Band-edge Modes Research Articles

Large-Area Perovskite Nanocrystal Metasurfaces for Direction-Tunable Lasing.

Perovskite nanocrystals (PNCs) are attractive emissive materials for developing compact lasers. However, manipulation of PNC laser directionality has been difficult, which limits their usage in photonic devices that require on-demand tunability. Here we demonstrate PNC metasurface lasers with engineered emission angles. We fabricated millimeter-scale CsPbBr3 PNC metasurfaces using an all-solution-processing technique based on soft nanoimprinting lithography. By designing band-edge photonic modes at the high-symmetry X point of the reciprocal lattice, we achieved four linearly polarized lasing beams along a polar angle of ∼30° under optical pumping. The device architecture further allows tuning of the lasing emission angles to 0° and ∼50°, respectively, by adjusting the PNC thickness to shift other high-symmetry points (Γ and M) to the PNC emission wavelength range. Our laser design strategies offer prospects for applications in directional optical antennas and detectors, 3D laser projection displays, and multichannel visible light communication.

Photonic defect modes in cholesteric liquid crystal resonators with embedded isotropic layers

Photonic defect modes are explored as a viable alternative to standard photonic band edge modes in photonic crystal applications, especially due to their typically high Q-factors and local density of states. For example, they can be used in nonlinearity enhancement, lasing, and cavity quantum electrodynamics. However, they are strongly dependent on any structural change and need to be well-controlled to ensure the desired resonance frequency. Here, we present a study of the photonic defect modes that appear in a structure where a layer of isotropic material is embedded between two layers of cholesteric liquid crystal (CLC), using full electrodynamics numerical simulations. We present typical transmission spectra and electric field profiles of selected defect modes and then analyze the influence of geometrical and material parameters on the eigenfrequencies and Q-factors of the modes within and around the photonic bandgap, including refractive indices and thicknesses of isotropic and liquid crystal layers, and different anchoring orientations at the boundaries of the isotropic defect layer. Additionally, a connection of such defect modes to previously extensively analyzed twist defect modes is given. Eigenmodes in asymmetric resonators are also presented, where CLC layers surrounding the intermediate isotropic layer are not equally thick, enabling biasing of specific directional light emission. More generally, this work aims to contribute to the understanding and design capability in topological soft matter photonics where defect mode lasing could be realized in CLC geometries with different singular and solitonic topological defect structures.

Statistics of Lyapunov exponent in random Fibonacci multilayer

Abstract We numerically investigated the localization properties of band-gap and band-edge modes in a one-dimensional random Fibonacci optical multilayer. The statistics of the Lyapunov Exponent (LE) reveal distinct behaviors of localization effects for band-edge and band-gap modes as a function of disorder strength. In particular, a deviation from the single parameter scaling theory (SPST) of localization was observed within a frequency window corresponding to the band-gap of an ordered Fibonacci multilayer. To provide a physical explanation for the violation of SPST, a close correlation between the frequency distribution of the resonant modes in the band-gap and the variance of the LE has been found. The spatial distribution of resonant modes has been reported and discussed. Finally, the dynamics of the gap closing of the two main band-gaps as a function of the disorder strength has been analyzed.

Topological phases and edge modes of an uneven ladder

Abstract We investigate the topological properties of a two-chain quantum ladder with uneven legs, i.e., the two chains differ in their periods by a factor of 2. Such an uneven ladder presents rich band structures classified by the closure of either direct or indirect bandgaps. It also provides opportunities to explore fundamental concepts concerning band topology and edge modes, including the difference of intracellular and intercellular Zak phases, and the role of the inversion symmetry (IS). We calculate the Zak phases of the two kinds and find excellent agreement with the dipole moment and extra charge accumulation. We also find that configurations with IS feature a pair of degenerate two-side edge modes emerging as the closure of the direct bandgap, while configurations without IS feature one-side edge modes emerging as not only the closure of both direct and indirect bandgaps but also within the band continuum. Furthermore, by projecting to the two sublattices, we find that the effective Bloch Hamiltonian corresponds to that of a generalized Su–Schrieffer–Heeger model or the Rice–Mele model whose hopping amplitudes depend on the quasimomentum. In this way, the topological phases can be efficiently extracted through winding numbers. We propose that uneven ladders can be realized by spin-dependent optical lattices and their rich topological characteristics can be examined by near future experiments.

