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Borrmann effect in Laue diffraction in one-dimensional photonic crystals under a topological phase transition
Abstract
We present experimental and theoretical studies of the anomalous high transmission of light (the Borrmann effect) under the Laue diffraction in a one-dimensional photonic crystal (PhC) characterized by spatial modulation of both refractive index and absorption. We show that a strong modulation of the refractive index along with the large PhC period provide new features of the Borrmann effect as compared to the well-known x-ray Borrmann effect in crystals appearing in PhC wavelength-angular transmission spectra. Namely, the maximal transmission is attained at the Bragg angles of incidence and corresponds alternatively to even or odd orders of the Bragg angles depending on the light wavelength. Second, a dramatic decrease of the angular width of the high transmission areas in the spectrum appear near the diabolic points. According to our description, this effect can be treated as a result of the topological phase transition accompanied by exchange of the parity of spatial distribution of the electromagnetic field of the two eigenmodes experiencing degeneracy. We demonstrate that these peculiarities are inherent to the PhC with the optical losses located in layers with higher refractive index, and disappear if the losses are specific for the PhC layers with lower refractive index. The suggested underlying mechanism involves the contribution of the waveguide PhC modes to the PhC transmission spectra.
... A well-known effect of that type in X-ray crystallography, called the Borrmann effect, is the anomalous transmission of waves across a crystal slab at the Bragg frequency [9,10]. More recently, a similar anomalous transmission was observed in photonic crystals [11][12][13]. In these works, a light wave is sent on a slab made of successive pairs of layers made of a high-absorbing and a low-absorbing material. ...
... In particular, a noticeable change occurs when the base medium undergoes a topological phase transition. Indeed, it was observed in [13] that the location of the anomalous transmission peaks change across a topological phase transition. Such a transition is characterized by a gap closing and reopening when varying a parameter (such as the cross-section ratio ν here), while the wave functions at the edges of the gap exchange symmetry [21]. ...
... Such a transition is characterized by a gap closing and reopening when varying a parameter (such as the cross-section ratio ν here), while the wave functions at the edges of the gap exchange symmetry [21]. Therefore, from what precedes, we conclude that the anomalous transmission frequency will change from the lower edge of the gap to the upper edge of the gap, in agreement with what was observed in [13]. ...
This work investigates anomalous transmission effects in periodic dissipative media, which is identified as an acoustic analogue of the Borrmann effect. For this, the scattering of acoustic waves on a set of equidistant resistive sheets is considered. It is shown both theoretically and experimentally that at the Bragg frequency of the system, the transmission coefficient is significantly higher than at other frequencies. The optimal conditions are identified: one needs a large number of sheets, which induce a very narrow peak, and the resistive sheets must be very thin compared to the wavelength, which gives the highest maximal transmission. Using the transfer matrix formalism, it is shown that this effect occurs when the two eigenvalues of the transfer matrix coalesce, i.e. at an exceptional point. Exploiting this algebraic condition, it is possible to obtain similar anomalous transmission peaks in more general periodic media. In particular, the system can be tuned to show a peak at an arbitrary long wavelength.
... Apparently, this method is not limited by the low IR absorption crosssections of the molecular vibration. Compared with the plasmon-molecule coupling methods such as Kerker effect, 8 Borrmann effect, 9 and Rabi splitting & Autler-Townes effect, 10 Fano resonance can be observed without scathing excitation conditions and has advantages in handling with objects that have multiple resonances. Hence, it attracts wide attention. ...
Metamaterials have proven their ability to possess extraordinary physical properties distinct from naturally available materials, leading to exciting sensing functionalities and applications. However, metamaterial-based sensing applications suffer from severe performance limitations due to noise interference and design constraints. Here, we propose a dual-phase strategy that leverages loss-induced different Fano-resonant phases to access both destructive and constructive signals of molecular vibration. When the two reverse signals are innovatively combined, the noise in the detection system is effectively suppressed, thereby breaking through the noise-related limitations. Additionally, by utilizing loss optimization of the plasmon-molecule coupling system, our dual-phase strategy enhances the efficiency of infrared energy transfer into the molecule without any additional fabrication complex, thereby overcoming the trade-off dilemma between performance and fabrication cost. Thanks to the pioneering breakthroughs in the limitations, our dual-phase strategy possesses an overwhelming competitive advantage in ultrasensitive vibrational spectroscopy over traditional metamaterial technology, including strong signal strength (Â4), high sensitivity (Â4.2), effective noise suppression (30%), low detection limit (13 ppm), and excellent selectivity among CO 2 , NH 3 , and CH 4 mixtures. This work not only opens the door to various emerging ultrasensitive detection applications, including ultrasensitive in-breath diagnostics and high-information analysis of molecular information in dynamic reactions, but also Hong Zhou and Dongxiao Li contributed equally to this work.
... Resonances in nanophotonics and nanoplasmonics are the fundamental phenomena that play a critical role in defining the operating mechanism, quality, and performance of the tailored tools. In recent years, several types of radiating and nonradiating resonances and spectral effects have been successfully excited and introduced by scientists such as Fano resonances [8][9][10], electromagnetically induced transparency (EIT) [11][12][13], Bormann and Kerker effects [14][15][16][17][18][19][20], toroidal multipoles [21][22][23][24], anapoles [23,[25][26][27], and charge transfer plasmons (CTPs) [28][29][30]. Excluding the later instance (CTP), other resonances can be induced based on robust coupling of optically driven modes between proximal metallic nanoparticles (NPs) with sharp protrusions in the near-field regime. ...
