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Phase field method to optimize dielectric devices for electromagnetic wave propagation
We discuss a phase field method for shape optimization in the context of electromagnetic wave propagation. The proposed method has the same functional capabilities as the level set method for shape optimization. The first advantage of the method is the simplicity of computation, since extra operations such as re-initialization of functions are not required. The second is compatibility with the topology optimization method due to the similar domain representation and the sensitivity analysis. Structural shapes are represented by the phase field function defined in the design domain, and this function is optimized by solving a time-dependent reaction diffusion equation. The artificial double-well potential function used in the equation is derived from sensitivity analysis. We study four types of 2D or 2.5D (axisymmetric) optimization problems. Two are the classical problems of photonic crystal design based on the Bloch theory and photonic crystal wave guide design, and two are the recent topics of designing dielectric left-handed metamaterials and dielectric ring resonators.
The magnetic, electronic, and light-induced topological properties in two-dimensional hexagonal FeX 2 (X = Cl, Br, I) monolayers
Using Floquet–Bloch theory, we propose to realize chiral topological phases in two-dimensional (2D) hexagonal FeX 2 (X = Cl, Br, I) monolayers under irradiation of circularly polarized light. Such 2D FeX 2 monolayers are predicted to be dynamically stable and exhibit both ferromagnetic and semiconducting properties. To capture the full topological physics of the magnetic semiconductor under periodic driving, we adopt ab initio Wannier-based tight-binding methods for the Floquet–Bloch bands, with the light-induced bandgap closings and openings being obtained as the light field strength increases. The calculations of slabs with open boundaries show the existence of chiral edge states. Interestingly, the topological transitions with branches of chiral edge states changing from zero to one and from one to two by tuning the light amplitude are obtained, showing that the topological Floquet phase of high Chern number can be induced in the present Floquet–Bloch systems.
Realizing high-quality ultralarge momentum states and ultrafast topological transitions using semiconductor hyperbolic metamaterials
We employ both the effective medium approximation (EMA) and Bloch theory to compare the dispersion properties of semiconductor hyperbolic metamaterials (SHMs) at mid-infrared frequencies and metallic hyperbolic metamaterials (MHMs) at visible frequencies. This analysis reveals the conditions under which the EMA can be safely applied for both MHMs and SHMs. We find that the combination of precise nanoscale layering and the longer infrared operating wavelengths puts the SHMs well within the effective medium limit and, in contrast to MHMs, allows for the attainment of very high photon momentum states. Additionally, SHMs allow for new phenomena such as ultrafast creation of the hyperbolic manifold through optical pumping. Furthermore, we examine the possibility of achieving ultrafast topological transitions through optical pumping which can photo-dope appropriately designed quantum wells on the femtosecond time scale.
R-Matrix Theory from the Green-Bloch Perspective
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Predicting the stability of a compressible periodic parallel jet flow
It is known that mixing enhancement in compressible free shear layer flows with high convective Mach numbers is difficult. One design strategy to get around this is to use multiple nozzles. Extrapolating this design concept in a one dimensional manner, one arrives at an array of parallel rectangular nozzles where the smaller dimension is omega and the longer dimension, b, is taken to be infinite. In this paper, the feasibility of predicting the stability of this type of compressible periodic parallel jet flow is discussed. The problem is treated using Floquet-Bloch theory. Numerical solutions to this eigenvalue problem are presented. For the case presented, the interjet spacing, s, was selected so that s/omega =2.23. Typical plots of the eigenvalue and stability curves are presented. Results obtained for a range of convective Mach numbers from 3 to 5 show growth rates omega(sub i)=kc(sub i)/2 range from 0.25 to 0.29. These results indicate that coherent two-dimensional structures can occur without difficulty in multiple parallel periodic jet nozzles and that shear layer mixing should occur with this type of nozzle design.
