Zero-order Mode Research Articles

An analytical model for dispersion relation of parallel plate Waveguide with periodic metallic cylinder nails

Abstract In this letter, a novel analytical model for a parallel plate waveguide composed of periodic metallic cylinder nails is developped, which is especially effective for sparse nails at higher frequencies. Based on the proposed model, one can effectively and precisely derive the dispersion relation of parallel plate Waveguide with the periodic metallic cylinder nails.The waveguide is modeled as a transmission line with periodically loaded parallel impedances. These impedances correspond to the periodic metallic cylinder nails arranged in a plane perpendicular to the propagation direction. To solve for the parallel impedance, the mirror principle is employed to extend the periodic metallic cylinder nails into the full space. Subsequently, based on the current distribution on the metallic nails, Fourier transformation and Poisson summation techniques are utilized to express the radiated field in terms of multiple Floquet modes. The boundary condition for the metallic nails is then applied to derive the analytical expression for the parallel impedance. Simulation results strongly support the proposed theory. Notably, the transmission line theory stipulates that the zero-order free mode, or TEM wave, should dominate the waveguide with minimal high-order coupling along the propagation direction.Compared to existing methods that treat dense nails as three-dimensional homogenized materials, this study is more applicable to scenarios involving relatively sparse nails at higher frequencies.

Elastic spin angular momentum of zero-order flexural mode in thin rod system

The exploration of elastic wave behaviors in solid materials has revealed their intricate topological properties in recent years, particularly highlighting the significance of a previously underappreciated characteristic known as elastic spin angular momentum. This aspect plays a crucial role in the dynamics of elastic waves. Our research has focused on elucidating the theoretical aspects of elastic spin angular momentum, especially concerning the zero-order flexural mode in thin rod systems. Through meticulous theoretical analysis, we have deduced the nature of this angular momentum and successfully calculated the distribution of spin within these systems. The implications of our findings are substantial, as they contribute to an enhanced physical comprehension of the topological attributes associated with the flexural mode in thin rod structures, thereby offering new avenues for understanding material behaviors and their potential technological applications.

Experimental observation of parabolic wakes in thin plates

Wakes are medium perturbations created by a moving object, such as wave patterns behind boats, or wingtip vortices following an aircraft. Here, we report about an experimental study of an uncharted form of parabolic wakes occurring in media with the group velocity twice larger than the phase velocity, as opposed to the conventional case of Kelvin wakes. They are formed by moving a laser spot on a thin plate, which excites a unique wake pattern made of confocal parabolas, due to the quadratic dispersion of the zero-order flexural Lamb mode. If the spatial dimensions are rescaled by the perturbation velocity and material constant, we obtain a single universal wake with constant parabolic focal lengths. We demonstrate an evanescent regime above the critical frequency where the wave components oscillate exclusively in the direction parallel to the perturbation path, with an opening angle of 90∘. We define a dimensionless number, analogous to Froude and Mach numbers, which determines whether or not the complete parabolic wake pattern will be excited by the moving source. Finally, we generalize the physics of wake shapes to arbitrary dispersion relations. Published by the American Physical Society 2024

Imaging of annulus-formation interface using reverse time migration based on ultrasonic pitch-catch measurements: Case studies from an experimental well and a field well

Cased-hole logging using ultrasonic pitch-catch modality is a proven technique for cement bond evaluation in cased holes. However, complex measuring environments such as tool and casing eccentering makes it difficult to precisely separate and pick the third interface echoes from full ultrasonic Lamb waves, leading to ambiguous identification of annulus-formation interface. To overcome this problem, we propose an improved cased-hole reverse time migration approach for ultrasonic pitch-catch measurements to image the annulus-formation interface. The missing ultrasonic Lamb waveforms between far and near receivers due to insufficient spatial sampling are reconstructed based on the optimized theoretical phase velocity of zero-order anti-symmetric Lamb mode waves. Additionally, we apply the hybrid illumination imaging condition to mitigate the imaging noises around the true reflectors and sources. Data examples from a physical experimental well and a field well demonstrate that the proposed approach is an effective method for characterizing the annulus-formation interface without requiring precise knowledge of the velocity distribution in the region behind the casing. Furthermore, test on an experimental well has indicated that the method has the potential to detect the absence of cement in the annulus medium.

Enhanced Transmission at the Zeroth-Order Mode of a Terahertz Fabry-Perot Cavity.

