The valleys of two-dimensional transition metal dichalcogenides (TMDCs) offer a new degree of freedom for information processing. To take advantage of this valley degree of freedom, on one hand, it is feasible to control valleys by utilizing different external stimuli like optical and electric fields. On the other hand, nanostructures are also used to separate the valleys by near field coupling. However, for both above methods, either required low-temperature environment or low degree of coherence properties limit their further applications. Here, we demonstrate all-dielectric photonic crystal (PhC) slabs without in-plane inversion symmetry (C2 symmetry) could separate and route valley photons in a WS2 monolayer at room temperature. Coupling with circularly polarized photonic Bloch modes of such PhC slabs, valley photons emitted by a WS2 monolayer are routed directionally and efficiently separated in the far field. In addition, the far-field emission is directionally enhanced and with long-distance spatial coherence property.
Eigenvalue problems for electromagnetic resonant states on open dielectric structures are non-Hermitian and may have exceptional points (EPs) at which two or more eigenfrequencies and the corresponding eigenfunctions coalesce. EPs of resonant states for photonic structures give rise to a number of unusual wave phenomena and have potentially important applications. It is relatively easy to find a few EPs for a structure with parameters, but isolated EPs provide no information about their formation and variation in parameter space, and it is always difficult to ensure that all EPs in a domain of…
We show that, taking a two-dimensional photonic-crystal slab system as an example, surprisingly high quality factors (Q) over 10^5 are achievable, even in the absence of a rigorous photonic-band-gap. We find that the density of in-plane Bloch modes can be controlled by creating additional photon feedback from a finite-size photonic-crystal boundary that serves as a low-Q resonator. This mechanism enables significant reduction in the coupling strength between the bound state and the extended Bloch modes by more than a factor of 40.
We develop a semi-analytical model to describe bound states in the continuum (BICs) in photonic crystal slabs. We model leaky modes supported by photonic crystal slabs as a transverse Fabry-Perot resonance composed of a few propagative Bloch waves bouncing back and forth vertically inside the slab. This multimode Fabry-Perot model accurately predicts the existence of BICs and their positions in the parameter space. We show that, regardless of the slab thickness, BICs cannot exist below a cut-off frequency, which is related to the existence of the second-order Bloch wave in the photonic crystal…
A photonic-crystal slab can support bound states in the continuum (BICs) which have infinite lifetimes but embedded into the continuous spectrum of optical modes in free space. The formation of BICs requires a total internal reflection (TIR) condition at both interfaces between the slab and free space. Here, we show that the TIR of Bloch waves can be directly obtained based on the generalized Fresnel equations proposed. If each of these Bloch waves picks up a phase with integer multiples of 2pi for traveling a round trip, light can be perfectly guided in the slab, namely, forming a BIC. A BIC …
We present a systematic comparison between guided modes supported by slab waveguides and Bloch Surface Waves (BSWs) propagating at the surface of truncated periodic multilayers. We show that, contrary to common belief, the best surface field enhancement achievable for guided modes in a slab waveguide is comparable to that observed for BSWs. At the same time, we demonstrate that, if one is interested in maximizing the electromagnetic energy density at a generic point of a dielectric planar structure, BSWs are often preferable to modes in which light is confined uniquely by total internal reflec…
This work concentrates on numerical simulations of Photonic Crystal structures using basis-expansion methods, with a main focus on simulating disorder. The plane-wave and guided-mode expansions are outlined as tools to compute the Bloch modes of a structure, on the basis of which the Bloch-mode expansion formalism is outlined - the latter allowing for simulations of large structures in presence of disorder. As a first illustration of the method, we apply it to three gentle-confinement cavities, to obtain results for their quality factors similar to the theoretically predicted in the literature…
We present a method to map the absolute electromagnetic field strength inside photonic crystals. We apply the method to map the electric field component Ez of a two-dimensional photonic crystal slab at microwave frequencies. The slab is placed between two mirrors to select Bloch standing waves and a subwavelength spherical scatterer is scanned inside the resulting resonator. The resonant Bloch frequencies shift depending on the electric field at the position of the scatterer. To map the electric field component Ez we measure the frequency shift in the reflection and transmission spectrum of th…