Collective Interaction of a Compressible Periodic Parallel Jet Flow
A linear instability model for multiple spatially periodic supersonic rectangular jets is solved using Floquet-Bloch theory. The disturbance environment is investigated using a two dimensional perturbation of a mean flow. For all cases large temporal growth rates are found. This work is motivated by an increase in mixing found in experimental measurements of spatially periodic supersonic rectangular jets with phase-locked screech. The results obtained in this paper suggests that phase-locked screech or edge tones may produce correlated spatially periodic jet flow downstream of the nozzles which creates a large span wise multi-nozzle region where a disturbance can propagate. The large temporal growth rates for eddies obtained by model calculation herein are related to the increased mixing since eddies are the primary mechanism that transfer energy from the mean flow to the large turbulent structures. Calculations of growth rates are presented for a range of Mach numbers and nozzle spacings corresponding to experimental test conditions where screech synchronized phase locking was observed. The model may be of significant scientific and engineering value in the quest to understand and construct supersonic mixer-ejector nozzles which provide increased mixing and reduced noise.
Collective Interaction in a Linear Array of Supersonic Rectangular Jets: A Linear Spatial Instability Study
A linear spatial instability model for multiple spatially periodic supersonic rectangular jets is solved using Floquet-Bloch theory. It is assumed that in the region of interest a coherent wave can propagate. For the case studied large spatial growth rates are found. This work is motivated by an increase in mixing found in experimental measurements of spatially periodic supersonic rectangular jets with phase-locked screech and edge tone feedback locked subsonic jets. The results obtained in this paper suggests that phase-locked screech or edge tones may produce correlated spatially periodic jet flow downstream of the nozzles which creates a large span wise multi-nozzle region where a coherent wave can propagate. The large spatial growth rates for eddies obtained by model calculation herein are related to the increased mixing since eddies are the primary mechanism that transfer energy from the mean flow to the large turbulent structures. Calculations of spacial growth rates will be presented for a set of relative Mach numbers and spacings for which experimental measurements have been made. Calculations of spatial growth rates are presented for relative Mach numbers from 1.25 to 1.75 with ratios of nozzle spacing to nozzle width ratios from s/w(sub N) = 4 to s/w(sub N) = 13.7. The model may be of significant scientific and engineering value in the quest to understand and construct supersonic mixer-ejector nozzles which provide increased mixing and reduced noise.
Unified theory of effective interaction
We present a unified description of effective interaction theories in both algebraic and graphic representations. In our previous work, we have presented the Rayleigh–Schrödinger and Bloch perturbation theories in a unified fashion by introducing the main frame expansion of the effective interaction. In this work, we start also from the main frame expansion, and present various nonperturbative theories in a coherent manner, which include generalizations of the Brandow, Brillouin–Wigner, and Bloch–Horowitz theories on the formal side, and the extended Krenciglowa–Kuo and the extended Lee–Suzuki methods on the practical side. We thus establish a coherent and comprehensive description of both perturbative and nonperturbative theories on the basis of the main frame expansion.
Partial secular Bloch-Redfield master equation for incoherent excitation of multilevel quantum systems
We present an efficient theoretical method for calculating the time evolution of the density matrix of a multilevel quantum system weakly interacting with incoherent light. The method combines the Bloch-Redfield theory with a partial secular approximation for one-photon coherences, resulting in a master equation that explicitly exposes the reliance on transition rates and the angles between transition dipole moments in the energy basis. The partial secular Bloch-Redfield master equation allows an unambiguous distinction between the regimes of quantum coherent vs. incoherent energy transfer under incoherent light illumination. The fully incoherent regime is characterized by orthogonal transition dipole moments in the energy basis, leading to a dynamical evolution governed by a coherence-free Pauli-type master equation. The coherent regime requires non-orthogonal transition dipole moments in the energy basis and leads to the generation of noise-induced quantum coherences and population-to-coherence couplings. As a first application, we consider the dynamics of excited state coherences arising under incoherent light excitation from a single ground state and observe population-to-coherence transfer and the formation of non-equilibrium quasisteady states in the regime of small excited state splitting. Analytical expressions derived earlier for the V-type system [T. V. Tscherbul and P. Brumer, Phys. Rev. Lett. 113, 113601 (2014)] are found to provide a nearly quantitative description of multilevel excited-state populations and coherences in both the small- and large-molecule limits.
