Vortex waves with orbital angular momentum (OAM) are a highly active research topic in various fields. In this paper, we design and investigate cylindrical metagratings (CMs) with an even number of unit cells that can efficiently achieve vortex localization and specific OAM selective conversion. The multifunctional manipulation of vortex waves and the new OAM conservation law have further been confirmed through analytical calculations and numerical simulations. In addition, we qualitatively and quantitatively determine the OAM range for vortex localization and the OAM value of vortex selective conversion and also explore the stability for performance and potential applications of the designed structure. This work holds potential applications in particle manipulation and optical communication.

To enhance the strength of chiral light–matter interaction for practical applications, the chirality and quality factors (Q-factors) of current methods need to be strengthened simultaneously. Here, we propose a design of photonic crystal slabs (PhCs) supporting chiral bound states in the continuum (BICs) of transverse electric (TE) and transverse magnetic (TM) modes, exhibiting maximal chiroptical responses with high Q-factors and near-unity circular dichroism (CD=0.98). Different from the past, the PhCs we employed only have reduced in-plane symmetry and can support simultaneously chiral quasi-BICs (q-BICs) of TE and TM mode with two-dimensional ultra-strong external and internal chirality. Based on the temporal coupled-mode theory, two analytical expressions of CD of chiral q-BICs response are revealed, which are consistent with the simulation results. Furthermore, we elucidate these results within the charge-current multipole expansion framework and demonstrate that the co-excitation of higher-order multipole electric/magnetic modes is responsible for near-perfect CD. Our results may provide more flexible opportunities for various applications requiring high Q-factors and chirality control, such as chiral lasing, chiral sensing, and enantiomer separation.

Effective medium theory is a powerful tool to solve various problems for achieving multifarious functionalities and applications. In this article, we present a concise empirical formula about effective permittivity of checkboard structures for different directions. To verify our empirical formula, we perform simulations of checkboard periodic structures in squares, rectangles, and sectors in two dimensions. Our results show that the formula is valid in a large range of parameters. This work provides a new way to understand and design composite materials, which might lead to further optical applications in transformation optics.