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We study the enhancement of third harmonic generation in indium tin oxide nanolayers coupled to Tamm plasmon polaritons (TPPs). The TPPs are excited at the interface between a thin gold mirror and a silicon dioxide/silicon nitride (SiO2/Si3N4) distributed Bragg reflector with a 30nm-thick indium tin oxide (ITO) nanolayer embedded in hte topmost dielectric layer under the metal mirror. This ITO nanolayer exhibits epsilon-near-zero (ENZ) behavior at nearinfrared wavelengths. By tuning the angle of incidence and resonance conditions, we achieve strong confinement and localization of the electromagnetic field at the TPP mode, which significantly boosts the local electric field and the nonlinear optical response of the structure. Our experiments reveal that the third harmonic generation (THG) efficiency is maximized when the TPP resonance coincides with the ENZ wavelength (i.e., the wavelength at which the real part of the ITO permittivity vanishes) of the ITO, resulting in a tenfold enhancement of the measured THG efficiency compared to a bare ITO nanolayer. We further investigate the dependence of the THG signal on the incident angle and sample orientation, confirming that the enhancement is directly related to the excitation of the TPP mode with nonreciprocal behaviour. Numerical simulations based on the transfer matrix method (TMM) support our findings. Our study demonstrates that the TPP-ENZ platform offers a versatile and highly efficient approach to enhancing nonlinear optical processes, with potential applications in frequency conversion, optical signal processing, and the development of quantum photonic devices.

In this article, we employ multiscale physics-informed neural networks (MscalePINNs) for the inverse retrieval of the spatially inhomogeneous effective permittivity and for the homogenization of finite-size photonic media with stealthy hyperuniform (SHU) disordered geometries. Specifically, we show that MscalePINNs can capture the fast spatial variations of complex fields scattered by arrays of dielectric nanocylinders arranged according to isotropic SHU point patterns, thus enabling a systematic methodology to inversely retrieve their effective dielectric profiles. Our approach extends the recently developed high-frequency homogenization theory of hyperuniform media and retrieves more general permittivity profiles for applications-relevant finite-size SHU systems, unveiling unique features related to their isotropic nature. In particular, we numerically corroborate the existence of a transparency region beyond the long-wavelength approximation, enabling effective and isotropic homogenization even without disorder-averaging, in contrast to the case of uncorrelated Poisson random patterns. The flexible multiscale network approach introduced here enables the efficient inverse design of more general effective media and finite-size metamaterials with isotropic electromagnetic responses beyond the limitations of traditional homogenization theories.

In this paper, we investigate the localization properties of optical waves in disordered systems with multifractal scattering potentials. In particular, we apply the localization landscape theory to the classical Helmholtz operator and, without solving the associated eigenproblem, show accurate predictions of localized eigenmodes for one- and two-dimensional multifractal structures. Finally, we design and fabricate nanoperforated photonic membranes in silicon nitride (SiN) and image directly their multifractal modes using leaky-mode spectroscopy in the visible spectral range. The measured data demonstrate optical resonances with multiscale intensity fluctuations in good qualitative agreement with numerical simulations. The proposed approach provides a convenient strategy to design multifractal photonic membranes, enabling rapid exploration of extended scattering structures with tailored disorder for enhanced light-matter interactions.

We present compact integrated speckle spectrometers based on monofractal and multifractal scattering media in a silicon-on-insulator platform. Through both numerical and experimental studies we demonstrate enhanced optical throughput, and hence signal-to-noise ratio, for a number of random structures with tailored multifractal geometries without affecting the spectral decay of the speckle correlation functions. Moreover, we show that the developed multifractal media outperform traditional scattering spectrometers based on uniform random distributions of scattering centers. Our findings establish the potential of low-density random media with multifractal correlations for integrated on-chip applications beyond what is possible with uncorrelated random disorder.

In this paper we introduce a fully non-perturbative approach for the description of the optical nonlinearity of epsilon-near-zero (ENZ) media. In particular, based on the rigorous Feynman path integral method, we develop a dressed Lagrangian field theory for light-matter interactions and discuss its application to dispersive Kerr-like media with order-of-unity light-induced refractive index variations. Specifically, considering the relevant case of Indium Tin Oxide (ITO) nonlinearities, we address the novel regime of non-perturbative refractive index variations in ENZ media and establish that it follows naturally from a scalar field theory with a Born-Infeld (BI) Lagrangian. Moreover, we developed a predctive model that includes the intrinsic saturation effects originating from the light-induced modification of the Drude terms in the linear dispersion of ITO materials. Our results extend the Huttner-Barnett-Bechler electrodynamics model to the case of non-perturbative optical Kerr-like media providing an intrinsically nonlinear, field-theoretic framework for understanding the exceptional nonlinearity of ITO materials beyond traditional perturbation theory.

