arXiv subjects

Fabio Biancalana

Publications and source records attributed to Fabio Biancalana.

At least 19 recordsLinked to original sources

arXiv2026

Nonlinear wave dynamics in photonic time crystals

Maxwell's wave equation in the presence of a cubic nonlinearity and a periodically time-varying refractive index (a photonic time crystal) is reduced, for spatially monochromatic waves, to a nonlinear Mathieu equation. Near the principal momentum gap this equation admits an autonomous two-dimensional reduction whose complete Hamiltonian phase portrait can be obtained analytically. We derive the two homoclinic separatrices corresponding to temporally localised momentum gap solitons, identify the nonlinear centres and the critical Hamiltonian value $H_c$, and calculate the point of maximum linear parametric gain. We then consider spatially localised pulses and show how the nucleation of multiple spatiotemporal gap solitons can produce a broad supercontinuum in momentum space; for stronger seeds, transient extreme nonlinear localisation can accompany an abrupt additional broadening of this momentum spectrum. These results establish a direct connection between Floquet amplification, nonlinear saturation, homoclinic dynamics, and momentum space spectral broadening in nonlinear photonic time crystals.

physics.optics↗

arXiv2026

Real-time identification of the onset of financial rogue waves

Extreme events in financial systems, often captured by indicators such as volatility, remain difficult to identify close to their onset. Volatility shares many statistical properties with other natural, complex systems which experience extreme events, which we explore in this manuscript. We extend the analogy between rogue waves in optical and hydrodynamical systems to financial volatility by identifying rogue-wave-like peaks with similar statistical properties. We use a Schrödinger equation where the potential follows the shape of a Kerr nonlinearity to examine the properties of financial volatility indices within a moving time window. We see evidence of Anderson localisation as a rogue peak approaches in the VIX, and show that the numerical gradient of the system's minimum eigenvalue reliably spikes at the onset of an extreme event. We adapt our methodology to simulate the real-time arrival of data, and show that all but one of the VIX's major peaks can be detected given a reasonable amount of history. We then perform two out-of-sample tests, one for the VXO index, and one for the VSTOXX index, and successfully replicate our initial results, identifying all but one major peak (87.5% or 7/8) in both cases. This method of analysis shows considerable promise as a tool for identifying potential financial crises, aiding in their mitigation.

q-fin.ST↗

arXiv2026

The Quantum Split-Step Fourier Algorithm for Nonlinear Optical Waveguides

We introduce the Quantum Split-Step Fourier (QSSF) algorithm for nonlinear optical waveguides, a numerical framework that combines split-step propagation of the nonlinear Schrödinger equation with a commutator-preserving Bogoliubov evolution of Gaussian quantum fluctuations. The method propagates the classical mean field together with the Bogoliubov matrices $U$ and $V$, from which reduced second moments, covariance matrices, symplectic eigenvalues, and entropic measures are constructed for arbitrary spectral windows. Applied to soliton-driven resonant radiation, QSSF shows that the selected radiation band acquires a steadily increasing von Neumann entropy and a corresponding loss of purity, quantifying its entanglement with the rest of the spectrum in the lossless Gaussian setting. The analysis also reveals a surprisingly pronounced low-dimensional structure: although the radiation occupies many Fourier bins, its reduced Gaussian state is dominated by only a few Williamson modes. QSSF therefore provides a practical information-theoretic diagnostic for quantum correlations in nonlinear frequency conversion, supercontinuum generation, and multimode squeezed-light formation in ultrafast waveguide platforms.

