Photonic Surface States Research Articles

Surface potential-adjusted surface states in 3D topological photonic crystals

Surface potential in a topological matter could unprecedentedly localize the waves. However, this surface potential is yet to be exploited in topological photonic systems. Here, we demonstrate that photonic surface states can be induced and controlled by the surface potential in a dielectric double gyroid (DG) photonic crystal. The basis translation in a unit cell enables tuning of the surface potential, which in turn regulates the degree of wave localization. The gradual modulation of DG photonic crystals enables the generation of a pseudomagnetic field. Overall, this study shows the interplay between surface potential and pseudomagnetic field regarding the surface states. The physical consequences outlined herein not only widen the scope of surface states in 3D photonic crystals but also highlight the importance of surface treatments in a photonic system.

Chiral Topological Surface States on a Finite Square Photonic Crystal Bounded by Air

Chiral, topologically protected, photonic surface states can be found at the boundary between gyrotropic photonic crystals where a changing magnetic field induces different topology across the interface. Typically, photonic crystals with either a suitable band structure on both sides of the interface to provide a band gap and evanescent decay of the surface states away from the interface, or an outer layer with engineered material properties is required. In this paper, we show the emergence of topological, unidirectional surface states at the termination of finite gyrotropic photonic crystals with a simple square lattice and ${\mathcal{C}}_{4}$ rotational symmetry bounded by a vacuum, eliminating the need for an outside layer to enable chiral surface modes. We start from an infinite, time-reversal-symmetry-breaking photonic crystal with a band gap associated with bands with nonzero Chern numbers, different from all-zero Chern numbers in air. We then modify the photonic crystal to move this band gap below the light line, while maintaining the Chern-number discontinuities. Band-structure calculations for a supercell approximating a photonic crystal finite in the direction normal to the surface demonstrate the existence, dispersion, and chirality of the surface mode. Extensive direct scattering calculations for a point source and spatial Fourier analysis further reveal a unidirectional free-space topological surface state, which propagates counterclockwise around the surface of a finite photonic crystal, providing a nearly foolproof way to cross-check the surface-mode band structure unaffected by backscattering from local defects. Additionally, scattering simulations allow an independent characterization of the state dispersion and unveil the robustness of the topological plasmonic mode propagation around the ${90}^{\ensuremath{\circ}}$ bends of the structure, being due to only radiation leakage. In contrast to buried topological surface states, the observed surface modes at the photonic crystal--air interface have the advantage of being accessible to the outside world, allowing one to take advantage of the defect-tolerant backscattering-free surface modes to engineer emission from photonic crystal surfaces into arbitrary free-space beam shapes and directions.

Realization of a three-dimensional photonic topological insulator.

Confining photons in a finite volume is highly desirable in modern photonic devices, such as waveguides, lasers and cavities. Decades ago, this motivated the study and application of photonic crystals, which have a photonic bandgap thatforbids light propagation in all directions1-3. Recently, inspired by the discoveries of topological insulators4,5, the confinement of photons with topological protection has been demonstrated in two-dimensional (2D) photonic structures known as photonic topological insulators6-8, with promising applications in topological lasers9,10 and robust optical delay lines11. However, a fully three-dimensional (3D) topological photonic bandgap has not been achieved. Here we experimentally demonstrate a 3D photonic topological insulator with an extremely wide (more than 25 per cent bandwidth) 3D topological bandgap. The composite material (metallic patterns on printed circuit boards) consists of split-ring resonators (classical electromagnetic artificial atoms) with strong magneto-electric coupling and behaves like a 'weak' topological insulator (that is, with an even number of surface Dirac cones), or a stack of 2D quantum spin Hall insulators. Using direct field measurements, we map out both the gapped bulk band structure and the Dirac-like dispersion of the photonic surface states, and demonstrate robust photonic propagation along a non-planar surface. Our work extends the family of 3D topological insulators from fermions to bosons and paves the way for applications in topological photonic cavities, circuits and lasers in 3D geometries.