Enhanced Photon-Pair Generation Based on Thin-Film Lithium Niobate Doubly Resonant Photonic Crystal Cavity

In this work, a doubly resonant photonic crystal (PhC) cavity is proposed to enhance second harmonic generation (SHG) efficiency and photon pair generation rate (PGR). Through the exploration of geometry parameters, a band-edge mode within the light cone is identified as the first harmonic (FH) mode, and a band-edge mode outside the light cone is designated as the second harmonic (SH). Subsequently, by increasing the layers of the core region, a heterostructure PhC cavity is designed. The results showcase a doubly resonant PhC cavity achieving a 133/W SHG efficiency and a photon pair generation rate of 3.7 × 108/s. The exceptional conversion efficiency is attributed to the high quality factors Q observed in the FH and SH modes with values of approximately 280,000 and 2100, respectively. The remarkably high Q factors compensate for nonlinear efficiency degradation caused by detuning, simultaneously making the manufacturing process easier and more feasible. This work is anticipated to provide valuable insights into efficient nonlinear conversion and photon pair generation rates.

Control of band-edge surface plasmons and their influences on photoluminescence of colloidal quantum dots on metal gratings

We holographically fabricated metal gratings demonstrating clear bandgaps and controlled resonances of band-edge surface plasmons (SP), and studied their influences on photoluminescence (PL) of colloidal quantum dots (cQDs) on the gratings. It is verified by numerical simulations that intrinsically existing but indiscernible bandgaps of SPs on sinusoidal metal gratings get distinctly open by introducing second harmonic components in their surface profiles. We elucidated roles of spatial harmonic components of the metal gratings on the bandgaps and their experimental manifestations. The band-edge SP resonance modes are shown to enhance PL of the cQDs and have the PL linearly polarized in direction parallel to grating vector. By systematically varying position of the bandgap relative to intrinsic PL peak of the cQDs, effects of the bandgap and band-edge SPs on PL of the cQDs in modifying the spectral profiles are demonstrated. It's also verified, by varying strength of coupling between the cQDs and the SP modes, that polarization of the PL is induced by the SPs, instead of selectivity of the gratings in diffractive coupling of the emitted photons in different polarization states. In additioin, it's interestingly found that excitation light coupled to the band-edge SPs can evidently improve linear polarization degree of the PL.

Design and Observation of Topological Band Gaps and Edge Modes of SOI Photonic Crystal Slabs in the Mid-Infrared Range

Design and Observation of Topological Band Gaps and Edge Modes of SOI Photonic Crystal Slabs in the Mid-Infrared Range

Deep Subwavelength Anti-Slot Photonic Crystals Fabricated in Monolithic Silicon Photonics Technology

We report the scalable fabrication and characterization of photonic crystal (PhC) nanobeam waveguides incorporating subwavelength-scale dielectric anti-slot unit cells. These anti-slot PhCs were fabricated using deep UV lithography on a monolithic silicon photonics technology. The dielectric band edge mode is characterized by strong field localization in the anti-slot region where the minimum dielectric feature size is approximately 70 nm. This demonstration opens the door to further investigation of subwavelength engineered photonic structures fabricated using commercial foundry processes for integrated photonics applications that benefit from enhanced light-matter interaction.

Topological band gaps and edge modes materialized by symmetric silicon-on-insulator photonic crystal slabs in the mid-IR range

We successfully fabricated silicon-on-insulator (SOI) photonic crystal (PhC) slabs in which electromagnetic topological band gaps and edge modes were materialized for symmetric transverse-electric-like modes. Because the structure of our specimens can be regarded as symmetric about the horizontal middle plane of the PhC slab, their symmetric and antisymmetric eigenmodes were rigorously separated, so we could achieve genuine photonic band gaps for the former. We fabricated those specimens by electron beam lithography of the top Si layer of SOI wafers and successive plasma-enhanced chemical vapor deposition of a ${\mathrm{SiO}}_{2}$ capping layer. We confirmed the complete common band gap of topologically trivial and nontrivial PhCs and the topological edge modes on the boundary between them by angle-resolved reflection spectroscopy in the mid-infrared range. This is an observation of the common band gap and edge modes that materialized in symmetric PhC slabs without a membrane structure, that is, without the etching of a sacrificial layer under the PhC to increase the refractive-index contrast and the width of the common band gap.