Recently, materials with vanishingly small permittivity, known as epsilon-near-zero (ENZ) media, emerged as promising candidates to achieve nonlinear optical effects of unprecedented magnitude on a solid-state platform. In particular, the ENZ behavior of Indium Tin Oxide (ITO) thin films resulted in Kerr-type nonlinearity with non-perturbative refractive index variations that are key to developing more efficient Si-compatible devices with sub-wavelength dimensions such as all-optical switchers, modulators, and novel photon detectors. In this contribution, we propose and demonstrate enhancement of the nonlinear index variation of 30 nm-thick ITO nanolayers by silicon dioxide/silicon nitride (SiO2/SiN) Tamm plasmon-polariton structures fabricated by radio-frequency magnetron sputtering on transparent substrates under different annealing conditions. In particular, we investigate the linear and nonlinear optical properties of ITO thin films and resonant photonic structures using broadband spectroscopic ellipsometry and intensity dependent Z-scan nonlinear characterization demonstrating enhancement of optical nonlinearity with refractive index variations as large as in the non-perturbative regime. Our study reveals that the efficient excitation of strongly confined plasmon-polariton Tamm states substantially boost the nonlinear optical response of ITO nanolayers providing a stepping stone for the engineering of more efficient infrared devices and nanostructures for a broad range of applications including all-optical data processing, nonlinear spectroscopy, sensing, and novel photodetection modalities.

In this paper, we develop and employ auxiliary physics-informed neural networks (APINNs) to solve forward, inverse, and coupled integro-differential problems of radiative transfer theory (RTE). Specifically, by focusing on the relevant slab geometry and scattering media described by different types of phase functions, we show how the proposed APINN framework enables the efficient solution of Boltzmann-type transport equations through multi-output neural networks with multiple auxiliary variables associated to the Legendre expansion terms of the considered phase functions. Furthermore, we demonstrate the successful application of APINN to the coupled radiation-conduction problem of a participating medium and find distinctive temperature profiles beyond the Fourier thermal conduction limit. Finally, we solve the inverse problem for the Schwarzschild-Milne integral equation and retrieve the single scattering albedo based solely on the knowledge of boundary data, similar to what is often available in experimental settings. The present work significantly expands the current capabilities of physics-informed neural networks for radiative transfer problems that are relevant to the design and understanding of complex scattering media and photonic structures with applications to metamaterials, biomedical imaging, thermal transport, and semiconductor device modeling.

We propose a rigorous approach for the inverse design of functional photonic structures by coupling the adjoint optimization method and the two-dimensional generalized Mie theory (2D-GMT) for the multiple scattering problem of finite-size arrays of dielectric nanocylinders optimized to display desired functions. We refer to these functional scattering structures as "photonic patches". We briefly introduce the formalism of 2D-GMT and the critical steps necessary to implement the adjoint optimization algorithm to photonic patches with designed radiation properties. In particular, we showcase several examples of periodic and aperiodic photonic patches with optimal nanocylinder radii and arrangements for radiation shaping, wavefront focusing in the Fresnel zone, and for the enhancement of the local density of states (LDOS) at multiple wavelengths over micron-size areas. Moreover, we systematically compare the performances of periodic and aperiodic patches with different sizes and find that optimized aperiodic Vogel spiral geometries feature significant advantages in achromatic focusing compared to their periodic counterparts. Our results show that adjoint optimization coupled to 2D-GMT is a robust methodology for the inverse design of compact photonic devices that operate in the multiple scattering regime with optimal desired functionalities. Without the need of spatial meshing, our approach provides efficient solutions at strongly reduced computational burden compared to standard numerical optimization techniques and suggests compact device geometries for on-chip photonics and metamaterials technologies.

We propose the inverse design of ultracompact, broadband focusing spectrometers based on adaptive deep diffractive neural networks (a-D$^2$NNs). Specifically, we introduce and characterize two-layer diffractive devices with engineered angular dispersion that focus and steer broadband incident radiation along predefined focal trajectories with desired bandwidth and $5$ nm spectral resolution. Moreover, we systematically study the focusing efficiency of two-layer devices with side length $L=100~\mu\mathrm{m}$ and focal length $f=300~\,\mu\mathrm{m}$ across the visible spectrum and we demonstrate accurate reconstruction of the emission spectrum from a commercial superluminescent diode. The proposed a-D$^2$NNs design method extends the capabilities of efficient multi-focal diffractive optical devices to include single-shot focusing spectrometers with customized focal trajectories for applications to ultracompact multispectral imaging and lensless microscopy.

