Consider a plane monochromatic wave incident on a semi-infinite periodic structure. What happens if the normal component of the transmitted wave group velocity vanishes? At first sight, zero normal component of the transmitted wave group velocity simply implies total reflection of the incident wave. But we demonstrate that total reflection is not the only possible outcome. Instead, the transmitted wave can appear in the form of a frozen mode with very large diverging amplitude and either zero, or purely tangential energy flux. The field amplitude in the transmitted wave can exceed that of the incident wave by several orders of magnitude. There are two qualitatively different kinds of frozen mode regime. The first one is associated with a stationary inflection point of electromagnetic dispersion relation. This phenomenon has been analyzed in our previous publications. Now, our focus is on the frozen mode regime related to a degenerate photonic band edge. An advantage of this new phenomenon is that it can occur in much simpler periodic structures. This spectacular effect is extremely sensitive to the frequency and direction of propagation of the incident plane wave. These features can be very attractive in a variety practical applications, such as higher harmonic generation and wave mixing, light amplification and lasing, highly efficient superprizms, etc.
Slow light in photonic crystals and other periodic structures is associated with stationary points of the photonic dispersion relation, where the group velocity of light vanishes. We show that in certain cases, the vanishing group velocity is accompanied by the so-called frozen mode regime, when the incident light can be completely converted into the slow mode with huge diverging amplitude. The frozen mode regime is a qualitatively new wave phenomenon -- it does not reduce to any known electromagnetic resonance. Formally, the frozen mode regime is not a resonance, in a sense that it is not par…
Experimental Measurement of Enhanced Group Delay Silicon Photonic Waveguides Indicative of the Frozen Mode Regime Around the Stationary Inflection Point
University of California, Irvine（加州大学尔湾分校）；Air Force Research Laboratory（空军研究实验室）；University of Dayton（代顿大学）；UES, a BlueHalo company（UES（BlueHalo旗下公司））
We propose a degenerate version of the Bragg condition, associated to a degenerate band edge (DBE). A standard Bragg condition can be implemented using a periodic grating that operates at the regular band edge. The structure we propose to realize a DBE is made of two stacked identical gratings that form two coupled periodic waveguides with broken mirror symmetry. The occurrence of the DBE is verified by using both an eigenmode solver and the calculations of scattering parameters, using full-wave simulations. The proposed structure is a good candidate to conceive a degenerate distributed feedba…
A tetragonal photonic crystal composed of high-index pillars can exhibit a frequency-isolated accidental degeneracy at a high-symmetry point in the first Brillouin zone. A photonic band gap can be formed there by introducing a geometrical anisotropy in the pillars. In this gap, gapless surface/domain-wall states emerge under a certain condition. We analyze their physical property in terms of an effective hamiltonian, and a good agreement between the effective theory and numerical calculation is obtained.
Wave propagation in spatially periodic media, such as photonic crystals, can be qualitatively different from any uniform substance. The differences are particularly pronounced when the electromagnetic wavelength is comparable to the primitive translation of the periodic structure. In such a case, the periodic medium cannot be assigned any meaningful refractive index. Still, such features as negative refraction and/or opposite phase and group velocities for certain directions of light propagation can be found in almost any photonic crystal. The only reservation is that unlike hypothetical unifo…
The problem of slowing down light by orders of magnitude has been extensively discussed in the literature. Such a possibility can be useful in a variety of optical and microwave applications. Many qualitatively different approaches have been explored. Here we discuss how this goal can be achieved in linear dispersive media, such as photonic crystals. The existence of slowly propagating electromagnetic waves in photonic crystals is quite obvious and well known. The main problem, though, has been how to convert the input radiation into the slow mode without loosing a significant portion of the i…
We numerically study supercontinuum (SC) generation in photonic crystal fibers pumped with low-power 30-ps pulses close to the zero dispersion wavelength 647nm. We show how the efficiency is significantly improved by designing the dispersion to allow widely separated spectral lines generated by degenerate four-wave-mixing (FWM) directly from the pump to broaden and merge. By proper modification of the dispersion profile the generation of additional FWM Stokes and anti-Stokes lines results in efficient generation of an 800nm wide SC. Simulations show that the predicted efficient SC generation i…
Low-Threshold Degenerate Optical Parametric Oscillations in Bichromatically-Pumped Normal-Dispersion Photonic-Crystal Microresonator
Russian Quantum Center（俄罗斯量子中心）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）；Faculty of Physics, Lomonosov Moscow State University（莫斯科国立大学物理系）
We propose a new approach leading to giant gain enhancement. It is based on unconventional slow wave resonance associated to a degenerate band edge (DBE) in the dispersion diagram for a special class of photonic crystals supporting two modes at each frequency. We show that the gain enhancement in a Fabry-Perot cavity (FPC) when operating at the DBE is several orders of magnitude stronger when compared to a cavity of the same length made of a standard photonic crystal with a regular band edge (RBE). The giant gain condition is explained by a significant increase in the photon lifetime and in th…
We report on singular and nonsingular flat bands in a Sierpinski fractal-like photonic lattice. We demonstrate that the the lowest two bands, being isolated and degenerate due to geometrical frustration, are nonsingular and thus can be spanned by a complete set of compact localized states. We experimentally prove these states to propagate diffractionless in the photonic lattice. Our results reveal the interplay between geometrical frustration, degenerate flat bands and compact localized states in a single photonic lattice, and pave the way to photonic spin liquid ground states.
