The concept of gauge field is a cornerstone of modern physics and the synthetic gauge field has emerged as a new way to manipulate particles in many disciplines. In optics, several schemes of Abelian ...synthetic gauge fields have been proposed. Here, we introduce a new platform for realizing synthetic SU(2) non-Abelian gauge fields acting on two-dimensional optical waves in a wide class of anisotropic materials and discover novel phenomena. We show that a virtual non-Abelian Lorentz force arising from material anisotropy can induce light beams to travel along Zitterbewegung trajectories even in homogeneous media. We further design an optical non-Abelian Aharonov-Bohm system which results in the exotic spin density interference effect. We can extract the Wilson loop of an arbitrary closed optical path from a series of gauge fixed points in the interference fringes. Our scheme offers a new route to study SU(2) gauge field related physics using optics.
In this paper, we develop an efficient and accurate procedure of electromagnetic multipole decomposition by using the Lebedev and Gaussian quadrature methods to perform the numerical integration. ...Firstly, we briefly review the principles of multipole decomposition, highlighting two numerical projection methods including surface and volume integration. Secondly, we discuss the Lebedev and Gaussian quadrature methods, provide a detailed recipe to select the quadrature points and the corresponding weighting factor, and illustrate the integration accuracy and numerical efficiency (that is, with very few sampling points) using a unit sphere surface and regular tetrahedron. In the demonstrations of an isotropic dielectric nanosphere, a symmetric scatterer, and an anisotropic nanosphere, we perform multipole decomposition and validate our numerical projection procedure. The obtained results from our procedure are all consistent with those from Mie theory, symmetry constraints, and finite element simulations.
Graphical Abstract
Given a constitutive relation of the bianisotropic medium, it is not trivial to study how light interacts with the photonic bianisotropic structure due to the limited available means of studying ...electromagnetic properties in bianisotropic media. In this paper, we study the electromagnetic properties of photonic bianisotropic structures using the finite element method. We prove that the vector wave equation with the presence of bianisotropic is self-adjoint under scalar inner product. we propose a balanced formulation of weak form in the practical implementation, which outperforms the standard formulation in finite element modeling. Furthermore, we benchmark our numerical results obtained from finite element simulation in three different scenarios. These are bianisotropy-dependent reflection and transmission of plane waves incident onto a bianisotropic slab, band structure of bianisotropic photonic crystals with valley-dependent phenomena, and the modal properties of bianisotropic ring resonators. The first two simulated results obtained from our modified weak form yield excellent agreements either with theoretical predictions or available data from the literature, and the modal properties in the last example, i.e., bianisotropic ring resonators as a polarization-dependent optical insulator, are also consistent with the theoretical analyses.
In the absence of random mode mixing (RMM), linearization of the cross-mode modulation (XMM) under pump-probe configuration is in general complicated because the evolution of the pump light depends ...on the local mode decomposition of itself. In this work, general derivation of the Hamiltonian of the XMM system without RMM is carried out and discussed under two interesting scenarios where the pump evolution can be effectively linearized, leading to spatial dependent Hamiltonian of the probe light. Representative evolutions of pump and probe light over transmission are investigated with the assistance of Poincaré sphere based on the Hamiltonian approach. Our results are benchmarked against the results given by precession equations examined by Lin and Agrawal and numerical simulations using nonlinear coupled mode equations (CMEs). By highlighting the eigenstates as well as eigenvalues of the system, our approach provides an intuitive yet powerful approach to understand the XMM nonlinear problems and to dynamically manipulate the spatial profiles of the probe light.
Particular waveguide structures and refractive index distribution can lead to specified degeneracy of eigenmodes. To obtain an accurate understanding of this phenomenon, we propose a simple yet ...effective approach, i.e., generalized eigenvalue approach based on Maxwell’s equations, for the analysis of waveguide mode symmetry. In this method, Maxwell’s equations are reformulated into generalized eigenvalue problems. The waveguide eigenmodes are completely determined by the generalized eigenvalue problem given by two matrices (
M
,
N
), where
M
is 6 × 6 waveguide Hamiltonian and
N
is a constant singular matrix. Close examination shows that
N
usually commute with the corresponding matrix of a certain symmetry operation, thus the waveguide eigenmode symmetry is essentially determined by
M
, in contrast to the tedious and complex procedure given in the previous work
Opt. Express
25
,
29822
(
2017
)
10.1364/OE.25.029822
. Based on this new approach, we discuss several symmetry operations and the corresponding symmetries including chiral, parity-time reversal, rotation symmetry, wherein the constraints of symmetry requirements on material parameters are derived in a much simpler way. In several waveguides with balanced gain and loss, anisotropy, and geometrical symmetry, the analysis of waveguide mode symmetry based on our simple yet effective approach is consistent with previous results, and shows perfect agreement with full-wave simulations.