We investigate the localization of waves in aperiodic structures that manifest the characteristic multiscale complexity of certain arithmetic functions with a central role in number theory. In particular, we study the eigenspectra and wave localization properties of tight-binding Schr\"{o}dinger equation models with on-site potentials distributed according to the Liouville function $\lambda(n)$, the M\"{o}bius function $\mu(n)$, and the Legendre sequence of quadratic residues modulo a prime (QRs). We employ Multifractal Detrended Fluctuation Analysis (MDFA) and establish the multifractal scaling properties of the energy spectra in these systems. Moreover, by systematically analyzing the spatial eigenmodes and their level spacing distributions, we show the absence of level repulsion with broadband localization across the entire energy spectra. Our study introduces deterministic aperiodic systems whose eigenmodes are all strongly localized in realistic finite one-dimensional systems and provides opportunities for novel quantum and classical devices of particular importance to cold-atom experiments in engineered speckle potentials and enhanced light-matter interactions.

In this paper we study the structural, scattering, and wave localization properties of multifractal arrays of electric point dipoles generated from multiplicative random fields with different degrees of multiscale correlations. Specifically, using the rigorous Green's matrix method, we investigate the scattering resonances and wave localization behavior of systems with $N=10^{4}$ dipoles and demonstrate an enhanced localization behavior in highly inhomogeneous multifractal structures compared to homogeneous fractals, or monofractals. We show distinctive spectral properties, such as the absence of level repulsion in the strong multiple scattering regime and power-law statistics of level spacings, which indicate a clear localization transition enhanced in non-homogeneous multifractals. Our findings unveil the importance of multifractal structural correlations in the multiple scattering regime of electric dipole arrays and provide an efficient model for the design of multiscale nanophotonic systems with enhanced light-matter coupling and localization phenomena beyond what is possible with traditional fractal systems.

We propose an efficient inverse design approach for multifunctional optical elements based on adaptive deep diffractive neural networks (a-D$^2$NNs). Specifically, we introduce a-D$^2$NNs and design two-layer diffractive devices that can selectively focus incident radiation over two well-separated spectral bands at desired distances. We investigate focusing efficiencies at two wavelengths and achieve targeted spectral lineshapes and spatial point-spread functions (PSFs) with optimal focusing efficiency. In particular, we demonstrate control of the spectral bandwidths at separate focal positions beyond the theoretical limit of single-lens devices with the same aperture size. Finally, we demonstrate devices that produce super-oscillatory focal spots at desired wavelengths. The proposed method is compatible with current diffractive optics and doublet metasurface technology for ultracompact multispectral imaging and lensless microscopy applications.

In this paper, we develop a deep learning approach for the accurate solution of challenging problems of near-field microscopy that leverages the powerful framework of physics-informed neural networks (PINNs) for the inversion of the complex optical parameters of nanostructured environments. Specifically, we show that PINNs can be flexibly designed based on the full-vector Maxwell's equations to inversely retrieve the spatial distributions of the complex electric permittivity and magnetic permeability of unknown scattering objects in the resonance regime from near-field data. Moreover, we demonstrate that PINNs achieve excellent convergence to the true material parameters under both plane wave and point source (localized) excitations, enabling parameter retrieval in scanning near-field optical microscopy (SNOM). Our method is computationally efficient compared to traditional data-driven deep learning approaches as it requires only a single dataset for training. Furthermore, we develop and successfully demonstrate adaptive PINNs with trainable loss weights that largely improve the accuracy of the inverse reconstruction for high-index materials compared to standard PINNs. Finally, we demonstrate the full potential of our approach by retrieving the space-dependent permittivity of a three-dimensional (3D) unknown object from near-field data. The presented framework paves the way to the development of a computationally-driven, accurate, and non-invasive platform for the simultaneous retrieval of the electric and magnetic parameters of resonant nanostructures from measured optical images, with applications to biomedical imaging, optical remote sensing, and characterization of metamaterial devices.

