Suppression and restoration of disorder‐induced light localization mediated by ‐symmetry breaking

We uncover that the breaking point of the ‐symmetry in optical waveguide arrays has a dramatic impact on light localization induced by the off‐diagonal disorder. Specifically, when the gain/loss control parameter approaches a critical value at which ‐symmetry breaking occurs, a fast growth of the coupling between neighboring waveguides causes diffraction to dominate to an extent that light localization is strongly suppressed and the statistically averaged width of the output pattern substantially increases. Beyond the symmetry‐breaking point localization is gradually restored, although in this regime the power of localized modes grows upon propagation. The strength of localization monotonically increases with disorder at both broken and unbroken ‐symmetry. Our findings are supported by statistical analysis of parameters of stationary eigenmodes of disordered‐symmetric waveguide arrays and by analysis of dynamical evolution of single‐site excitations in such structures.

     

Nonlinear absorption and refraction in crystalline silicon in the mid‐infrared

The wavelength dependence of the nonlinear absorption and the third order nonlinear refraction of crystalline silicon between m and m as well as at m have been measured. It was found that at all wavelengths multi‐photon and free carrier absorption can be significant. In particular nonlinear absorption can affect silicon devices designed for the mid‐infrared that require strong nonlinear response, such as for the generation of a supercontinuum.     

Observation of optomechanical coupling in a microbottle resonator

In this work, we report optomechanical coupling, resolved sidebands and phonon lasing in a solid‐core microbottle resonator fabricated on a single mode optical fiber. Mechanical modes with quality factors (Q_m) as high as 1.57 × 10⁴ and 1.45 × 10⁴ were observed, respectively, at the mechanical frequencies and . The maximum  Hz is close to the theoretical lower bound of 6 × 10¹² Hz needed to overcome thermal decoherence for resolved‐sideband cooling of mechanical motion at room temperature, suggesting microbottle resonators as a possible platform for this endeavor. In addition to optomechanical effects, scatter‐induced mode splitting and ringing phenomena, which are typical for high‐quality optical resonances, were also observed in a microbottle resonator.

     

Three‐dimensional ultra‐broadband integrated tapered mode multiplexers

The demonstration of a three‐dimensional tapered mode‐selective coupler in a photonic chip is reported. This waveguide‐based, ultra‐broadband mode multiplexer was fabricated using the femtosecond laser direct‐write technique in a boro‐aluminosilicate glass chip. A three‐core coupler has been shown to enable the multiplexing of the LP₀₁, LP and LP spatial modes of a multimode waveguide, across an extremely wide bandwidth exceeding 400 nm, with low loss, high mode extinction ratios and negligible mode crosstalk. Linear cascades of such devices on a single photonic chip have the potential to become a definitive technology in the realization of broadband mode‐division multiplexing for increasing optical fiber capacity.     

Splitting of magnetic dipole modes in anisotropic TiO2 micro‐spheres

Monocrystalline titanium dioxide (TiO₂) micro‐spheres support two orthogonal magnetic dipole modes at terahertz (THz) frequencies due to strong dielectric anisotropy. For the first time, we experimentally detected the splitting of the first Mie mode in spheres of radii m through near‐field time‐domain THz spectroscopy. By fitting the Fano lineshape model to the experimentally obtained spectra of the electric field detected by the sub‐wavelength aperture probe, we found that the magnetic dipole resonances in TiO₂ spheres have narrow linewidths of only tens of gigahertz. Anisotropic TiO₂ micro‐resonators can be used to enhance the interplay of magnetic and electric dipole resonances in the emerging THz all‐dielectric metamaterial technology.

     

Control of surface charge for high‐fidelity nanostructuring of materials

The universal problem of surface charging during focused ion milling has been fully resolved using a flood‐gun approach based on simultaneous co‐illumination with a UV light‐emitting diode (LED). Non‐distorted as‐designed nano‐patterns were milled using Ga⁺ ions on dielectric materials which charge up strongly. Deep‐UV (250–280 nm) LED co‐illumination during the ion beam milling fully discharges optically the surface under standard Ga⁺ ion‐milling conditions. Photo‐ionization of electrons trapped at the sub‐surface defects to the free vacuum state is a key to the phenomenon ( nm corresponds to a photon energy  eV). The method is applicable as a solution to other charging problems where electrons (primary or secondary) and their spatial redistribution affect nanofabrication or imaging.     