We consider propagating bound states in the continuum in dielectric gratings. The gratings consist of a slab with ridges periodically arranged ether on top or on the both sides of the slab. Based on the Fourier modal approach we recover the leaky zones above the line of light to identify the geometries of the gratings supporting Bloch bound states propagating in the direction perpendicular to the ridges. Most importantly, it is demonstrated that if a two-side grating possesses either mirror or glide symmetry the Bloch bound states are stable to variation of parameters as far as the above symme…
A uniform or periodic dielectric slab can serve as an optical waveguide for which guided modes are important, and it can also be used as a diffraction structure for which resonant modes with complex frequencies are relevant. Guided modes are normally studied below the lightline where they exist continuously and emerge from points on the lightline, but isolated guided modes may exist above the lightline and they are the so-called bound states in the continuum. Resonant modes are usually studied above the lightline (defined using the real part of the complex frequency), but they are not connecte…
We propose a new method based on variational principle for analysis of photonic crystal (PC) slabs. Most of the methods used today treat PC slab as a three-dimensional (3D) crystal and this makes them very time and/or memory consuming. In this method we use Bloch theorem to expand the field on infinite plane waves which their amplitudes depend on the component perpendicular to the slab surface. By approximating these amplitudes with appropriate functions, we can find modes of PC slabs almost as fast as we can find modes of a two-dimensional (2D) crystal. Besides this advantage, we can also cal…
Effective magnetic fields have enabled unprecedented manipulation of neutral particles including photons. In most studied cases, the effective gauge fields are defined through the phase of mode coupling between spatially discrete elements, such as optical resonators and waveguides in the case for photons. Here, in the paradigm of Bloch-wave modulated photonic crystals, we show creation of effective magnetic fields for photons in conventional dielectric continua for the first time, via Floquet band engineering. By controlling the phase and wavevector of Bloch waves, we demonstrated anomalous qu…
Emission of high-order harmonics from solids provides a new avenue in attosecond science. On one hand, it allows to investigate fundamental processes of the non-linear response of electrons driven by a strong laser pulse in a periodic crystal lattice. On the other hand, it opens new paths toward efficient attosecond pulse generation, novel imaging of electronic wave functions, and enhancement of high-order harmonic generation (HHG) intensity. A key feature of HHG in a solid (as compared to the well-understood phenomena of HHG in an atomic gas) is the delocalization of the process, whereby an e…
We present a detailed theoretical study of the effects of structural disorder on LN photonic crystal slab cavities, ranging from short to long length scales, using a fully-3D Bloch mode expansion technique. We compute the optical density of states, quality factors and effective mode volumes of the cavity modes, with and without disorder, and compare with the localized modes of the corresponding disordered photonic crystal waveguide. We demonstrate how the quality factors and effective mode volumes saturate at a specific cavity length and become bounded by the corresponding values of the Anders…
Metamaterials with an effective zero refractive index associated to their electromagnetic response are sought for a number of applications in communications and nonlinear optics. A promising way that this can be achieved in all-dielectric photonic crystals is through the design of a Dirac cone at zero Bloch wave-vector in the photonic band structure. In the optical frequency range, the natural way to implement this design is through the use of a photonic crystal slab. In the existing implementation, however, the zero-index photonic modes also radiate strongly into the environment due to intrin…
There has been remarkable recent progress in the formation of nano-resonators that support ultra-low-loss, compact dielectric photonic crystals with exceptional high-Q modes that operate at visible or telecom wavelengths. New insights into modal engineering have recently emerged from researchers exploring exotic electronic phases in 2D materials. The phenomenon relates to a twist in the angle between two layers of materials with high periodic spatial ordering, such as graphene. A moire pattern forms, and at a particular magic angle of twist, the electronic behavior significantly changes, enjoy…
Under the action of a weak constant force a wavepacket in periodic potential undergoes periodic oscillations in space, returning to the initial position after one oscillation cycle. This wave phenomenon, known as Bloch oscillations (BOs), pertains to many physical systems. Can BOs also occur in topological insulators with topologically protected edge states? This question is highly nontrivial, because in topological insulators with broken time-reversal symmetry, the edge states propagate unidirectionally without backscattering, hence BOs that typically involve stages, where wavepacket moves al…
We study the classical scattering problem of a plane electromagnetic wave incident on the surface of semi-infinite periodic stratified media incorporating anisotropic dielectric layers with special oblique orientation of the anisotropy axes. We demonstrate that an obliquely incident light, upon entering the periodic slab, gets converted into an abnormal grazing mode with huge amplitude and zero normal component of the group velocity. This mode cannot be represented as a superposition of extended and evanescent contributions. Instead, it is related to a general (non-Bloch) Floquet eigenmode wit…