The purpose of this work is to understand the fundamental connection between structural correlations and light localization in three-dimensional (3D) open scattering systems of finite size. We numerically investigate the transport of vector electromagnetic waves scattered by resonant electric dipoles spatially arranged in 3D space by stealthy hyperuniform disordered point patterns. Three-dimensional stealthy hyperuniform disordered systems (3D-SHDS) are engineered with different structural correlation properties determined by their degree of stealthiness $\chi$. Such fine control of exotic states of amorphous matter enables the systematic design of optical media that interpolate in a tunable fashion between uncorrelated random structures and crystalline materials. By solving the electromagnetic multiple scattering problem using Green's matrix spectral method, we establish a transport phase diagram that demonstrates a distinctive transition from a diffusive to a weak localization regime beyond a critical scattering density that depends on $\chi$. The transition is characterized by studying the Thouless number and the spectral statistics of the scattering resonances. In particular, by tuning the $\chi$ parameter, we demonstrate large spectral gaps and suppressed sub-radiant proximity resonances, facilitating light localization. Moreover, consistently with previous studies, our results show a region of the transport phase diagram where the investigated scattering systems become transparent. Our work provides a systematic description of the transport and weak localization properties of light in stealthy hyperuniform structures and motivates the engineering of novel photonic systems with enhanced light-matter interactions for applications to both classical and quantum devices., Comment: 12 pages, 7 figures

We propose a novel framework for the systematic design of lensless imaging systems based on the hyperuniform random field solutions of nonlinear reaction-diffusion equations from pattern formation theory. Specifically, we introduce a new class of imaging point-spread-functions (PSFs) with enhanced isotropic behavior and controllable sparsity. We investigate the PSFs and the modulated transfer functions (MTFs) for a number of nonlinear models and demonstrate that two-phase isotropic random fields with hyperuniform disorder are ideally suited to construct imaging PSFs with improved performances compared to PSFs based on the Perlin noise. Additionally, we introduce a phase retrieval algorithm based on the non-paraxial Rayleigh-Sommerfeld diffraction theory and introduce diffractive phase plates with PSFs designed from hyperuniform random fields, called hyperuniform phase plates (HPPs). Finally, using high-fidelity object reconstruction, we demonstrate improved image quality using engineered HPPs across the visible range. The proposed framework is suitable for high-performance lensless imaging systems for on-chip microscopy and spectroscopy applications., Comment: Optics Letters in review

In this paper, we study the wave transport and localization properties of novel aperiodic structures that manifest the intrinsic complexity of prime number distributions in imaginary quadratic fields. In particular, we address structure-property relationships and wave scattering through the prime elements of the nine imaginary quadratic fields (i.e., of their associated rings of integers) with class number one, which are unique factorization domains (UFDs). Our theoretical analysis combines the rigorous Green's matrix solution of the multiple scattering problem with the interdisciplinary methods of spatial statistics and graph theory analysis of point patterns to unveil the relevant structural properties that produce wave localization effects. The onset of a Delocalization-Localization Transition (DLT) is demonstrated by a comprehensive study of the spectral properties of the Green's matrix and the Thouless number as a function of their optical density. Furthermore, we employ Multifractal Detrended Fluctuation Analysis (MDFA) to establish the multifractal scaling of the local density of states in these complex structures and we discover a direct connection between localization, multifractality, and graph connectivity properties. Finally, we use a semi-classical approach to demonstrate and characterize the strong coupling regime of quantum emitters embedded in these novel aperiodic environments. Our study provides access to engineering design rules for the fabrication of novel and more efficient classical and quantum sources as well as photonic devices with enhanced light-matter interaction based on the intrinsic structural complexity of prime numbers in algebraic fields., Comment: 11 figures, 24 pages

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 temporarily (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., Comment: 8 pages, 3 figures

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 the 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 multiscale-invariant vacuum for quantum nanophotonics applications., Comment: 14 pages, 9 Figures

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., Comment: 9 pages, 7 figures

