper. The proposed method is demonstrated to be an attractive alternative to conventional uncertainty quantification methods because of its considerable advantage in the computational expense and speed.

Volume integral equations for modeling biological tissues in the frequency domain typically suffer from illconditioning for high dielectric contrasts and low frequencies. These conditioning breakdowns severely compromise the accuracy and applicability of these models and render them impractical despite their numerous advantages. In this work, we present an electric flux volume integral equation (D-VIE) free from these shortcomings when computed on biologically compatible simply connected objects. This new formulation leverages on careful spectral analysis to obtain volume quasi-Helmholtz projectors capable of curing both sources of ill-conditioning. In particular, the normalization of the projectors by the material permittivity allows for an inhomogeneous re-scaling of the equation which stabilises the high contrast breakdown together with the lowfrequency breakdown. Numerical results show the applicability of this new formulation in realistic brain imaging.

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In this paper we present a new regularized electric flux volume integral equation (D-VIE) for modeling high-contrast conductive dielectric objects in a broad frequency range. This new formulation is particularly suitable for modeling biological tissues at low frequencies, as it is required by brain epileptogenic area imaging, but also at higher ones, as it is required by several applications including, but not limited to, transcranial magnetic and deep brain stimulation (TMS and DBS, respectively). When modeling inhomogeneous objects with high complex permittivities at low frequencies, the traditional D-VIE is illconditioned and suffers from numerical instabilities that result in slower convergence and in less accurate solutions. In this work we address these shortcomings by leveraging a new set of volume quasi-Helmholtz projectors. Their scaling by the material permittivity matrix allows for the re-balancing of the equation when applied to inhomogeneous scatterers and thereby makes the proposed method accurate and stable even for high complex permittivity objects until arbitrarily low frequencies. Numerical results, canonical and realistic, corroborate the theory and confirm the stability and the accuracy of this new method both in the quasi-static regime and at higher frequencies.