Fano interference governs wave transport in disordered systems

Fano-Like Resonance from Disorder Correlation in Vacancy-Doped Photonic Crystals

By preparing colloidal crystals with random missing scatterers, crystals are created where disorder is embodied as vacancies in an otherwise perfect lattice. In this special system, there is a critical defect concentration where light propagation undergoes a transition from an all but perfect reflector (for the spectral range defined by the Bragg condition), to a metamaterial exhibiting an enhanced transmission phenomenon. It is shown that this behavior can be phenomenologically described in terms of Fano-like resonances. The results show that the Fano's parameter q experiences a sign change signaling the transition from a perfect crystal exhibiting a reflectance Bragg peak, through a state where background scattering is maximum and Bragg reflectance reaches a minimum to a point where the system reenters a low scattering state recovering ordinary Bragg diffraction. A simple dipolar model considering the correlation between scatterers and vacancies is proposed and the reported evolution of the Fano-like scattering is explained in terms of the emerging covariance between the optical paths and polarizabilities and the effect of field enhancement in photonic crystal (PhC) defects.

High-Q Quasi-Bound States in the Continuum in Terahertz All-Silicon Metasurfaces

Bound states in the continuum (BIC)-based all-silicon metasurfaces have attracted widespread attention in recent years because of their high quality (Q) factors in terahertz (THz) frequencies. Here, we propose and experimentally demonstrate an all-silicon BIC metasurface consisting of an air-hole array on a Si substrate. BICs originated from low-order TE and TM guided mode resonances (GMRs) induced by (1,0) and (1,1) Rayleigh diffraction of metagratings, which were numerically investigated. The results indicate that the GMRs and their Q-factors are easily excited and manipulated by breaking the lattice symmetry through changes in the position or radius of the air-holes, while the resonance frequencies are less sensitive to these changes. The measured Q-factor of the GMRs is as high as 490. The high-Q metasurfaces have potential applications in THz modulators, biosensors, and other photonic devices.

Large-scale fabrication of an ultrathin broadband absorber using quasi-random dielectric Mie resonators

Ultrathin broadband absorber maintaining a near-uniform low reflectivity over a broadband wavelength is essential for many optical applications, such as light harvesting and nanoscale imaging. Recently, there has been considerable interest in employing arrays of high-index dielectric Mie resonators on surfaces to trap light and reduce the reflectivity. For such Mie-resonant metasurfaces, however, antireflection properties featuring both a flat low reflectance curve and a wide bandwidth are hard to be satisfied simultaneously, and an efficient large-scale nanofabrication technique rarely exists. Here, we present a high-throughput laser interference induced quasi-random patterning (LIIQP) technique to fabricate quasi-random Mie resonators in large scale. Mie resonators with feature sizes down to sub-100 nm have been fabricated using a 1064 nm laser source. Each Mie resonator concentrates light at its shape-dependent resonant frequency, and all such resonators are arranged quasi-randomly to provide both rich (with broadband Fourier components) and strong (with large intensities) Fourier spectra. Specifically, a near-uniform broadband reflectivity over 400-1100 nm spectrum region has been confined below 3% by fabricating a large-scale ultrathin (around 400 nm) absorber. Our concept and high-throughput fabrication technique allows the rapid production of quasi-random dielectric Mie-resonant metasurfaces in a controllable way, which can be used in various promising applications including thin-film solar cells, display, and imaging.