physics.optics↗

arXiv2025

Spatio-spectral optical fission in time-varying subwavelength layers

Transparent conducting oxides are highly doped semiconductors that exhibit favourable characteristics when compared to metals, including reduced material losses, tuneable electronic and optical properties, and enhanced damage thresholds. Recently, the photonic community has renewed its attention towards these materials, recognizing their remarkable nonlinear optical properties in the near-infrared spectrum, a feature previously overlooked despite their long-standing application in photovoltaics and touchscreens. The exceptionally large and ultra-fast change of the refractive index, which can be optically induced in these compounds, extends beyond the boundaries of conventional perturbative analysis and makes this class of materials the closest approximation to a time-varying system, and a unique playground for studying a variety of novel phenomena within the domain of photon acceleration. Here we report the spatio-spectral fission of an ultra-fast pulse trespassing a thin film of aluminium zinc oxide with a non-stationary refractive index. By applying phase conservation to this time-varying layer, our model can account for both space and time refraction and explain in quantitative terms, the spatial separation of both the spectrum and energy. Our findings represent an example of extreme nonlinear phenomena on subwavelength propagation distances and shed light on the nature of several nonlinear effects recently reported not accounting for the full optical field distribution. Our work also provides new important insights into transparent conducting oxides transient optical properties which are critical for the ongoing research in photonic time crystals, on-chip generation of nonclassical states of light, integrated optical neural networks as well as ultra-fast beam steering and frequency division multiplexing

physics.optics↗

arXiv2022

Convergence of Combinatorial Gravity

We present a new regularisation of Euclidean Einstein gravity in terms of (sequences of) graphs. In particular, we define a discrete Einstein-Hilbert action that converges to its manifold counterpart on sufficiently dense random geometric graphs (more generally on any sequence of graphs that converges to the manifold in the sense of Gromov-Hausdorff). Our construction relies crucially on the Ollivier curvature of optimal transport theory. Our methods also allow us to define an analogous discrete action for Klein-Gordon fields. These results may be taken as the basis for a combinatorial approach to quantum gravity where we seek to generate graphs that approximate manifolds as metric-measure structures.

gr-qc↗

arXiv2021

New Insights into the Nature of Nonlinear Gravitational Waves

We study the evolution equations for gravitational waves, which are derived using the full metric to raise and lower indices. This method ensures full consistency between the Ricci tensor and all gauge restrictions and requirements, and allows a meaningful expansion of all tensors up to second order, avoiding several inconsistencies and contradictions observed in previous work. Taking the harmonic gauge to second order in the perturbation theory results in a new nonlinear equation. We show that non-trivial solutions to this equation are necessarily non-plane wave modes with a non-zero trace. These solutions must contain both longitudinal and transverse components, as both are permitted by the gauge restrictions.

gr-qc↗

arXiv2021

Reduction of nonlinear field theory equations to envelope models: towards a universal understanding of analogues of relativistic systems

We investigate a novel mapping between solutions to several members of the Klein-Gordon family of equations and solutions to equations describing their reductions via the slowly varying envelope approximation. This mapping creates a link between the study of interacting relativistic fields and that of systems more amenable to laboratory-based analogue research, the latter described by nonlinear Schrödinger equations. A new evolution equation is also derived, emerging naturally from the sine-Gordon formula, possessing a Bessel-function nonlinearity; numerical investigations show that solutions to this novel equation include quasi-solitary waves, breather solutions, along with pulse splittings and recombinations.

math-ph↗

arXiv2021

Generation of Half-Integer Harmonics and Efficient THz-to-Visible Frequency Conversion in Strained Graphene

We study the generation of harmonics from graphene under the influence of an artificial magnetic field, generated via bending of a graphene flake. We show how the Landau level structure induced by the pseudomagnetic field breaks the centrosymmetry of graphene, thus allowing the generation of even harmonics. We also show, that depending on the impinging pulse duration, the nonlinear signal does not only contain the integer harmonics of the impinging pulse, but also its half-integer ones, due to the peculiar square-root-like nature of Landau levels in graphene.

cond-mat.mes-hall↗

arXiv2021

Emergence of the Circle in a Statistical Model of Random Cubic Graphs

We consider a formal discretisation of Euclidean quantum gravity defined by a statistical model of random $3$-regular graphs and making using of the Ollivier curvature, a coarse analogue of the Ricci curvature. Numerical analysis shows that the Hausdorff and spectral dimensions of the model approach $1$ in the joint classical-thermodynamic limit and we argue that the scaling limit of the model is the circle of radius $r$, $S^1_r$. Given mild kinematic constraints, these claims can be proven with full mathematical rigour: speaking precisely, it may be shown that for $3$-regular graphs of girth at least $4$, any sequence of action minimising configurations converges in the sense of Gromov-Hausdorff to $S^1_r$. We also present strong evidence for the existence of a second-order phase transition through an analysis of finite size effects. This -- essentially solvable -- toy model of emergent one-dimensional geometry is meant as a controllable paradigm for the nonperturbative definition of random flat surfaces.

