arXiv subjects

Riccardo Franchi

Publications and source records attributed to Riccardo Franchi.

13 recordsLinked to original sources

arXiv2026

Quantum Theory of Third-harmonic Generation in Epsilon-Near-Zero Materials

We present a theoretical framework, based on the Green's tensor quantization method, to describe third-harmonic generation in epsilon-near-zero (ENZ) materials and derive analytical, closed-form solutions for the generation efficiency. We validate our model against experimental measurements of wavelength- and angle-resolved third-harmonic generation efficiency from 30 nm-thin ITO nanolayers at low pump intensity, described under the undepleted pump approximation. Our results provide a local and scalar effective model for quantum nonlinear processes in dispersive and lossy ENZ media, and establishes a simple and reliable framework for investigating a variety of nonlinear optical phenomena with applications to quantum sensing, quantum information, and quantum nondemolition measurements.

physics.optics↗

arXiv2026

Component structure and percolation in block models

The stochastic block model is a widely studied model of community structure in networks. Here we study the component structure and percolation properties of networks generated from this model and its variants, using exact methods based on probability generating functions. In particular, we derive expressions for the size of the giant component and the distribution of small components in such networks and for the size of the percolating cluster and position of the percolation threshold for both node and edge percolation, for the original stochastic block model and for its degree-corrected versions. In passing, we also develop a mapping between generating functions for microcanonical and canonical block models that allows us to generalize results for the former to the latter with minimal effort.

cs.SI↗

arXiv2026

Mid-Infrared Single-Photon Detection via Enhanced Cross-Phase Modulation in Topology-Optimized Epsilon-Near-Zero Dual-Wavelength Nanocavities

We use the Green's tensor quantization theory for open resonant nanostructures with absorption losses to study cross-phase modulation (XPM) at the single-photon level in nanoscale Kerr-type epsilon-near-zero (ENZ) materials with an effective nonlinear susceptibility integrated inside dual-wavelength nanocavities. We obtain analytical formulas for the XPM frequency shifts in hybrid nanocavities that simultaneously trap a classical probe beam at 1.5 $\mu$m and single-photon pump at 3 $\mu$m wavelengths. We present a comprehensive analysis of the fundamental limits for mid-infrared single-photon detection in the quantum nondemolition modality for nanostructured cadmium oxide (CdO) regions with ENZ-enhanced nonlinearity embedded in a silicon (Si) environment inversely designed by free-form topology optimization. We numerically implement our theoretical results using finite element simulations within the rigorous framework of quasi-normal modes, demonstrating a single-photon XPM frequency shift $\Delta f_s \approx 55.6 \text{ GHz}$ with fractional shift (i.e., frequency pulling) $\Delta f_s / f_s \approx 2.78 \times 10^{-4}$ and addressing the feasibility of detection in the hybrid Si-CdO dual-wavelength nanocavity, either with a classical probe beam or a squeezed probe state, including the contributions of traditional limitations from self-phase modulation noise, thermorefractive noise, shot noise, and free-carrier absorption effects. Finally, we present a comparative size scaling analysis of the XPM phase shift and phase noise contributions for dual-wavelength nanocavities based on CdO and indium tin oxide (ITO) nonlinear ENZ materials. This work establishes a robust benchmark for the engineering of mid-infrared single-photon nonlinear devices such as nondemolition quantum detectors, sensors, and all-optical gates on a solid state photonic platform.

physics.optics↗

arXiv2026

Structural and physical properties of gyromorphs and disordered stealthy hyperuniform media

Disordered stealthy hyperuniform materials combine liquid-like statistical isotropy with crystal-like homogeneity, suppressed density fluctuations at large length scales, bounded holes, and an isotropic structure factor that vanishes for a finite range of wavevectors. This combination yields unusual physical properties, including optical transparency, effective delocalization, ultrafast spreadability, optimal conductivity, and complete isotropic photonic bandgaps. Gyromorphs, point patterns whose structure factor includes rings of Bragg-like peaks arranged with discrete $G$-fold rotational symmetry, were recently introduced as counterexamples: disordered media that can somehow achieve the same physical properties, in some cases with higher performance, without stealthiness or hyperuniformity. In this paper, we resolve the puzzle of how gyromorphs fit consistently with the stealthy hyperuniform studies. We first show that gyromorphs are actually hyperuniform and, in the large-$G$ limit where they become nearly isotropic, belong to the weakest form of hyperuniformity, known as Class III. Thus, gyromorphs should have comparatively degraded physical properties compared to stealthy hyperuniform media, which belong to the strongest form of hyperuniformity, known as Class I. We verify this expectation using the rigorous spectral Green's matrix method for the calculation of the density of states (DOS) and Purcell factors in large arrays of electric dipoles. We find that gyromorphs display size-dependent pseudogaps richly populated by localized states rather than smooth band gaps like those found for highly stealthy hyperuniform materials or in deterministic structures such as Vogel spiral and triangular lattices. Furthermore, we predict similar disorder-induced degradation relative to stealthy hyperuniformity with regard to transparency, spreadability and diffusion properties.

