Bloch Wave Research Articles

Non-reciprocity in photonic crystal due to parity time symmetric defect state

In this article, defect state of photonic crystal regarding parity time known as PT-symmetric is explored thoroughly. For this purpose, transfer matrix technique in setting Bloch theorem is employed to characterize the dispersion relation regarding PT-symmetric defect state. The study uncovers the norteworthy wave phenomenon entitle “non-reciprocity” is exhibited. Moreover, an increasing the in-plane component of wavevector contributes two or more branches in the short wavelength boundary of the stop-band which is not observed in conventional structures. The reflectance of structure is conducted across the optical regime leads to minimum point that aligns with the wavelength of the eigen mode for wavevector value (kx = 0). These findings of research may have significant applications in various areas of photonics and optics likes filters, modern optical photonic cavity resonators and thermo-photovoltaic devices etc.

Two-dimensional altermagnets from high throughput computational screening: Symmetry requirements, chiral magnons, and spin-orbit effects

We present a high throughput computational search for altermagnetism in two-dimensional (2D) materials based on the Computational 2D Materials Database (C2DB). We start by showing that the symmetry requirements for altermagnetism in 2D are somewhat more strict compared to bulk materials and applying these yields a total of seven altermagnets in the C2DB. The collinear ground state in these monolayers is verified by spin spiral calculations using the generalized Bloch theorem. We focus on four d-wave altermagnetic materials belonging to the P21′/c′ magnetic space group—RuF4, VF4, AgF2, and OsF4. The first three of these are known experimentally as van der Waals bonded bulk materials and are likely to be exfoliable from their bulk parent compounds. We perform a detailed analysis of the electronic structure and non-relativistic spin splitting in k-space exemplified by RuF4. The magnon spectrum of RuF4 is calculated from the magnetic force theorem, and it is shown that the symmetries that enforce degenerate magnon bands in anti-ferromagnets are absent in altermagnets and give rise to the non-degenerate magnon spectrum. We then include spin–orbit effects and show that these will dominate the splitting of magnons in RuF4. Finally, we provide an example of i-wave altermagnetism in the 2H-phase of FeBr3.

Measure pseudoasymptotically Bloch periodic functions in the sense of Stepanov and applications

UDC 517.9 We focus on the measures of Stepanov-like pseudoasymptotically Bloch τ -periodicity and its applications. First, we define a new notion of measures of Stepanov-like pseudoasymptotically Bloch periodic functions and diccuss some of its fundamental properties. Then the obtained results are applied to investigate the existence and uniqueness of the measure Stepanov-like pseudoasymptotically Bloch periodic mild solutions to semilinear delay differential equation in Banach spaces. Finally, an application is presented to illustrate the efficiency of the results.

Controllable magnetic ground states in metal diiodide MI2 (M: Fe, Co, and Ni) monolayers by electric field

We investigated the controllable magnetic ground states of 1T metal diiodide MI2 (M: Fe, Co, and Ni) monolayers by applying the electric field. To do so, we utilized the generalized Bloch theorem within the density functional theory on the primitive unit cell to examine the appearance of three possible magnetic ground states, namely, ferromagnetic, spiral, and antiferromagnetic states from the specified spiral vector. We found that the ground state can be changed as the electric field increases but depends on the lattice parameter. In general, the spiral ground state exists as the electric field is taken into account, thus all these materials are prominent as multiferroics. Also, based on the competition between ferromagnetic and antiferromagnetic exchange interactions, we observed that for FeI2, the transition from the ferromagnetic exchange to the antiferromagnetic exchange happens as the electric field increases, while CoI2 and NiI2 tend to preserve their original exchange interaction. This implies that only the magnetic state in FeI2 sensitively depends on the electric field.