A planar Fabry-Perot cavity with intermirror spacing of d ≪ λ is explored for its "zero-order mode" terahertz transmission. The enhanced transmission observed as d → 0 indicates that such cavities satisfy the resonance conditions across a broad terahertz bandwidth. The experimental signatures from this elusive, "technically challenging" regime are evidenced using time-domain terahertz spectroscopy and are complemented by numerical calculations. The results raise intriguing possibilities for terahertz field modulation and pave new paths for strong coupling of multiple transition frequencies simultaneously.

Topological vortex mode for flexural waves in pillared plates

Localized topological modes with high robustness to various perturbations are receiving increasing attention. Recently, zero-order topological vortex modes have been designed in phononic structures, in analogy with zero-energy fermionic states modulated by Jackiw-Rossi binding mechanism. Such localized modes may have potential applications for biosensing, bioimaging and on-chip communication. In this work, we propose a pillared phononic plate with a Kekulé distortion of pillars position to bind topological modes at a vortex core via dispersion engineering. The phase winding and amplitude diagrams of the topological vortex mode are observed experimentally. It is found that existence of vibration peaks and corresponding mode patterns are strongly robust against the random perturbation of resonant frequencies of pillars at the vortex core. We further design a topological resonant sensor for mass sensitivity. The frequency of the topological vortex mode is almost linearly sensitive to added small mass at the vortex core in terms of mass values and positions. The proposed pillared plates provide a platform for potential applications such as energy localization and harvesting, remote health monitoring.

Plastic-Rock Complexes as Hotspots for Microplastic Generation.

Discarded plastics and microplastics (MPs) in the environment are considered emerging contaminants and indicators of the Anthropocene epoch. This study reports the discovery of a new type of plastic material in the environment─plastic-rock complexes─formed when plastic debris irreversibly sorbs onto the parent rock after historical flooding events. These complexes consist of low-density polyethylene (LDPE) or polypropylene (PP) films stuck onto quartz-dominated mineral matrices. These plastic-rock complexes serve as hotspots for MP generation, as evidenced by laboratory wet-dry cycling tests. Over 1.03 × 108 and 1.28 × 108 items·m-2 MPs were generated in a zero-order mode from the LDPE- and PP-rock complexes, respectively, following 10 wet-dry cycles. The speed of MP generation was 4-5 orders of magnitude higher than that in landfills, 2-3 orders of magnitude higher than that in seawater, and >1 order of magnitude higher than that in marine sediment as compared with previously reported data. Results from this investigation provide strong direct evidence of anthropogenic waste entering geological cycles and inducing potential ecological risks that may be exacerbated by climate change conditions such as flooding events. Future research should evaluate this phenomenon regarding ecosystem fluxes, fate, and transport and impacts of plastic pollution.

A compact metamaterial SIW diplexer with transmission zeros

ABSTRACT A compact low-loss microstrip diplexer with four controllable transmission zeros (TZs), all less than 41 dB, is presented. The diplexer circuit consists of two coupled gap bandpass filters with a T-junction as a combining circuit. Channels’ filters metalize SIW resonators loaded with metamaterial cells operated at zeroth order mode for compactness and low loss operation. For each channel, a fractional bandwidth of 1.9% is obtained. Also, two TZs at both sides of the resonant frequency are obtained by mixed electric and magnetic coupling between channels’ resonators. Design methodology for filtering response and placing TZs at certain frequencies are discussed in detail. There is a good agreement between simulation and measurement with isolation better than 40 dB. Moreover, the diplexer has a small size of (1.1×1.43 λg 2 ). Lower and higher TZs are located at 4.75 and 5.69 GHz, for the lower channel, and at 5.4 GHz and 6.2 GHz for the higher channel, respectively.

Evolution of high-order Tamm plasmon modes with a metal-PhC cavity

We put forward the concept of high-order Tamm plasmon (TP) modes which are illustrated with a simple metal-Bragg mirror cavity. Results show series orders of TP modes are gradually generated through adjusting the thickness of the cavity, for which traditional TP modes only corresponds to the zero-order modes. The reflectance spectra and electric field distributions are compared to demonstrate the consistency of these series of TP modes. Meanwhile, the excitation intensity of different order TP modes are studied. Results show that the excitation intensity is related directly to the TP mode wavelength, and has no relation to the order number. These results might provide new ideas to the study of TP modes and guide the design and optimization of TP based devices.