physics.optics↗

arXiv2026

On-Chip Interferometric Excitation of an Infinity-Loop Microresonator

Integrated photonics is a powerful platform for exploring Hermitian and non-Hermitian physics. Beyond device geometry, controlling how resonators are driven is crucial to access and tailor their modes. Coherent excitation via multiple input ports (interferometric excitation) enables such control, but its accurate description requires extending standard temporal coupled-mode theory to include interference between excitation pathways. Experimental realizations have so far been limited by phase-unstable, off-chip interferometers. Here we implement a fully integrated, phase-stable interferometric excitation scheme for an infinity-loop-microresonator, an established structure operating on an exceptional surface, and use it to test the extended theory. Phase-resolved measurements in the linear and thermo-optic nonlinear regimes show that the relative phase between inputs governs the intracavity energy distribution, enabling up to a twofold increase of the circulating power compared to single-port excitation. This integrated platform enables reproducible studies of phase-dependent effects and coherent-control schemes in non-Hermitian photonic devices.

physics.optics↗

arXiv2025

Roadmap on Neuromorphic Photonics

This roadmap consolidates recent advances while exploring emerging applications, reflecting the remarkable diversity of hardware platforms, neuromorphic concepts, and implementation philosophies reported in the field. It emphasizes the critical role of cross-disciplinary collaboration in this rapidly evolving field.

cs.ET↗

arXiv2024

Nonlinear Quantum Electrodynamics of Epsilon-Near-Zero Nanocavities

We investigate single-photon nonlinear refractive index change and frequency shift of Epsilon-Near-Zero (ENZ) sub-wavelength nanocavities. We apply the rigorous quantum Langevin-noise approach in the framework of Green's tensor quantization method to realistic ENZ materials with causal dispersion and derive closed-form analytical solutions for cavities with spherical geometry. This is achieved by employing a fully nonperturbative methodology for the analysis of open quantum systems with single-photon Kerr-type nonlinearity. The analytical results are validated numerically using the established quasi-normal mode expansion method and extended to nonspherical nanocavity geometries that can be experimentally fabricated using state-of-the-art electron lithography. Our findings establish a rigorous benchmark for understanding single-photon nonlinear optical effects in Kerr-type ENZ nanostructures with losses and are of importance to emerging quantum technology applications, including on-chip single-photon nondemolition detection, quantum sensing, and controlled quantum gates driven by enhanced photon blockade effects at the nanoscale.

physics.optics↗

arXiv2024

The Taiji microresonator as an unidirectional spiking neuron

While biological neurons ensure unidirectional signalling, scalable integrated photonic neurons, such as silicon microresonators, respond the same way regardless of excitation direction due to the Lorentz reciprocity principle. Here, we show that a non-linear Taiji microresonator is a proper optical analogous of a biological neuron showing both a spiking response as well as a direction dependence response.

physics.optics↗

arXiv2023

An array of microresonators as a Photonic Extreme Learning Machine

Machine learning technologies have found fertile ground in optics due to its promising features based on speed and parallelism. Feed-forward neural networks are one of the most widely used machine learning algorithms due to their simplicity and universal approximation capability. However, the typical training procedure, where all weights are optimized, can be time and energy consuming. An alternative approach is the Extreme Learning Machine, a feed-forward neural network in which only the output weights are trained, while the internal connections are random. Here we present an experimental implementation of a photonic extreme learning machine (PELM) in an integrated silicon chip. The PELM is based on the processing of the image of the scattered light by an array of 18 gratings coupled to microresonators. Light propagation in the microresonator array is a linear process while light detection by the video camera is a nonlinear process. Training is done offline by analyzing the recorded scattered light image with a linear classifier. We provide a proof-of-concept demonstration of the PELM by solving both binary and analog tasks, and show how the performance depends on the number of microresonators used in the readout procedure.

cs.ET↗

arXiv2023

The infinity-loop microresonator: A new integrated photonic structure working on an exceptional surface