The scattering and resonant properties of optical scatterers/resonators are determined by the relative ratios among the associated multipole components, the calculation of which usually is ...analytically tedious and numerically complicated for complex structures. Here we identify the constraints as well as the relative relations among electromagnetic multipoles for the eigenmodes of symmetric scatterers/resonators. By reducing the symmetry properties of the vector spherical harmonic waves to those of the modified generating functions, we systematically study the required conditions for electromagnetic multipoles under several fundamental symmetry operations, i.e., 2D rotation and reflection operations and 3D proper and improper rotations. Taking a 2D scatterer with C
as an example, we show that each irreducible representation of C
can be assigned to corresponding electromagnetic multipoles, and consequently the constraints of the electromagnetic multipoles can be easily extracted. Such group approach can easily be extended to more complex 3D scatterers with higher symmetry group. Subsequently, we use the same procedure to map out the complete relation and constraint on the electromagnetic multipoles of a 3D scatterer imposed by D
symmetry. Our theoretical analyses are in perfect agreements with the fullwave finite element calculations of the eigenmodes of the symmetric scatters.
Scattering immune propagation of light in topological photonic systems may revolutionize the design of integrated photonic circuits for information processing and communications. In optics, various ...photonic topological circuits have been developed, which were based on classical emulation of either quantum spin Hall effect or quantum valley Hall effect. On the other hand, the combination of both the valley and spin degrees of freedom can lead to a new kind of topological transport phenomenon, dubbed spin-valley Hall effect (SVHE), which can further expand the number of topologically protected edge channels and would be useful for information multiplexing. However, it is challenging to realize SVHE in most known material platforms, due to the requirement of breaking both the (pseudo)fermionic time-reversal (T) and parity symmetries (P) individually, but leaving the combined symmetry S ≡ TP intact. Here, we propose an experimentally feasible platform to realize SVHE for light, based on coupled ring resonators mediated by optical Kerr nonlinearity. Thanks to the inherent flexibility of cross-mode modulation, the coupling between the probe light can be engineered in a controllable way such that spin-dependent staggered sublattice potential emerges in the effective Hamiltonian. With delicate yet experimentally feasible pump conditions, we show the existence of spin-valley Hall-induced topological edge states. We further demonstrate that both degrees of freedom, i.e., spin and valley, can be manipulated simultaneously in a reconfigurable manner to realize spin-valley photonics, doubling the degrees of freedom for enhancing the information capacity in optical communication systems.
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We study the symmetric properties of waveguide modes in presence of gain/losses, anisotropy/bianisotropy, or continuous/discrete rotational symmetry. We provide a comprehensive approach to identity ...the modal symmetry by constructing a 4 × 4 waveguide Hamiltonian and searching the symmetric operation in association with the corresponding waveguides. We classify the chiral/time reversal/parity/parity time/rotational symmetry for different waveguides, and provide the criterion for the aforementioned symmetry operations. Lastly, we provide examples to illustrate how the symmetry operations can be used to classify the modal properties from the symmetric relation between modal profiles of several different waveguides.
Response surface methodology was applied to study the extrusion product of peanut–buckwheat–rice by a twin screw extruder. Effects of peanut–buckwheat flour (PBF) (25%–35%), feed moisture (18%–22%), ...barrel temperature (120–140°C), and screw speed (15–25 Hz) on the expansion ratio (ER), breaking strength (BS), bulk density (BD), and overall acceptability (OA) of extrusion product were studied based on the central composite rotatable design. Remarkable regression models that explored influences of peanut–buckwheat, feed moisture, barrel temperature, and screw speed were established. A desired product was obtained by 25% PBF, 22% feed moisture, 120°C extruder barrel temperature, and 25 Hz screw speed. The corresponding reactions were 2.983 ER, 0.472 kgf BS, 0.105 g cm3 BD, and 7.707 OA.
Practical applications
This project studied that peanut and buckwheat can effectively use basic extrusion conditions to produce extruded snacks by choosing appropriate extrusion parameters. The selected ingredients are easy to obtain and cheap. As a potential functional food, it will be favored by the consumer.
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