Optimal slope angles of the air-coupled transducer from viewpoint of the effective Lamb waves propagation in different materials

Air-coupled transducers (ACT) allow for non-contact generation of acoustic waves which can be later transferred into elastic waves due to interactions with the solid specimen. Proper slope of the ACT in relation to the investigated specimen surface during acoustic waves generation is important as it leads to the possibility of generation of desired Lamb wave modes in the form of elastic waves with selected propagation velocity values. Effective generation of these modes ease the analysis of elastic waves propagation in specimens, simultaneously helping in detection of material defects if they exist. The attempt to determine optimal slope angles was undertaken in case of aluminum (Al), carbon fiber-reinforced polymer (CFRP) and glass fiber-reinforced polymer (GFRP) plate-like structure. Due to relatively low excitation frequency of the used ACT (40 kHz) the investigation was focused on the slope angles referred to the generation of zero-order modes - antisymmetric A0 and symmetric S0. In CFRP plate case the issue of efficient generation of shear horizontal (SH0) wave mode was additionally considered. In Al and CFRP plate case optimal slope angles were considered numerically (Comsol, Matlab) and experimentally (lab investigations, Matlab) while in GFRP plate case they were estimated experimentally. Although not all of the slope angles were successfully determined within different approaches, the results helped to form some interesting conclusions. After determination of the slope angles the performance of sloped/non-sloped ACT was compared in full wavefield measurements (comparison of signal energy maps calculated with the usage of root mean square (RMS) formula). Recommendations for further work were depicted within the summary section.

Analytical prediction for quasi-TE mode in silicon nanowire optical rectangular waveguide

Theoretical and numerical mode estimation performed on silicon nanowire optical rectangular waveguide (SNORW) is presented for on-chip communication in photonic integrated circuits. The propagation behavior of electric and magnetic field is investigated, where zeroth order mode is found dominating inside the nanoslot region of SNORW, for the circularly symmetric quasi-TE mode to propagate. This SNORW structure supports hybrid mode, which derives its behavioral root from the rectangular waveguide and functional root from the slot waveguide. In periodic silicon nanowire-based waveguide, it is found that the envelope of mode field intensity closely matches with rectangular waveguide, and the guiding properties closely match with slot waveguide. The type of mode is analyzed by full-vectorial finite element method (FEM) and the analytical expression is derived using effective index method. Analytical expressions are used to express Quasi-TE mode in terms of material profile and waveguide physical parameters. The results obtained for SNORW are in S, C and L wavelength bands and are compared with the earlier reported work on slot waveguide, and the field intensity obtained with the theoretical equations is also compared with that of FEM results.

A slender body theory for the motion of special Cosserat filaments in Stokes flow

The motion of filament-like structures in fluid media has been a topic of interest since long. In this regard, a well known slender body theory exists, wherein the fluid flow is assumed to be Stokesian while the filament is modeled as a Kirchhoff rod which can bend and twist but remains inextensible and unshearable. In this work, we relax the inextensibility and unshearability constraints on filaments, i.e., the filament is modeled as a special Cosserat rod. Starting with the boundary integral formulation of Stokes flow involving the filament’s surface velocity and fluid traction that acts on the filament surface, the method of matched asymptotic expansion is used to first obtain a leading-order representation of the boundary integral kernels in the filament’s aspect ratio. We then substitute Fourier series expansion (in filament’s circumferential coordinate) of both the filament’s surface velocity and fluid traction in the aforementioned leading-order representation and further linearize it in the rod’s shear strains to reduce the two-dimensional boundary integral over the filament surface into a line integral over the filament’s centerline. Upon further collecting the coefficients of sine and cosine terms, the zeroth-order Fourier mode yields a line integral equation relating the rod’s centerline velocity with the distributed fluid force that acts on the filament. The presence of line integral makes the relation non-local in nature. On the contrary, the first-order Fourier mode yields a simpler local relation between the rod’s angular velocity and the distributed fluid couple. The line integral equation is shown to reduce to the classical slender body theory when shear strains and axial strain are set to zero. The non-dimensional governing equations of the special Cosserat rod are also derived accounting for the distributed fluid force and distributed fluid couple in them which are solved to obtain the filament motion. The presented theory is demonstrated with an example problem of the tumbling of filaments in background shear flow. We show that for relatively shorter filaments where the effect of shear and axial stretch is more dominant, the obtained results deviate from the ones based on the classical slender body theory.