Performance optimization of Bloch surface wave based devices using an XGBoost machine learning model

Bloch surface wave (BSW) based photonic devices have attracted significant interest for bio-sensing, spectroscopy, and light manipulation applications due to their ability to confine light at dielectric interfaces. However, optimizing the geometry of BSW structures to achieve desired optical properties can be computationally expensive using conventional simulation methods for multi-parameter design spaces. In this work, we develop machine learning models based on the gradient boosting algorithm XGBoost to predict key optical characteristics of BSW devices and expedite the design process. Finite element method simulations are used to generate a dataset relating BSW structures’ excitation angle, sensitivity, and spectral response to their geometric parameters, including thickness, porosity, and surrounding refractive index. This dataset trains and validates different XGBoost regression models for photonic structure optimization. Our results demonstrate that a model utilizing deep decision trees achieves the highest predictive accuracy, with a mean absolute error of 0.09° in estimating the excitation angle for new structures. We apply this optimized model to uncover the thickness-porosity combinations, enabling a maximum sensitivity of 171-degree/RIU. This machine learning approach provides a powerful tool for the inverse design and performance enhancement of BSW photonic structures beyond the capabilities of conventional simulation-based optimization.

Towards the fast buckling load prediction of composite shells via Bloch wave based numerical vibration correlation technique

The buckling load revealing structural capacity bears significant value for the design of engineering composite shells, especially in the aerospace industry. Non-destructive methods are prevailing for critical buckling load prediction. However, the experimental costs and computational time for the analysis are unaffordable, especially for large-scale and complex shells. Despite the numerical vibration correlation technique (NVCT) and its modifications proposed for faster critical buckling load prediction, the efficiency requires further improvement. For composite shells with rotational periodicity, analyzing one substructure based on the Bloch wave method can be an alternate for the analysis of the entire shell. Since the NVCT comprises the linear buckling analysis and repeated frequency analyses, twofold acceleration can be performed. Thus, the Bloch wave based numerical vibration correlation technique (BW-NVCT) is proposed. Firstly, the formulations for the Bloch wave method and the NVCT are derived. As the curve of Bloch wave numbers and buckling loads is monotonous or principally comprise a single peak, the computations in the Bloch wave method to determine the minimum buckling load are further reduced. Then, the implementation of BW-NVCT is presented wherein the Bloch wave calculations are simplified compared with the Bloch wave buckling analysis method. Secondly, three types of composite shells including the Z33 composite cylindrical shell, the pressure vessel and the nozzle are analyzed by the proposed method. By applying Bloch boundary conditions to the substructure, the linear buckling loads, natural frequencies are in high accuracy with respect to results by finite element analyses directly. In addition, predicted critical buckling loads by the BW-NVCT are in excellent precision and most importantly, remarkable efficiency is achieved compared with both the NVCT and the dynamic explicit analysis. Results show that the proposed method can capture both global and local buckling modes, even when bend-twist coupling exists. It is concluded that the BW-NVCT is widely applicable for composite shells and is substantiated as an effective method for fast buckling load prediction.

Observation of an acoustic topological Euler insulator with meronic waves

Topological band theory has conventionally been concerned with the topology of bands around a single gap. Only recently non-Abelian topologies that thrive on involving multiple gaps were studied, unveiling a new horizon in topological physics beyond the conventional paradigm. Here, we report on the first experimental realization of a topological Euler insulator phase with unique meronic characterization in an acoustic metamaterial. We demonstrate that this topological phase has several nontrivial features: First, the system cannot be described by conventional topological band theory, but has a nontrivial Euler class that captures the unconventional geometry of the Bloch bands in the Brillouin zone. Second, we uncover in theory and probe in experiments a meronic configuration of the bulk Bloch states for the first time. Third, using a detailed symmetry analysis, we show that the topological Euler insulator evolves from a non-Abelian topological semimetal phase via. the annihilation of Dirac points in pairs in one of the band gaps. With these nontrivial properties, we establish concretely an unconventional bulk-edge correspondence which is confirmed by directly measuring the edge states via. pump-probe techniques. Our work thus unveils a nontrivial topological Euler insulator phase with a unique meronic pattern and paves the way as a platform for non-Abelian topological phenomena.

Temporal and spectral signatures of the interaction between ultrashort laser pulses and Bloch surface waves

The resonant excitation of Bloch Surface Waves (BSWs) in dielectric one-dimensional photonic crystals is becoming a realistic photonic solution for surface integration in many domains, from spectroscopy to local field management. Bringing BSWs to ultrafast and nonlinear regimes requires a deep knowledge of the effects that the photonic crystal dispersion and the resonant surface wave excitation have on the ultrashort laser pulses. We report on the experimental evidence of spectral and temporal modifications of the radiation leaving a planar one-dimensional photonic crystal after coupling to BSWs. In such a resonant condition, a characteristic long temporal tail is observed in the outgoing pulses. Observations are performed by employing both frequency-resolved optical gating and field cross-correlation techniques.

