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Topological insulators constitute one of the most intriguing phenomena in modern condensed matter theory. The unique and exotic properties of topological states of matter allow for unidirectional gapless electron transport and extremely accurate measurements of the Hall conductivity. Recently, new topological effects occurring at Dirac/Weyl points have been better understood and demonstrated using artificial materials such as photonic and phononic crystals, metamaterials and electrical circuits. In comparison, the topological properties of nodal lines, which are one-dimensional degeneracies in momentum space, remain less explored. Here, we explain the theoretical concept of topological nodal lines and review recent and ongoing progress using artificial materials. The review includes recent demonstrations of non-Abelian topological charges of nodal lines in momentum space and examples of nodal lines realized in photonic and other systems. Finally, we will address the challenges involved in both experimental demonstration and theoretical understanding of topological nodal lines., Comment: 21 pages, 11 figures

A quantum emitter placed in a nanophotonic structure can result in non-reciprocal phenomena like chiral light excitation. Here, we present a theoretical model to couple circularly polarized emitters described by the density matrix formalism to the electromagnetic fields within a finite-difference time-domain (FDTD) simulation. In particular, we discuss how to implement complex electric fields in the simulation to make use of the rotating wave approximation. By applying our model to a quantum emitter in a dielectric waveguide and an optical circulator, we show how the excitation of the quantum system depends on its position and polarization. In turn, the backcoupling can result in strongly asymmetric light excitation. Our framework and results will help better understand spatio-temporal dynamics of light field in nanophotonic structures containing quantum emitters.

Although a large class of topological materials have uniformly been identified using symmetry properties of wave functions, the past two years have seen the rise of multi-gap topologies beyond this paradigm. Given recent reports of unexplored features of such phases, platforms that are readily implementable to realize them are therefore desirable. Here, we demonstrate that multi-gap topological phase transitions of non-Abelian charged nodal lines arise in classical phonon waves. By adopting a simple spring-mass system, we construct nodal lines of a three-band system. The braiding process of the nodal lines is readily performed by adjusting the spring constants. The generation and annihilation of the nodal lines are then analyzed using Euler class. Finally, we retrieve topological transitions from trivial nodal lines to a nodal link. Our work provides a simple platform that can offer diverse insights to not only theoretical but also experimental studies on multi-gap topology.

The prime example of a two-dimensional photonic crystal featuring Dirac cones is based on the honeycomb lattice. Colloidal self-assembly can produce a two-dimensional colloidal structure over a large area but is limited to hexagonal-close-packed structures. Therefore, it has been challenging to fabricate honeycomb monolayers by colloidal self-assembly. Here, we fabricate a dielectric honeycomb lattice in a large area by template-assisted self-assembly and analyze its photonic structure. Although the Dirac point occurring at the K point is not accessible by light in free space, a part of the upper Dirac cone above the light line is verified by a Fourier analysis of the back-focal-plane image. Because the template-assisted self-assembly enables additional geometrical perturbations in the honeycomb lattice, various lattices can be fabricated. This additional degree of freedom may provide an alternative way of fabricating photonic topological insulators.

A gyroid crystal possesses a peculiar structural feature that can be conceptualized as a triply periodic surface with a constant mean curvature of zero. The exotic optical properties such as the photonic bandgap and optical chirality can emerge from this three-dimensional (3D) morphological feature. As such, gyroid crystals have been considered as the promising structures for photonic crystals and optical metamaterials. To date, several methods have been proposed to materialize gyroid crystals, including 3D printing, layer-by-layer stacking, two-photon lithography, interference lithography, and self-assembly. Furthermore, the discovery of Weyl points in gyroid crystals has further stimulated these advancements. Among such methods, the self-assembly of block copolymers (BCPs) is unique, because this soft approach can provide an easy-to-craft gyroid, especially at the nanoscale. The unit-cell scale of a gyroid ranging within 30–300 nm can be effectively addressed by BCP self-assembly, whereas other methods would be challenging to achieve this size range. Therefore, a BCP gyroid has provided a material platform for metamaterials and photonic crystals functioning at optical frequencies. Currently, BCP gyroid nanophotonics is ready to take the next step toward topological photonics beyond the conventional photonic crystals and metamaterials. In particular, the intrinsic lattice transformations occurring during the self-assembly of BCP into a gyroid crystal could promise a compelling advantage for advancing Weyl photonics in the optical regime. Lattice transformations are routinely considered as limitations, but in this review, we argue that it is time to widen the scope of the lattice transformations for the future generation of nanophotonics. Thus, our review provides a comprehensive understanding of the gyroid crystal and its lattice transformations, the relevant optical properties, and the recent progress in BCP gyroid self-assembly.

