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.

     

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.

     

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.     

Mapping the near fields of plasmonic nanoantennas by scattering‐type scanning near‐field optical microscopy

Near‐field optical microscopy techniques provide information on the amplitude and phase of local fields in samples of interest in nanooptics. However, the information on the near field is typically obtained by converting it into propagating far fields where the signal is detected. This is the case, for instance, in polarization‐resolved scattering‐type scanning near‐field optical microscopy (s‐SNOM), where a sharp dielectric tip scatters the local near field off the antenna to the far field. Up to now, basic models have interpreted S‐ and P‐polarized maps obtained in s‐SNOM as directly proportional to the in‐plane ( or ) and out‐of‐plane () near‐field components of the antenna, respectively, at the position of the probing tip. Here, a novel model that includes the multiple‐scattering process of the probing tip and the nanoantenna is developed, with use of the reciprocity theorem of electromagnetism. This novel theoretical framework provides new insights into the interpretation of s‐SNOM near‐field maps: the model reveals that the fields detected by polarization‐resolved interferometric s‐SNOM do not correlate with a single component of the local near field, but rather with a complex combination of the different local near‐field components at each point (, and ). Furthermore, depending on the detection scheme (S‐ or P‐polarization), a different scaling of the scattered fields as a function of the local near‐field enhancement is obtained. The theoretical findings are corroborated by s‐SNOM experiments which map the near field of linear and gap plasmonic antennas. This new interpretation of nanoantenna s‐SNOM maps as a complex‐valued combination of vectorial local near fields is crucial to correctly understand scattering‐type near‐field microscopy measurements as well as to interpret the signals obtained in field‐enhanced spectroscopy.

     

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.

     

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.     

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.

     

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.

     

A broadband,quasi‐continuous,mid‐infrared supercontinuum generated in a chalcogenide glass waveguide

The production of a broadband supercontinuum spanning from 1.8 μm to >7.5 μm is reported which was created by pumping a chalcogenide glass waveguide with ≈320 fs pulses at 4 μm. The total power was ≈20 mW and the source brightness was 100 that of current synchrotrons. This source promises to be an excellent laboratory tool for infrared microspectroscopy.     

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”.     

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.     

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.     

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.     

Higher‐Dimensional Unification with continuous and fuzzy coset spaces as extra dimensions

We first review the Coset Space Dimensional Reduction (CSDR) programme and present the best model constructed so far based on the , 10‐dimensional E₈ gauge theory reduced over the nearly‐Kähler manifold with the additional use of the Wilson flux mechanism. Then we present the corresponding programme in the case that the extra dimensions are considered to be fuzzy coset spaces and the best model that has been constructed in this framework too. In both cases the best model appears to be the trinification GUT .     

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.     

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.     

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.     

Room temperature all‐silicon photonic crystal nanocavity light emitting diode at sub‐bandgap wavelengths

Silicon is now firmly established as a high performance photonic material. Its only weakness is the lack of a native electrically driven light emitter that operates CW at room temperature, exhibits a narrow linewidth in the technologically important 1300–1600 nm wavelength window, is small and operates with low power consumption. Here, an electrically pumped all‐silicon nano light source around 1300–1600 nm range is demonstrated at room temperature. Using hydrogen plasma treatment, nano‐scale optically active defects are introduced into silicon, which then feed the photonic crystal nanocavity to enhance the electrically driven emission in a device via Purcell effect. A narrow ( nm) emission line at 1515 nm wavelength with a power density of is observed, which represents the highest spectral power density ever reported from any silicon emitter. A number of possible improvements are also discussed, that make this scheme a very promising light source for optical interconnects and other important silicon photonics applications.     

algebras and field theory

We review and develop the general properties of algebras focusing on the gauge structure of the associated field theories. Motivated by the homotopy Lie algebra of closed string field theory and the work of Roytenberg and Weinstein describing the Courant bracket in this language we investigate the structure of general gauge invariant perturbative field theories. We sketch such formulations for non‐abelian gauge theories, Einstein gravity, and for double field theory. We find that there is an algebra for the gauge structure and a larger one for the full interacting field theory. Theories where the gauge structure is a strict Lie algebra often require the full algebra for the interacting theory. The analysis suggests that algebras provide a classification of perturbative gauge invariant classical field theories.