PT symmetry in a fractional Schrödinger equation

We investigate the fractional Schrödinger equation with a periodic ‐symmetric potential. In the inverse space, the problem transfers into a first‐order nonlocal frequency‐delay partial differential equation. We show that at a critical point, the band structure becomes linear and symmetric in the one‐dimensional case, which results in a nondiffracting propagation and conical diffraction of input beams. If only one channel in the periodic potential is excited, adjacent channels become uniformly excited along the propagation direction, which can be used to generate laser beams of high power and narrow width. In the two‐dimensional case, there appears conical diffraction that depends on the competition between the fractional Laplacian operator and the ‐symmetric potential. This investigation may find applications in novel on‐chip optical devices.

     

Microresonator Kerr frequency combs with high conversion efficiency

Microresonator‐based Kerr frequency comb (microcomb) generation can potentially revolutionize a variety of applications ranging from telecommunications to optical frequency synthesis. However, phase‐locked microcombs have generally had low conversion efficiency limited to a few percent. Here we report experimental results that achieve conversion efficiency ( on‐chip comb power excluding the pump) in the fiber telecommunication band with broadband mode‐locked dark‐pulse combs. We present a general analysis on the efficiency which is applicable to any phase‐locked microcomb state. The effective coupling condition for the pump as well as the duty cycle of localized time‐domain structures play a key role in determining the conversion efficiency. Our observation of high efficiency comb states is relevant for applications such as optical communications which require high power per comb line.

     

Spectral engineering of coupled open‐access microcavities

Open‐access microcavities are emerging as a new approach to confine and engineer light at mode volumes down to the λ³ regime. They offer direct access to a highly confined electromagnetic field while maintaining tunability of the system and flexibility for coupling to a range of matter systems. This article presents a study of coupled cavities, for which the substrates are produced using Focused Ion Beam milling. Based on experimental and theoretical investigation the engineering of the coupling between two microcavities with radius of curvature of 6 m is demonstrated. Details are provided by studying the evolution of spectral, spatial and polarisation properties through the transition from isolated to coupled cavities. Normal mode splittings up to 20 meV are observed for total mode volumes around . This work is of importance for future development of lab‐on‐a‐chip sensors and photonic open‐access devices ranging from polariton systems to quantum simulators.

     

The Spin‐Charge‐Family Theory Offers Understanding of the Triangle Anomalies Cancellation in the Standard Model

The standard model has for massless quarks and leptons “miraculously” no triangle anomalies due to the fact that the sum of all possible traces — where and are the generators of one, of two or of three of the groups and U (1) — over the representations of one family of the left handed fermions and anti‐fermions (and separately of the right handed fermions and anti‐fermions), contributing to the triangle currents, is equal to zero. 1 - 4 It is demonstrated in this paper that this cancellation of the standard model triangle anomaly follows straightforwardly if the and are the subgroups of the orthogonal group , as it is in the spin‐charge‐family theory. 5 - 22 We comment on the anomaly cancellation, which works if handedness and charges are related “by hand”.     

Towards the Standard Model in F‐theory

This article explores possible embeddings of the Standard Model gauge group and its matter representations into F‐theory. To this end we construct elliptic fibrations with gauge group as suitable restrictions of a ‐fibration with rank‐two Mordell‐Weil group. We analyse the five inequivalent toric enhancements to gauge group along two independent divisors W₃ and W₂ in the base. For each of the resulting smooth fibrations, the representation spectrum generically consists of a bifundamental , three types of representations and five types of representations (plus conjugates), in addition to charged singlet states. The precise spectrum of zero‐modes in these representations depends on the 3‐form background. We analyse the geometrically realised Yukawa couplings among all these states and find complete agreement with field theoretic expectations based on their U(1) charges. We classify possible identifications of the found representations with the Standard Model field content extended by right‐handed neutrinos and extra singlets. The linear combination of the two abelian gauge group factors orthogonal to hypercharge acts as a selection rule which, depending on the specific model, can forbid dangerous dimension‐four and ‐five proton decay operators.     