A nodal link is a special form of a line degeneracy (a nodal line) between adjacent bands in the momentum space of a three-dimensional topological crystal. Unlike nodal chains or knots, a nodal link consists of two or more mutually-linked rings that do not touch each other. Recent studies on non-Abelian band topology revealed that the topological charges of the nodal links can have the properties of quaternions. However, a photonic crystal that has a nodal link with non-Abelian charges has not been reported. Here, we propose dielectric photonic crystals in forms of double diamond structures which realize the nodal links in the momentum space. By examining the evolution of the eigenstate correlations along the closed loops which enclose the nodal line(s) of the links, their non-Abelian topological charges are also analyzed. The proposed design scheme and theoretical approach in this work will allow for experimental observation of photonic non-Abelian charges in purely dielectric materials and facilitate the control of the degeneracy in complex photonic structures., 35 pages, 12 figures

The dispersion relation of surface plasmon polaritons in graphene that includes optical losses is often obtained for complex wave vectors while the frequencies are assumed to be real. This approach, however, is not suitable for describing the temporal dynamics of optical excitations and the spectral properties of graphene. Here, we propose an alternative approach that calculates the dispersion relation in the complex frequency and real wave vector space. This approach provides a clearer insight into the optical properties of a graphene layer and allows us to find the surface plasmon modes of a graphene sheet in the full frequency range, thus removing the earlier reported limitation (1.667 < $\hbar��/��$ < 2) for the transverse-electric mode. We further develop a simple analytic approximation which accurately describes the dispersion of the surface plasmon polariton modes in graphene. Using this approximation, we show that transverse-electric surface plasmon polaritons propagate along the graphene sheet without losses even at finite temperature., 13 pages, 7 figures

We propose a dynamic model for photonic topological insulators (PTIs) with Kerr nonlinearity. Using the model, we demonstrate the bistability and spontaneous symmetry breaking in the Su-Schrieffer-Heeger model and two-dimensional nonlinear PTIs.

We show linked nodal rings in momentum space with a dielectric photonic crystal. From evolutions of the eigenstates polarizations along the loops which enclose the nodal line(s) of the rings, their non-Abelian topological charges are also analyzed.

By introducing an imaginary gauge field, we demonstratet opologically pro-tected bulk modes extended over a two-dimensional kagome lattice with rhombus geometry. Using the kagome lattice with gain/loss, a phase-locked broad-area topological laser can be realized.

The realization of topological edge states (TESs) in photonic systems has provided unprecedented opportunities for manipulating light in novel manners. The Su-Schrieffer Heeger (SSH) model has recently gained significant attention and has been exploited in a wide range of photonic platforms to create TESs. We develop a photonic topological insulator strategy based on SSH photonic crystal nanobeam cavities. In contrast to the conventional photonic SSH schemes which are based on alternately tuned coupling rength in one dimensional lattice, our proposal provides higher flexibility and allows tailoring TESs by manipulating mode coupling in a two-dimensional manner. We reveal that the proposed hole array based nanobeams in a dielectric membrane can selectively tailor single or double TESs in the telecommunication region by controlling the coupling strength of the adjacent SSH nanobeams in both vertical and horizontal directions. Our finding provides an additional degree of freedom in exploiting the SSH model for integrated topological hotonic devices and functionalities based on the well-established photonic crystal nanobeam cavity platforms.

Topological photonics has recently been proved a robust framework for manipulating light. Active topological photonic systems, in particular, enable richer fundamental physics by employing nonlinear light-matter interactions, thereby opening a new landscape for applications such as topological lasing. Here we propose an all-dielectric topological insulator laser scheme in telecommunication region based on semiconductor cavities formed by topologically distinct Kagome photonic crystals. Our theoretical results show that the proposed planar semiconductor Kagome lattice can lift degeneracy with geometrical perturbation and open broad photonic bandgaps, and valley-dependent edge states and topologically robust transport with subwavelength scale confinement are observed at the edge of the perturbed Kagome lattices with distinct valley Chern numbers. An interesting feature of the Kagome lattices is that it supports two different types of valley Hall edge modes, which enables the coexistence of high Q ring-resonator modes and lossy Fabry–Perot resonator modes in the proposed topological cavities. Moreover, we explore pumping and lasing dynamics of the topological cavities by means of a four-level two-electron model and demonstrate that this model offers a powerful platform to investigate non-Hermitian topological laser cavities with arbitrary geometry. The proposed topological semiconductor scheme provides a new route to study non-Hermitian topological photonics and to develop integrated topological systems for robust light generation and transport.