Reducing the capacitive opening between subwavelength metallic objects down to atomic scales or bridging the gap by a conductive path reveals new plasmonic spectral features, known as charge transfer plasmon (CTP). We review the origin, properties, and trending applications of this modes and show how they can be well-understood by classical electrodynamics and quantum mechanics principles. Particularly important is the excitation mechanisms and practical approaches of such a unique resonance in tailoring high-response and efficient extreme-subwavelength hybrid nanophotonic devices. While the quantum tunneling-induced CTP mode possesses the ability to turn on and off the charge transition by varying the intensity of an external light source, the excited CTP in conductively bridged plasmonic systems suffers from the lack of tunability. To address this, the integration of bulk plasmonic nanostructures with optothermally and optoelectronically controllable components has been introduced as promising techniques for developing multifunctional and high-performance CTP-resonant tools. Ultimate tunable plasmonic devices such as metamodulators and metafilters are thus in prospect.
We study theoretically the second-order correlation function g(2)(t) for photons transmitted through a periodic Bragg-spaced array of superconducting qubits, coupled to a waveguide. We demonstrate that photon bunching and antibunching persist much longer than both radiative and nonradiative lifetimes of a single qubit. Due to the Borrmann effect, that is a strongly non-Markovian collective feature of light-qubit coupling inherent to the Bragg regime, the photon-photon correlations become immune to nonradiative dissipation. This persistence of quantum correlations opens new avenues for enhancing the performance of setups of waveguide quantum electrodynamics.
The ability to manipulate the frequency of light is a cornerstone of a wide range of applications in photonics expanding spectral ranges of the light sources. To boost the second harmonic generation efficiency, intense efforts toward exploiting artificial microstructures for frequency doubling were carried out. The sought-after approach of utilizing photonic crystals is inspired by their unusual light dispersion. In such structures, the dynamics of the field of femtosecond laser pulses is of paramount importance for frequency conversion. In this work, we investigate the phase-matched second harmonic generation under the effect of diffraction-induced femtosecond laser pulse splitting in one-dimensional photonic crystals at the Bragg diffraction in the Laue geometry. We demonstrate that the interaction of the two pulses at the fundamental frequency that appears in photonic crystals through the dynamical light diffraction leads to a nonmonotonic dependence of the frequency up-conversion efficiency with respect to the laser pulse duration, thus allowing to increase the second harmonic power by tuning the pulse duration.
This work investigates anomalous transmission effects in periodic dissipative media, which is identified as an acoustic analogue of the Borrmann effect. For this, the scattering of acoustic waves on a set of equidistant resistive sheets is considered. It is shown both theoretically and experimentally that at the Bragg frequency of the system, the transmission coefficient is significantly higher than at other frequencies. The optimal conditions are identified: one needs a large number of sheets, which induce a very narrow peak, and the resistive sheets must be very thin compared to the wavelength, which gives the highest maximal transmission. Using the transfer matrix formalism, it is shown that this effect occurs when the two eigenvalues of the transfer matrix coalesce (i.e., at an exceptional point). Exploiting this algebraic condition, it is possible to obtain similar anomalous transmission peaks in more general periodic media. In particular, the system can be tuned to show a peak at an arbitrary long wavelength.
The parity-time (PT)-symmetric optical properties are significantly restored for broadband radiation if the width of the field spectrum is substantially less than the width of the spectral line of a resonant medium. This is the so-called quasi-PT-symmetry for broadband radiation. Under the quasi-PT-symmetric light-matter interaction, we describe the dynamics of a short spatially localized pulse propagating in the extended medium, when the length of propagation significantly exceeds the pulse size. As an example, the boundary problem of dynamical Bragg diffraction in the Laue geometry for a short laser pulse in a photonic crystal (PhC) with strong material dispersion is solved. It is shown that at exceptional point of the PT-symmetry breaking, the dynamics and parameters of the pulse change dramatically when the sign of the Bragg angle of incidence θB changes. Unidirectional zero Bragg reflection and unidirectional Bragg-diffraction-induced pulse splitting are revealed. At a positive angle, θB>0, the localized short pulse propagates in a quasi-PT-symmetric PhC with gain and loss under Bragg diffraction condition as in a conservative transparent homogeneous medium. A change in the sign θB<0 leads to the appearance of an amplified diffracted pulse. In the case of a small detuning from the exact Bragg condition, at θB<0, the directions and magnitudes of the group velocities of different field modes change and, as a result, the temporal and spatial diffraction-induced pulse splitting occurs. Such asymmetric dynamics of the pulse propagation in a quasi-PT-symmetric PhC can be used to effectively control the parameters and dynamics of short optical pulses by small changes in its frequency, in the magnitude of the gain and loss parameter of the medium, etc.
Topological edge states exist at the interfaces between two topologically distinct materials. The presence and number of such modes are deterministically predicted from the bulk band topologies, known as the bulk-edge correspondence. This principle is highly useful for predictably controlling optical modes in resonators made of photonic crystals (PhCs), leading to the recent demonstrations of microscale topological lasers. Meanwhile, zero-dimensional topological trapped states in the nanoscale remained unexplored, despite its importance for enhancing light–matter interactions and for wide applications including single-mode nanolasers. Here, we report a topological PhC nanocavity with a near-diffraction-limited mode volume and its application to single-mode lasing. The topological origin of the nanocavity, formed at the interface between two topologically distinct PhCs, guarantees the existence of only one mode within its photonic bandgap. The observed lasing accompanies a high spontaneous emission coupling factor stemming from the nanoscale confinement. These results encompass a way to greatly downscale topological photonics.
