Intertwining operators for Sklyanin algebra and elliptic hypergeometric series

Intertwining operators for infinite-dimensional representations of the Sklyanin algebra with spins ?$?$ and −?−1$-?-1$ are constructed using the technique of intertwining vectors for elliptic L$L$-operator. They are expressed in terms of elliptic hypergeometric series with operator argument. The intertwining operators obtained (W$W$-operators) serve as building blocks for the elliptic R$R$-matrix which intertwines tensor product of two L$L$-operators taken in infinite-dimensional representations of the Sklyanin algebra with arbitrary spin. The Yang–Baxter equation for this R$R$-matrix follows from simpler equations of the star–triangle type for the W$W$-operators. A natural graphic representation of the objects and equations involved in the construction is used.     

Electric-field-induced symmetry breaking of angular momentum distribution in atoms

We report the experimental observation of alignment to orientation conversion in the 7D3/2 and 9D3/2 states of Cs in the presence of an external dc electric field and without the influence of magnetic fields or atomic collisions. Initial alignment of angular momentum states was created by two-step excitation with linearly polarized laser radiation. The appearance of transverse orientation of angular momentum was confirmed by the observation of circularly polarized light. We present experimentally measured signals and compare them with the results of a detailed theoretical model based on the optical Bloch equations. The effect is odd under time reversal and should be taken into account in ever more sensitive searches for an electron electric dipole moment.     

Morphology-dependent photonic circuit elements

We theoretically propose and experimentally demonstrate the design of a novel one-dimensional ringlike macroscopic optical circuit element. The similarity between morphologies of an optical planar waveguide and a whispering-gallery axially symmetric solid-state resonator is used.     

Enabling arbitrary wavelength frequency combs on chip

A necessary condition for generation of bright soliton Kerr frequency combs in microresonators is to achieve anomalous group velocity dispersion (GVD) for the resonator modes. This condition is hard to implement in the visible as well as ultraviolet since the majority of optical materials are characterized with large normal GVD in these wavelength regions. We overcome this challenge by borrowing ideas from strongly dispersive coupled systems in solid state physics and optics. We show that photonic compound ring resonators can possess large anomalous GVD at any desirable wavelength, even if each individual resonator is characterized with normal GVD. Based on this concept, we design a mode‐locked frequency comb with thin‐film silicon nitride compound ring resonators in the vicinity of the rubidium D₁ line (794.6 nm) and propose to use this optical comb as a flywheel for chip‐scale optical clocks.

     

Surface bound states in the continuum

We introduce a novel concept of surface bound states in the continuum, i.e., surface modes embedded into the linear spectral band of a discrete lattice. We suggest an efficient method for creating such surface modes and the local bounded potential necessary to support the embedded modes. We demonstrate that the surface embedded modes are structurally stable, and the position of their eigenvalues inside the spectral band can be tuned continuously by adding weak nonlinearity.     

High-frequency behavior of magnetic composites

The paper reviews recent progress in the field of microwave magnetic properties of composites. The problem under discussion is developing composites with high microwave permeability that are needed in many applications. The theory of magnetic composites is briefly sketched with the attention paid to the laws governing the magnetic frequency dispersion in magnetic materials and basic mixing rules for composites. Recent experimental reports on the microwave performance of magnetic composites, as well as data on the agreement of the mixing rules with the measured permeability of composites that are available from the literature are discussed. From the data, a conclusion is made that the validity of a mixing rule is determined by the permeability contrast in the composite, i.e., the difference between permeability of inclusions and that of the host matrix. When the contrast is low, the Maxwell Garnet mixing rule is frequently valid. When the contrast is high, which is of the most interest for obtaining high microwave permeability of a composite, no conventionally accepted theory is capable of accurately predicting the permeability of the composites. Therefore, the mixing rules do not allow the microwave properties of magnetic composites to be predicted when the permeability of inclusions is high, that is the case of the most interest. Because of that, general limitations to the microwave performance of composites are of importance. In particular, an important relation constraining the microwave permeability of composites follows from Kittel's theory of ferromagnetic resonance and analytical properties of frequency dependence of permeability. Another constraint concerning the bandwidth of electromagnetic wave absorbers follows from the Kramers-Kronig relations for the reflection coefficient. The constraints are of importance in design and analysis of electromagnetic wave absorbers and other devices that employ the microwave magnetic properties of composites, such as magnetic substrates for microwave antennas, microwave inductors, etc.     

CdxHg(1−x)Te Alloy Colloidal Quantum Dots: Tuning Optical Properties from the Visible to Near‐Infrared by Ion Exchange

The energy gap between valence and conduction levels in colloidal semiconductor quantum dots can be tuned via the nanoparticle diameter when this is comparable to or less than the Bohr radius. In materials such as cadmium mercury telluride, which readily forms a single phase ternary alloy, this quantum confinement tuning can also be augmented by compositional tuning, which brings a further degree of freedom in the bandgap engineering. Here it is shown that compositional control of 2.3 nm diameter Cd_xHg_(1?x)Te nanocrystals by exchange of Hg²⁺ in place of Cd²⁺ ions can be used to tune their optical properties across a technologically useful range, from 500 nm to almost 1200 nm. Data on composition‐dependent changes in the optical properties are provided, including bandgap, extinction coefficient, emission energy and spectral shape, Stokes shift, quantum efficiency, and radiative lifetimes as the exchange process occurs, which are highly relevant for those seeking to use these technologically important QD materials.     

Observation of nonlinear self-trapping in triangular photonic lattices

We experimentally study light self-trapping in triangular photonic lattices induced optically in nonlinear photorefractive crystals. We observe the formation of two-dimensional discrete and gap spatial solitons originating from the first and second bands of the linear transmission spectrum.