Photonic topological insulators are a promising photonic platform due to the possibility of unidirectional edge states with insensitivity to bending, fabrication imperfections or environmental fluctuation. Here we demonstrate highly efficient unidirectional photonic edge mode propagation facilitated by an optical analogue of the quantum valley Hall effect. With an all-dielectric kagome lattice design, we demonstrate broadband suppressed reflection in the presence of sharp corners and further show negligible vertical losses in a semiconductor-based device at telecommunication wavelengths., 9 pages, 13 figures

Recent interest in optical analogs to the quantum spin Hall and quantum valley Hall effects is driven by the\ud promise to establish topologically protected photonic edge modes at telecommunication and optical wavelengths\ud on a simple platform suitable for industrial applications. While first theoretical and experimental efforts have\ud been made, these approaches so far both lack a rigorous understanding of the nature of topological protection and\ud the limits of backscattering immunity. We here use a generic group theoretical methodology to fill this gap and\ud obtain general design principles for purely dielectric two-dimensional topological photonic systems. The method\ud comprehensively characterizes possible two-dimensional hexagonal designs and reveals their topological nature,\ud potential, and limits.

Metamaterials with classical analogues of electromagnetically induced transparency open new avenues in photonics for realizing smaller, more efficient slow light devices without quantum approaches. However, most of the metamaterial-based slow light devices are passive, which limits their practical applications. Here, by combining diatomic metamaterials with a gated single-layer graphene, we demonstrate that the group delay of terahertz light can be dynamically controlled under a small gate voltage. Using a two coupled harmonic oscillators model, we show that this active control of group delay is made possible by an effective control of the dissipative loss of the radiative dark resonator by varying the graphene’s optical conductivity. Our work may provide opportunities in the design of various applications such as compact slow light devices and ultrasensitive sensors and switches.

Nanophotonic engineering of light–matter interaction at subwavelength scale allows thermal radiation that is fundamentally different from that of traditional thermal emitters and provides exciting opportunities for various thermal-photonic applications. We propose a new kind of integrated and electrically controlled thermal emitter that exploits layered metamaterials with lithography-free and dielectric/metallic nanolayers. We demonstrate both theoretically and experimentally that the proposed concept can create a strong photonic bandgap in the visible regime and allow small impedance mismatch at the infrared wavelengths, which gives rise to optical features of significantly enhanced emissivity at the broad infrared wavelengths of 1.4–14 μm as well as effectively suppressed emissivity in the visible region. The electrically driven metamaterial devices are optically and thermally stable at temperatures up to ∼800 K with electro-optical conversion efficiency reaching ∼30%. We believe that the proposed high-efficiency thermal emitters will pave the way toward integrated infrared light source platforms for various thermal-photonic applications and particularly provide a novel alternative for cost-effective, compact, low glare, and energy-efficient infrared heating.

The presence of topological edge modes at the interface of two perturbed honeycomb photonic crystals with $C_6$ symmetry is often attributed to the different signs of Berry curvature at the K and K$'$ valleys. In contrast to the electronic counterpart, the Chern number defined in photonic valley Hall effect is not a quantized quantity but can be tuned to finite values including zero simply by changing geometrical perturbations. Here, we argue that the edge modes in photonic valley Hall effect can exist even when Berry curvature vanishes. We numerically demonstrate the presence of the zero-Berry-curvature edge modes in triangular lattice photonic crystal slab structures in which $C_3$ symmetry is maintained but inversion symmetry is broken. We investigate the evolution of the Berry curvature from the honeycomb-lattice photonic crystal slab to the triangular-lattice photonic crystal slab and show that the triangular-lattice photonic crystals still support edge modes in a very wide photonic bandgap. Additionally, we find that the edge modes with zero Berry curvature can propagate with extremely low bending loss., Comment: 8 pages, 10 figures including supplementary information

Photonic topological insulators are promising photonic structures which can exhibit unidirectional propagation of edge states insensitive to bendings, fabrication imperfections or temperature variations. Recently, an all-dielectric perturbed honeycomb topological photonic crystal has attracted attention due to its simplicity of fabrication. However, its edge states intrinsically suffer from back-reflection due to the symmetry breaking at the interface. Here, we propose an all-dielectric reciprocal photonic topological insulator based on the geometry of a kagome lattice in which the topological edge modes do not undergo back-reflection for termination along the $\Gamma - K$ direction. In contrast to the perturbed honeycomb, the edge modes in our kagome-based structure are below the light cone leading to improved vertical mode confinement.