Refractory materials exhibit high damage tolerance, which is attractive for the creation of nanoscale field-emission electronics and optoelectronics applications that require operation at high peak current densities and optical intensities. Recent results have demonstrated that the optical properties of titanium nitride, a refractory and CMOS-compatible plasmonic material, can be tuned by adding silicon and oxygen dopants. However, to fully leverage the potential of titanium (silicon oxy)nitride, a reliable and scalable fabrication process with few-nm precision is needed. In this work, we developed a fabrication process for producing engineered nanostructures with gaps between 10 and 15 nm, aspect ratios larger than 5 with almost 90{\deg} steep sidewalls. Using this process, we fabricated large-scale arrays of electrically-connected bow-tie nanoantennas with few-nm free-space gaps. We measured a typical variation of 4 nm in the average gap size. Using applied DC voltages and optical illumination, we tested the electronic and optoelectronic response of the devices, demonstrating sub-10-V tunneling operation across the free-space gaps, and quantum efficiency of up to 1E-3 at 1.2 {\mu}m, which is comparable to a bulk silicon photodiode at the same wavelength. Tests demonstrated that the titanium silicon oxynitride nanostructures did not significantly degrade, exhibiting less than 5 nm of shrinking of the average gap dimensions over few-{\mu}m^2 areas after roughly 6 hours of operation. Our results will be useful for developing the next generation of robust and CMOS-compatible nanoscale devices for high-speed and low-power field-emission electronics and optoelectronics applications.

The polarization- and angle- resolved optical response of the anapole mode in silicon nano-disks array have been experimentally and theoretically investigated. The good agreement betweenmeasured data and simulations yields to a consistent description of the anapole mode behaviorthat exhibits different features for TE or TM polarization excitation. Scattering matrix calculationallows us to disentangle scattered and diffused light contributions and to provide a quantitativeestimation of the absorbance enhancement associated to 2D excitation of the anapole mode. Weperformed the multipolar decomposition of the far-field scattered radiation for both TE and TMpolarizations and unambiguously identified the anapole resonant condition in excellent agreementwith the experimental results over a large range of incident angles. Our findings demonstrate thecontrolled excitation of electromagnetic anapole modes in engineered arrays of silicon nano-disksfor the development of optical nanostructures with enhanced light-matter interaction, Comment: 10 pages, 4 figures and 1 table, submitted to Phys.Rev.B

We design, fabricate, and characterize multifunctional and compact diffractive microlenses with sub-wavelength thickness and the capability to simultaneously focus visible and near-infrared spectral bands at two different focal positions with 24% and 15% measured focusing efficiency, respectively. Our technology utilizes high-index and low-loss sputtered hydrogenated amorphous Si, enabling a sub-wavelength thickness of only 235nm. Moreover, the proposed flat lens concept is polarization insensitive and can be readily designed to operate across any desired wavelength regime. Imaging under broadband illumination with independent focal planes for two targeted spectral bands is experimentally demonstrated, enabling the encoding of the depth information of a sample into different spectral images. In addition, with a small footprint of only 100$\mu$m and a minimum feature size of 400nm, the proposed multifunctional and compact diffractive microlenses can be readily integrated with vertical detector arrays to simultaneously concentrate and spectrally select electromagnetic radiation. This provides novel opportunities for spectroscopic and multispectral imaging systems with advanced detector architectures.

We design and characterize phase-modulated, ultra-compact, silicon-based axilens devices that combine efficient point focusing and grating selectivity within scalable 4-level phase mask configurations. The proposed designs are polarization insensitive and maintain a large focusing efficiency over a broad spectral band. Specifically, we select and systematically characterize structures designed for visible and near-infrared (NIR) operation in the $750nm-950nm$ wavelength range. These devices are ideally suited for monolithic integration atop the substrate layers of focal plane arrays (FPAs) for use in multi-band photo-detection and imaging. We demonstrate linear control of multi-wavelength focusing on a single achromatic plane and provide an application consisting of a proof-of-concept ultra-compact single-lens spectrometer with only 300 nm thickness and 70${\mu}m$ diameter, achieving a minimum distinguishable wavelength $\Delta\lambda=40nm$ at $\lambda_0=850nm$. The proposed devices add fundamental spectroscopic capabilities to compact imaging devices for a number of applications ranging from spectral sorting to visible and NIR multispectral imaging and detection.

We investigate light transport in novel three-dimensional scattering systems generated according to subrandom sequences and demonstrate subdiffusive behavior typical of wave transport in disordered systems at the critical point for metal-insulator-transitions but in a wider range of parameters. Specifically, we solve the electromagnetic multiple scattering problem using the Green's matrix spectral theory for aperiodic systems based on Halton, Sobol, and stochastic Latin-Hypercube sequences. By studying the Thouless number and the level spacing statistics of the electromagnetic resonances at different scattering density we demonstrate that light transport in deterministic Halton and Sobol structures exhibit multifractal behavior characterized by inverse power law scaling of level spacing statistics across a wide range of densities of dipolar scatterers. On the other hand, this scenario is absent in the stochastic Latin-Hypercube array, whose behavior resembles instead standard diffusion in uniform random media. Our findings establish a connection between subdiffusion and subrandom aperiodic order and provide a novel strategy to design three-dimensional structures with multifractal properties over a broad spectral range., Comment: 11 pages, 5 figures