Generalized temporal coupled-mode theory for a P T-symmetric optical resonator and Fano resonance in a P T-symmetric photonic heterostructure

We have proposed generalized temporal coupled-mode theory for P T-symmetric optical resonator, and on this basis we have explained the Fano resonance in P T-symmetric photonic heterostructure. Our theoretical predictions agree very well with the simulated results obtained by transfer matrix method, which confirms the correctness of our theory. Compared with conventional Fano resonance in optical resonator with time-reversal symmetry, in this Fano resonance the amplitudes of scattering coefficients can be tuned in much larger range, which can be much larger than one, and tend to infinity at singular scattering point, where the rates of dissipation and accumulation are equal to each other and the difference of the phases of the coupling coefficients between output fields and resonant mode is equal to ±π/2. Not only that, the quality factor Q here can be negative out of accumulation, and approaches infinity at this singular scattering point. The phases of reflections jump π in the vicinity of the minima of corresponding amplitudes. We believe that we open a new door to study Fano resonance in non-Hermitian optics and inspire relevant study in other non-Hermitian wave systems.

Full manipulation of transparency and absorption through direct tuning of dark modes in high-Q Fano metamaterials

Controlling the line shape of Fano resonance has continued to attract significant research attention in recent years owing to its practical applications such as lasing, biosensing, and slow-light devices. However, controllable Fano resonances always require stringent alignment of complex symmetry-breaking structures; therefore, the manipulation can only be performed with limited degrees of freedom and a narrow tuning range. This work demonstrates dark-mode excitation tuning independent of the bright mode for the first time, to the authors' knowledge, in asymmetric Fano metamaterials. Metallic subwavelength slits are arranged to form asymmetric unit cells and generate a broad and bright (radiative) Fabry-Perot mode and a sharp and dark (non-radiative) surface mode. The introduction of the independent radial and angular asymmetries realizes independent control of the Fano phase (q) and quality factor (Q). This tunability provides a dynamic phase shift while maintaining a high-quality factor, enabling switching between nearly perfect transmission and absorption, which is confirmed both numerically and experimentally. The proposed scheme for fully controlled Fano systems can aid practical applications such as phase-sensitive switching devices.

Efficiency enhancement of perovskite solar cells based on opal-like photonic crystals

Perovskite solar cells have shown a tremendous interest for photovoltaics since the past decade. However, little is known on the influence of light management using photonic crystals inside such structures. We present here numerical simulations showing the effect of photonic crystal structuring on the integrated quantum efficiency of perovskite solar cells. The photo-active layer is made of an opal-like perovskite structure (monolayer, bilayer or trilayer of perovskite spheres) built in a T i O ₂ matrix. Fano resonances are exploited in order to enhance the absorption, especially near the bandgap of perovskite material. The excitation of quasi-guided modes inside the absorbing spheres enhances the integrated quantum efficiency and the photonic enhancement factor. More specifically, a photonic enhancement factor as high as 6.4% is predicted in the case of spheres monolayer compared to an unstructured perovskite layer. The influences of sphere's radius and incident angle on the absorbing properties are also estimated. Those numerical results can be applied to the nascent field of photonic structuring inside perovskite solar cells.

Disorder-Immune Photonics Based on Mie-Resonant Dielectric Metamaterials

When the feature size of photonic structures becomes comparable or even smaller than the wavelength of light, the fabrication imperfections inevitably introduce disorder that may eliminate many functionalities of subwavelength photonic devices. Here we suggest a novel concept to achieve a robust band gap which can endure disorder beyond 30% as a result of the transition from photonic crystals to Mie-resonant metamaterials. By utilizing Mie-resonant metamaterials with high refractive index, we demonstrate photonic waveguides and cavities with strong robustness to position disorder, thus providing a novel approach to the band-gap-based nanophotonic devices with new properties and functionalities.

Tuning high-Q nonlinear dynamics in a disordered quantum magnet

Quantum states cohere and interfere. Atoms arranged imperfectly in a solid rarely display these properties. Here we demonstrate an exception in a disordered quantum magnet that divides itself into nearly isolated subsystems. We probe these coherent spin clusters by driving the system nonlinearly and measuring the resulting hole in the linear spectral response. The Fano shape of the hole encodes the incoherent lifetime as well as coherent mixing of the localized excitations. For the Ising magnet LiHo0.045Y0.955F4, the quality factor Q for spectral holes can be as high as 100,000. We tune the dynamics by sweeping the Fano mixing parameter q through zero via the ac pump amplitude as well as a dc transverse field. The zero crossing of q is associated with a dissipationless response at the drive frequency. Identifying localized two-level systems in a dense and disordered magnet advances the search for qubit platforms emerging from strongly interacting, many-body systems.