Metamaterial-based theoretical description of light scattering by metallic nano-hole array structures
We have experimentally and theoretically investigated the light-matter interaction in metallic nano-hole array structures. The scattering cross section spectrum was measured for three samples each having a unique nano-hole array radius and periodicity. Each measured spectrum had several peaks due to surface plasmon polaritons. The dispersion relation and the effective dielectric constant of the structure were calculated using transmission line theory and Bloch's theorem. Using the effective dielectric constant and the transfer matrix method, the surface plasmon polariton energies were calculated and found to be quantized. Using these quantized energies, a Hamiltonian for the surface plasmon polaritons was written in the second quantized form. Working with the Hamiltonian, a theory of scattering cross section was developed based on the quantum scattering theory and Green's function method. For both theory and experiment, the location of the surface plasmon polariton spectral peaks was dependant on the array periodicity and radii of the nano-holes. Good agreement was observed between the experimental and theoretical results. It is proposed that the newly developed theory can be used to facilitate optimization of nanosensors for medical and engineering applications.
The quantum Hall effect at a weak magnetic field
Using a weak limit for the hopping integral in one direction in the Hofstadter model, we show that the fermion states in the gaps of the spectrum are determined within the Kitaev chain. The proposed approach allows us to study the behavior of Chern insulators (CI) in different classes of symmetry. We consider the Hofstadter model on the square and honeycomb lattices in the case of rational and irrational magnetic fluxes ϕ, and discuss the behavior of the Hall conductance at a weak magnetic field in a sample of finite size. We show that in the semiclassical limit at the center of the fermion spectrum, the Bloch states of fermions turn into chiral Majorana fermion liquid when the magnetic scale (1/ϕ) is equal to the sample size N. We are talking about the dielectric–metal phase transition, which is determined by the behavior of the Landau levels in 2D fermion systems in a transverse magnetic field. When a magnetic scale, which determines the wave function of fermions, exceeds the size of the sample, a jump in the longitudinal conductance occurs. The wave function describes non-localized states of fermions, the sample becomes a conductor, the system changes from the dielectric state to the metallic one. It is shown, that at 1∕ϕ>N the quantum Hall effect and the Landau levels are not realized, which makes possibility to study the behavior of CI in irrational magnetic fluxes.
Surface-wave-assisted nonreciprocity in spatio-temporally modulated metasurfaces
Emerging photonic functionalities are mostly governed by the fundamental principle of Lorentz reciprocity. Lifting the constraints imposed by this principle could circumvent deleterious effects that limit the performance of photonic systems. Most efforts to date have been limited to waveguide platforms. Here, we propose and experimentally demonstrate a spatiotemporally modulated metasurface capable of complete violation of Lorentz reciprocity by reflecting an incident beam into far-field radiation in forward scattering, but into near-field surface waves in reverse scattering. These observations are shown both in nonreciprocal beam steering and nonreciprocal focusing. We also demonstrate nonreciprocal behavior of propagative-only waves in the frequency- and momentum-domains, and simultaneously in both. We develop a generalized Bloch-Floquet theory which offers physical insights into Lorentz nonreciprocity for arbitrary spatial phase gradients, and its predictions are in excellent agreement with experiments. Our work opens exciting opportunities in applications where free-space nonreciprocal wave propagation is desired.
Dynamics of the two-spin spin-boson model with a common bath
Dynamics of the two-spin spin-boson model in the presence of Ohmic and sub-Ohmic baths is investigated by employing a multitude of the Davydov D{sub 1} trial states, also known as the multi-D{sub 1} Ansatz. Its accuracy in dynamics simulations of the two-spin SBM is improved significantly over the single D{sub 1} Ansatz, especially in the weak to moderately strong coupling regime. Validity of the multi-D{sub 1} Ansatz for various coupling strengths is also systematically examined by making use of the deviation vector which quantifies how faithfully the trial state obeys the Schrödinger equation. The time evolution of population difference and entanglement has been studied for various initial conditions and coupling strengths. Careful comparisons are carried out between our approach and three other methods, i.e., the time-dependent numerical renormalization group (TD-NRG) approach, the Bloch-Redfield theory, and a method based on a variational master equation. For strong coupling, the multi-D{sub 1} trial state yields consistent results as the TD-NRG approach in the Ohmic regime while the two disagree in the sub-Ohmic regime, where the multi-D{sub 1} trial state is shown to be more accurate. For weak coupling, the multi-D{sub 1} trial state agrees with the two master-equation methods in the presence of both Ohmic and sub-Ohmic baths, but shows considerable differences with the TD-NRG approach in the presence of a sub-Ohmic bath, calling into question the validity of the TD-NRG results at long times in the literature.