We study the nonlinear frequency up-conversion in a plasmonic thin film sandwiched between one-dimensional photonic crystals (PCs) of different Zak phases by rigorous numerical time-domain nonlinear hydrodynamic calculations. We show that the proposed hetero-structure can support robust fundamental and high-order topological edge modes that simultaneously enhance the third-harmonic generation. Numerical simulations also show that femtosecond pulses can excite double topological edge modes through optical tunneling in band gaps, leading to a large nonlinear response. The obtained third harmonic generation (THG) conversion efficiency of the hetero-structure is three orders of magnitude larger than that of a single plasmonic film. The results presented here may open new avenues for designing high-efficiency nonlinear photonic devices.
The molecular organization in thermally annealed films of poly(9,9-bis((S)-3,7-dimethyloctyl)-2,7-fluorene-alt-benzothiadiazole) is investigated using polarized light. Measurement of linear polarization in transmission and reflection as function of layer thickness and orientation directly show a left handed cholesteric organization with a pitch length of 600 nm. Results are corroborated by measurements of circularly polarized reflection and generalized ellipsometry and are compared to calculations of the optical properties based on the Maugin-Oseen-DeVries model. For wavelengths near the lowest allowed optical transition, light with the same handedness as the cholesteric arrangement (left) is found to be reflected and transmitted with a probability higher than right circularly polarized light. The high transmission for left polarized light is interpreted as an optical manifestation of the Borrmann effect.
Topological semimetals are materials whose band structure contains touching points that are topologically nontrivial and can host quasiparticle excitations that behave as Dirac or Weyl fermions1,2,3,4,5,6,7. These so-called Weyl points not only exist in electronic systems, but can also be found in artificial periodic structures with classical waves, such as electromagnetic waves in photonic crystals8,9,10,11 and acoustic waves in phononic crystals12,13. Due to the lack of spin and a difficulty in breaking time-reversal symmetry for sound, however, topological acoustic materials cannot be achieved in the same way as electronic or optical systems. And despite many theoretical predictions12,13, experimentally realizing Weyl points in phononic crystals remains challenging. Here, we experimentally realize Weyl points in a chiral phononic crystal system, and demonstrate surface states associated with the Weyl points that are topological in nature, and can host modes that propagate only in one direction. As with their photonic counterparts, chiral phononic crystals bring topological physics to the macroscopic scale.
Exploring photonic topology
Scattering topological effects are being explored in a variety of electronic and optical materials systems owing to their robustness against defects (see the Perspective by Özdemir). Yang et al. designed and fabricated an ideal optical analog of a three-dimensional Weyl system. Angular transmission measurements revealed four Weyl points at the same energy, as well as the signature helicoidal arcs associated with such an exotic topological system. Zhou et al. theoretically proposed and experimentally demonstrated the formation of a topologically protected bulk Fermi arc. They attributed the formation of the arc to the topological nature of paired exceptional points (points at which gain and loss in the system are matched). Photonic crystals may provide a powerful platform for studying exotic properties of topological electronic systems and may also be used to develop optical devices that exploit topological properties of light-matter interactions.
Science , this issue p. 1013 , p. 1009 ; see also p. 995
Weyl fermions have not been found in nature as elementary particles, but they emerge as nodal points in the band structure of electronic and classical wave crystals. Novel phenomena such as Fermi arcs and chiral anomaly have fueled the interest in these topological points which are frequently perceived as monopoles in momentum space. Here we report the experimental observation of generalized optical Weyl points inside the parameter space of a photonic crystal with a specially designed four-layer unit cell. The reflection at the surface of a truncated photonic crystal exhibits phase vortexes due to the synthetic Weyl points, which in turn guarantees the existence of interface states between photonic crystals and any reflecting substrates. The reflection phase vortexes have been confirmed for the first time in our experiments which serve as an experimental signature of the generalized Weyl points. The existence of these interface states is protected by the topological properties of the Weyl points and the trajectories of these states in the parameter space resembles those of Weyl semimetal "Fermi arcs surface states" in momentum space. Tracing the origin of interface states to the topological character of the parameter space paves the way for a rational design of strongly localized states with enhanced local field.
We present the experimental observation of the optical Borrmann effect in 1D porous silica-based photonic crystals (PhC) composed of several hundreds of dielectric layers with different porosity. Two mechanisms of the effect are demonstrated, which involve the optical losses associated with light scattering and absorption in nanoporous layers. Absorption is introduced by a small amount of silicon in partially annealed porous silicon PhC. We show that the PhC transmittance increases substantially under the Bragg diffraction condition, which is a manifestation of the Borrmann effect. The observed effects along with their polarization sensitivity are confirmed by numerical calculations.
Light propagating in PT-symmetric photonic crystals (PhCs) under Bragg diffraction in the Laue geometry has been studied theoretically using the spectral method. The PT-symmetric solutions describing propagating modes have been found in the PhCs with gain and loss beyond paraxial approximation. We described the pendulum effect - the periodical spatial localization of the total field intensity in a PhC - near the PT-symmetry-breaking point. It is shown that, due to PT-symmetric properties of the medium, an asymmetric change in the amplitudes of the diffracted waves in PhCs is observed when the sign of the Bragg incidence angle is changed from positive to negative. Thus, the intensity of a spatially periodic field in a medium radically alters under the pendulum effect. Moreover, when the sign of the Bragg incidence angle changes, a PhC of a certain thickness is turned from an absorbing structure into an amplifying one, also a PhC of any thickness evolves from completely transparent into amplifying in the vicinity of the PT-symmetry-breaking point. Under a small change of the imaginary part of permittivity, the light switching from a transmitted wave into a gain or loss diffracted wave is possible in a diffraction-thick PhC.