hep-th↗

arXiv2020

Ultra-broadband supercontinuum generation in gas-filled photonic-crystal fibers: The epsilon-near-zero regime

In this Letter, we show theoretically that the nonlinear photoionisation process of a noble gas inside a hollow-core photonic crystal fibre can be exploited in obtaining broadband supercontinuum generation via pumping close to the mid-infrared regime. The interplay between the Kerr and photoionisation nonlinearities is strongly enhanced in this regime. Photoionisation continuously modifies the medium dispersion, in which the refractive index starts to significantly decrease and approach the epsilon-near-zero regime. Subsequently, the self-phase modulation induced by the Kerr effect is boosted because of the accompanied slow-light effect. As a result of this interplay, an output spectrum that comprises of a broadband light with multiple dispersive-wave emission is obtained.

physics.optics↗

arXiv2020

Long-lived Nonlinear Oscillatory States in Interacting Relativistic Bose-Einstein Condensates

In this paper we study a mean field model for the dynamics of an interacting Bose-Einstein condensate in two dimensional pseudo-relativistic materials. This model is relatively simple, but contains stable solutions called oscillons which are absent in non-relativistic condensates. We report on a variety of scenarios including interactions between pairs of oscillons and oscillons propagating across an inhomogeneous material boundary. Hitherto relativistic oscillons have been studied only in high energy physics and cosmology and their relevance has not been highlighted so far in condensed matter physics.

nlin.PS↗

arXiv2020

Stationary States and Instabilities of a Mobius Fibre Resonator

We examine the steady state and dynamic behaviour of an optical resonator comprised of two interlinked fibre loops sharing a common pump. A coupled Ikeda map models with great accuracy the field evolution within and exchange between both fibres over a single roundtrip. We find this supports a range of rich multi-dimensional bistability in the continuous wave regime, as well as previously unseen cavity soliton states. Floquet analysis reveals that modulation and parametric instabilities occur over wider domains than in single-fibre resonators, which can be tailored by controlling the relative dispersion and resonance frequencies of the two fibre loops. Parametric instability gives birth to train of pulses with a peculiar period-doubling behavior.

physics.optics↗

arXiv2020

Role of Anisotropy in Nonlinear Harmonic Generation Across TMD Monolayers

Recent techniques have allowed transition metal dichalcogenides (TMD) monolayers to be grown and adequately characterised. Of particular interest, their nonlinear optical response presents many promising opportunities for future nanophotonic devices and technology. The dispersion of the carriers is trigonally-warped, leading to an anisotropic Fermi surface for low-lying states. In this paper, the effects of such a deformation on the nonlinear harmonic generation are studied by considering a tight-binding model expanded up to third order in $\mathbf{k} \cdot \mathbf{p}$. By solving exactly the free-carrier dynamics of the carriers when interacting with intense and ultrashort pulses of light, we predict the photogenerated current in a nonperturbative way and study its harmonic composition. We find frequency and amplitude modulation of the nonlinear current in quadratic and cubic models. Furthermore, we demonstrate anisotropy-induced modulation of the intensity of higher-order harmonics and the existence of harmonic crossovers, depending on the incident light polarisation. The methodology presented in this paper may be applied to any general effective two-band model and offer a pathway to identify signatures of electronic features in optical output.

cond-mat.mes-hall↗

arXiv2019

Angular Momentum Supercontinuum from Fibre Rings

Broadband, coherent light carrying optical angular momentum is of potential utility for a variety of classical and quantum communication applications, but at present few such sources exist. We study the generation of supercontinua in a ring array of coupled optical fibres. Short pulses carrying discrete angular momentum undergo soliton fission, spontaneously breaking azimuthal symmetry. This results in a train of pulses with a broadband frequency spectrum as well as a non-trivial angular momentum distribution. These spatio-temporal solitary waves, localised around a single fibre core, emit an unusual form of resonant radiation which can be present even in the absence of intrinsic higher order dispersion, being induced by the lattice dispersion of the ring array. We explore how the coupling properties between fibre cores affect the resulting supercontinuum, in particular how mildly twisting the array can effectively manipulate its angular momentum content and resonant frequencies through the induced Peierls phase.