All-Dielectric Active Terahertz Photonics Driven by Bound States in the Continuum

The remarkable emergence of all-dielectric meta-photonics governed by the physics of high-index dielectric materials offers a low-loss platform for efficient manipulation and subwavelength control of electromagnetic waves from microwaves to visible frequencies. Dielectric metasurfaces can focus electromagnetic waves, generate structured beams and vortices, enhance local fields for advanced sensing, and provide novel functionalities for classical and quantum technologies. Recent advances in meta-photonics are associated with the exploration of exotic electromagnetic modes called the bound states in the continuum (BICs), which offer a simple interference mechanism to achieve large quality factors (Q) through excitation of supercavity modes in dielectric nanostructures and resonant metasurfaces. Here, a BIC-driven terahertz metasurface with dynamic control of high-Q silicon supercavities that are reconfigurable at a nanosecond timescale is experimentally demonstrated. It is revealed that such supercavities enable low-power, optically induced terahertz switching and modulation of sharp resonances for potential applications in lasing, mode multiplexing, and biosensing.

Fano resonance and polarization transformation induced by interpolarization coupling of Bloch surface waves

In this work, the resonant coupling behaviors between the transverse-electric (TE) and transverse-magnetic (TM) Bloch surface waves (BSWs) on a dielectric multilayer have been theoretically studied. Due to the different penetration depths in the dielectric multilayer, the TM BSWs and TE BSWs can act as the radiative and dark electromagnetic modes, respectively. By using a rectangular grating on the dielectric multilayer, both Rabi splitting and Fano resonance phenomena based on the coupling of the two BSW modes were demonstrated, through tuning the period of the grating and the azimuthal angle of the incoming wave. Furthermore, by using the temporal coupled-mode theory, we show that the anti-Hermitian coupling between the two BSW modes contributes to the enhanced diffraction and the huge polarization transformation efficiency of incoming waves in the weak coupling regime.

Manipulation of transmission by engineered disorder in one-dimensional photonic crystals

Uncovering how disorder affects light propagation is a key step to manipulating light transportation and localization utilizing engineered disorder in photonics. Herein, we study the disorder-induced localization, delocalization and inter-transition between them in the regions of photonic band gaps (PBGs) and their associated passbands of one-dimensional (1D) Photonic crystals (PhCs) under different types of disorder effect. We introduce two parameters to quantitatively evaluate how disorder effect can be exploited to tailor the localization and delocalization of light in 1D PhCs. Such parameters can clearly indicate the inter-transition between extended states and localized states. It is shown that both nontrivial and trivial disorder-induced transport scenarios exist depending on the types of disorder introduced to the otherwise periodic system. The disorder-induced band tailing, which is correlated with the disorder-induced redistribution of electric energy compared with periodic case, is crucial for observing these interesting disorder-induced light transportation scenarios. Our results might provide positive insight to the manipulation of light transmission in nanophotonics by engineered disorder.

Exploring the effect of hole localization on the charge-phonon dynamics of hole doped delafossite

For weak or moderate doping, electrical measurement is not suitable for detecting changes in the charge localization inside a semiconductor. Here, to investigate the nature of charge-phonon coupling in the presence of gradually delocalized holes within a weak doping regime (~10¹⁶ cm^-3), we examine the temperature dependent Raman spectra (303-817 K) of prototype hole doped delafossite [Formula: see text] (x  =  0/0.03, y  =  0/0.01). For both [Formula: see text] and [Formula: see text] phonons, negative lineshape asymmetry and relative thermal hardening are distinctly observed upon [Formula: see text] and [Formula: see text] doping. Using Allen formalism, charge density of states at the Fermi level per spin and molecule, and charge delocalization associated to [Formula: see text] plane, are estimated to increase appreciably upon codoping compared to the [Formula: see text]-axis. We delineate the interdependence between charge-phonon coupling constant ([Formula: see text]) and anharmonic phonon lifetime ([Formula: see text]), and deduce that excitation of delocalized holes weakly coupled with phonons of larger [Formula: see text] is the governing feature of observed Fano asymmetry ([Formula: see text]) reversal.