Quantum-Geometry-Induced Anomalous Hall Effect in Nonunitary Superconductors and Application to Sr_{2}RuO_{4}.

The polar Kerr effect and the closely related anomalous charge Hall effect are among the most distinguishing signatures of the superconducting state in Sr_{2}RuO_{4}, as well as in several other compounds. These effects are often thought to be derived from chiral superconducting pairing, and different mechanisms have been invoked for the explanation. However, the intrinsic mechanisms proposed previously often involve unrealistically strong interband Cooper pairing. We show in this Letter that, even without interband pairing, nonunitary superconducting states can support the intrinsic anomalous charge Hall effect, thanks to the quantum geometric properties of the Bloch electrons. The key here is to have a normal-state spin Hall effect, for which a nonzero spin-orbit coupling is essential. A finite charge Hall effect then naturally arises at the onset of a spin-polarized nonunitary superconducting pairing. It depends on both the spin polarization and the normal-state electron Berry curvature, the latter of which is the imaginary part of the quantum geometric tensor of the Bloch states. Applying our results to the weakly paired Sr_{2}RuO_{4} we conclude that, if the reported Kerr effect is of intrinsic origin, the superconducting state is most likely nonunitary and has odd parity. Our theory may be generalized to other superconductors that exhibit the polar Kerr effect.

Inheritance of the exciton geometric structure from Bloch electrons in two-dimensional layered semiconductors

Inheritance of the exciton geometric structure from Bloch electrons in two-dimensional layered semiconductors

Efficient second-harmonic generation of quasi-bound states in the continuum in lithium niobate thin film enhanced by Bloch surface waves

Abstract Nonlinear optics has generated a wide range of applications in the fields of optical communications, biomedicine, and materials science, with nonlinear conversion efficiency serving as a vital metric for its progress. However, the weak nonlinear response of materials, high optical loss, and inhomogeneous distribution of the light field hamper the improvement of the conversion efficiency. We present a composite grating waveguide structure integrated into a Bragg reflector platform. This design achieves high Q in the spectral range by exploiting the unique properties exhibited by the bound states in the Bloch surface wave-enhanced continuum, and efficient second-harmonic generation by close-field amplification with the optical field tightly localized in a nonlinear material. By manipulating the symmetry of the grating, a precise tune over the near field within a designated wavelength range can be achieved. Specifically, we select a photonic crystal configuration supporting surface waves, employing TE polarization conditions and an asymmetry factor of −0.1 between the composite gratings. This configuration resonates at a fundamental wavelength of 783.5 nm, exhibiting an impressive Q-factor of 106. Notably, at an incident light intensity of 1.33 GW/cm2, we achieve a normalized electric field strength of up to 940 at the fundamental frequency and a second-harmonic conversion efficiency of up to 6 × 10−3, significantly amplifying the second-harmonic response. The proposed configuration in this investigation has the potential to be integrated into the field of nonlinear optics for sensing frequency conversion applications.

Sensing of volatile organic compounds using one-dimensional photonic crystal Bloch surface waves and internal optical modes

Bloch surface wave (BSW) and internal optical modes (IOMs) of one-dimensional photonic crystals (1DPhCs) have been explored for sensing purposes in the photonic crystal coupled reflectance (PCCR) geometry using the Kretschmann-Raether (KR) prism-coupling configuration. 1DPhCs coated with polyvinyl alcohol (PVA) thin films of two distinct thicknesses: 18 nm (referred to as PhC18) and 24 nm (referred to as PhC24) were fabricated. The response of the PCCR to the changes occurring in the PVA coated 1DPhC structures were studied by spraying volatile organic compounds, 1-propanol and 2-propanol onto the surface of the 1DPhCs. The BSWs excited under TE polarization are found to be very sensitive to perturbations at the 1DPhC interface. 1-propanol displays larger wavelength shifts and longer recovery times of the 1DPhC modes than 2-propanol because of its lower vapor pressure and higher reactivity to PVA.