Witnessing topological Weyl semimetal phase in a minimal circuit-QED lattice

We present an experimentally feasible protocol to mimic topological Weyl semimetal phase in a small one-dimensional circuit-QED lattice. By modulating the photon hopping rates and on-site photon frequencies in parametric spaces, we demonstrate that the momentum space of this one-dimensional lattice model can be artificially mapped to three dimensions accompanied by the emergence of topological Weyl semimetal phase. Furthermore, via a lattice-based cavity input-output process, we show that all the essential topological features of Weyl semimetal phase, including the topological charges associated with Weyl points and the photonic surface states connecting the Weyl points as open arcs, can be unambiguously detected in a circuit with four dissipative resonators by measuring the reflection spectra. These remarkable features may open up a new prospect for simulating topological phases with well-controlled small quantum artificial lattices.

Topological Photonic Phase in Chiral Hyperbolic Metamaterials

Recently, the possibility of achieving one-way backscatter immune transportation of light by mimicking the topological properties of certain solid state systems, such as topological insulators, has received much attention. Thus far, however, demonstrations of nontrivial 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 nontrivial 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.

Theory of Wave Propagation in Magnetized Near-Zero-Epsilon Metamaterials: Evidence for One-Way Photonic States and Magnetically Switched Transparency and Opacity

We study propagation of transverse-magnetic electromagnetic waves in the bulk and at the surface of a magnetized epsilon-near-zero (ENZ) medium in a Voigt configuration. We reveal that in a certain range of material parameters novel regimes of wave propagation emerge; we show that the transparency of the medium can be altered with the magnetization leading either to magnetically induced Hall opacity or Hall transparency of the ENZ. In our theoretical study, we demonstrate that surface waves at the interface between either a transparent or an opaque Hall medium and a homogeneous medium may, under certain conditions, be predominantly one way. Moreover, we predict that one-way photonic surface states may exist at the interface of an opaque Hall ENZ and a regular metal, giving rise to the possibility for backscattering immune wave propagation and isolation.

Nonreciprocal photonic surface states in periodic structures of magnetized plasma nanospheres

We report on the occurrence and properties of photonic surface states in periodic structures of magnetized plasma nanospheres by means of rigorous calculations using the full-electrodynamic layer-multiple-scattering method, properly extended to treat gyrotropic spheres with arbitrarily oriented gyration vector. More specifically, dispersion diagrams of Tamm states at the (001) surface of a semi-infinite fcc crystal of plasma nanospheres and of guided modes of a square array of such spheres supported by a quartz substrate, without and under the action of an in-plane static uniform magnetic field, are analyzed and nonreciprocal optical response, which emerges as a result of the simultaneous lack of space-inversion and time-reversal symmetries, is demonstrated in the Voigt geometry.

Photonic surface states in plasmonic crystals of metallic nanoshells

We report on the occurrence and properties of photonic surface states in fcc crystals of metallic nanoshells, by means of full-electrodynamic calculations using the layer-multiple-scattering method, properly extended. Detailed dispersion diagrams of the surface states associated with the $(001)$ and $(111)$ surfaces are calculated for such semi-infinite crystals and corresponding finite slabs, and convergence by increasing the slab thickness is discussed. It is shown that these states can be tuned over a broad frequency range by varying the shell thickness and can be characterized, along high-symmetry directions, according to their symmetry. Absorption in the metallic material limits the propagation length which can, however, be as long as several tens of lattice constants for low-loss metals and relatively broad bands.

Dirac-cone photonic surface states in three-dimensional photonic crystal slab

We present a multiple-scattering method in conjunction with supercell calculations to study the electromagnetic surface states in three-dimensional photonic crystal slab. Using our technique, we obtain the first prediction of Dirac-cone photonic surface state in some three-dimensional photonic crystal slabs. Such a state can be used to investigate some extremal transmission phenomena of electromagnetic waves near the Dirac point on the surface of the crystal, which is similar to the case of electron on the surface of topological insulators.

Coupling into the slow light mode in slab-type photonic crystal waveguides

Coupling external light signals into a photonic crystal (PhC) waveguide becomes increasingly inefficient as the group velocity of the waveguiding mode slows down. We have systematically studied the efficiency of coupling in the slow light regime for samples with different truncations of the photonic lattice at the coupling interface between a strip waveguide and a PhC waveguide. An inverse power law dependence is found to best fit the experimental scaling of the coupling loss on the group index. Coupling efficiency is significantly improved up to group indices of 100 for a truncation of the lattice that favors the appearance of photonic surface states at the coupling interface in resonance with the slow light mode.