Doubly resonant photonic crystal cavity using merged bound states in the continuum

In this work, a doubly resonant photonic crystal (PhC) cavity using the merged bound states in the continuum (BICs) is proposed to obtain a higher second harmonic generation (SHG) efficiency. Firstly by scanning geometry parameters the accidental BICs and a band-edge mode outside the light cone can be obtained. Then as the lattice constant or the thickness of the slab is adjusted the accidental BICs will merge. A supercell with large and small holes is constructed and the band-edge mode outside the light cone can be mode-matched with the merged BICs mode. Finally the heterostructure PhC cavity is designed. The merged BICs show a high quality factor for the photonic crystal with finite size. Consequently, the SHG efficiency of the lattice constant near merged BICs of ~6000% W-1 is higher than the one of the isolated BIC.

Flat band induced topological photonic Tamm states in stubbed structures: Theory and experiment

We provide theoretical and experimental evidence for the existence of topological Tamm states at the interface between two stubbed photonic crystals (PCs) as a function of the period and length of the stubs. Several works have addressed these states in the well-known Su-Schrieffer-Heeger model, a dimerized chain based on two resonators per unit cell where the opening of a gap at a Dirac cone results in a symmetry inversion of bulk bands between two topologically different crystals. Here, we give a detailed theoretical analysis of a mechanism based on band-edge symmetry inversion around a flat band, i.e., when the width of the pass band vanishes, while using only one resonator (stub) per unit cell. Then, we propose a simple versatile experimental platform to observe such interface states, which is based on coaxial cables operating in the radio-frequency domain. The investigation of these states was performed by using different approaches: (i) the topology of the bands based on the Zak phase and the symmetry of the band-edge modes, (ii) the sign of the reflection phase between each PC and a waveguide, and (iii) the dips or peaks in the reflection and transmission spectra when two finite photonic crystals are connected together either horizontally or vertically along a waveguide. Furthermore, we give a general rule about the existence of interface states when two PCs exhibit two common gaps with a flat band in their middle and different bulk-edge symmetries. Also, we provide closed-form expressions of the geometrical parameters and the frequency for which the interface state becomes bound state in the continuum (BIC). We show that these topological BIC states are stationary states of the cavity between the two PCs, and are very robust to any perturbation on both sides of the cavity. Finally, we show the impossibility of existence of interface states between two PCs with identical periods and different stubs. The theoretical and experimental results are discussed for both Neumann and Dirichlet boundary conditions at the end of the stubs.

Bloch Surface Waves in Open Fabry-Perot Microcavities.

Thanks to the increasing availability of technologies for thin film deposition, all-dielectric structures are becoming more and more attractive for integrated photonics. As light-matter interactions are involved, Bloch Surface Waves (BSWs) may represent a viable alternative to plasmonic platforms, allowing easy wavelength and polarization manipulation and reduced absorption losses. However, plasmon-based devices operating at an optical and near-infrared frequency have been demonstrated to reach extraordinary field confinement capabilities, with localized mode volumes of down to a few nanometers. Although such levels of energy localization are substantially unattainable with dielectrics, it is possible to operate subwavelength field confinement by employing high-refractive index materials with proper patterning such as, e.g., photonic crystals and metasurfaces. Here, we propose a computational study on the transverse localization of BSWs by means of quasi-flat Fabry-Perot microcavities, which have the advantage of being fully exposed toward the outer environment. These structures are constituted by defected periodic corrugations of a dielectric multilayer top surface. The dispersion and spatial distribution of BSWs' cavity mode are presented. In addition, the hybridization of BSWs with an A exciton in a 2D flake of tungsten disulfide (WS2) is also addressed. We show evidence of strong coupling involving not only propagating BSWs but also localized BSWs, namely, band-edge and cavity modes.