We present a systematic numerical approach to compute the eigenmodes and the related eigenfrequencies of a disordered photonic crystal, characterized by small fluctuations of the otherwise periodic dielectric profile. The field eigenmodes are expanded on the basis of Bloch modes of the corresponding periodic structure, and the resulting eigenvalue problem is diagonalized on a truncated basis including a finite number of Bloch bands. The Bloch-mode expansion is very effective for modeling modes of very extended disordered structures in a given frequency range, as only spectrally close bands mus…
Nanoscale light-matter interaction in the weak-coupling regime has been achieved with unique hyperbolic metamaterial modes possessing a high density of states. Here, we show strong coupling between intersubband transitions (ISBTs) of a multiple quantum well (MQW) slab and the bulk polariton modes of a hyperbolic metamaterial (HMM). These HMM modes have large wave vectors (high-k modes) and are normally evanescent in conventional materials. We analyze a metal-dielectric practical multilayer HMM structure consisting of a highly doped semiconductor acting as a metallic layer and an active multipl…
It has recently been predicted that a conical singularity (= Dirac point) in the band structure of a photonic crystal produces an unusual 1/L scaling of the photon flux transmitted through a slab of thickness L. This inverse-linear scaling is unusual, because it is characteristic of radiative transport via diffusion modes through a disordered medium -- while here it appears for propagation of Bloch modes in an ideal crystal without any disorder. We present a quantitative numerical test of the predicted scaling, by calculating the scattering of transverse-electric (TE) modes by a two-dimensiona…
Out-of-plane gap solitons in 2D photonic crystals are optical beams localized in the plane of periodicity of the medium and delocalized in the orthogonal direction, in which they propagate with a nonzero velocity. We study such gap solitons as described by the Kerr nonlinear Maxwell system. Using a model of the nonlinear polarization, which does not generate higher harmonics, we obtain a closed curl-curl problem for the fundamental harmonic of the gap soliton. For gap solitons with frequencies inside spectral gaps and in an asymptotic vicinity of a gap edge we use a slowly varying envelope app…
The Single Gyroid, or srs, nanostructure has attracted interest as a circular-polarisation sensitive photonic material. We develop a group theoretical and scattering matrix method, applicable to any photonic crystal with symmetry I432, to demonstrate the remarkable chiral-optical properties of a generalised structure called 8-srs, obtained by intergrowth of eight equal-handed srs nets. Exploiting the presence of four-fold rotations, Bloch modes corresponding to the irreducible representations E- and E+ are identified as the sole and non-interacting transmission channels for right- and left-cir…
We build an effective medium theory for two-dimensional photonic crystals comprising a rectangular lattice of dielectric cylinders with the incident electric field polarized along the axis of the cylinders. In particular, we discuss the feasibility of constructing an effective medium theory for the case where the Bloch wave vector is far away from the center of Brillouin zone, where the optical response of the photonic crystal is necessarily anisotropic and hence the effective medium description becomes inevitability angle dependent. We employ the scattering theory and treat the two-dimensiona…
Systems with strong light-matter interaction opens up new avenues for studying topological phases of matter. Examples include exciton-polaritons, mixed light-matter quasiparticles, where the topology of the polaritonic band structure arises from the collective coupling between matter wave and optical fields strongly confined in periodic dielectric structures. Distinct from light-matter interaction in a uniform environment, the spatially varying nature of the optical fields leads to a fundamental modification of the well-known optical selection rules, which were derived under the plane wave app…
Chirality refers to a geometric phenomenon in which objects are not superimposable on their mirror image. Structures made of nano-scale chiral elements can display chiroptical effects, such as dichroism for left- and right- handed circularly polarized light, which makes them of high interest for applications ranging from quantum information processing and quantum optics to circular dichroism spectroscopy and molecular recognition. At the same time, strong effects have been challenging to achieve even in synthetic optical media and chiroptical effects for light with normal incidence has been sp…
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 Gamma ($Γ$) point. This paper address the fundamental properties of the fourth stop band accompanied by BICs at the third-order $Γ$ point in one-dimensional (1D) leaky-mode photonic lattices. At the fourth stop band, one band edge mode suffers radiation loss, thereby generating a Fano resonance, while the ot…