Many natural patterns and shapes, such as meandering coastlines, clouds, or turbulent flows, exhibit a characteristic complexity mathematically described by fractal geometry. In recent years, the engineering of self-similar structures in photonics and nano-optics technology enabled the manipulation of light states beyond periodic or disordered systems, adding novel functionalities to complex optical media with applications to nano-devices and metamaterials. Here, we extend the reach of fractal "photonics" by experimentally demonstrating multifractality of light in engineered arrays of dielectric nanoparticles. Our findings stimulate fundamental questions on the nature of transport and localization of wave excitations with multi-scale fluctuations beyond what is possible in traditional fractal systems. Moreover, our approach establishes structure-property relationships that can readily be transferred to planar semiconductor electronics and to artificial atomic lattices, enabling the exploration of novel quantum phases and many-body effects that emerge directly from fundamental structures of algebraic number theory., Comment: 15 pages, 23 pages

Enhancing light-matter interactions on a chip is of paramount importance to study nano- and quantum optics effects and to realise integrated devices, for instance, for classical and quantum photonics, sensing and energy harvesting applications. Engineered nano-devices enable the efficient confinement of light and the control of the spontaneous emission dynamics of single emitters, which is crucial for cavity quantum electrodynamics experiments and for the development of classical and quantum light sources. Here, we report on the demonstration of enhanced light-matter interaction and Purcell effects on a chip, based on bio-inspired aperiodic devices fabricated in silicon nitride and gallium arsenide. Internal light sources, namely optically-active defect centers in silicon nitride and indium arsenide single quantum dots, are used to image and characterize, by means of micro-photoluminescence spectroscopy, the individual optical modes confined by photonic membranes with Vogel-spiral geometry. By studying the statistics of the measured optical resonances, in partnership with rigorous multiple scattering theory, we observe log-normal distributions and report quality factors with values as high as 2201+/-443. Building on the strong light confinement achieved in this novel platform, we further investigate the coupling of single semiconductor quantum dots to the confined optical modes. Our results show cavity quantum electrodynamics effects providing strong modifications of the spontaneous emission decay of single optical transitions: we show control of the decay lifetime of single emitters with a dynamic range reaching 20. Our findings improve the understanding of the fundamental physical properties of light-emitting Vogel-spiral systems, show their application to quantum photonic devices, and form the basis for the further development of classical and quantum active devices on a chip., Comment: 32 pages, 11 figures

We design and characterize a novel axilens-based diffractive optics platform that flexibly combines efficient point focusing and grating selectivity and is compatible with scalable top-down fabrication based on a 4-level phase mask configuration. This is achieved using phase-modulated compact axilens devices that simultaneously focus incident radiation of selected wavelengths at predefined locations with larger focal depths compared to traditional Fresnel lenses. In addition, the proposed devices are polarization insensitive and maintain a large focusing efficiency over a broad spectral band. Specifically, here we discuss and characterize modulated axilens configurations designed for long-wavelength infrared (LWIR) in the $6~\mu$m--12~$\mu$m wavelength range and in the $4~\mu$m--6~$\mu$m mid-wavelength infrared (MWIR) range. These devices are ideally suited for monolithic integration atop the substrate layers of infrared focal plane arrays (IR-FPAs) and for use as compact microspectrometers. We systematically study their focusing efficiency, spectral response, and cross talk ratio, and we demonstrate linear control of multi-wavelength focusing on a single plane. Our design method leverages Rayleigh-Sommerfeld (RS) diffraction theory and is validated numerically using the Finite Element Method (FEM). Finally, we demonstrate the application of spatially modulated axilenses to the realization of compact, single-lens spectrometer. By optimizing our devices, we achieve a minimum distinguishable wavelength interval of $\Delta\lambda=240nm$ at $\lambda_0=8{\mu}m$ and $\Delta\lambda=165nm$ at $\lambda_0=5{\mu}m$. The proposed devices add fundamental spectroscopic capabilities to compact imaging devices for a number of applications ranging from spectral sorting to LWIR and MWIR phase contrast imaging and detection.