Topologically protected surface states in photonic systems, with unique properties such as unidirectional propagation and light confinement insensitive to thermal or fabrication imperfections, have attracted immense attention over the past ten years. We introduce the notion of weak protection where a topological invariant predicts the existence of surface states in the photonic bulk gap, and strong protection which instead corresponds to the number of glueing points of a surface band with the bulk edges. While strong protection is desired for many key applications such as topologically protected loss-free cavities to boost non-linear interactions, it requires optical reciprocity breaking in two dimensions. We here provide a group theoretical recipe to design weakly protected states on purely dielectric metasurfaces, and genuinely strongly protected states in fully connected 3D photonic crystals. Both design principles can be readily realized by current direct manufacturing techniques, such as electron beam lithography and direct laser writing, respectively.

Taming laser instabilities Broad-area and high-power lasers often suffer from instabilities owing to the chaotic interference of multiple modes within the cavity. Such instabilities can ultimately limit the operation of the laser or damage the cavity. The usual approach to minimizing such instabilities is to limit the number of modes in the cavity. Bittner et al. designed a chaotic cavity that disrupts the formation of self-organized structures that lead to instabilities (see the Perspective by Yang). This approach of fighting chaos with chaos by using the boundary condition of the cavity shape may provide a robust route to stabilizing lasers at high operating powers. Science , this issue p. 1225 ; see also p. 1201

The suppression of spatio-temporal instabilities of broad-area semiconductor lasers is demonstrated for microcavities with chaotic ray dynamics. We attribute the stabilization to the disruption of coherent instabilities by complex wave interference.

A unidirectional chiral edge mode in photonic topological insulators can be selectively excited by a circularly-polarized dipole source. We show that the directionality is also determined by the position of the dipole source.

We demonstrated that metamaterial technology enables us to tailor infrared thermal emission and provides a promising strategy towards novel, cost-effective and highly efficient mid-infrared source for optical gas sensing.

Introduction of a gain medium in lossy plasmonic metamaterials reduces and compensates losses or even amplifies an incident light often with nonlinear optical effect. Here, optical gain in a pump-probe experimental setup is effectively calculated in the frequency-domain by approximating a gain material as an inhomogeneous medium. Spatially varying local field amplitudes of the pump and probe beams are included in the model to reproduce the inhomogeneous gain effect, in which population inversion occurs most strongly near the surface and decays along the propagation direction. We demonstrate that transmission spectra calculated by this method agree well with finite-difference time-domain simulation results. This simplified approach of gain modelling offers an easy and reliable way to analyze wave propagation in a gain medium without nonlinear time-domain calculation.

Graphene, which is a two-dimensional crystal of carbon atoms arranged in a hexagonal lattice, has attracted a great amount of attention due to its outstanding mechanical, thermal and electronic properties. Moreover, graphene shows an exceptionally strong tunable light-matter interaction that depends on the Fermi level - a function of chemical doping and external gate voltage - and the electromagnetic resonance provided by intentionally engineered structures. In the optical regime, the nonlinearities of graphene originated from the Pauli blocking have already been exploited for mode-locking device applications in ultrafast laser technology, whereas nonlinearities in the terahertz regime, which arise from a reduction in conductivity due to carrier heating, have only recently been confirmed experimentally. Here, we investigated two key factors for controlling nonlinear interactions of graphene with an intense terahertz field. The induced transparencies of graphene can be controlled effectively by engineering meta-atoms and/or changing the number of charge carriers through electrical gating. Additionally, nonlinear phase changes of the transmitted terahertz field can be observed by introducing the resonances of the meta-atoms.

The optical properties of metamaterials made by block copolymer self-assembly are tuned by structural and environmental variations. The plasma frequency red-shifts with increasing lattice constant and blue-shifts as the network filling fraction increases. Infiltration with dielectric liquids leads also to a red-shift of the plasma edge. A 300 nm-thick slab of gyroid-structured gold has a remarkable transmission of 20%.

Orbital angular momentum of light has recently been recognized as a new degree of freedom to encode information in quantum communication using light pulses. Methods to extract this information include reversing the process by which such twisted light was created in the first place or interference with other beams. Here, we propose an alternative new way to directly read out the extra information encoded in twisted light using plasmonic nanoantennas by con- verting the information about the orbital angular momentum of light into spectral information using bright and dark modes. Exemplarily considering rotation-symmetrical nanorod nanoan- tennas we show that their scattering cross-section is sensitive to the value of the orbital angular momentum combined with the polarisation of an incident twisted light beam. Explaining the twist-dependence of the excited modes with a new analytical model our results pave the way to twisted light nanoplasmonics, which is of central importance for future on-chip communication using orbital angular momentum of light.