We introduce a class of unidirectional lasing modes associated with the frozen mode regime of non-reciprocal slow-wave structures. Such asymmetric modes can only exist in cavities with broken time-reversal and space inversion symmetries. Their lasing frequency coincides with a spectral stationary inflection point of the underlying passive structure and is virtually independent of its size. These unidirectional lasers can be indispensable components of photonic integrated circuitry.
Inspired by complete graph theory, we demonstrate that a metallic claw "meta-atom" structure can carry a high number of nearly degenerate resonant modes. A photonic meta-crystal composing of a lattice of such meta-atoms exhibits a large number of flat bands that are squeezed into a narrow frequency window, and these flat bands can be designed to locate in a wide complete 3D bandgap. The degeneracy dimension (Nf) of the flat bands is determined by the number of branches (Nb) of the metallic claw with Nf=Nb-3, which is geometrically related to the complete graph theory. Different from those flat…
Non-abelian gauge fields emerge naturally in the description of adiabatically evolving quantum systems having degenerate levels. Here we show that they also play a role in Thouless pumping in the presence of degenerate bands. To this end we consider a photonic Lieb lattice having two degenerate non-dispersive modes and we show that, when the lattice parameters are slowly modulated, the propagation of the photons bear the fingerprints of the underlying non-abelian gauge structure. The non-dispersive character of the bands enables a high degree of control on photon propagation. Our work paves th…
Max Planck Institute for the Science of Light（马克斯·普朗克光科学研究所）；Friedrich-Alexander-Universität Erlangen-Nürnberg（埃尔朗根-纽伦堡大学）；Ruprecht-Karls University Heidelberg（海德堡大学）；Leibniz Institute of Photonic Technology（莱布尼茨光子技术研究所）；Institute of Applied Optics and Biophysics（应用光学与生物物理研究所）；Otto Schott Institute of Materials Research（奥托·肖特材料研究所）
We measured the angle- and polarization-resolved reflection and photoluminescence spectra of ZnO inverse opals. Significant enhancement of spontaneous emission is observed. The enhanced emission not only has good directionality but also can be linearly polarized. A detailed theoretical analysis and numerical simulation reveal that such enhancement is caused by the abnormal dispersion of a high-order photonic band. The frozen mode at a stationary inflection point of a dispersion curve can strongly modify the intensity, directionality and polarization of spontaneous emission.
We consider transmission band edge resonance in periodic layered structures involving birefringent layers. Previously we have shown that the presence of birefringent layers with misaligned in-plane anisotropy can dramatically enhance the performance of the photonic-crystal Fabry-Perot resonator. It allows to reduce its size by an order of magnitude without compromising on its performance. The key characteristic of the enhanced photonic-crystal cavity is that its Bloch dispersion relation displays a degenerate photonic band edge, rather than only regular ones. This can be realized in specially …
We report phase sensitive amplification in a 1.5mm long, $Ga_{0.5}In_{0.5}P$ dispersion engineered photonic crystal waveguide which has a flattened dispersion profile. A signal degenerate configuration with pulsed pumps whose total peak power is only 0.5W yields a phase sensitive extinction ratio of 10dB.