Light propagation through a finite-width periodically modulated layer obeying parity-time ( P T ) symmetry is considered. We consider the configuration when the resonant conditions of mode coupling by the grating are satisfied. It is shown that the dependence of the transmission and reflection coefficients on the slab width has resonant character featuring strong amplification of reflected and transmitted waves with negative angles. The dependence of the scattering data on the gain-and-loss intensity also feature strong resonances near the P T -symmetry breaking point, when the slab strongly amplifies waves reflected and transmitted with negative angles, provided the incident wave has a positive angle of incidence.
There is no known simple rule that assures the existence of interface states in photonic crystals (PCs). We show here that one can control the existence or absence of interface states in 1D PCs through engineering the bulk geometrical phase such that interface states can be guaranteed in some or all photonic bandgaps. We verify experimentally the interface state design paradigm in 1D multilayered PCs fabricated by electron beam vapor deposition. We obtain the geometrical phases by measuring the reflection phases at the bandgaps of the PCs and achieve good agreement with the theory. Our approach could provide a platform for generating a PC interface state for various applications.
We show theoretically that, in the limit of weak dispersion, one-dimensional binary centrosymmetric photonic crystals can support topological edge modes in all photonic bandgaps. By analyzing their bulk band topology, these “harmonic” topological edge modes can be designed in a way that they exist at all photonic bandgaps opened at the center of the Brillouin zone, at all gaps opened at the zone boundaries, or both. The results may suggest a new approach to achieve robust multi-frequency coupled modes for applications in nonlinear photonics, such as frequency upconversion.
For a one-dimensional (1D) periodic system with inherent mirror symmetry, the value of the geometric “Zak” phase in a bulk band is related to the sign of reflection phase for wavelengths inside the bandgaps sandwiching the bulk band. Here, we designed an interference setup which allows us to measure the reflection phase of 1D phonic crystal fabricated for the optical range; this, in turn, enabled us to determine the Zak phases of the bands. We then found interface states whose existence can be traced to the topological properties of the bandgaps and the geometric phases of the bulk bands.
The localized opical modes in photonic liquid crystals are studied for the certainty at the example of chiral liquid crystals (CLCs). The chosen here model (absence of dielectric interfaces in the studied structures) allows one to get rid off the polarization mixing at the surfaces of the CLC layer and the defect structure (DMS) and to reduce the corresponding equations to the equations for the light of diffracting in the CLC polarization only. The dispersion equations determining connection of the EM and DM frequencies with the CLC layer parameters and other parameters of the DMS are obtained. Analytic expressions for the transmission and reflection coefficients of the DMS are presented and analyzed. As specific cases are considered DMS with an active (i.e. transforming the light intensity or polarization) defect layer and CLC layers with locally anisotropic absorption. It is shown that the active layer (excluding an amplifying one) reduces the DM lifetime (and increase the lasing threshold) in comparison with the case of DM at an isotropic defect layer. The case of CLC layers with an anisotropic local absorption is also analyzed and, in particular, shown that due to the Borrmann effect the EM life-times for the EM frequncies at the opposite stop-bans edges may be signifinately different. The options of experimental observations of the theoretically revealed phenomena are discussed.
The Dirac cone underlies many unique electronic properties of graphene and topological insulators, and its band structure—two conical bands touching at a single point—has also been realized for photons in waveguide arrays, atoms in optical lattices, and through accidental degeneracy. Deformation of the Dirac cone often reveals intriguing properties; an example is the quantum Hall effect, where a constant magnetic field breaks the Dirac cone into isolated Landau levels. A seemingly unrelated phenomenon is the exceptional point, also known as the parity–time symmetry breaking point, where two resonances coincide in both their positions and widths. Exceptional points lead to counter-intuitive phenomena such as loss-induced transparency, unidirectional transmission or reflection, and lasers with reversed pump dependence or single-mode operation. Dirac cones and exceptional points are connected: it was theoretically suggested that certain non-Hermitian perturbations can deform a Dirac cone and spawn a ring of exceptional points. Here we experimentally demonstrate such an ‘exceptional ring’ in a photonic crystal slab. Angle-resolved reflection measurements of the photonic crystal slab reveal that the peaks of reflectivity follow the conical band structure of a Dirac cone resulting from accidental degeneracy, whereas the complex eigenvalues of the system are deformed into a two-dimensional flat band enclosed by an exceptional ring. This deformation arises from the dissimilar radiation rates of dipole and quadrupole resonances, which play a role analogous to the loss and gain in parity-time symmetric systems. Our results indicate that the radiation existing in any open system can fundamentally alter its physical properties in ways previously expected only in the presence of material loss and gain.
