Three-Dimensional All-Dielectric Photonic Topological Insulator (1602.00049v1)

Abstract: The discovery of two-dimensional topological photonic systems has transformed our views on electromagnetic propagation and scattering of classical waves, and a quest for similar states in three dimensions, known to exist in condensed matter systems, has been put forward. Here we demonstrate that symmetry protected three-dimensional topological states can be engineered in an all-dielectric platform with the electromagnetic duality between electric and magnetic fields ensured by the structure design. Magneto-electric coupling playing the role of a synthetic gauge field leads to a topological transition to an insulating regime with a complete three-dimensional photonic bandgap. An emergence of surface states with conical Dirac dispersion and spin-locking is unimpeded. Robust propagation of surface states along two-dimensional domain walls defined by the reversal of magneto-electric coupling is confirmed numerically by first principle studies. It is shown that the proposed system represents a table-top platform for emulating relativistic physics of massive Dirac fermions and the surface states revealed can be interpreted as Jackiw-Rebbi states confined to the interface between two domains with opposite particle masses.

• The paper introduces novel symmetry-protected topological state engineering in an all-dielectric 3D photonic system.
• It demonstrates that bianisotropy induces effective spin-orbit interaction, creating a complete 3D bandgap with Dirac-like surface states.
• Rigorous numerical and analytical validations confirm robust photon propagation along curved domain walls for lossless photonic circuits.

Three-Dimensional All-Dielectric Photonic Topological Insulator

This paper presents a significant advancement in the field of photonic topological insulators, demonstrating the realization of a three-dimensional (3D) topological photonic system using an all-dielectric platform. The paper focuses on engineering symmetry-protected topological (SPT) states in such a system, eschewing the need for magnetism or temporal modulation typically required in similar 2D structures, thereby facilitating practical implementation across a wide range of the electromagnetic spectrum.

Core Contributions and Findings

1. SPT Phase Engineering: The work introduces a novel approach to engineer nontrivial symmetry-protected topological states in photonic crystals through the realization of electromagnetic duality. By designing all-dielectric metamaterials, the researchers achieve a structure capable of supporting pseudo-spin degrees of freedom, which are crucial for the topological order.
2. Bianisotropy, Spin-Orbit Interaction, and Bandgap Formation: Introducing bianisotropy into the structure induces an effective spin-orbit interaction, resulting in a topological transition accompanied by the emergence of a complete 3D photonic bandgap. This allows surface states with Dirac-like conical dispersion, a haLLMark of robust topological phases, to exist without backscattering or localization.
3. Numerical and Analytical Validation: The authors utilize rigorous first-principle numerical simulations and complimentary analytical techniques, including effective Hamiltonian and effective medium approaches, to validate the existence of the surface states on domain walls defined by the reversal of bianisotropy. The results confirm that these states exhibit polarization-locking analogously to hypothetical Jackiw-Rebbi states in relativistic quantum systems.
4. Robust Photonic Propagation: The paper validates the robustness of the surface states through simulations of wave propagation along curved domain walls featuring sharp bends, demonstrating uniform intensity distribution and lack of back-reflection, underscoring their potential for use in robust photonic circuits.
5. System Classification and Comparison: The 3D metacrystal is shown to be equivalent to a weak topological insulator classified under the weak $\mathbb{Z}_2$ class, closely paralleling condensed matter systems like graphene in terms of band topology. Nonetheless, it offers prospects of observing and utilizing exotic Dirac fermion states in tailored photonic systems.

Implications and Future Directions

The realization of a 3D all-dielectric photonic topological insulator marks a pivotal step toward practical applications of topological photonics in 3D circuits, with contributions extending to the design of lossless optical pathways, robust waveguides, and elements in quantum emulation platforms. The absence of metallic and magnetic components circumvents issues of Ohmic loss and integration complexity, enhancing applicability in dielectric and semiconductor-based photonic devices.

Speculating on future developments, this work lays the groundwork for extensive research in the development of photonic systems that emulate complex quantum phenomena, such as spintronics and advanced quantum computing architectures. Further exploration might focus on optimizing material parameters for more robust surface states, refining fabrication techniques for higher spectral domains, and exploring interactions with other physical systems for enhanced functionalities.

Overall, the paper provides compelling evidence of the practical potential of employing topological principles in photonics, heralding the future of robust, ultra-compact, and flexible three-dimensional optical devices.