We experimentally demonstrate phase sensitive amplification (PSA) in a silicon photonic crystal waveguide based on pump-degenerate four-wave mixing. An 11 dB phase extinction ratio is obtained in a record compact 196 μm nanophotonic device due to broadband slow-light, in spite of the presence of two-photon absorption and free-carriers. Numerical calculations show good agreement with the experimental results.
Crystal-symmetry-protected photonic topological edge states (PTESs) based on air rods in conventional dielectric materials are designed as photonic topological waveguides (PTWs) coupled with side optical cavities. We demonstrate that the cavity coupled with the PTW can change the reflection-free transport of the PTESs, where the cavities with single mode and twofold degenerate modes are taken as examples. The single-mode cavities are able to perfectly reflect the PTESs at their resonant frequencies, forming a dip in the transmission spectra. The dip full width at half depth depends on the coup…
We performed non-degenerate pump-probe experiments on a GaAs/AlAs photonic structure. We switched the photonic properties using the optical Kerr effect and free carriers excited by three photon absorption. From these measurements we extracted the non-degenerate Kerr coefficients over a broad wavelength range and we extracted the three photon absorption coefficient for GaAs at three wavelengths in the near infrared. We show that the optical Kerr effect is large enough to switch a cavity resonance with a high \emph{Q} ($Q>1000$) photonic cavity.
We consider a plane electromagnetic wave incident on a periodic stack of dielectric layers. One of the alternating layers has an anisotropic refractive index with an oblique orientation of the principal axis relative to the normal to the layers. It was shown recently (A. Figotin and I. Vitebskiy, Phys. Rev. E68, 036609 2003) that an obliquely incident light, upon entering such a periodic stack, can be converted into an abnormal axially frozen mode with drastically enhanced amplitude and zero normal component of the group velocity. The stack reflectivity at this point can be very low, implying …
Bound states in the continuum (BICs), circularly polarized states (C points) and degenerate states are all of three types of singular points of polarization in the momentum space. For photonic crystal slabs (PhCSs) with linearly polarized far fields, BICs were found to be the centers of polarization vortices and attracted more attention in the previous studies. Here, we theoretically demonstrate that the far fields of PhCSs can exhibit remarkably diverse polarizations due to the robust existences of C points in the continuum. Only a pair of C points with identical handedness and opposite topol…
Silicon is a common material for photonics due to its favorable optical properties in the telecom and mid-wave IR bands, as well as compatibility with a wide range of complementary metal-oxide semiconductor (CMOS) foundry processes. Crystalline inversion symmetry precludes silicon from natively exhibiting second-order nonlinear optical processes. In this work, we build on recent work in silicon photonics that break this material symmetry using large bias fields, thereby enabling $χ^{(2)}$ interactions. Using this approach, we demonstrate both second-harmonic generation (with a normalized effic…
We investigate, theoretically and experimentally, a photonic realization of a Sawtooth lattice. This special lattice exhibits two spectral bands, with one of them experiencing a complete collapse to a highly degenerate flat band for a special set of inter-site coupling constants. We report the ob- servation of different transport regimes, including strong transport inhibition due to the appearance of the non-diffractive flat band. Moreover, we excite localized Shockley surfaces states, residing in the gap between the two linear bands.
The principal use of photonic crystals is to engineer the photonic density of states, which controls light-matter coupling. We theoretically show that strained 2D photonic crystals can generate artificial electromagnetic fields and highly degenerate Landau levels. Since photonic crystals are not described by tight-binding, we employ a multiscale expansion of the full wave equation. Using numerical simulations, we observe dispersive Landau levels which we show can be flattened by engineering a pseudoelectric field. Artificial fields yield a design principle for aperiodic nanophotonic systems.