Anharmonic Bloch oscillations in a waveguide array
Using the coupled-wave method, we consider anharmonic Bloch oscillations of light in an array of waveguides, taking into account the coupling between waveguides up to the third order. It is shown that the beam trajectory is periodic, with the trajectory oscillating within a single period. (paper)
Helical antiferromagnetic ordering in EuNi 1.95 As 2 single crystals
The Eu + 2 spins-7/2 in EuNi 2 As 2 with the body-centered tetragonal ThCr 2 Si 2 structure order antiferromagnetically below the Néel temperature T N = 15 K into a helical antiferromagnetic (AFM) structure with the helix axis aligned along the tetragonal c axis and the Eu ordered moments aligned ferromagnetically within the ab plane as previously reported from neutron diffraction measurements [T. Jin et al., Phys. Rev. B 99, 014425 (2019)]. Here we study the crystallographic, magnetic, thermal, and electronic transport properties of Bi-flux-grown single crystals using single-crystal x-ray diffraction, anisotropic magnetic susceptibility χ, isothermal magnetization M, heat capacity Cp, and electrical resistivity ρ measurements versus applied magnetic field H and temperature T. Vacancies are found on the Ni sites corresponding to the composition EuNi 1.95 (1) As 2. A good fit of the ρ (T) data by the Bloch-Grüneisen theory for metals was obtained. The χab (T) data below T N are fitted well by molecular field theory (MFT), and the helix turn angle kd and the Eu-Eu Heisenberg exchange constants are extracted from the fit parameters. The kd value is in good agreement with the neutron-diffraction result. The magnetic contribution to the zero-field heat capacity below T N is also fitted by MFT. The isothermal in-plane magnetization M ab exhibits two metamagnetic transitions versus H, whereas M c (T = 2 K ) is nearly linear up to H = 14 T, both behaviors being consistent with MFT. The M c (H, T) , ρ(H c , T) , and Cp (H c , T) data yielded a H c - T phase diagram separating the AFM and paramagnetic phases in good agreement with MFT. Anisotropic χ(T) literature data for the ThCr 2 Si 2 -type helical antiferromagnet EuRh 2 As 2 were also fitted well by MFT. A comparison is made between the crystallographic and magnetic properties of ThCr 2 Si 2 -type Eu M 2 Pn 2 compounds with M = Fe , Co, Ni, Cu, or Rh, and Pn = P or As, where only ferromagnetic and c -axis helical AFM structures are found.
KCo 2 As 2 : A new portal for the physics of high-purity metals
High-quality single crystals of KCo 2 As 2 with the body-centered tetragonal ThCr 2 Si 2 structure were grown using KAs self flux. Structural, magnetic, thermal, and electrical transport properties were investigated. No clear evidence for any phase transitions was found in the temperature range 2–300 K. The in-plane electrical resistivity ρ versus temperature T is highly unusual, showing a T 4 behavior below 30 K and an anomalous positive curvature up to 300 K, which is different from the linear behavior expected from the Bloch-Grüneisen theory for electron scattering by acoustic phonons. This positive curvature has been previously observed in the in-plane resistivity of high-conductivity layered delafossites such as PdCoO 2 and PtCoO 2 . The in-plane ρ(T → 0) = 0.36μΩ cm of KCo 2 As 2 is exceptionally small for this class of compounds. The material also exhibits a magnetoresistance at low T which attains a value of about 40% at T = 2 K and magnetic field H = 80 kOe. The magnetic susceptibility χ of KCo 2 As 2 is isotropic and about an order of magnitude smaller than the values for the related compounds SrCo 2 As 2 and BaCo 2 As 2 . The χ increases above 100 K, which is found from our first-principles calculations to arise from a sharp peak in the electronic density of states just above the Fermi energy E F . Heat capacity C p (T) data at low T yield an electronic density of states N(E F ) that is about 36% larger than predicted by the first-principles theory. The C p (T) data near room temperature suggest the presence of excited optic vibration modes, which may also be the source of the positive curvature in ρ(T). Angle-resolved photoemission spectroscopy measurements are compared with the theoretical predictions of the band structure and Fermi surfaces. In conclusion, our results show that KCo 2 As 2 provides a new avenue for investigating the physics of high-purity metals.
Recent Updates to the Los Alamos EDA 𝑅-Matrix Code
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