On the Influence of Certain Geometric Characteristics of the Resonator on the Impedance Determined by the Dean’s Method

This article considers the influence of the orifice arrangement in a cover of a cylindrical resonator on the impedance determined by the Dean’s method. A resonator with a small height and a low perforation degree is studied. This geometry provides different non-uniformity of the sound field at the resonator backing depending on the orifice arrangement in the resonator cover, while the number of orifices does not change. It is shown that, with different orifice arrangements, the impedance values determined by Dean’s method at high frequencies (3000 Hz and more) differ greatly. The authors propose the modification of Dean’s formula by using the amplitude coefficient of the zeroth order mode instead of the acoustic pressure at the resonator backing. The computations performed demonstrate that, in this case, the impedance does not depend on the orifice arrangement in the resonator cover. The computations consist of three stages: numerical simulation of the plane wave incidence onto the resonator (simulating a full-scale experiment); carrying out a modal analysis of the sound field at the resonator backing to extract the zeroth order mode; and determination of the resonator impedance according to the modified Dean’s formula.

A Broadband Antenna Based on a Single CRLH TL Unit Cell and a Parasitic Strip for Sub-1GHz DVB and LTE Applications

A Broadband and slim profile antenna based-on a single composite right/left-handed transmission line unit cell and parasitic shorted strip is presented for sub-1 GHz digital video broadcasting and long-term evolution applications (470-970 MHz). It is comprised of an ungrounded coplanar waveguide that feeds a meandered strip (distributed series inductors), which is connected through capacitive coupling (series capacitance) with a virtual small ground, while an upper shorted meandered strip represents a parallel inductor. A shorted meandered strip (parasitic inductor) is added to create a third resonant frequency. A broadband operation is achieved by merging three different resonant modes frequencies (zeroth-order mode and two quarter wavelength monopole modes) to satisfy 6 dB bandwidth criterion. A prototype is constructed and measured in order to verify the achieved results. The results of reflection parameter, gain, efficiency, patterns and bandwidth efficiency product are presented, discussed, and evaluated with respect to literature. The results show that the proposed antenna is a potential candidate for recent broadband digital video broadcasting applications.

Collinear acousto-optical filtration of polychromatic Bessel light beams in lithium niobate crystals

The features of collinear acousto - optical filtration of quasi - diffractive Bessel light beams of o- and e-type in uniaxial crystals are investigated. Using the method of overlap integrals, an expression is found for the diffraction efficiency depending on the parameters of the acousto-optical interaction, as well as on the values of the overlap integrals. It is shown that for the zero-order mode of a Bessel light beam for a lithium niobate crystal under conditions of transverse phase synchronism and in the optical spectrum range of 0.4-0.7 μm, the filter bandwidth of ∼0.2 nm is achievable; with an increase in the order of the mode m≥1, the increase in the bandwidth is insignificant and is ∼0.23 -0.24 nm.

Attenuation of Orbital Angular Momentum Beam Transmission With a Parabolic Antenna

In order to evaluate the transmission performance of orbital angular momentum (OAM) beams with a parabolic antenna, this letter investigates the attenuation of OAM beams reflected by the parabolic reflector. Specifically, the system structure and mathematical models of the OAM transmission with a parabolic antenna are established. According to the geometrical optics approximation and aperture field method, the electric field strength after the parabolic antenna is solved. In the case of the paraxial approximation, for the zero-order OAM mode, the receiving power is inversely proportional to the square of the transmission distance. However, for all the nonzero-order OAM modes, the receiving power is inversely proportional to the fourth power of the transmission distance. Compared with OAM beams generated by the traditional antenna array without the parabolic reflector, the receiving power can be improved greatly by the proposed structure with the parabolic reflector used for the OAM beam convergence. Especially for OAM beams with the high orders, the attenuation is no longer related to the OAM mode.