Metallic single gyroids, a new class of self-assembled nanoplasmonic metamaterials, are analyzed on the basis of a tri-helical metamaterial model. The physical mechanisms underlying the chiral optical behavior of the nanoplasmonic single gyroid are identified and it is shown that the optical chirality in this metallic structure is primarily determined by structural chirality and the connectivity of helices along the main cubic axes.

The authors thank Prof. H. Y. Park, Korea Advanced Institute of Science and Technology, and Dr. C.-S. Kee, Advanced Photonics Research Institute, for assistance with the FDTD simulations. This work was supported by an ERC grant of the National Research Foundation of Korea NRF) funded by the Korea Ministry of Education, Science and Technology (MEST) (No. R11–2007-045–01002-0(2009)).

We fabricated micro-lens arrays which have moth-eye antireflective nanostructures on their surfaces using thermal imprinting process and plasma treatment and characterized the morphology of the micro-lens arrays. After a micro-lens array shape was fabricated on a photoresist using photolithography and thermal reflow process, patterns were transferred onto a Ni stamp, and then micro-lens patterns were replicated on a polycarbonate film using thermal imprinting lithography. Using reactive ion etching, we were able to form the moth-eye antireflective nanostructures on the surface of polycarbonate films and polycarbonate micro-lens arrays. The AFM and SEM images of the plasma treated samples clearly show that the moth-eye nanostructures are formed on the surface. By measuring the transmittance spectrum using a UV-visible spectrometer, we also show that the moth-eye structures really act as antireflection coatings.

Antireflection (AR) nanostructures are fabricated on a glass substrate using hybrid nano-patterning lithography (H-NPL) consisting of nanosphere lithography (NSL) and UV-nanoimprint lithography (UV-NIL). The shape and diameter of the AR nanostructures were controlled by fabricating Si masters with different RIE conditions. The shapes of the AR nanostructures were a pillar-type and a corn-type. The diameters of the AR nanostructures were about 350 and 250nm, respectively. AR nanostructures were successfully nanoimprinted on glass in accordance with Si master prepared by NSL. The pillar-type AR nanostructure with diameter of 350nm exhibited the transmittance of over 98% in the wavelength range from 1100 to 2200nm. From the results, the fabricated AR nanostructures demonstrate the possibility to improve the efficiency of optoelectronic devices such as a photo-detector and an IR-LED.

For the purpose of carbon-dioxide (CO 2 ) sensors, we propose a photonic crystal (PhC)-type filter that has a narrow pass band at a wavelength of 4.26 mu m in the infrared region. Using the finite-difference time-domain (FDTD) method, we obtained the transmission spectra for various shapes and sizes of the air holes in the PhC type filters. On the basis of the numerical results, we designed and fabricated a PhC-type filter. By measuring the transmission spectra of the fabricated devices, we confirmed that the PhC-type filter could be a candidate for an element of an optical gas sensor. The behavior of the spectral response of the filter with respect to the shape and the size of the air holes was also analyzed.

At infrared wavelengths, we demonstrate subwavelength scale localization of spoof surface plasmon polaritons. Based on an analytical model and numerical simulations, we show that the defect mode has toroidal dipole moment and high Q factor.

We numerically and experimentally demonstrate subwavelength scale waveguiding of spoof surface plasmon polaritons at a line defect in a two-dimensional groove metal array that exhibits a band gap region.

The control of the optical activity and ellipticity of a medium has drawn considerable attention due to the recent\ud developments in metamaterial design techniques and a deeper understanding of the light matter interaction in\ud composite metallic structures. Indeed, recently proposed designs of metaatoms have enabled the realisation of\ud materials with unprecedented chiral optical properties e.g. strong optical activity, broadband optical activity, and\ud nondispersive zero ellipticity. Combining chiral metamaterials with nonlinear materials has opened up new\ud possibilities in the field of nonlinear chirality as well as provided the foundation for switchable chiral devices.\ud Furthermore, chirality together with hyperbolicity can be used to realise new exciting materials such as photonic\ud topological insulators. In this review, we will outline the fundamental principles of chiral metamaterials and report on\ud recent progress in providing the foundations for promising applications of switchable chiral metamaterials.