Exceptional points, where eigenvalues and eigenvectors coalesce, impact the behavior of different photonics components that show, e.g., enhanced sensing, coherent perfect absorption, unidirectional lasing, and chirality. However, only a few passive geometries have been developed that work on these points. Here, we introduce a novel non-Hermitian structure based on a microresonator shaped as the infinity symbol twice coupled to a bus waveguide: the infinity-loop microresonator. Unlike other structures working on an exceptional surface, the infinity-loop microresonator can achieve either high- or low-contrast unidirectional reflection with a negligible or identical reflection for counterpropagating light. It allows an easy walking through the Riemann sheet by simply controlling the phase of the light propagating in the bus waveguide, which makes it a tunable component to build more complex topological structures. Furthermore, the infinity-loop microresonator allows sensors that show the features of both an exceptional point device and a diabolic point device simultaneously.

physics.optics↗

arXiv2022

Interferometric cavity ring-down technique for ultra-high Q-factor microresonators

Microresonators (MRs) are key components in integrated optics. As a result, the estimation of their energy storage capacity as measured by the quality factor (Q) is crucial. However, in MR with high/ultra-high Q, the surface-wall roughness dominates the intrinsic Q and generates a coupling between counter-propagating modes. This splits the usual sharp single resonance and makes difficult the use of classical methods to assess Q. Here, we theoretically show that an interferometric excitation can be exploited in a Cavity Ring-Down (CRD) method to measure the ultimate Q of a MR. In fact, under suitable conditions, the resonant doublet merges into a single Lorentzian and the time dynamics of the MR assumes the usual behavior of a single-mode resonator unaffected by backscattering. This allows obtaining a typical exponential decay in the charging and discharging time of the MR, and thus, estimating its ultimate Q by measuring the photon lifetime.

physics.optics↗

arXiv2021

An interferometric method to estimate the eigenvalues of a Non-Hermitian two-level optical system

Non-Hermitian physics has found a fertile ground in optics. Recently, the study of mode degeneracies, i.e. exceptional points, has led to the discovery of intriguing and counterintuitive phenomena. Degeneracies are typically modeled through the coupled mode theory to determine the behaviour of eigenstates and eigenvalues. However, the complex nature of the eigenvalues makes hard their direct characterization from the response spectrum. Here, we demonstrate that a coherent interferometric excitation allows estimating both the real and imaginary parts of the eigenvalues. We studied the clockwise and counter-clockwise modes in an optical microresonators both in the case of Hermitian and non-Hermitian intermodal coupling. We show the conditions by which a resonant doublet, due to the dissipative coupling of counter-propagating modes caused by surface roughness backscattering, merges to a single Lorentzian. This permits to estimate the optimal quality factor of the microresonator in the absence of modal coupling caused by backscattering. Furthermore, we demonstrate that a taiji microresonator working at an exceptional point shows a degeneracy splitting only in one propagation direction and not in the other. This follows from the strongly non-Hermitian intermodal coupling caused by the inner S-shaped waveguide.

physics.optics↗

arXiv2021

Influence of the bus waveguide on the linear and nonlinear response of a taiji microresonator

We study the linear and nonlinear response of a unidirectional reflector where a nonlinear breaking of the Lorentz reciprocity is observed. The device under test consists of a racetrack microresonator, with an embedded S-shaped waveguide, coupled to an external bus waveguide (BW). This geometry of the microresonator, known as "taiji" microresonator (TJMR), allows to selectively couple counter-propagating modes depending on the propagation direction of the incident light and, at the nonlinear level, leads to an effective breaking of Lorentz reciprocity. Here, we show that a full description of the device needs to consider also the role of the BW, which introduces (i) Fabry-Perot oscillations (FPOs) due to reflections at its facets, and (ii) asymmetric losses, which depend on the actual position of the TJMR. At sufficiently low powers the asymmetric loss does not affect the unidirectional behavior, but the FP interference fringes can cancel the effect of the S-shaped waveguide. However, at high input power, both the asymmetric loss and the FPOs contribute to the redistribution of the energy between the clockwise and counterclockwise modes within the TJMR. This strongly modifies the nonlinear response, giving rise to counter-intuitive features where, due to the FP effect and the asymmetric losses, the BW properties can determine the violation of the Lorentz reciprocity and, in particular, the difference between the transmittance in the two directions of excitation. The experimental results are explained by using an analytical model based on the transfer matrix approach, a numerical finite-element model and exploiting intuitive interference diagrams.

physics.optics↗