Simultaneous detection of complex refractive index and temperature using a compact side-coupled photonic crystal nanobeam cavity

In this paper, we theoretically propose a compact photonic crystal nanobeam cavity (PCNC) side coupled with a waveguide for sensing complex refractive index (CRI) and temperature ( T ). Two Fano resonances are achieved by coupling two discrete states (zeroth-order mode and first-order mode) in a PCNC and the continuous state in the waveguide with a partial transmitting element. The transmission expression is derived based on the temporal coupled-mode theory. By measuring the wavelength shifts and shape changes of two Fano resonances in the transmission spectrum, not only the real part of the refractive index (RRI) and the imaginary part of the refractive index (IRI) can be sensed simultaneously, but also the effect of T on CRI is considered. The sensitivities of RRI for zeroth-order mode and first-order mode are 152.7 nm/refractive index unit (RIU) and 183.7 nm/RIU, respectively. The sensitivities of IRI are − 461 / R I U and − 198 / R I U for zeroth-order mode and first-order mode, respectively. The T sensitivities for zeroth-order mode and first-order mode are 58.6 pm/K and 55.6 pm/K, respectively. The fringe visibility values of both modes are more than 0.5. The relationship between structural parameters and coupling effect is studied and the effect of T on detection accuracy is discussed. To the best of our knowledge, this is the first geometry to simultaneously sense CRI and T . Moreover, the total footprint of the device is only 11 × 1.45 × 0.22 ( l e n g t h × w i d t h × h e i g h t ) µ m 3 , which will contribute to the large-scale integrated sensor array on chip.

Mode characteristics of nested eccentric waveguides constructed by two cylindrical nanowires coated with graphene

A kind of nested eccentric waveguide constructed with two cylindrical nanowires coated with graphene was designed. The mode characteristics of this waveguide were studied using the multipole method. It was found that the three lowest modes (mode 0, mode 1 and mode 2) can be combined by the zero-order mode or/and the first-order modes of two single nanowires. Mode 0 has a higher figure of merit and the best performance among these modes within the parameter range of interest. The mode characteristics can be adjusted by changing the parameters of the waveguide. For example, the propagation length will be increased when the operating wavelength, the minimum spacing between the inner and outer cylinders, the inner cylinder radius and the Fermi energy are increased. However, when the outer cylinder radius, the dielectric constants of region I, or the dielectric constants of region III are increased, the opposite effect can be seen. These results are consistent with the results obtained using the finite element method (FEM). The waveguide structure designed in this paper is easy to fabricate and can be applied to the field of micro/nano sensing.

Numerical investigation of comb-like optical filters based on guided-mode resonances enabled in thick slab waveguide gratings

We numerically investigate innovative comb-like filters working in the telecommunication region based on guided-mode resonances in thick slab waveguide gratings, with emphasis on their resonant properties such as number of resonances, full width at half-maximum, and free spectral range. The slab waveguide gratings with various thicknesses and grating depths are designated and analyzed using a finite-difference time-domain method. Since the slab waveguide is much thicker than the wavelength of operation, a large number of resonances are obtained in the spectral region of interest. By adding an antireflection coating having thickness of quarter-wavelength on the back side of the waveguiding slab, we observe that a usual interference between the directly transmitted zero-order mode and the diffracted order generating the guided mode is eliminated. As a consequence, the sharp resonances and undisturbed comb-like spectra are achieved. The incident and polarization angles, and the surrounding medium’s refractive index influence on the resonant properties are also examined. The guided-mode resonance-based comb-like filters may find applications in optical clocks, optical spectroscopy, optical communications, and lasers. Our systematic investigation provides useful guidelines for designing grating-based frequency comb devices.

Wideband Circularly Polarized Microstrip Patch Antenna With Multimode Resonance

A novel wideband circularly polarized microstrip patch antenna (MPA) with multimode resonance is proposed in this letter. The TM1/2,0 mode, the zeroth-order mode, and the TM1,0 mode are excited by inserting the shorting pins underneath the driven patch and the parasitic patch. Therefore, a wide impedance bandwidth is achieved under triple-mode resonance. By sequentially rotating the triple-mode elements, a circularly polarized MPA is developed with a four-feed network. Additionally, four metallic side walls are employed to obtain desirable radiation performances. For demonstration, a prototype of the proposed antenna is fabricated and measured. The measured −10 dB impedance bandwidth is 96% (1.53–4.39 GHz) and 3 dB axial ratio bandwidth is 86% (1.74–4.36 GHz). Meanwhile, a low profile with the height of 0.037 λ 0 ( λ 0 is the wavelength in free space at the lowest operating frequency) is obtained. Such a wideband, low-profile, and circularly polarized antenna is very promising for modern wireless communication applications.