Inverse design of high-Q wave filters in two-dimensional phononic crystals by topology optimization

Topology optimization of a waveguide-cavity structure in phononic crystals for designing narrow band filters under the given operating frequencies is presented in this paper. We show that it is possible to obtain an ultra-high-Q filter by only optimizing the cavity topology without introducing any other coupling medium. The optimized cavity with highly symmetric resonance can be utilized as the multi-channel filter, raising filter and T-splitter. In addition, most optimized high-Q filters have the Fano resonances near the resonant frequencies. Furthermore, our filter optimization based on the waveguide and cavity, and our simple illustration of a computational approach to wave control in phononic crystals can be extended and applied to design other acoustic devices or even opto-mechanical devices.

Suppression of scattering for small dielectric particles: anapole mode and invisibility

We reveal that an isotropic, homogeneous, subwavelength particle with high refractive index can produce ultra-small total scattering. This effect, which follows from the inhibition of the electric dipole radiation, can be identified as a Fano resonance in the scattering efficiency and is associated with the excitation of an anapole mode in the particle. This anapole mode is non-radiative and emerges from the destructive interference of electric and toroidal dipoles. The invisibility effect could be useful for the design of highly transparent optical materials.This article is part of the themed issue 'New horizons for nanophotonics'.

Interplay between evanescence and disorder in deep subwavelength photonic structures

Deep subwavelength features are expected to have minimal impact on wave transport. Here we show that in contrast to this common understanding, disorder can have a dramatic effect in a one-dimensional disordered optical system with spatial features a thousand times smaller than the wavelength. We examine a unique regime of Anderson localization where the localization length is shown to scale linearly with the wavelength instead of diverging, because of the role of evanescent waves. In addition, we demonstrate an unusual order of magnitude enhancement of transmission induced due to localization. These results are described for electromagnetic waves, but are directly relevant to other wave systems such as electrons in multi-quantum-well structures.

Features much smaller than the wavelength are not expected to have a significant impact on the transport of a wave. Here, the authors show that Anderson localization can dominate light transport in a one-dimensional disordered system, even when the disordered features are a thousand times smaller than the wavelength.

Metadisorder for designer light in random systems

Disorder plays a critical role in signal transport by controlling the correlation of a system, as demonstrated in various complex networks. In wave physics, disordered potentials suppress wave transport, because of their localized eigenstates, from the interference between multiple scattering paths. Although the variation of localization with tunable disorder has been intensively studied as a bridge between ordered and disordered media, the general trend of disorder-enhanced localization has remained unchanged, and the existence of complete delocalization in highly disordered potentials has not been explored. We propose the concept of "metadisorder": randomly coupled optical systems in which eigenstates can be engineered to achieve unusual localization. We demonstrate that one of the eigenstates in a randomly coupled system can always be arbitrarily molded, regardless of the degree of disorder, by adjusting the self-energy of each element. Ordered waves with the desired form are then achieved in randomly coupled systems, including plane waves and globally collective resonances. We also devise counterintuitive functionalities in disordered systems, such as "small-world-like" transport from non-Anderson-type localization, phase-conserving disorder, and phase-controlled beam steering.

