Odd Modes Research Articles

Metasurface for Engineering Superimposed Ince-Gaussian Beams.

Ince-Gaussian beams (IGBs) are the third complete family of exact and orthogonal solutions of the paraxial wave equation and have been applied in many fields ranging from particle trapping to quantum optics. IGBs play a very important role in optics as they represent the exact and continuous transition modes connecting Laguerre-Gaussian and Hermite-Gaussian beams. The method currently in use suffers from the high cost, complexity, and large volume of the optical system. The superposition of IGBs can generate complicated structured beams with multiple phase and polarization singularities. A metasurface approach is proposed to realizing various superpositions of IGBs without relying on a complicated optical setup. By superimposing IGBs with even and odd modes, multiple phase, and polarization singularities are observed in the resultant beams. The phase and polarization singularities are modulated by setting the initial phase in the design and controlling the incident linear polarization. The compactness of the developed metasurface devices and the unique properties of the generated beams have the potential to impact many practical applications such as particle manipulation, orbital angular momentum spectrum manipulation, and optical communications.

Tri-arm MIMO array antenna pair for mobile phone applications

Abstract An 8 × 8 tri-arm multiple-input multiple-output (MIMO) array using novel even–odd mode decouplers is presented. To decouple the directly connected driven ports on the tri-arm antenna pair, a T-shaped stub working as an even-mode decoupler and a narrow strip working as an odd-mode decoupler are elaborately introduced. Therefore, the even-mode and odd-mode impedances cross with the antenna input impedance, and a deep coupling zero is achieved at this cross frequency. Finally, the proposed 8 × 8 MIMO array was developed, fabricated, and measured for further performance verification. The measured results show that the proposed array can have a wide isolation bandwidth of 17.2 % with a compact size of 0.44λ 0 × 0.08λ 0 and zero clearance requirement on the ground plane. The diversity performances are also investigated with the measured worst envelope correlation coefficient less than 0.05.

Deformations of the Kerr-(A)dS near horizon geometry

We investigate deformations of the Kerr-(A)dS near horizon geometry and derive partial infinitesimal rigidity results for it. The proof comprises two parts. First, we follow the analysis of Jezierski and Kamiński (2013 Gen. Rel. Grav. 45 987–1004) to eliminate all but a finite number of Fourier modes of linear perturbations. In the second part, we give an argument using analyticity to prove that there are no odd Fourier modes.

A falling fluid droplet in an oscillating flow field

We examine the flow in and around a falling fluid droplet in a vertically oscillating flow. We assume axisymmetric Stokes flow, and for small deformations to the droplet, the governing equations can be linearized leading to an infinite system of linear ordinary differential equations. In this study, we have analytically solved the problem in the small-capillary limit. We note that the solution locally breaks down at the poles of the droplet. The drag and center of the mass were also obtained. In the case when only odd modes are present, the droplet shows three-dimensional axisymmetric heart-shaped solutions oscillating vertically in time. When only even modes are present, the droplet exhibits axisymmetric stretching and squeezing.

Spoof Surface Plasmon Polariton-Based Antenna and Array by Exciting Both Even- and Odd-Mode Resonances

Spoof Surface Plasmon Polariton-Based Antenna and Array by Exciting Both Even- and Odd-Mode Resonances

Low-Profile, Pattern-Reconfigurable, Electrically Small Antenna Based on Equivalent Even and Odd Modes

Low-Profile, Pattern-Reconfigurable, Electrically Small Antenna Based on Equivalent Even and Odd Modes

Wideband n-Way filtering power dividers with good isolation and arbitrary power ratios

This paper presents a n-way filtering power divider (FPD) with arbitrary power ratios and good in-band isolation using modified Luzzato power dividers. Three-line coupled lines are introduced at the output ports to improve the impedance matching and out-of-band rejection. And half-wavelength stepped-impedance transmission lines and resistors are used to form the entire isolation network. To explore the mechanism of the topology, the even–odd mode method is applied. To obtain a wide isolation bandwidth, two transmission zeros are introduced to widen the isolation by changing the values of resistors of the isolation networks. Finally, three FPDs with different splitting ways and power ratios are designed and fabricated. And the simulated and measured results agree well with each other.