The geometric phase that specifically characterizes the topological property of bulk bands in one-dimensional periodic systems is known as the Zak phase. Recently, it has been found that topological notions can also characterize the topological phase of mechanical isostatic lattices. Here, we present a theoretical framework and two experimental methods to determine the Zak phase in a periodic acoustic system. We constructed a phononic crystal with a topological transition point in the acoustic band structure where the band inverts and the Zak phase in the bulk band changes following a shift in system parameters. As a consequence, the topological characteristics of the bandgap change and interface states form at the boundary separating two phononic crystals having diierent bandgap topological characteristics. Such acoustic interface states with large sound intensity enhancement are observed at the phononic crystal interfaces. We use a simple photonic crystal system to demonstrate geometric phase effects and the existence of topological transition points in acoustic systems.
The massless solutions to the Dirac equation are described by the so-called Weyl Hamiltonian. The Weyl equation requires a particle to have linear dispersion in all three dimensions (3D) while being doubly degenerate at a single momentum point. These Weyl points are topological monopoles of quantized Berry flux exhibiting numerous unusual properties. We performed angular-resolved microwave transmission measurements through a double-gyroid photonic crystal with inversion-breaking, where Weyl points have been theoretically predicted to occur. The excited bulk states show two linear dispersion bands touching at four isolated points in the 3D Brillouin zone, indicating the observation of Weyl points. This work paves a way to a variety of photonic topological phenomena in 3D.
Copyright © 2015, American Association for the Advancement of Science.
We study the propagation of waves in a periodic array of absorbing layers. We report an anomalous increase of wave transmission through the structure related to a decrease of the absorption around the Bragg frequencies. The effect is first discussed in terms of a generic coupled wave model extended to include losses, and its predictions can be applied to different types of waves propagating in media with periodic modulation of the losses at the wavelength scale. The particular case of sound waves in an array of porous layers embedded in air is considered. An experiment designed to test the predictions demonstrates the existence of the enhanced transmission band.
Topological features—global properties not discernible locally—emerge in systems ranging from liquid crystals to magnets to fractional quantum Hall systems. A deeper understanding of the role of topology in physics has led to a new class of matter—topologically ordered systems. The best known examples are quantum Hall effects, where insensitivity to local properties manifests itself as conductance through edge states that is insensitive to defects and disorder. Current research into engineering topological order primarily focuses on analogies to quantum Hall systems, where the required magnetic field is synthesized in non-magnetic systems. Here, we realize synthetic magnetic fields for photons at room temperature, using linear silicon photonics. We observe, for the first time, topological edge states of light in a two-dimensional system and show their robustness against intrinsic and introduced disorder. Our experiment demonstrates the feasibility of using photonics to realize topological order in both non-interacting and many-body regimes.
Surface impedance is an important concept in classical wave systems such as
photonic crystals (PCs). For example, the condition of an interface state
formation in the interfacial region of two different one-dimensional PCs is
simply Z_SL +Z_SR=0, where Z_SL (Z_SR)is the surface impedance of the
semi-infinite PC on the left- (right-) hand side of the interface. Here, we
also show a rigorous relation between the surface impedance of a
one-dimensional PC and its bulk properties through the geometrical (Zak) phases
of the bulk bands, which can be used to determine the existence or
non-existence of interface states at the interface of the two PCs in a
particular band gap. Our results hold for any PCs with inversion symmetry,
independent of the frequency of the gap and the symmetry point where the gap
lies in the Brillouin Zone. Our results provide new insights on the
relationship between surface scattering properties, the bulk band properties
and the formation of interface states, which in turn can enable the design of
systems with interface states in a rational manner.
The polarization effects in the diffraction-induced pulse splitting (DIPS) observed under the dynamical Bragg diffraction in the Laue geometry in linear one-dimensional photonic crystals (PCs) are studied theoretically and experimentally. It is demonstrated that the characteristic length of the laser pulse path in a PC, or splitting length, used to describe the temporal pulse splitting, as well as the number of the outgoing femtosecond pulses, are influenced significantly by the polarization of the incident laser pulse. We have observed that the characteristic splitting time in porous quartz PCs for the s -polarized probe pulse is approximately 1.5 times smaller as compared with that measured for the p -polarized radiation. These results are supported by the theoretical description and ensure that the polarization sensitivity of the DIPS effect is due to a large lattice-induced dispersion of the PC. It is also shown that the number of output pulses can be varied from two up to four in both transmission and diffraction directions depending on the polarization of incident femtosecond pulses.
Recent progress in understanding the topological properties of condensed matter has led to the discovery of time-reversal-invariant topological insulators. A remarkable and useful property of these materials is that they support unidirectional spin-polarized propagation at their surfaces. Unfortunately topological insulators are rare among solid-state materials. Using suitably designed electromagnetic media (metamaterials) we theoretically demonstrate a photonic analogue of a topological insulator. We show that metacrystals-superlattices of metamaterials with judiciously designed properties-provide a platform for designing topologically non-trivial photonic states, similar to those that have been identified for condensed-matter topological insulators. The interfaces of the metacrystals support helical edge states that exhibit spin-polarized one-way propagation of photons, robust against disorder. Our results demonstrate the possibility of attaining one-way photon transport without application of external magnetic fields or breaking of time-reversal symmetry. Such spin-polarized one-way transport enables exotic spin-cloaked photon sources that do not obscure each other.
We consider one-dimensional photonic crystals in which the contrast of layer impedances is due to differ-ences in imaginary parts of layer dielectric permittivities. We show that even though in such structures there is no noticeable increase in the imaginary part of the Bloch wave number, there are frequency regions in which the transmission coefficient can rise or fall compared with a homogeneous slab of the same thickness and total absorption.