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 paper we employ the emerging paradigm of physics-informed neural networks (PINNs) for the solution of representative inverse scattering problems in photonic metamaterials and nano-optics technologies. In particular, we successfully apply mesh-free PINNs to the difficult task of retrieving the effective permittivity parameters of a number of finite-size scattering systems that involve many interacting nanostructures as well as multi-component nanoparticles. Our methodology is fully validated by numerical simulations based on the Finite Element Method (FEM). The development of physics-informed deep learning techniques for inverse scattering can enable the design of novel functional nanostructures and significantly broaden the design space of metamaterials by naturally accounting for radiation and finite-size effects beyond the limitations of traditional effective medium theories.

We study the compact localized scattering resonances of periodic and aperiodic chains of dipolar nanoparticles by combining the powerful Equitable Partition Theorem (EPT) of graph theory with the spectral dyadic Green's matrix formalism for the engineering of embedded quasi-modes in non-Hermitian open scattering systems in three spatial dimensions. We provide analytical and numerical design of the spectral properties of compact localized states in electromagnetically coupled chains and establish a connection with the distinctive behavior of Bound States in the Continuum. Our results extend the concept of compact localization to the scattering resonances of open systems with arbitrary aperiodic order beyond tight-binding models, and are relevant for the efficient design of novel photonic and plasmonic metamaterial architectures for enhanced light-matter interaction., Comment: 5 pages,3 figures

We propose a real-space approach explaining and controlling the occurrence of edge-localized gap states between the spectral quasibands of binary tight binding chains with deterministic aperiodic long-range order. The framework is applied to the Fibonacci, Thue-Morse and Rudin-Shapiro chains, representing different structural classes. Our approach is based on an analysis of the eigenstates at weak inter-site coupling, where they are shown to generically localize on locally reflection-symmetric substructures which we call local resonators. A perturbation theoretical treatment demonstrates the local symmetries of the eigenstates. Depending on the degree of spatial complexity of the chain, the proposed local resonator picture can be used to predict the occurrence of gap-edge states even for stronger couplings. Moreover, we connect the localization behavior of a given eigenstate to its energy, thus providing a quantitative connection between the real-space structure of the chain and its eigenvalue spectrum. This allows for a deeper understanding, based on local symmetries, of how the energy spectra of binary chains are formed. The insights gained allow for a systematic analysis of aperiodic binary chains and offers a pathway to control structurally induced edge states.

We study the scattering resonances of one-dimensional deterministic aperiodic chains of electric dipoles using the vectorial Green's matrix method, which accounts for both short- and long-range electromagnetic interactions in open scattering systems. We discover the existence of edge-localized scattering states within fractal energy gaps with characteristic topological band structures. Notably, we report and characterize edge-localized modes in the classical wave analogues of the Su-Schrieffer-Heeger (SHH) dimer model, quasiperiodic Harper and Fibonacci crystals, as well as in more complex Thue-Morse aperiodic systems. Our study demonstrates that topological edge-modes with characteristic power-law envelope appear in open aperiodic systems and coexist with traditional exponentially localized ones. Our results extend the concept of topological states to the scattering resonances of complex open systems with aperiodic order, thus providing an important step towards the predictive design of topological optical metamaterials and devices beyond tightbinding models., Comment: 4 pages, 4 figures

We present a theory for the cloaking of arbitrarily-shaped objects and demonstrate electromagnetic scattering-cancellation through designed homogeneous coatings. First, in the small-particle limit, we expand the dipole moment of a coated object in terms of its resonant modes. By zeroing the numerator of the resulting rational function, we accurately predict the permittivity values of the coating layer that abates the total scattered power. Then, we extend the applicability of the method beyond the small-particle limit, deriving the radiation corrections of the scattering-cancellation permittivity within a perturbation approach. Our method permits the design of invisibility cloaks for irregularly-shaped devices such as complex sensors and detectors.

We present a full-wave analytical solution for the problem of second-harmonic generation from spherical nanoparticles. The sources of the second-harmonic radiation are represented through an effective nonlinear polarization. The solution is derived in the framework of the Mie theory by expanding the pump field, the nonlinear sources and the second-harmonic fields in series of spherical vector wave functions. We use the proposed solution for studying the second-harmonic radiation generated from gold nanospheres as function of the pump wavelength and the particle size, in the framework of the Rudnick-Stern model. We demonstrate the importance of high-order multipolar contributions to the second-harmonic radiated power. Moreover, we investigate the p- and s- components of the SH radiation as the Rudnick-Stern parameters change, finding a strong variation. This approach provides a rigorous methodology to understand second-order optical processes in metal nanoparticles, and to design novel nanoplasmonic devices in the nonlinear regime., Comment: 16 pages, 10 figures

