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Hybridization of Atomic Orbitals I

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The mathematical expression known as the wave function, ψ, contains information about each orbital and the wavelike properties of electrons in an isolated atom. When atoms are bound together in a molecule, the wave functions combine to produce new mathematical descriptions that have different shapes. This process of combining the wave functions for atomic orbitals is called hybridization and is mathematically accomplished by the linear combination of atomic orbitals. The new orbitals that...

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A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

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Published on: September 5, 2019

High-Order Bound States in the Continuum by Merging Hybrid Polarization Singularities.

Zengping Su¹, Yongkang Wang¹, Bo Li^1,2

¹Tsinghua Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, China.

|March 5, 2026

Summary

Researchers merged distinct singularity types, like bound states in the continuum (BICs), to create higher-order topological charges in photonic crystals. This novel method enables precise control over topological charges for advanced photonic applications.

Keywords:

bound states in the continuum photonic crystal slabs polarization singularities quadratic degeneracy point

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Area of Science:

Photonics
Topological Photonics
Condensed Matter Physics

Background:

Merging polarization singularities is key for higher-order topological charges in photonics.
Previous research focused on merging identical singularities, limiting hybrid approaches.
The hybrid merging of distinct singularities, like bound states in the continuum (BICs), is unexplored.

Purpose of the Study:

To demonstrate the systematic construction of higher-order merging BICs.
To engineer the coalescence of accidental BICs with a quadratic degeneracy point in photonic crystal slabs.
To explore topological charge manipulation via hybrid singularity merging.

Main Methods:

Utilizing conventional photonic crystal slabs.
Engineering the coalescence of accidental bound states in the continuum (BICs) with a quadratic degeneracy point.
Employing C4v and C2v symmetric lattice structures.

Main Results:

Successfully constructed higher-order merging BICs.
Achieved a merging BIC with topological charge +3 in a C4v-symmetric lattice.
Engineered a +2 charged BIC by breaking symmetry to C2v on nondegenerate bands.

Conclusions:

Established a versatile and controllable methodology for topological charge manipulation.
Significantly expanded the capacity for nonlocal vortex beam generation.
Opened new avenues for hybrid singularity merging in photonic systems.