We experimentally demonstrate that networks of identical photonic spiking neurons based on coupled degenerate parametric oscillators can show various chimera states, in which, depending on their local synchronization and desynchronization, different kinds of spiking dynamics can develop in a self-organized manner. Even when only a static interaction is implemented, through synchronized inputs from connected neurons, the spiking mode of photonic neurons can be spontaneously and adaptively changed between the Class-I and Class-II modes classified by A. L. Hodgkin. This spontaneous spiking-mode s…
Recently, the gapless Dirac/Weyl nodal semimetals with linear dispersion and topologically protected modes degeneracy are rapidly growing frontiers of topological physics. Especially, type-I, type-II, and critical type-III nodal semimetals are discovered according to the tilt angles of the Dirac/Weyl cones. Here, by introducing hyperbolic metamaterials into one-dimensional photonic crystals, we design the "hyper-crystal" and study the photonic four-fold degenerate Dirac nodal line semimetals (DNLSs) with two types of perpendicularly polarized waves. Moreover, the flexibly controlled photonic D…
We identify different types of the photonic band gaps (PBGs) of two dimensional magnetic photonic crystals (MPCs) consisting of arrays of magnetic cylinders and study the different tunability (by an external static magnetic field) of these PBGs. One type of the band gaps comes from infinitely degenerate flat bands and is closely related to those in the study of plasmonics. In addition, such PBGs are magnetically tunable and robust against position disorder. We calcualte the transmission of the PBG's and found excellent agreement with the results of the photonic band structure calculation. Posi…
Optically-active spin systems coupled to photonic cavities with high cooperativity can generate strong light-matter interactions, a key ingredient in quantum networks. But obtaining high cooperativities for quantum information processing often involves the use of photonic crystal cavities that feature a poor optical access from the free space, especially to circularly polarized light required for the coherent control of the spin. Here, we demonstrate coupling with cooperativity as high as $8$ of an InAs/GaAs quantum dot to a fabricated bullseye cavity that provides nearly degenerate and Gaussi…
In recent times, we experimentally realized a quite efficient modeling of the shape of diffraction-resistant optical beams; thus generating for the first time the so-called Frozen Waves (FW), whose longitudinal intensity pattern can be arbitrarily chosen, within a prefixed space interval of the propagation axis. Such waves possess a host of potential applications: in medicine, biomedical optics, optical tweezers, atom guiding, remote sensing, tractor beams, optical communications or metrology, and other topics in photonic areas. In this work, we extend our theory of FWs -- which led to beams e…
We calculate that an appropriate modification of the field associated with only one of the photons of a photon pair can suppress generation of the pair entirely. From this general result, we develop a method for suppressing the generation of undesired photon pairs utilizing photonic stop bands. For a third-order nonlinear optical source of frequency-degenerate photons we calculate the modified frequency spectrum (joint spectral intensity) and show a significant increase in a standard metric, the coincidence to accidental ratio. These results open a new avenue for photon-pair frequency correlat…
We present a $\mathbf{k} \cdot \mathbf{p}$ theory of photonic crystals containing gain and loss in which the gain and loss are added to separate primitive cells of the underlying Hermitian system, thereby creating a supercell photonic crystal. We show that the supercell bands of this system can merge outward from the degenerate contour formed from folding the bands of the underlying Hermitian system into the supercell Brillouin zone, but that other accidental degeneracies in the band structure of the underlying Hermitian system do not yield band merging behavior. Finally, we show that the moda…
Hyperbolic metamaterials (HMMs), an unusual class of electromagnetic metamaterials, have found important applications in various fields due to their distinctive properties. A surprising feature of HMMs is that even continuous HMMs can possess topological edge modes. However, previous studies based on equal-frequency surface (analogy of Fermi surface) may not correctly capture the topology of entire bands. Here we develop a topological band description for continuous HMMs that can be described by a non-Hermitian Hamiltonian formulated from Maxwell's equations. We find two types of three dimensi…
We develop a general microscopic theory describing the phonon decoherence of quantum dots and indistinguishability of the emitted photons in photonic structures. The coherence is found to depend fundamentally on the dimensionality of the structure resulting in vastly different performance for quantum dots embedded in a nano-cavity (0D), waveguide (1D), slab (2D), or bulk medium (3D). In bulk, we find a striking temperature dependence of the dephasing rate scaling as $T^{11}$ implying that phonons are effectively 'frozen out' for $T \lesssim 4 \mathrm{K}$. The phonon density of states is strong…