physics.optics↗

arXiv2019

Polarisation and Transparency of Relativistically Rotating Two-Level Atoms

Electromagnetism and light-matter interaction in rotating systems is a rich area of ongoing research. We study the interaction of light with a gas of non-interacting two-level atoms confined to a rotating disk. We numerically solve the optical Bloch equations to investigate the how relativistic rotation affects the atoms' polarisation and inversion. The results are used to predict the steady-state stimulated emission seen by an observer at rest with the optical source in the laboratory frame. Competing physical effects due to time dilation and motion-induced detuning strongly modify solutions to the Bloch equations when the gas's velocity becomes relativistic. We account for the non-inertial motion by including acceleration-dependent excitation and emission rates, arising from a generalised Unruh effect. The effective thermal vacuum resulting from large accelerations de-polarises the gas while driving it towards population inversion, negating coherent driving due to the external light source. The results illustrate the intuitive, special-relativistic approach of assigning instantaneously comoving frames to understand non-inertial motion's influence when only local fields are physically significant.

physics.optics↗

arXiv2019

Self-Assembly of Geometric Space from Random Graphs

We present a Euclidean quantum gravity model in which random graphs dynamically self-assemble into discrete manifold structures. Concretely, we consider a statistical model driven by a discretisation of the Euclidean Einstein-Hilbert action; contrary to previous approaches based on simplicial complexes and Regge calculus our discretisation is based on the Ollivier curvature, a coarse analogue of the manifold Ricci curvature defined for generic graphs. The Ollivier curvature is generally difficult to evaluate due to its definition in terms of optimal transport theory, but we present a new exact expression for the Ollivier curvature in a wide class of relevant graphs purely in terms of the numbers of short cycles at an edge. This result should be of independent intrinsic interest to network theorists. Action minimising configurations prove to be cubic complexes up to defects; there are indications that such defects are dynamically suppressed in the macroscopic limit. Closer examination of a defect free model shows that certain classical configurations have a geometric interpretation and discretely approximate vacuum solutions to the Euclidean Einstein-Hilbert action. Working in a configuration space where the geometric configurations are stable vacua of the theory, we obtain direct numerical evidence for the existence of a continuous phase transition; this makes the model a UV completion of Euclidean Einstein gravity. Notably, this phase transition implies an area-law for the entropy of emerging geometric space. Certain vacua of the theory can be interpreted as baby universes; we find that these configurations appear as stable vacua in a mean field approximation of our model, but are excluded dynamically whenever the action is exact indicating the dynamical stability of geometric space. The model is intended as a setting for subsequent studies of emergent time mechanisms.

gr-qc↗

arXiv2019

The Hawking Temperature of Anti-de Sitter Black Holes: Topology and Phase Transitions

In this work we determine how the description of a four-dimensional Schwarzschild-anti de Sitter black hole affects the topological calculation of its Hawking temperature. It is shown that a two-dimensional approach is required due to the presence of the Hawking-Page phase transition which destabilises the spacetime's topology. We prove that a dimensional reduction removes the phase transition and hence stabilises the system. This hints at a previously unknown feature of black hole thermodynamics, namely that certain black holes may demand a lower-dimensional description in order to define their Hawking temperatures.

gr-qc↗

arXiv2019

Global Hawking Temperature of Schwarzschild-de Sitter Spacetime: a Topological Approach

We introduce a calculation, based on purely topological reasoning, of the global equilibrium Hawking temperature of the Schwarzschild-de Sitter spacetime, where a Schwarzschild black hole horizon coexists with a de Sitter cosmological horizon. Our method is based on the careful calculation of the Euler characteristic of the total system, showing that this quantity completely determines the thermodynamical features of the system. The method is universal and can be applied to any structure possessing multiple horizons in general relativity.

gr-qc↗