Electromagnetically induced transparency and quantum enhancement of transmission via dressed bloch photons in an array of three-level Λ-type atoms.

We investigate the interactions between an array of three-level atoms and two photon fields with distinct frequencies employing quantum electrodynamics (QED). The control beam, as expected, has a considerably higher intensity than the probe beam, and the probe photon's eigenstate notably then appears as a distinctive dressed Bloch wave. We calculate the dispersion relation and quantum amplitude of the probe photons for their transmission. At positions predicting electromagnetically induced transparency (EIT) phenomena, we unveil remarkable enhancements in the transmission of the probe beam. Crucially, these enhancements are intricately linked to the unique characteristics of the dressed Bloch wave eigenstate. Moreover, we demonstrate that modulating frequency and intensity of the control beam and the lattice constant would further tune these enhancements. Our study highlights the crucial role of the dressed Bloch wave eigenstate in substantially amplifying targeted light beams, thereby significantly enhancing the detection sensitivity for minute electromagnetic signals and emphasizing its pivotal role in unveiling intriguing phenomena.

Solvable non-Hermitian skin effects and real-space exceptional points: non-Hermitian generalized Bloch theorem

Non-Hermitian systems can exhibit extraordinary boundary behaviors, known as the non-Hermitian skin effects, where all the eigenstates are localized exponentially at one side of lattice model. To give a full understanding and control of non-Hermitian skin effects, we have developed the non-Hermitian generalized Bloch theorem to provide the analytical expression for all solvable eigenvalues and eigenstates, in which translation symmetry is broken due to the open boundary condition. By introducing the Vieta’s theorem for any polynomial equation with arbitrary degree, our approach is widely applicable for one-dimensional non-Hermitian tight-binding models. With the non-Hermitian generalized Bloch theorem, we can analyze the condition of existence or non-existence of the non-Hermitian skin effects at a mathematically rigorous level. Additionally, the non-Hermitian generalized Bloch theorem allows us to explore the real-space exceptional points. We also establish the connection between our approach and the generalized Brillouin zone method. To illustrate our main results, we examine two concrete examples including the Su–Schrieffer–Heeger chain model with long-range couplings, and the ladder model with non-reciprocal interaction. Our non-Hermitian generalized Bloch theorem provides an efficient way to analytically study various non-Hermitian phenomena in more general cases.

Orbital Magneto-Nonlinear Anomalous Hall Effect in Kagome Magnet Fe_{3}Sn_{2}.

It has been theoretically predicted that perturbation of the Berry curvature by electromagnetic fields gives rise to intrinsic nonlinear anomalous Hall effects that are independent of scattering. Two types of nonlinear anomalous Hall effects are expected. The electric nonlinear Hall effect has recently begun to receive attention, while very few studies are concerned with the magneto-nonlinear Hall effect. Here, we combine experiment and first-principles calculations to show that the kagome ferromagnet Fe_{3}Sn_{2} displays such a magneto-nonlinear Hall effect. By systematic field angular and temperature-dependent transport measurements, we unambiguously identify a large anomalous Hall current that is linear in both applied in-plane electric and magnetic fields, utilizing a unique in-plane configuration. We clarify its dominant orbital origin and connect it to the magneto-nonlinear Hall effect. The effect is governed by the intrinsic quantum geometric properties of Bloch electrons. Our results demonstrate the significance of the quantum geometry of electron wave functions from the orbital degree of freedom and open up a new direction in Hall transport effects.

Energy spectrum theory of incommensurate systems

ABSTRACT Because of the lack of translational symmetry, calculating the energy spectrum of an incommensurate system has always been a theoretical challenge. Here, we propose a natural approach to generalize energy band theory to incommensurate systems without reliance on the commensurate approximation, thus providing a comprehensive energy spectrum theory of incommensurate systems. Except for a truncation-dependent weighting factor, the formulae of this theory are formally almost identical to that of Bloch electrons, making it particularly suitable for complex incommensurate structures. To illustrate the application of this theory, we give three typical examples: one-dimensional bichromatic and trichromatic incommensurate potential models, as well as a moiré quasicrystal. Our theory establishes a fundamental framework for understanding incommensurate systems.

