Topological Photonic Phase in Chiral Hyperbolic Metamaterials (1401.5448v2)

Abstract: Recently the possibility of achieving one-way backscatter immune transportation of light by mimicking the topological order present within certain solid state systems, such as topological insulators, has received much attention. Thus far however, demonstrations of non-trivial topology in photonics have relied on photonic crystals with precisely engineered lattice structures, periodic on the scale of the operational wavelength and composed of finely tuned, complex materials. Here we propose a novel effective medium approach towards achieving topologically protected photonic surface states robust against disorder on all length scales and for a wide range of material parameters. Remarkably, the non-trivial topology of our metamaterial design results from the Berry curvature arising from the transversality of electromagnetic waves in a homogeneous medium. Our investigation therefore acts to bridge the gap between the advancing field of topological band theory and classical optical phenomena such as the Spin Hall effect of light. The effective medium route to topological phases will pave the way for highly compact one-way transportation of electromagnetic waves in integrated photonic circuits.

• The paper introduces a novel approach that uses chiral hyperbolic metamaterials to generate topologically protected photonic surface states.
• It leverages Berry curvature and Chern numbers to quantify robust topological invariants, leading to non-trivial equi-frequency surfaces.
• Full-wave simulations confirm that the design enables backscattering-immune, unidirectional surface states suitable for integrated photonic circuits.

Topological Photonic Phase in Chiral Hyperbolic Metamaterials: A Formal Examination

The research document under scrutiny explores a novel approach to realizing topological photonic phases using chiral hyperbolic metamaterials. This innovative methodology circumvents the limitations of traditional photonic crystals by employing effective medium theory to achieve topologically protected photonic surface states. The work is situated in the broader context of extending topological concepts from condensed matter physics into the field of photonics, with implications for the development of integrated photonic circuits offering one-way transmission of light with immunity to backscattering.

The paper begins by grounding its theoretical foundation in the principles of topological order, leveraging attributes of Berry curvature and Chern numbers. The authors argue that the transverse nature of electromagnetic waves in a homogeneous medium is instrumental in generating non-trivial topological effects. The paper diverges from conventional reliance on gyromagnetic effects or lattice engineering at the operational wavelength scale.

The metamaterial design proposed by the authors introduces chirality into a hyperbolic medium, which facilitates the lifting of polarization degeneracy for waves propagating along the optical axis. This leads to the emergence of topologically non-trivial equi-frequency surfaces (EFS) in k-space, which the authors draw an analogy to Fermi surfaces in topological semimetals. Remarkably, these EFSs support robust, unidirectional surface states at the interface with a topologically trivial medium like a vacuum, reminiscent of Fermi arcs.

Key Numerical Observations and Claims

• Topological Invariants: The paper delineates the evolution of EFSs and their associated Chern numbers. Specifically, the chiral hyperbolic metamaterial exhibits well-separated, topologically non-trivial EFSs. These are mathematically quantified through the preservation and determination of Chern numbers, highlighting the robustness of the resultant topological phases.
• Surface State Immunity: The metamaterial's surface states exhibit immunity to backscattering, demonstrated through full-wave simulations. The simulations show that right-moving surface waves navigate sharp corners without reflection, a property predicated on the spatial separation of left and right-moving modes.
• Robustness: The paper claims the metamaterial's design is highly resilient to spatial deformations and material parameter variations. This robustness extends across length scales and includes low symmetry structures, positing the approach as a likely candidate for practical application in photonic circuits.

Implications and Future Directions

The findings of this research introduce substantial theoretical and practical implications for the field of photonics. By dissociating topological protection from lattice structures and time-reversal symmetry breaking, this design affords greater flexibility and scalability in frequency applications. The simplicity of control over non-trivial topology via effective medium parameters, namely permittivity tensor and chirality, promises a versatile platform for future exploration.

The theoretical underpinnings found in the transversality conditions of Maxwell's equations could inspire the pursuit of subwavelength resolution applications in photonic devices. The research suggests a new vector for studying highly confined topological surface states, which might be realized experimentally due to the feasible design and fabrication of metamaterials with significant chirality and hyperbolicity.

In summary, the paper presents a compelling argument for the integration of chirality into hyperbolic metamaterials as a pathway to achieve topologically non-trivial phases. The paper makes substantive contributions to the burgeoning field of topological photonics, suggesting that the experimental realization of these concepts is within reach, potentially heralding advancements in efficient light manipulation and compact photonic device design.