Fabrizio Sgrignuoli

We investigate the spatial decay and temporal localization properties of quasimodes (i.e., scattering resonances) of two-dimensional Vogel spirals, composed of deterministic, aperiodic arrays of electric dipoles. By determining the structural entropy and localization maps of Vogel spirals using the Green's matrix method, we show that three distinctive decay types of quasimodes coexist in Vogel spirals: exponential, power law, and Gaussian. While the exponential and the power-law decays typically occur in disordered media and multifractal systems, respectively, the Gaussian decay is demonstrated to characterize, on average, the most localized quasimodes of Vogel spirals, both spatially (smallest participation ratios) and temporally (longest lifetimes). These decay forms are demonstrated by a no-fitting analysis of the localization maps, independently corroborated by calculating the electric field in real space, which also provides a direct evidence of the algebraic spatial decay of critical quasimodes. Altogether our findings unveil a rich spectrum of both long-lived and spatially localized quasimodes that coexist in Vogel spirals and can be of direct relevance to novel optical functionalities for applications to light sources and sensing devices.

In this paper, we propose a novel approach to enhance the efficiency of the two-photon spontaneous emission process that is driven by the multifractal optical mode density of photonic structures based on the aperiodic distributions of Eisenstein and Gaussian primes. In particular, using the accurate Mie–Lorenz multipolar theory in combination with multifractal detrended fluctuation analysis, we compute the local density of states of periodic and aperiodic systems and demonstrate the formation of complete bandgaps with distinctive fractal scaling behavior for scattering arrays of dielectric nanocylinders. Moreover, we systematically study the Purcell enhancement and the most localized optical mode resonances in these novel aperiodic photonic systems and compute their two-photon spontaneous emission rates based on the general Green’s tensor approach. Our results demonstrate that excitation of the highly resonant critical states of Eisenstein and Gaussian photonic arrays across broadband multifractal spectra gives rise to significantly enhanced emission rates compared to what is possible at the band edges of periodic structures with comparable size. Besides defining a novel approach for enhanced quantum two-photon sources on the chip, the engineering of aperiodic bandgap structures with multifractal mode density may provide access to novel electromagnetic resonant phenomena in a multi-scale-invariant vacuum for quantum nanophotonics applications.

Optical rogue waves are demonstrated in the far-field scattered radiation from photonic arrays designed according to the aperiodic distributions of prime elements in complex quadratic fields. Specifically, by studying light diffraction from Eisenstein and Gaussian prime arrays, we establish a connection between the formation of optical rogue waves and multifractality in the visible single-scattering regime. We link strong multifractality with the heavy-tail probability distributions that describe the fluctuations of scattered radiation from the fabricated arrays. Our findings pave the way to control high-intensity rogue waves using deterministic arrays of dielectric nanostructures for enhanced sensing and lithographic applications.

In this paper we propose a novel approach to aperiodic order in optical science and technology that leverages the intrinsic structural complexity of certain non-polynomial (hard) problems in number theory and cryptography for the engineering of optical media with novel transport and wave localization properties. In particular, we address structure-property relationships in a large number (900) of light scattering systems that physically manifest the distinctive aperiodic order of elliptic curves and the associated discrete logarithm problem over finite fields. Besides defining an extremely rich subject with profound connections to diverse mathematical areas, elliptic curves offer unprecedented opportunities to engineer light scattering phenomena in aperiodic environments beyond the limitations of traditional random media. Our theoretical analysis combines the interdisciplinary methods of point patterns spatial statistics with the rigorous Green’s matrix solution of the multiple wave scattering problem for electric and magnetic dipoles and provides access to the spectral and light scattering properties of novel deterministic aperiodic structures with enhanced light-matter coupling for nanophotonics and metamaterials applications to imaging and spectroscopy.

In this article, we demonstrate that a grating fabricated through nanoscale volumetric cross-linking of a liquid crystalline polymer enables remote polarization control over the diffracted channels. This functionality is a consequence of the responsivity of liquid crystal networks upon light stimuli. Tuning of the photonic response of the device is achieved thanks to both a refractive index and a shape change of the grating elements induced by a molecular rearrangement under irradiation. In particular, the material anisotropy allows for nontrivial polarization state management over multiple beams. The absence of any liquid component and a time response down to 0.2 ms make our device appealing in the fields of polarimetry and optical communications.

By using the dyadic Green's matrix spectral method, we demonstrate that aperiodic deterministic Vogel spirals made of electric dipoles support a light localization transition in three dimensions, an effect that does not occur in traditional uniform random media. We discover a light localization transition in Vogel spiral arrays embedded in three-dimensional space by evaluating the Thouless conductance, the level spacing statistics, and by performing a finite-size scaling. We probe light localization in the plane of the array by analyzing the behavior of the scattering resonances in three-dimensional space. This light localization transition is different from the Anderson transition because Vogel spirals are aperiodic deterministic structures characterized by nonuniform geometries. Moreover, this transition occurs when the vector character of light is fully taken into account, in contrast to what is expected for traditional uniform random media of pointlike scatterers. We show that light localization in Vogel arrays is a collective phenomenon that involves the contribution of multiple length scales. Vogel spirals are suitable photonic platforms to localize light thanks to their distinctive structural correlation properties that enable collective electromagnetic excitations with strong light-matter coupling. Our results unveil the importance of aperiodic correlations for the engineering of photonic media with strongly enhanced light-matter coupling compared to the traditional periodic and homogeneous random media.

Random dielectrics defines a class of non‐absorbing materials where the index of refraction is randomly arranged in space. Whenever the transport mean free path is sufficiently small, light can be confined in modes with very small volume. Random photonic modes have been investigated for their basic physical insights, such as Anderson localization, and recently several applications have been envisioned in the field of renewable energies, telecommunications, and quantum electrodynamics. An advantage for optoelectronics and quantum source integration offered by random systems is their high density of photonic modes, which span a large range of spectral resonances and spatial distributions, thus increasing the probability to match randomly distributed emitters. Conversely, the main disadvantage is the lack of deterministic engineering of one or more of the many random photonic modes achieved. This issue is solved by demonstrating the capability to electrically and mechanically control the random modes at telecom wavelengths in a 2D double membrane system. Very large and reversible mode tuning (up to 50 nm), both toward shorter or longer wavelength, is obtained for random modes with modal volumes of the order of few tens of (λ/n)³.