Beryllium Silicate,Be2SiO4 (phenakite) – a Novel Trigonal SRS‐Active Crystal

In single crystals of the beryllium silicate Be₂SiO₄ with trigonal symmetry , known also as the mineral phenakite, χ⁽³⁾‐nonlinear lasing by stimulated Raman scattering (SRS) is investigated. All observed Stokes and anti‐Stokes lasing components are identified and ascribed to a single SRS‐promoting vibration mode with ω_SRS ≈876 cm⁻¹. With picosecond single‐wavelength pumping at one micrometer the generation of an octave‐spanning Stokes and anti‐Stokes comb is observed.     

Half‐Maximal Supersymmetry from Exceptional Field Theory

We study ‐dimensional half‐maximal flux backgrounds using exceptional field theory. We define the relevant generalised structures and also find the integrability conditions which give warped half‐maximal Minkowski_D and AdS_D vacua. We then show how to obtain consistent truncations of type II / 11‐dimensional SUGRA which break half the supersymmetry. Such truncations can be defined on backgrounds admitting exceptional generalised structures, where , and N is the number of vector multiplets obtained in the lower‐dimensional theory. Our procedure yields the most general embedding tensors satisfying the linear constraint of half‐maximal gauged SUGRA. We use this to prove that all half‐maximal warped AdS_D and Minkowski_D vacua of type II / 11‐dimensional SUGRA admit a consistent truncation keeping only the gravitational supermultiplet. We also show to obtain heterotic double field theory from exceptional field theory and comment on the M‐theory / heterotic duality. In five dimensions, we find a new SO(5, N ) double field theory with a ‐dimensional extended space. Its section condition has one solution corresponding to 10‐dimensional supergravity and another yielding six‐dimensional SUGRA.     

Hodge numbers for CICYs with symmetries of order divisible by 4

We compute the Hodge numbers for the quotients of complete intersection Calabi‐Yau three‐folds by groups of orders divisible by 4. We make use of the polynomial deformation method and the counting of invariant Kähler classes. The quotients studied here have been obtained in the automated classification of V. Braun. Although the computer search found the freely acting groups, the Hodge numbers of the quotients were not calculated. The freely acting groups, G, that arise in the classification are either or contain , , or as a subgroup. The Hodge numbers for the quotients for which the group G contains or have been computed previously. This paper deals with the remaining cases, for which or . We also compute the Hodge numbers for 99 of the 166 CICY's which have quotients.     

inflation from scale invariant supergravity and anomaly free superstrings with fluxes

The scale invariant gravity theory coupled to conformally invariant matter is investigated. We show that in the non‐supersymmetric case the conformally coupled scalars belong to an manifold, while in the supersymmetric case the scalar manifold becomes isomorphic to the Kählerian space =. In both cases when the underlying scale symmetry is preserved the vacuum corresponds to de Sitter space. Once the scale symmetry is broken by quantum effects, a transition to flat space becomes possible. We argue that the scale violating terms are induced by anomalies related to a symmetry. The anomaly is resolved via the gauging of a Peccei‐Quinn axion shift symmetry. The theory describes an inflationary transition from de Sitter to flat Minkowski space, very similar to the Starobinsky inflationary model. The extension to metastable de Sitter superstring vacua is also investigated. The scalar manifold is extended to a much richer manifold, but it contains always as a sub‐manifold. In superstrings the metastability is induced by axions that cure the anomalies in chiral (or even ) supersymmetric vacua via a Green‐Schwarz/Peccei‐Quinn mechanism generalized to four dimensions. We present some typical superstring models and discuss the possible stabilization of the no‐scale modulus.     