We demonstrate high-efficiency, degenerate four-wave mixing in triply resonant Kerr $χ^(3)$ photonic crystal (PhC) nanobeam cavities. Using a combination of temporal coupled mode theory and nonlinear finite-difference time-domain (FDTD) simulations, we study the nonlinear dynamics of resonant four-wave mixing processes and demonstrate the possibility of observing high-efficiency limit cycles and steady-state conversion corresponding to $\approx 100$% depletion of the pump light at low powers, even including effects due to losses, self- and cross-phase modulation, and imperfect frequency matchi…
Modal coupling between frequency-degenerate resonances of an optical ring resonator is a commonly observed phenomenon that results in adverse mode splitting. Traditionally, this coupling is attributed to Rayleigh scattering of a propagating electromagnetic wave into its associated degenerate counter-propagating mode from small perturbations to the dielectric material of the resonator. We have chosen to reframe the problem of intracavity Rayleigh scattering by considering the optical ring resonator as an infinitely-long, one-dimensional photonic crystal (PhC) that possesses a lattice constant e…
Degeneracy is an omnipresent phenomenon in various physical systems, which has its roots in the preservation of geometrical symmetry. In electronic and photonic crystal systems, very often this degeneracy can be broken by virtue of strong interactions between photonic modes of the same energy, where the level repulsion and the hybridization between modes causes the emergence of photonic bandgaps. However, most often this phenomenon does not lead to a complete and inverted bandgap formation over the entire Brillouin zone. Here, by systematically breaking the symmetry of a two-dimensional square…
Some years after the appearance of the so-called non-diffracting beams, there was the development of methods capable of structuring them spatially, being the so called Frozen Waves method the first and, perhaps, the most efficient one. That method allowed modelling the longitudinal intensity pattern of non-diffracting beams, being, however, little efficient in controlling their transverse spatial pattern, granting only the possibility of choosing their transverse dimensions, which remain invariant throughout the propagation. In this work, we have extended the Frozen Wave method in such a way t…
In this paper, we report on the first evidence of guided resonances (GRs) in aperiodically-ordered photonic crystals, tied to the concept of "quasicrystals" in solid-state physics. Via a full-wave numerical study of the transmittance response and the modal structure of a photonic quasicrystal (PQC) slab based on a representative aperiodic geometry (Ammann-Beenker octagonal tiling), we demonstrate the possibility of exciting GR modes, and highlight similarities and differences with the periodic case. In particular, we show that, as for the periodic case, GRs arise from the coupling of the incid…
Weyl points are the degenerate points in three-dimensional momentum space with nontrivial topological phase, which are usually realized in classical system with structure and symmetry designs. Here we proposed a one-dimensional layer-stacked photonic crystal using anisotropic materials to realize ideal type-II Weyl points without structure designs. The topological transition from two Dirac points to four Weyl points can be clearly observed by tuning the twist angle between layers. Besides, on the interface between the photonic type-II Weyl material and air, gappless surface states have also be…
We report results of the study of solitons in a system of two nonlinear-Schrodinger (NLS) equations coupled by the XPM interaction, which models the co-propagation of two waves in metamaterials(MMs). The same model applies to photonic crystals (PCs), as well as to ordinary optical fibers, close to the zero-dispersion point. A peculiarity of the system is a small positive or negative value of the relative group-velocity dispersion (GVD) coefficient in one equation, assuming that the dispersion is anomalous in the other. In contrast to earlier studied systems of nonlinearly coupled NLS equations…
In this paper, we propose a method for tailoring the absorption in a photonic crystal membrane. For that purpose, we first applied Time Domain Coupled Mode Theory to such a subwavelength membrane and demonstrated that 100% resonant absorption can be reached even for a symmetric membrane, if degenerate modes are involved. Design rules were then derived from this model in order to tune the absorption. Subsequently, Finite Difference Time Domain simulations were used as a proof of concept and carried out on a low absorbing material (extinction coefficient=10-2) with a high refractive index corres…
The induction of synthetic magnetic fields on lattice structures allows to effectively control their localization and transport properties. In this work, we generate effective $π$ magnetic fluxes on a multi-orbital diamond lattice, where first ($S$) and second ($P$) order modes effectively interact. We implement a $z$-scan method on femtosecond laser written photonic lattices and experimentally observe Aharonov-Bohm caging for $S$ and $P$ modes, as a consequence of a band transformation and the emergence of a spectrum composed of three degenerated flat bands. As an application, we demonstrate …
Photonic molecules are composed of two or more optical resonators, arranged such that some of the modes of each resonator are coupled to those of the other. Such structures have been used for emulating the behaviour of two-level systems, lasing, and on-demand optical storage and retrieval. Coupled resonators have also been used for dispersion engineering of integrated devices, enhancing their performance for nonlinear optical applications. Delicate engineering of such integrated nonlinear structures is required for developing scalable sources of non-classical light to be deployed in quantum in…
