This study aims to present a theoretical investigation of a feasible electromagnetic wavepacket with toroidal-type dual vortices. The paper begins with a discussion on geometric phases and angular momenta of electromagnetic vortices in free space and periodic structures, and introduces topological photonic media with a review on topological phenomena of electron systems in solids, such as quantum Hall systems and topological insulators. Representative simulations demonstrate both the characteristics of electromagnetic vortices in a periodic structure and of exotic boundary modes of a topological photonic crystal, on a Y-shaped waveguide configuration. Those boundary modes stem from photonic helical surface modes, i.e., a photonic analog of electronic helical surface states of topological insulators. Then, we discuss the possibility of toroidal electromagnetic wavepackets via topological photonic media, based on the dynamics of an electronic wavepacket around the boundary of a topological insulator and a correspondence relation between electronic helical surface states and photonic helical surface modes. Finally, after introducing a simple algorithm for the construction of wavepacket solutions to Maxwell’s equations with multiple types of vortices, we examine the stability of a toroidal electromagnetic wavepacket against reflection and refraction, and further discuss the transformation laws of its topological properties in the corresponding processes.
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