Quantifying the photocurrent fluctuation in quantum materials by shot noise

The DC photocurrent can detect the topology and geometry of quantum materials without inversion symmetry. Herein, we propose that the DC shot noise (DSN), as the fluctuation of photocurrent operator, can also be a diagnostic of quantum materials. Particularly, we develop the quantum theory for DSNs in gapped systems and identify the shift and injection DSNs by dividing the second-order photocurrent operator into off-diagonal and diagonal contributions, respectively. Remarkably, we find that the DSNs can not be forbidden by inversion symmetry, while the constraint from time-reversal symmetry depends on the polarization of light. Furthermore, we show that the DSNs also encode the geometrical information of Bloch electrons, such as the Berry curvature and the quantum metric. Finally, guided by symmetry, we apply our theory to evaluate the DSNs in monolayer GeS and bilayer MoS2 with and without inversion symmetry and find that the DSNs can be larger in centrosymmetric phase.

Propagation characteristics of elastic longitudinal wave in a piezoelectric semiconductor metamaterial rod and its tuning

Elastic metamaterial structures have many distinct wave properties such as band gap structure and topological phase inversion. The coexistence and interaction of piezoelectricity and semiconductor behavior in piezoelectric semiconductor (PS) materials endow metamaterials with some new physical effects. We investigate the propagation characteristics of elastic longitudinal waves in a metamaterial rod made of n-type PS material and piezoelectric (PE) dielectric material. Based on one-dimensional rod model, we present the transfer matrixes for the PS and PE phases as well as the interfacial transfer matrix of unit cell. The analytical dispersion relations of the considered PS-PE metamaterial rod are obtained by utilizing Bloch's theorem. Numerical results show that band gap structures of the metamaterial rod are dependent on the initial electron concentration, length ratio of PE phase, interfacial condition, and capacitor connected with the PE phase. The selection of certain initial electron concentration, length ratio of PE phase, and capacitor can lead to the appearance of topological phase inversion, highlighting the potential for controlling and manipulating the wave propagation properties of PS metamaterial structures. This paper provides a theoretical guidance on the development of smart devices based on PS metamaterial structures. The novel combination of piezoelectricity and semiconductor behavior in these materials opens up new avenues for designing and engineering advanced devices with tailored wave properties and functionalities.

Pseudo-spin polarized one-way elastic wave eigenstates in one-dimensional phononic superlattices

We use a one-dimensional discrete binary elastic superlattice bridging continuous models of superlattices that showcase one-way propagation character and the discrete elastic Su-Schrieffer-Heeger model that does not. By considering Bloch wave solutions of the superlattice wave equation, we demonstrate conditions supporting elastic eigenmodes that do not satisfy translational invariance of Bloch waves over the entire Brillouin zone, unless their amplitude vanishes for some wave number. These modes are characterized by a pseudo-spin, and occur only on one side of the Brillouin zone for given spin, leading to spin-selective one-way wave propagation. We demonstrate how these features result from the interplay of translational invariance of Bloch waves, pseudo-spin, and a Fabry-Pérot resonance condition in the superlattice unit cell.

Bridging the gap between annular and can-annular acoustic spectra.

In the literature on thermoacoustic instabilities in combustors, a distinction is typically made between annular and can-annular systems because these are the most common gas turbine architectures. In reality, however, annular combustors typically feature discretely symmetric elements, such as burner tubes, and can-annular combustors feature an azimuthally symmetric plenum at the turbine inlet. To better understand the general case in between the annular and can-annular extremes, we analyze the acoustic spectrum of an idealized can-annular combustion chamber with variable geometry, where the length of the axial gap distance beyond the ends of the cans-hence, the coupling strength-may be adjusted. For small gap sizes, the geometry approaches a set of isolated combustor cans, whereas for large gap sizes, it approaches that of pure annular systems. We present two theoretical models based on Bloch wave theory and validate them against finite-element simulations of the Helmholtz equation. We demonstrate that the azimuthal modes transform into the eigenmodes of an annular chamber as the gap is fully opened, and we show that below a certain frequency, all the modes in between the can-annular and annular limits can be classified by their axial and azimuthal mode orders.