Lower bound for the spatial extent of localized modes in photonic-crystal waveguides with small random imperfections

Light localization due to random imperfections in periodic media is paramount in photonics research. The group index is known to be a key parameter for localization near photonic band edges, since small group velocities reinforce light interaction with imperfections. Here, we show that the size of the smallest localized mode that is formed at the band edge of a one-dimensional periodic medium is driven instead by the effective photon mass, i.e. the flatness of the dispersion curve. Our theoretical prediction is supported by numerical simulations, which reveal that photonic-crystal waveguides can exhibit surprisingly small localized modes, much smaller than those observed in Bragg stacks thanks to their larger effective photon mass. This possibility is demonstrated experimentally with a photonic-crystal waveguide fabricated without any intentional disorder, for which near-field measurements allow us to distinctly observe a wavelength-scale localized mode despite the smallness (~1/1000 of a wavelength) of the fabrication imperfections.

Purcell effect and Lamb shift as interference phenomena

The Purcell effect and Lamb shift are two well-known physical phenomena which are usually discussed in the context of quantum electrodynamics, with the zero-point vibrations as a driving force of those effects in the quantum approach. Here we discuss the classical counterparts of these quantum effects in photonics, and explain their physics trough interference wave phenomena. As an example, we consider a waveguide in a planar photonic crystal with a side-coupled defect, and demonstrate a perfect agreement between the results obtained on the basis of quantum and classic approaches and reveal their link to the Fano resonance. We find that in such a waveguide-cavity geometry the Purcell effect can modify the lifetime by at least 25 times, and the Lamb shift can exceed 3 half-widths of the cavity spectral line.

Weak lasing in one-dimensional polariton superlattices

Bosons with finite lifetime exhibit condensation and lasing when their influx exceeds the lasing threshold determined by the dissipative losses. In general, different one-particle states decay differently, and the bosons are usually assumed to condense in the state with the longest lifetime. Interaction between the bosons partially neglected by such an assumption can smear the lasing threshold into a threshold domain--a stable lasing many-body state exists within certain intervals of the bosonic influxes. This recently described weak lasing regime is formed by the spontaneously symmetry breaking and phase-locking self-organization of bosonic modes, which results in an essentially many-body state with a stable balance between gains and losses. Here we report, to our knowledge, the first observation of the weak lasing phase in a one-dimensional condensate of exciton-polaritons subject to a periodic potential. Real and reciprocal space photoluminescence images demonstrate that the spatial period of the condensate is twice as large as the period of the underlying periodic potential. These experiments are realized at room temperature in a ZnO microwire deposited on a silicon grating. The period doubling takes place at a critical pumping power, whereas at a lower power polariton emission images have the same periodicity as the grating.

Switching from visibility to invisibility via Fano resonances: theory and experiment

Subwavelength structures demonstrate many unusual optical properties which can be employed for engineering of a new generation of functional metadevices, as well as controlled scattering of light and invisibility cloaking. Here we demonstrate that the suppression of light scattering for any direction of observation can be achieved for a uniform dielectric object with high refractive index, in a sharp contrast to the cloaking with multilayered plasmonic structures suggested previously. Our finding is based on the novel physics of cascades of Fano resonances observed in the Mie scattering from a homogeneous dielectric rod. We observe this effect experimentally at microwaves by employing high temperature-dependent dielectric permittivity of a glass cylinder with heated water. Our results open a new avenue in analyzing the optical response of high-index dielectric nanoparticles and the physics of cloaking.

Mode parity-controlled Fano- and Lorentz-like line shapes arising in plasmonic nanorods

We present the experimental observation of spectral lines of distinctly different shapes in the optical extinction cross-section of metallic nanorod antennas under near-normal plane wave illumination. Surface plasmon resonances of odd mode parity present Fano interference in the scattering cross-section, resulting in asymmetric spectral lines. Contrarily, modes with even parity appear as symmetric Lorentzian lines. Finite element simulations are used to verify the experimental results. The emergence of either constructive or destructive mode interference is explained with a semianalytical 1D line current model. This simple model directly explains the mode-parity dependence of the Fano-like interference. Plasmonic nanorods are widely used as half-wave optical dipole antennas. Our findings offer a perspective and theoretical framework for operating these antennas at higher-order modes.