We demonstrate analytically a linear optical property of photonic crystals—diffraction-induced incident optical pulse splitting in two pulses propagating with different group velocities in a linear photonic crystal. The reason of this phenomenon is in spatially inhomogeneous field localization within the photonic crystal in case of the Bragg diffraction at the Laue scheme. The field of the fast first pulse is mainly localized within low refractive index layers, whereas the slow second pulse field is mostly in high refractive index layers. Changing optical properties of either high-index or low-index layers of periodical multilayer structure, it is possible to control parameters of each propagating pulse separately. The distance between two transmitted and two dif-fractively reflected output pulses can be controlled by varying the crystal thickness and modulation depth of the refractive index.
Nonlinear-optical manifestations of the Borrmann effect that are consequences of the spectral dependence of the spatial distributions
of the electromagnetic field in a structure are observed in one-dimensional photonic crystals. The spectrum of the light self-focusing
effect corresponding to the propagation-matrix calculations has been measured near the edge of the photonic gap.
PACS numbers7.57.Lm-76.60.-k
Results of the study of second harmonic generation by femtosecond laser pulses in a lithium niobate crystal with a regular
domain structure in the Laue scheme are presented. The angular distribution of the intensity and the polarization properties
of the second harmonic radiation are studied. The orders of the corresponding phase-matching conditions and the angular width
of the second harmonic maxima are calculated theoretically. The theoretical results are compared with experimental data.
Weyl points, i.e., peculiar nodal degenerate points in three-dimensional reciprocal space, carry topological charges, therefore giving rise to many intriguing phenomena including topologically protected surface states and chiral anomaly. More importantly, the concept of the Weyl point can be applied in systems with reduced geometrical dimensionality by means of synthetic dimension. Such generalized synthetic Weyl points therefore provide a versatile platform to explore the Weyl-point physics in one or two-dimensional structures. In this work, we study the synthetic Weyl points in one-dimensional plasmonic-dielectric crystals with broken inversion symmetry and further demonstrate that the synthetic Weyl points can ensure the emergence of topological interface states. Instead of using the Zak phase, the emergence of a Weyl point in synthetic space is helpful to understand the underlying physics and the topological properties of the interface states in one-dimensional crystals with broken inversion symmetry. Due to the opposite sign of the surface impedance for plasmonic and dielectric cover medium, the surface states demonstrate distinct properties and locate in separated parameter space regions. Our results show that the synthetic Weyl point provides a potential approach for studying novel electromagnetic modes and facilitates the formation of topologically protected interface states in systems with reduced geometrical dimensions.
Topological protection for lasers
Ideas based on topology, initially developed in mathematics to describe the properties of geometric space under deformations, are now finding application in materials, electronics, and optics. The main driver is topological protection, a property that provides stability to a system even in the presence of defects. Harari et al. outline a theoretical proposal that carries such ideas over to geometrically designed laser cavities. The lasing mode is confined to the topological edge state of the cavity structure. Bandres et al. implemented those ideas to fabricate a topological insulator laser with an array of ring resonators. The results demonstrate a powerful platform for developing new laser systems.
Science , this issue p. eaar4003 , p. eaar4005
Weyl fermions are hypothetical two-component massless relativistic particles in three-dimensional (3D) space, proposed by Hermann Weyl in 1929. Their band-crossing points, called ‘Weyl points’, carry a topological charge and are therefore highly robust. There has been much excitement over recent observations of Weyl points in microwave photonic crystals and the semimetal TaAs. Here, we report on the experimental observation of ‘type-II’ Weyl points of light at optical frequencies, with the photons having a strictly positive group velocity along one spatial direction. We use a 3D structure consisting of laser-written waveguides, and show the presence of type-II Weyl points by observing conical diffraction along one axis when the frequency is tuned to the Weyl point; and observing the associated Fermi arc-like surface states. The realization of Weyl points at optical frequencies allows these novel electromagnetic modes to be further explored in the context of linear, nonlinear, and quantum optics.
To describe the theory of topological band insulators we will use the language of adiabatic phases. In this chapter we review the basic concepts: the Berry phase, the Berry curvature, and the Chern number. We further describe the relation between the Berry phase and adiabatic dynamics in quantum mechanics. Finally, we illustrate these concepts using the two-level system as a simple example.
The geometric phase and topological property for the band structures of one-dimensional hybrid plasmonic-photonic crystals consisting of a simple lattice of graphene sheets are investigated systematically. For transverse magnetic (TM) waves, both the plasmonic and photonic modes exist in the momentum space spanned by (k||, q). The accidental degeneracy point of these two modes is identified to be a diabolic point accompanied with a topological phase transition. For a closed loop around this degeneracy point, the Berry phase is Pi as a consequence of the discontinuous jump of the geometric Zak phase. The wave impedance is calculated analytically for the semi-infinite system, and the corresponding topological interface states either start from or terminate at the degeneracy point.
Physical systems with loss or gain have resonant modes that decay or grow exponentially with time. Whenever two such modes coalesce both in their resonant frequency and their rate of decay or growth, an 'exceptional point' occurs, giving rise to fascinating phenomena that defy our physical intuition. Particularly intriguing behaviour is predicted to appear when an exceptional point is encircled sufficiently slowly, such as a state-flip or the accumulation of a geometric phase. The topological structure of exceptional points has been experimentally explored, but a full dynamical encircling of such a point and the associated breakdown of adiabaticity have remained out of reach of measurement. Here we demonstrate that a dynamical encircling of an exceptional point is analogous to the scattering through a two-mode waveguide with suitably designed boundaries and losses. We present experimental results from a corresponding waveguide structure that steers incoming waves around an exceptional point during the transmission process. In this way, mode transitions are induced that transform this device into a robust and asymmetric switch between different waveguide modes. This work will enable the exploration of exceptional point physics in system control and state transfer schemes at the crossroads between fundamental research and practical applications.
