Optical geometric phase encoded by in-plane spatial orientation of microstructures has promoted the rapid development of numerous functional meta-devices. However, pushing the concept of the geometric phase toward the acoustic community still faces challenges. In this work, we utilize two acoustic nonlocal metagratings that could support a direct conversion between an acoustic plane wave and a designated vortex mode to obtain the acoustic geometric phase, in which an orbital angular momentum conversion process plays a vital role. In addition, we realize the acoustic geometric phases of different orders by merely varying the orientation angle of the acoustic nonlocal metagratings. Intriguingly, according to our developed theory, we reveal that the reflective acoustic geometric phase, which is twice the transmissive one, can be readily realized by transferring the transmitted configuration to a reflected one. Both the theoretical study and experimental measurements verify the announced transmissive and reflective acoustic geometric phases. Moreover, the reconfigurability and continuous phase modulation that covers the 2π range shown by the acoustic geometric phases provide us with the alternatives in advanced acoustic wavefront control.

In this paper we give an overview over some aspects of the modern mathematical theory of Ruelle resonances for chaotic, i.e. uniformly hyperbolic, dynamical systems and their implications in physics. First we recall recent developments in the mathematical theory of resonances, in particular how invariant Ruelle distributions arise as residues of weighted zeta functions. Then we derive a correspondence between weighted and semiclassical zeta functions in the setting of negatively curved surfaces. Combining this with results of Hilgert, Guillarmou and Weich yields a high frequency interpretation of invariant Ruelle distributions as quantum mechanical matrix coefficients in constant negative curvature. We finish by presenting numerical calculations of phase space distributions in the more physical setting of 3-disk scattering systems.

While plasmonic particles can provide optical resonances in a wide spectral range from the lower visible up to the near-infrared, often, symmetry effects are utilized to obtain particular optical responses. By breaking certain spatial symmetries, chiral structures arise and provide robust chiroptical responses to these plasmonic resonances. Here, we observe strong chiroptical responses in the linear and nonlinear optical regime for chiral L-handed helicoid-III nanoparticles and quantify them by means of an asymmetric factor, the so-called g-factor. We calculate the linear optical g-factors for two distinct chiroptical resonances to −0.12 and –0.43 and the nonlinear optical g-factors to −1.45 and −1.63. The results demonstrate that the chirality of the helicoid-III nanoparticles is strongly enhanced in the nonlinear regime.

Inspired by plant grafting, grafted vortex beams can be formed through grafting two or more helical phase profiles of optical vortex beams. Recently, grafted perfect vortex beams (GPVBs) have attracted much attention due to their unique optical properties and potential applications. However, the current method to generate and manipulate GPVBs requires a complex and bulky optical system, hindering further investigation and limiting its practical applications. Here, a compact metasurface approach for generating and manipulating GPVBs in multiple channels is proposed and demonstrated, which eliminates the need for such a complex optical setup. A single metasurface is utilized to realize various superpositions of GPVBs with different combinations of topological charges in four channels, leading to asymmetric singularity distributions. The positions of singularities in the superimposed beam can be further modulated by introducing an initial phase difference in the metasurface design. The work demonstrates a compact metasurface platform that performs a sophisticated optical task that is very challenging with conventional optics, opening opportunities for the investigation and applications of GPVBs in a wide range of emerging application areas, such as singular optics and quantum science.

Subwavelength dielectric resonators assembled into metasurfaces have become a versatile tool for miniaturizing optical components approaching the nanoscale. An important class of metasurface functionalities is associated with asymmetry in both the generation and transmission of light with respect to reversals of the positions of emitters and receivers. The nonlinear light–matter interaction in metasurfaces offers a promising pathway towards miniaturization of the asymmetric control of light. Here we demonstrate asymmetric parametric generation of light in nonlinear metasurfaces. We assemble dissimilar nonlinear dielectric resonators into translucent metasurfaces that produce images in the visible spectral range on being illuminated by infrared radiation. By design, the metasurfaces produce different and completely independent images for the reversed direction of illumination, that is, when the positions of the infrared emitter and the visible light receiver are exchanged. Nonlinearity-enabled asymmetric control of light by subwavelength resonators paves the way towards novel nanophotonic components via dense integration of large quantities of nonlinear resonators into compact metasurface designs.

We study the DC conductivity in potassium titanyl phosphate (KTiOPO4, KTP) and its isomorphs KTiOAsO4 (KTA) and Rb1%K99%TiOPO4 (RKTP) and introduce a method by which to reduce the overall ionic conductivity in KTP by a potassium nitrate treatment. Furthermore, we create so-called gray tracking in KTP and investigate the ionic conductivity in theses areas. A local unintended reduction of the ionic conductivity is observed in the gray-tracked regions, which also induce additional optical absorption in the material. We show that a thermal treatment in an oxygen-rich atmosphere removes the gray tracking and brings the ionic conductivity as well as the optical transmission back to the original level. These studies can help to choose the best material and treatment for specific applications.