Plasmonic Fano resonances in nanohole quadrumers for ultra-sensitive refractive index sensing

Plasmonic Fano resonances arising from electromagnetic interactions in metallic nanostructures exhibit spectral characteristics analogous to those from the electron waves in oligomer molecules. Though a great deal of research interest has been attracted to study the optical properties and explore the associated applications of metallic nanoparticle oligomers, the plasmonic response of their complementary structures--nanohole clusters--remains largely unexplored. Here we show numerically by a full-wave finite element method that a nanohole quadrumer can sustain two Fano resonances when the incident electric field is oriented along the long-axis of the quadrumer system. The underlying physical mechanisms responsible for the Fano resonance formation are revealed explicitly by spectrally deconstructing the Fano lineshape, spatially decomposing the structure configuration and mapping the electric field profile and charge distribution, which collectively demonstrate a strong mode coupling between either two antiparallel dipolar modes or dipole-quadruple modes in the nanohole quadrumer. We further show that the spectral profile of the Fano resonance including the resonance linewidth and spectral contrast can be engineered flexibly by adjusting the geometrical parameters of the nanohole cluster, including the nanohole diameter, film thickness and interhole distance. With an optimized and realistic geometrical configuration, the nanohole quadrumer system exhibits an overall sensing figure of merit up to 14.25, far surpassing the value reported for conventional nanoparticle oligomers.

Fano resonance in anodic aluminum oxide based photonic crystals

Anodic aluminum oxide based photonic crystals with periodic porous structure have been prepared using voltage compensation method. The as-prepared sample showed an ultra-narrow photonic bandgap. Asymmetric line-shape profiles of the photonic bandgaps have been observed, which is attributed to Fano resonance between the photonic bandgap state of photonic crystal and continuum scattering state of porous structure. And the exhibited Fano resonance shows more clearly when the sample is saturated ethanol gas than air-filled. Further theoretical analysis by transfer matrix method verified these results. These findings provide a better understanding on the nature of photonic bandgaps of photonic crystals made up of porous materials, in which the porous structures not only exist as layers of effective-refractive-index material providing Bragg scattering, but also provide a continuum light scattering state to interact with Bragg scattering state to show an asymmetric line-shape profile.

Mie scattering as a cascade of Fano resonances

We reveal that the resonant Mie scattering by high-index dielectric nanoparticles can be presented through cascades of Fano resonances. We employ the exact solution of Maxwell's equations and demonstrate that the Lorenz-Mie coefficients of the Mie problem can be expressed generically as infinite series of Fano functions as they describe interference between the background radiation originated from an incident wave and narrow-spectrum Mie scattering modes that lead to Fano resonances.

Isotropic band gaps and freeform waveguides observed in hyperuniform disordered photonic solids

Recently, disordered photonic media and random textured surfaces have attracted increasing attention as strong light diffusers with broadband and wide-angle properties. We report the experimental realization of an isotropic complete photonic band gap (PBG) in a 2D disordered dielectric structure. This structure is designed by a constrained optimization method, which combines advantages of both isotropy due to disorder and controlled scattering properties due to low-density fluctuations (hyperuniformity) and uniform local topology. Our experiments use a modular design composed of Al2O3 walls and cylinders arranged in a hyperuniform disordered network. We observe a complete PBG in the microwave region, in good agreement with theoretical simulations, and show that the intrinsic isotropy of this unique class of PBG materials enables remarkable design freedom, including the realization of waveguides with arbitrary bending angles impossible in photonic crystals. This experimental verification of a complete PBG and realization of functional defects in this unique class of materials demonstrate their potential as building blocks for precise manipulation of photons in planar optical microcircuits and has implications for disordered acoustic and electronic band gap materials.