Efficient finite element modeling of photonic modal analysis augmented by combined symmetry.

In this work, we present an efficient numerical implementation of the finite element method for modal analysis that leverages various symmetry operations, including spatial symmetry in point groups and space-time symmetry in pseudo-hermiticity systems. We provide a formal and rigorous treatment, specifically deriving the boundary constraint conditions corresponding to symmetry constraints. Without loss of generality, we illustrate our approach via computing the modes of optical waveguides with complex cross-sections, accompanied by performance benchmark against the standard finite element method.

Hidden symmetry-induced effective moving double-zero-index metamaterials.

Materials possessing an effective zero refractive index are often associated with Dirac-like cone dispersion at the center of the Brillouin zone (BZ). It has been reported the presence of hidden symmetry-enforced triply degenerate points [nexus points (NP)] away from the Brillouin zone center with the stacked dielectric photonic crystals. The spin-1 Dirac-like dispersion in the xy plane near the nexus point suggests a method for achieving zero refractive index materials.

Efficient and accurate numerical-projection of electromagnetic multipoles for scattering objects.

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.

Simple yet effective analysis of waveguide mode symmetry: generalized eigenvalue approach based on Maxwell's equations.

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.

Optically Reconfigurable Spin-Valley Hall Effect of Light in Coupled Nonlinear Ring Resonator Lattice.

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.

Finite element modeling of electromagnetic properties in photonic bianisotropic structures.

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.

Hidden-symmetry-enforced nexus points of nodal lines in layer-stacked dielectric photonic crystals.

It was recently demonstrated that the connectivities of bands emerging from zero frequency in dielectric photonic crystals are distinct from their electronic counterparts with the same space groups. We discover that in an AB-layer-stacked photonic crystal composed of anisotropic dielectrics, the unique photonic band connectivity leads to a new kind of symmetry-enforced triply degenerate points at the nexuses of two nodal rings and a Kramers-like nodal line. The emergence and intersection of the line nodes are guaranteed by a generalized 1/4-period screw rotation symmetry of Maxwell's equations.

On the constraints of electromagnetic multipoles for symmetric scatterers: eigenmode analysis.

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.

Gauge-field description of Sagnac frequency shift and mode hybridization in a rotating cavity.

Active optical systems can give rise to intriguing phenomena and applications that are not available in conventional passive systems. Structural rotation has been widely employed to achieve non-reciprocity or time-reversal symmetry breaking. Here, we examine the quasi-normal modes and scattering properties of a dielectric disk under rotation.

Non-Abelian gauge field optics.

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.

S-parameters, non-Hermitian ports and the finite-element implementation in photonic devices with 𝒫𝒯-symmetry.

In Hermitian photonic devices, S-parameters, i.e., the elements of a scattering matrix based on integrated power flux and Hermitian modal orthogonality, are used to account for the transmission or reflection of light from one port to another.

Classification of symmetry properties of waveguide modes in presence of gain/losses, anisotropy/bianisotropy, or continuous/discrete rotational symmetry.

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.