Exceptional Calabi–Yau spaces: the geometry of backgrounds with flux

In this paper we define the analogue of Calabi–Yau geometry for generic , flux backgrounds in type II supergravity and M‐theory. We show that solutions of the Killing spinor equations are in one‐to‐one correspondence with integrable, globally defined structures in generalised geometry. Such “exceptional Calabi–Yau” geometries are determined by two generalised objects that parametrise hyper‐ and vector‐multiplet degrees of freedom and generalise conventional complex, symplectic and hyper‐Kähler geometries. The integrability conditions for both hyper‐ and vector‐multiplet structures are given by the vanishing of moment maps for the “generalised diffeomorphism group” of diffeomorphisms combined with gauge transformations. We give a number of explicit examples and discuss the structure of the moduli spaces of solutions. We then extend our construction to and flux backgrounds preserving eight supercharges, where similar structures appear, and finally discuss the analogous structures in generalised geometry.     

The c‐map,Tits Satake subalgebras and the search for inflaton potentials

In this paper we address the general problem of including inflationary models exhibiting Starobinsky‐like potentials into (symmetric) supergravities. This is done by gauging suitable abelian isometries of the hypermultiplet sector and then truncating the resulting theory to a single scalar field. By using the characteristic properties of the global symmetry groups of the supergravities we are able to make a general statement on the possible α‐attractor models which can obtained upon truncation. We find that in symmetric models group theoretical constraints restrict the allowed values of the parameter α to be . This confirms and generalizes results recently obtained in the literature. Our analysis heavily relies on the mathematical structure of symmetric supergravities, in particular on the so called c‐map connection between Quaternionic Kähler manifolds starting from Special Kähler ones. A general statement on the possible consistent truncations of the gauged models, leading to Starobinsky‐like potentials, requires the essential help of Tits Satake universality classes. The paper is mathematically self‐contained and aims at presenting the involved mathematical structures to a public not only of physicists but also of mathematicians. To this end the main mathematical structures and the general gauging procedure of supergravities is reviewed in some detail.     

New Gaugings and Non‐Geometry

We discuss the possible realisation in string/M theory of the recently discovered family of four‐dimensional maximal gauged supergravities, and of an analogous family of seven‐dimensional half‐maximal gauged supergravities. We first prove a no‐go theorem that neither class of gaugings can be realised via a compactification that is locally described by ten‐ or eleven‐dimensional supergravity. In the language of Double Field Theory and its M theory analogue, this implies that the section condition must be violated. Introducing the minimal number of additional coordinates possible, we then show that the standard S ³ and S ⁷ compactifications of ten‐ and eleven‐dimensional supergravity admit a new class of section‐violating generalised frames with a generalised Lie derivative algebra that reproduces the embedding tensor of the and gaugings respectively. The physical meaning, if any, of these constructions is unclear. They highlight a number of the issues that arise when attempting to apply the formalism of Double Field Theory to non‐toroidal backgrounds. Using a naive brane charge quantisation to determine the periodicities of the additional coordinates restricts the gaugings to an infinite discrete set and excludes all the gaugings other than the standard one.     

Supersymmetric M2‐branes with Englert fluxes,and the simple group PSL(2, 7)

A new class is introduced of M2‐branes solutions of d=11 supergravity that include internal fluxes obeying Englert equation in 7‐dimensions. A simple criterion for the existence of Killing spinors in such backgrounds is established. Englert equation is viewed as the generalization to d=7 of Beltrami equation defined in d=3 and it is treated accordingly. All 2‐brane solutions of minimal d=7 supergracity can be uplifted to d=11 and have supersymmetry. It is shown that the simple group PSL(2, 7) is crystallographic in d=7 having an integral action on the A7 root lattice. By means of this point‐group and of the T⁷ torus obtained quotiening with the A7 root lattice we were able to construct new M2 branes with Englert fluxes and . In particular we exhibit here an solution depending on 4‐parameters and admitting a large non abelian discrete symmetry, namely . The dual field theories have the same symmetries and have complicated non linear interactions.     

Minimal Bosonization of Supersymmetry with ‐graded Parity

In this paper we consider the ‐graded parity generalizing the ordinary (or Z₂‐graded ) parity. Using the ‐graded parity operator, we discuss the minimal bosonization of the N=2 SUSY with ‐graded parity. The lowest energy level is shown to be infinitely degenerate. In order to avoid the infinite degeneracy of the ground state we introduce the paraboson algebra to obtain the para‐supersymmetry. Finally, we discuss the hidden SUSY with Z₃‐graded parity.