Phase-matched second-harmonic generation (SHG) under the Bragg diffraction in the Laue geometry in one-dimensional photonic crystal (PhC) is studied theoretically and experimentally. We demonstrate that the phase-matched SHG can be realized in a PhC by compensation of the material dispersion of the PhC constituent layers of adjustable thickness. The second-order nonlinear susceptibility is introduced in the porous quartz-based PhC by its infiltration by sodium nitrite. We observed that two second-harmonic (SH) beams appear after passing through the PhC under the phase-matched process, which correspond to the transmission and diffraction angular directions. The appearance of the phase-matched SHG is confirmed by a pronounced SH spectral dependence and a narrow SH angular distribution, with the FWHM of the SH peak of approximately 3.5 times smaller as compared to the case of non-phase-matched SHG.
Second-harmonic generation (SHG) in the Laue scheme of the dynamical Bragg diffraction in one-dimensional photonic crystal (PhC) is studied. The experiments are performed for partially annealed porous-silicon PhC containing 250 periods of the structure. Our measurements confirm that the phase-matched optical SHG is observed under the Bragg conditions, which is evidenced by a narrow angular and spectral distribution of the diffracted SHG outgoing the PhC. This is confirmed by both the analytical description of the SHG process performed in the two-wave approximation, and by direct calculations of the PhC dispersion curves for the fundamental and SHG wavelengths by the revised plane wave method. Possible types of phase- and quasi-phase-matching realized in the studied PhC under the Laue diffraction scheme are discussed.
The discovery of topological photonic states has revolutionized our understanding of electromagnetic propagation and scattering. Endowed with topological robustness, photonic edge modes are not reflected from structural imperfections and disordered regions. Here we demonstrate robust propagation along reconfigurable pathways defined by synthetic gauge fields within a topological photonic metacrystal. The flow of microwave radiation in helical edge modes following arbitrary contours of the synthetic gauge field between bianisotropic metacrystal domains is unimpeded. This is demonstrated in measurements of the spectrum of transmission and time delay along the topological domain walls. These results provide a framework for freely steering electromagnetic radiation within photonic structures.
We present the realization of the multiperiodic optical pendulum effect in 1D porous silicon photonic crystals (PhCs) under dynamical Bragg diffraction in the Laue scheme. The diffraction-thick PhC contained 360 spatial periods with a large variation of the refractive index of adjacent layers of 0.4. The experiments reveal switching of the light leaving the PhC between the two spatial directions, which correspond to Laue diffraction maxima, as the fundamental wavelength or polarization of the incident light is varied. A similar effect can be achieved when the temperature of the sample or the intensity of the additional laser beam illuminating the crystal are changed. We show that in our PhC structures, the spectral period of the pendulum effect is down to 5 nm, while the thermal period is about 10 °C.
Topological insulators are insulating in the bulk but feature conducting
states on their surfaces. Standard methods for probing their topological
properties largely involve probing the surface, even though topological
invariants are defined via the bulk band structure. Here, we utilize
non-hermiticy to experimentally demonstrate a topological transition in an
optical system, using bulk behavior only, without recourse to surface
properties. This concept is relevant for a wide range of systems beyond optics,
where the surface physics is difficult to probe.
The magneto-optical Faraday effect is studied in one-dimensional magnetophotonic crystals (MPCs). Mechanisms of a strong enhancement of the Faraday rotation at the edges of the photonic band gap are considered. High difference of refractive indexes of bismuth-substituted yttrium iron garnet (Bi:YIG) and SiO2 layers provides a strong spatial localization of the optical field in Bi:YIG layers, which leads to manifold Faraday rotation enhancement at the photonic band edges. The Faraday rotation angle in the finite MPCs appears to be a nonlinear function of the total thickness of magnetic material in the stack that can be interpreted as the nonlinear Verdet law. Relation between the enhancement of the Faraday rotation and localization of optical field in magnetic layers is treated as a Borrmann-type effect. This relation shows that the Faraday rotation can be considered as a measure of the density of photonic states trapped within Bi:YIG layers.
In this work, we present the results on the fabrication and characterization of the structural and optical properties of thick mesoporous silicon-based 1D photonic crystals (PC) containing up to 2500 periods (400 μm thick) made by electrochemical etching in the hydrofluoric acid solution. The composition of multilayered structures with good spatial periodicity up to thousands of layers and with good reproducibility of porosity of alternate layers is demonstrated that is proven by SEM measurements. Comparative studies of the reflectivity spectra from the front and back sides of a thick free-standing PC also testify a good periodicity of the multilayer structure which manifests itself by the appearance of the photonic band gaps. We demonstrate that the main mechanism that restricts the fabrication of thick porous silicon-based photonic crystals is the local decreasing of the HF concentration in pores.