High-performance dielectric nano-cavities for near- and mid-infrared frequency applications

We present a judicious design approach for optimizing semiconductor nanocavities, starting from single photonic atoms to build photonic molecules functioning as high-performance nanocavities. This design approach is based on exact analytical solutions to the Maxwell equations for collective Mie resonances. Conceptually, we distinguish different concepts of cavity modes including Mie mode, collective Mie mode, photonic-crystal (PC) band-edge mode, and Feshbach-type bound states in the continuum (BIC) mode. Using the design approach, we present a unique structure of nanocavity supporting the Feshbach-type BIC mode, capable of enhancing the emission rate of a dipolar emitter by orders of magnitude. This high-performance nanocavity suppresses radiative loss channels strongly via destructive interference and consequently channels the emission light efficiently into an in-plane bi-directional beam with a divergence angle of 10°. Engineering the geometrical parameters of the nanocavity for near-infrared frequency applications requires a fabrication tolerance of ±5 nm. This high accuracy is challenging for the mass production of devices. The fabrication accuracy can be relaxed greatly for mid-infrared frequency devices. As a showcase, we analyze and optimize the well-known PC L3 defect nanocavity for mid-infrared frequency applications in the framework of Feshbach resonance. We show that the optimal structure of this defect nanocavity requires a fabrication tolerance of ±50 nm. Our nanocavity design approach may be useful for near- and mid-infrared frequency applications.

Nonlinear localized gap modes in width-modulated Fibonacci lattices

We address the properties of nonlinear localized gap modes supported by the width-modulated Fibonacci lattices, including their existence and stability. Linear system with the width-modulated Fibonacci lattices has multiple gaps. We find the existence of different families of nonlinear localized modes in two relatively large gaps. One of the nonlinear localized gap modes originates from the upper band-edge linear mode. Such gap modes are mostly stable in their entire existence domain, except for a small region in the middle of their existence. The other two families of nonlinear modes localized in the relatively large gap are pure nonlinear modes, and they have a narrow stable region near their upper cutoff. The results of the linear stability analysis are in good agreement with that of the propagation simulations.

Generation and modulation of non-classical light in a strongly coupled photon–emitter system

Non-classical light, especially its single photon and squeezing properties, plays a fundamental role in on-chip quantum networks. The single photon property has been widely studied in photonic cavities including photonic crystals (PhCs), micropillar cavities, nanowires, and plasmonic cavities. However, the generation and modulation of squeezing light in nanophotonic cavities remain to be explored. Here, we theoretically demonstrate a strongly coupled PhC–plasmonic-emitter system enabling non-classical light generation and modulation. The hybridization of a PhC waveguide and an Ag nanoparticle forms a band-edge mode with a narrow linewidth and a strong confined field, which enables strong light–emitter interaction, further resulting in simultaneous generation of squeezing and single photon properties for on-chip applications. Non-classical light emission can be modulated with the detuning between the band-edge mode and the emitter. The emission is efficiently channeled by the PhC waveguide with a high coupling efficiency, accompanying unidirectional transmission under excitation by a circularly polarized emitter. The system provides a candidate for tunable and bifunctional on-chip non-classical light sources at the nanoscale and may offer more possibilities to build versatile quantum networks.

Progress in Germanium Tin (GeSn) Photonic Crystal Lasers

We report on lasing in two types of Germanium-Tin (GeSn) photonic crystal lasers, with band-edge and H4 hexagonal cavities. A GeSn 16% step-graded structure was used as the optical gain material. The strong out-of-plane emission observed in the band-edge cavity was attributed to the thick optical gain layer, in addition with the presence of leaky band-edge modes above the light cones and a high photonic density of states. The maximum lasing temperature in both types of photonic crystal lasers, 180 K, was lower than in a micro-disk laser fabricated from the same stack, i.e., 230 K. Meanwhile, the lasing thresholds at low temperature (15 K) were very similar (120 kW/cm² for a band-edge cavity and 140 kW/cm² for a H4 cavity, to be compared with 134 kW/cm² for a micro-disk cavity). Since the injected carrier density is governed by the pump power, we suggest the strong variation of optical gain at low temperature, for a small variation of injected carrier density, as a possible cause of such a phenomenon.