<jats:p>Secret sharing is a well-established cryptographic primitive for storing highly sensitive information like encryption keys for encoded data. It describes the problem of splitting a secret into different shares, without revealing any information to its shareholders. Here, we demonstrate an all-optical solution for secret sharing based on metasurface holography. In our concept, metasurface holograms are used as spatially separable shares that carry encrypted messages in the form of holographic images. Two of these shares can be recombined by bringing them close together. Light passing through this stack of metasurfaces accumulates the phase shift of both holograms and optically reconstructs the secret with high fidelity. In addition, the hologram generated by each single metasurface can uniquely identify its shareholder. Furthermore, we demonstrate that the inherent translational alignment sensitivity between two stacked metasurface holograms can be used for spatial multiplexing, which can be further extended to realize optical rulers.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>For a compact Riemannian locally symmetric space $\mathcal M$ of rank 1 and an associated vector bundle $\mathbf V_{\tau }$ over the unit cosphere bundle $S^{\ast }\mathcal M$, we give a precise description of those classical (Pollicott–Ruelle) resonant states on $\mathbf V_{\tau }$ that vanish under covariant derivatives in the Anosov-unstable directions of the chaotic geodesic flow on $S^{\ast }\mathcal M$. In particular, we show that they are isomorphically mapped by natural pushforwards into generalized common eigenspaces of the algebra of invariant differential operators $D(G,\sigma )$ on compatible associated vector bundles $\mathbf W_{\sigma }$ over $\mathcal M$. As a consequence of this description, we obtain an exact band structure of the Pollicott–Ruelle spectrum. Further, under some mild assumptions on the representations $\tau$ and $\sigma$ defining the bundles $\mathbf V_{\tau }$ and $\mathbf W_{\sigma }$, we obtain a very explicit description of the generalized common eigenspaces. This allows us to relate classical Pollicott–Ruelle resonances to quantum eigenvalues of a Laplacian in a suitable Hilbert space of sections of $\mathbf W_{\sigma }$. Our methods of proof are based on representation theory and Lie theory.</jats:p>

Topological photonic crystals (TPhCs) provide robust manipulation of light with built-in immunity to fabrication tolerances and disorder. Recently, it was shown that TPhCs based on weak topology with a dislocation inherit this robustness and further host topologically protected lower-dimensional localized modes. However, TPhCs with weak topology at optical frequencies have not been demonstrated so far. Here, we use scattering-type scanning near-field optical microscopy to verify mid-bandgap zero-dimensional light localization close to 100 THz in a TPhC with nontrivial Zak phase and an edge dislocation. We show that because of the weak topology, differently extended dislocation centers induce similarly strong light localization. The experimental results are supported by full-field simulations. Along with the underlying fundamental physics, our results lay a foundation for the application of TPhCs based on weak topology in active topological nanophotonics, and nonlinear and quantum optic integrated devices because of their strong and robust light localization.

<jats:p>Compact and robust cold atom sources are increasingly important for quantum research, especially for transferring cutting-edge quantum science into practical applications. In this study, we report on a novel scheme that uses a metasurface optical chip to replace the conventional bulky optical elements used to produce a cold atomic ensemble with a single incident laser beam, which is split by the metasurface into multiple beams of the desired polarization states. Atom numbers ~10<jats:sup>7</jats:sup> and temperatures (about 35 μK) of relevance to quantum sensing are achieved in a compact and robust fashion. Our work highlights the substantial progress toward fully integrated cold atom quantum devices by exploiting metasurface optical chips, which may have great potential in quantum sensing, quantum computing, and other areas.</jats:p>

<jats:title>Abstract</jats:title><jats:p>Given a closed orientable hyperbolic manifold of dimension <jats:inline-formula><jats:alternatives><jats:tex-math>$$\ne 3$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>≠</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> we prove that the multiplicity of the Pollicott-Ruelle resonance of the geodesic flow on perpendicular one-forms at zero agrees with the first Betti number of the manifold. Additionally, we prove that this equality is stable under small perturbations of the Riemannian metric and simultaneous small perturbations of the geodesic vector field within the class of contact vector fields. For more general perturbations we get bounds on the multiplicity of the resonance zero on all one-forms in terms of the first and zeroth Betti numbers. Furthermore, we identify for hyperbolic manifolds further resonance spaces whose multiplicities are given by higher Betti numbers. </jats:p>

<jats:p>We consider a simple model of an open partially expanding map. Its trapped set <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0143385715000346_inline1" /><jats:tex-math>${\mathcal{K}}$</jats:tex-math></jats:alternatives></jats:inline-formula> in phase space is a fractal set. We first show that there is a well-defined discrete spectrum of Ruelle resonances which describes the asymptotic of correlation functions for large time and which is parametrized by the Fourier component <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0143385715000346_inline2" /><jats:tex-math>$\unicode[STIX]{x1D708}$</jats:tex-math></jats:alternatives></jats:inline-formula> in the neutral direction of the dynamics. We introduce a specific hypothesis on the dynamics that we call ‘minimal captivity’. This hypothesis is stable under perturbations and means that the dynamics is univalued in a neighborhood of <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0143385715000346_inline3" /><jats:tex-math>${\mathcal{K}}$</jats:tex-math></jats:alternatives></jats:inline-formula>. Under this hypothesis we show the existence of an asymptotic spectral gap and a fractal Weyl law for the upper bound of density of Ruelle resonances in the semiclassical limit <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0143385715000346_inline4" /><jats:tex-math>$\unicode[STIX]{x1D708}\rightarrow \infty$</jats:tex-math></jats:alternatives></jats:inline-formula>. Some numerical computations with the truncated Gauss map and Bowen–Series maps illustrate these results.</jats:p>