Frames, or lattices consisting of mass points connected by rigid bonds or
central force springs, are important model constructs that have applications in
such diverse fields as structural engineering, architecture, and materials
science. The difference between the number of bonds and the number of degrees
of freedom of these lattices determines the number of their zero-frequency
"floppy modes". When these are balanced, the system is on the verge of
mechanical instability and is termed isostatic. It has recently been shown that
certain extended isostatic lattices exhibit floppy modes localized at their
boundary. These boundary modes are insensitive to local perturbations, and
appear to have a topological origin, reminiscent of the protected electronic
boundary modes that occur in the quantum Hall effect and in topological
insulators. In this paper we establish the connection between the topological
mechanical modes and the topological band theory of electronic systems, and we
predict the existence of new topological bulk mechanical phases with distinct
boundary modes. We introduce model systems in one and two dimensions that
exemplify this phenomenon.
Since the appearance of Berry's seminal paper in 1984, geometric phases have been discovered in virtually all fields of physics. Here we address molecules and solids, and we limit our scope to the Berry's phases of the many-electron wavefunction. Many advances have occurred in very recent years relating to the theory of such phases and their observable consequences. After discussing the basic features of Berry's phases in a generic quantum system, we specialize to selected examples taken from molecular physics and condensed matter physics; in each of these cases, a Berry's phase of the electronic wavefunction leads to measurable effects.
`Accidental' degeneracies between energy levels E_j and Ej+1 of a real Hamiltonian can occur generically in a family of Hamiltonians labelled by at least two parameters X, Y, ... Energy-level surfaces in E, X, Y space have (locally) a double-cone (diabolo) connection and we refer to the degeneracies themselves as `diabolical points'. We studied the family of systems in which a particle moves freely within hard-walled triangles (vibrations of triangular membranes), with X and Y labelling two of the angles. Using an efficient Green-function technique to compute the levels, we found several diabolical points for low-lying levels (as well as some symmetry degeneracies); the lowest diabolical point occurred for levels 5 and 6 of the triangle 130.57^circ, 30.73^circ, 18.70^circ. The conical structure was confirmed by noting that the normal derivative u of the wavefunction psi at a boundary point changed sign during a small circuit of the diabolical point. The form of the variation of u around a circuit, and the changing pattern of nodal lines of psi, agreed with theoretical expectations. An estimate of the total number of degeneracies N_d(j), involving levels 1 through j, based on the energy-scaling of cone angles and the level spacing distribution, gave N_d(j) ~ (j+1/2)2.5, and our limited data support this prediction. Analytical theory confirmed that for thin triangles (where our computational method is slow) there are no degeneracies in the energy range studied.
It has been shown previously that in analogy with the Borrmann effect in X-ray diffraction from crystals there is an anomalous increase in the transmitted intensity near the Bragg reflection band in an absorbing cholesteric liquid crystal. In this communication detailed experimental studies of this effect carried out on thin films of mixtures of cholesteryl nonanoate and p-azoxyanisole of different concentrations are reported. Numerical calculations based on the dynamical theory of reflection are also presented. The theoretical curves of circular dichroism versus wavelength are in qualitative agreement with the experimentally observed features.
DOI:https://doi.org/10.1103/RevModPhys.36.681
The structure of holograms recorded in a three-dimensional photosensitive medium, is a combination of ideal three-dimensional periodics. By reconstruction of the images of those holograms phenomena of abnormal transmission and extinction were observed, i.e. effects characteristic for diffraction of X-rays in ideal crystals.
The rigorous coupled-wave analysis technique for describing the diffraction of electromagnetic waves by periodic grating structures is reviewed. Formulations for a stable and efficient numerical implementation of the analysis technique are presented for one-dimensional binary gratings for both TE and TM polarization and for the general case of conical diffraction. It is shown that by exploitation of the symmetry of the diffraction problem a very efficient formulation, with up to an order-of-magnitude improvement in the numerical efficiency, is produced. The rigorous coupled-wave analysis is shown to be inherently stable. The sources of potential numerical problems associated with underflow and overflow, inherent in digital calculations, are presented. A formulation that anticipates and preempts these instability problems is presented. The calculated diffraction efficiencies for dielectric gratings are shown to converge to the correct value with an increasing number of space harmonics over a wide range of parameters, including very deep gratings. The effect of the number of harmonics on the convergence of the diffraction efficiencies is investigated. More field harmonics are shown to be required for the convergence of gratings with larger grating periods, deeper gratings, TM polarization, and conical diffraction.
The Borrmann effect for obliquely incident light is qualitatively explained using the Optical Eigen Modes. Transmission spectra from an absorbing single-domain cholesteric liquid crystal are measured for obliquely incident light. The Borrmann effect is still found to be in exitence at a small angle of incidence. The transmission spectra at a large angle of incidence, however, show that the Borrmann effect has disappeared. Transmission spectra are numerically calculated by the 4× 4 matrix method and are in good agreement with the experiments.
The interdisciplinary theoretical and practical problems involved in the
development of devices analogous to lasers for generation of coherent
radiation in the 6- to 120-keV photon energy range by stimulated
emission of recoilless radiation from nuclear isomers are discussed in
depth with a comprehensive bibliography.
Weyl points and line nodes are three-dimensional linear point- and
line-degeneracies between two bands. In contrast to Dirac points, which are
their two-dimensional analogues, Weyl points are stable in the momentum space
and the associated surface states are predicted to be topologically
non-trivial. However, Weyl points are yet to be discovered in nature. Here, we
report photonic crystals, based on the double-gyroid structures, exhibiting
frequency-isolated Weyl points with intricate phase diagrams. The surface
states associated with the non-zero Chern numbers are demonstrated. Line nodes
are also found in similar geometries; the associated surface states are shown
to be flat bands. Our results are readily experimentally realizable at both
microwave and optical frequencies.