Quantum cryptography and quantum key distribution (QKD) have been the most successful applications of quantum information processing, highlighting the unique capability of quantum mechanics, through the no-cloning theorem, to protect the security of shared encryption keys. Here we present a new and fundamentally different approach to high-capacity, high-efficiency QKD by exploiting interplay between cross-disciplinary ideas from quantum information and light scattering of aperiodic photonic media. The novelty of the proposed approach relies on a unique type of entangled-photon source and a new physical mechanism for efficiently sharing keys. The new source produces entangled photons with orbital angular momenta (OAM) randomly distributed among Fibonacci numbers. Combining entanglement with the mathematical properties of Fibonacci sequences leads to a new QKD protocol. This Fibonacci protocol is immune to photon-number-splitting attacks and allows secure generation of long keys from few photons. Unlike other protocols, reference frame alignment and active modulation of production and detection bases are unnecessary, since security does not require use of non-orthogonal polarization measurements.

We present a numerical study on photonic bandgap and bandedge modes in the golden-angle spiral array of air cylinders in dielectric media. Despite the lack of long-range translational and rotational order, there is a large PBG for the TE polarized light. Due to spatial inhomogeneity in the air hole spacing, the bandedge modes are spatially localized by Bragg scattering from the parastichies in the spiral structure. They have discrete angular momenta that originate from different families of the parastichies whose numbers correspond to the Fibonacci numbers. The unique structural characteristics of the golden-angle spiral lead to distinctive features of the bandedge modes that are absent in both photonic crystals and quasicrystals., Comment: 12pages, 12 figures

One-dimensional nanobeam photonic crystal cavities are fabricated in an Er-doped amorphous silicon nitride layer. Photoluminescence from the cavities around 1.54 um is studied at cryogenic and room temperatures at different optical pump powers. The resonators demonstrate Purcell enhanced absorption and emission rates, also confirmed by time-resolved measurements. Resonances exhibit linewidth narrowing with pump power, signifying absorption bleaching and the onset of stimulated emission in the material at both 5.5 K and room temperature. We estimate from the cavity linewidths that Er has been pumped to transparency at the cavity resonance wavelength., Comment: 10 pages, 7 figures

Optical fiber tapers are used to collect photoluminescence emission at ~1.5 um from photonic crystal cavities fabricated in erbium doped silicon nitride on silicon. Photoluminescence collection via fiber taper is enhanced 2.5 times relative to free space, with a total taper collection efficiency of 53%. By varying the fiber taper offset from the cavity, a broad tuning range of coupling strength is obtained. This material system combined with fiber taper collection is promising for building on-chip optical amplifiers., Comment: 10 pages, 7 figures

Stimulated emission of sensitized Erbium atoms is reported in silicon-rich silicon nitride waveguides. Visible pump and infrared probe measurements are carried out in waveguides fabricated from erbium-doped silicon rich silicon nitride. A decrease in the photoinduced absorption of the probe in the wavelength range of the erbium emission is observed and is attributed to stimulated emission from erbium atoms excited indirectly via the silicon excess in an SiNx matrix. A near 50% decrease in absorption is measured, corresponding to an 8% fraction of inverted erbium atoms. This fraction is an order of magnitude higher than that obtained in counterpart oxide systems possessing observable nanocrystals. Our results indicate that population inversion and gain at 1.54 um might be possible by optimizing the silicon excess in the SiNx matrix.

Plasmonic gratings and nano-particle arrays in a metal-insulator-metal structures are fabricated on an erbium doped silicon nitride layer. This material system enables simple fabrication of the structure, since the active nitride layer can be directly grown on metal. Enhancement of collected emission of up to 12 is observed on resonance, while broad off-resonant enhancement is also present. The output polarization behavior of the gratings and nano-particle arrays is investigated and matched to plasmonic resonances, and the behavior of coupled modes as a function of inter-particle distance is also discussed., Comment: 9 pages, 6 figures updated because pdf was still non-functional

Based on the rigorous generalized Mie theory solution of Maxwell's equations for dielectric cylinders we theoretically investigate the optical properties of two-dimensional deterministic structures based on the Fibonacci, Thue-Morse and Rudin-Shapiro aperiodic sequences. In particular, we investigate band-gap formation and mode localization properties in aperiodic photonic structures based on the accurate calculation of their Local Density of States (LDOS). In addition, we explore the potential of photonic structures based on aperiodic order for the engineering of radiative rates and emission patterns in Erbium-doped silicon-rich nitride photonic structures., Comment: 4 pages with 5 figures (to appear in Physica E, 40, 2008)