Mechanism of Band Gaps in Self-Similar Triangular Lattice With Koch Fractal

Abstract Fractal lattice is a kind of lattices with multifunctional physical characteristics and superior mechanical properties. The wave propagation of the triangular lattice with Koch fractal is calculated by the finite element method and Bloch theorem. The effects of the iteration number on the band gaps and the band edge modes are studied. The finite element software was used to simulate the dynamic response of the triangular lattice with Koch fractal for verifying the vibration suppression performance. The results show that the triangular lattice with Koch fractal can produce multiple and low-frequency band gaps. As an increase of the iteration number, the band gap gradually shifts to a lower frequency. By comparing and analyzing the band edge modes and the eigenmodes of Koch fractal, the mechanisms of the band gaps within the low-frequency ranges are analyzed and discussed in detail. Additionally, the band edge modes exhibit similar vibration modes. Finally, the simulation results of the finite lattice verify the broadband vibration suppression performance of the triangular lattice with Koch fractal. This work provides insights into the lattice dynamic behavior adjusted by Koch fractal, which is beneficial to the periodic lattice for suppressing vibration in engineering applications.

High-Q Localized States in Finite Arrays of Subwavelength Resonators

We introduce a novel physical mechanism for achieving giant quality factors ($Q$-factors) in finite-length periodic arrays of subwavelength optical resonators. The underlying physics is based on interference between the band-edge mode and another standing mode in the array, and the formation of spatially localized states with dramatically suppressed radiative losses. We demonstrate this concept for an array of $N$ dipoles with simultaneous cancellation of multipoles up to $N$-th order and the $Q$ factor growing as $Q \propto N^{\alpha}$, where $\alpha \gtrsim 6.88$. Based on this finding, we propose a realistic array of Mie-resonant nanoparticles ($N \lesssim 29$) with a dramatic enhancement of the Purcell factor (up to $\sim $3400) achieved by tuning of the array parameters.

Plasmonic Nanoparticle Lattice Devices for White-Light Lasing.

A plasmonic nanolaser architecture that can produce white-light emission is reported. A laser device is designed based on a mixed dye solution used as gain material sandwiched between two aluminum nanoparticle (NP) square lattices of different periodicities. The (±1, 0) and (±1, ±1)band-edge surface lattice resonance (SLR) modes of one NP lattice and the (±1, 0) band-edge mode of the other NP lattice function as nanocavity modes for red, blue, and green lasing respectively. From a single aluminum NP lattice, simultaneous red and blue lasing is realized from a binary dye solution, and the relative intensities of the two colors are controlled by the volume ratio of the dyes. Also, a laser device is constructed by sandwiching dye solutions between two Al NP lattices with different periodicities, which enables red-green and blue-green lasing. With a combination of three dyes as liquid gain, red, green, and blue lasing for a white-light emission profile is realized.

Band dynamics accompanied by bound states in the continuum at the third-order Γ point in leaky-mode photonic lattices

Bound states in the continuum (BICs) and Fano resonances in planar photonic lattices, including metasurfaces and photonic-crystal slabs, have been studied extensively in recent years. Typically, the BICs and Fano resonances are associated with the second stop bands open at the second-order Γ point. This paper addresses the fundamental properties of the fourth stop band accompanied by BICs at the third-order Γ point in one-dimensional leaky-mode photonic lattices. At the fourth stop band, one band edge mode suffers radiation loss, thereby generating a Fano resonance, while the other band edge mode becomes a nonleaky BIC. The fourth stop band is controlled primarily by the Bragg processes associated with the first, second, and fourth Fourier harmonic components of the periodic dielectric constant modulation. The interplay between these three major processes closes the fourth band gap and induces a band flip whereby the leaky and BIC edges transit across the fourth band gap. At the fourth stop band, an accidental BIC is formed owing to the destructive interplay between the first and second Fourier harmonics. When the fourth band gap closes with strongly enhanced radiative Q factors, Dirac cone dispersions can appear at the third-order Γ point.