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., 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. Express25, 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.

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. 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.

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.e., 2D rotation and reflection operations and 3D proper and improper rotations. Taking a 2D scatterer with C4v as an example, we show that each irreducible representation of C4v 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 D3h symmetry. Our theoretical analyses are in perfect agreements with the fullwave finite element calculations of the eigenmodes of the symmetric scatters.

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. In addition to the familiar phenomenon of Sagnac frequency shift, we observe the the hybridization of the clockwise (CW) and counter-clockwise CCW) chiral modes of the cavity controlled by the rotation. The rotation tends to suppress one chiral mode while amplifying the other, and it leads to the variation of the far field. The phenomenon can be understood as the result of a synthetic gauge field induced by the rotation of the cavity. We explicitly derived this gauge field and the resulting Sagnac frequency shift. The analytical results are corroborated by finite element simulations. Our results can be applied in the measurement of rotating devices by probing the far field.

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. The definition of S-parameters in Hermitian settings becomes inappropriate in the non-Hermitian optical environment. Here we revisit the fundamental problems associated with extracting the S-parameters of light in photonic 𝒫𝒯-symmetric devices, i.e., waveguides or coupled waveguide-cavity systems, wherein the waveguide ports themselves may also be non-Hermitian. We first use the bi-orthogonal inner product that restores the modal orthogonality on the waveguide ports containing balanced gain and losses to quantify the modal overlapping instead of Hermitian inner product. Secondly, a finite element implementation is proposed and realized to extract the S-parameters on non-Hermitian ports. Lastly, we illustrate our approach of calculating the S-parameters on non-Hermitian ports via two waveguide-lattice structures. The numerical results of S-parameters are validated against the constraints imposed by reciprocity and 𝒫𝒯-symmetry.

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. 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.

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. 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.

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. 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.

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. The bands with a constant k z and iso-frequency surfaces near a nexus point both disperse as a spin-1 Dirac-like cone, giving rise to exotic transport features of light at the nexus point. We show that spin-1 conical diffraction occurs at the nexus point, which can be used to manipulate the charges of optical vortices. Our work reveals that Maxwell's equations can have hidden symmetries induced by the fractional periodicity of the material tensor components and hence paves the way to finding novel topological nodal structures unique to photonic systems.

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. 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.