Balanced Filtering Power Divider based on Odd-mode Hybrid Microstrip and Slotline Spoof Surface Plasmon Polaritons

In this paper, an ultra-wideband balanced filtering power divider (B-FPD) with high common mode (CM) suppression level is proposed. The B-FPD is designed based on the odd mode spoof surface plasmon polaritons (SSPPs), which are constructed by the hybrid folded microstrip and slotline (HFMS) structure. Firstly, the dispersion characteristic and electric field distribution of the HFMS SSPP unit cell are investigated, which can decrease the upper cut-off frequency for size reduction of nearly 50%. Next, an equal balanced power divider with low cut-off frequency is proposed based on the microstrip-to-slotline transition structure and slotline Y-junction. Then, the balanced power divider is used to excite the odd mode of HFMS SSPP structure. An equal B-FPD with center frequency of 4.0 GHz is implemented, and the 3-dB bandwidth covers 0.9 to 7.0 GHz. Finally, the B-FPD with advantages of high CM suppression level and compact size is fabricated and measured.

Dual‐polarised end‐fire antenna based on the high‐order mode of spoof surface plasmon polaritons

AbstractA planar antenna with dual‐linearly polarised end‐fire radiation is proposed. A tapered double‐sided symmetrical spoof surface plasmon polariton (SSPP) transmission line (TL) with tilted unit cells is proposed. The SSPP TL can operate in two types of first high‐order modes: the first high‐order even mode and the first high‐order odd mode. A two‐port feeding structure is designed to feed the SSPP TL. When the signal is fed from port 1, the energy travels through the substrate integrated waveguide and eventually excites the even mode on the SSPP TL, leading to vertically polarised radiation. Conversely, when the signal is input from port 2, the energy travels through the stripline‐to‐slotline transition and eventually excites the odd mode on the SSPP TL, generating horizontally polarised radiation. According to the measured results, a 54.6% overlapping bandwidth is obtained. The horizontal and the vertical polarisations achieve a maximum gain of 14.7 and 12.2 dBi, respectively.

Mode purity evaluation of high-power millimeter wave transmission line by 3-port directional coupler

In high-power millimeter wave systems, transmission lines based on the circular corrugated waveguide are widely used to realize efficient millimeter wave transmission. The mode purity is a very important parameter for the high-power millimeter wave transmission lines. The main mode in the corrugated waveguide is usually the LP01 mode, while the main spurious modes include the LP02 mode, the LP11 even mode, the LP11 odd mode, and so on. For the mode purity analysis, we designed a 3-port directional coupler, considering 3 major spurious modes. A calculation code was developed for the mode purity investigation. In addition, the error caused by ignoring the minor spurious modes was analyzed with some calculation examples. Finally, high-power experiments were carried out with a 105 GHz millimeter wave system. The mode purity was evaluated with the data measured by the 3-port directional coupler. The results indicated that the content of the main mode LP01 is up to 90.38%, which aligns with the parameters derived from the factory test results of 105 GHz high-power millimeter wave source. It shows that the 3-port directional coupler can be used as an optional method for mode purity estimation of the high-power millimeter wave systems.

Damping of liquid sloshing by floating balls

Sloshing in partially filled containers is a key phenomenon for the design of offshore structures such as liquefied natural gas carriers, floating production storage and offloading platforms, crude oil carriers, and floating liquefied natural gas vessels, due to large sloshing force acting on container's walls. Hence, violent sloshing motion needs to be mitigated for the safe operation of the floating structures. This study is focused on the experimental investigation of a sloshing damping device based on floating balls. The free-surface sloshing waves are generated in a rectangular tank filled with water, the free-surface of which is covered by a layer of floating balls. Three important sloshing regimes, namely, shallow, intermediate, and finite-water depth sloshing, are considered for investigation. Frequency responses of sloshing with and without balls are obtained to comprehend the effects of floating balls on damping of sloshing odd modes (first, third, fifth, and ninth modes). Further, physical processes enhancing damping mechanisms are also investigated in detail. It is found that the floating balls dampen shallow-water sloshing effectively. Different motions of the balls, ball–ball interactions, motions of ball–liquid interfaces, and liquid shear-flow motion between the tank wall and balls cause the dominant mechanism of energy dissipation.

Design of dual-mode dual-band filter based on multilayer groove gap waveguide

This paper presents a novel dual-mode dual-band filter (DBF) based on multilayer groove gap waveguide (GGW). Unlike other published planar GGW filters, the proposed filter achieves a vertically stacked duplicate topology by introducing a rectangular aperture in the common wall and traditional inductive irises on the same layer, with perfect central symmetry in the overall structure. This reduces machining difficulty while having a smaller size. By optimizing the dimensions of the coupling structure and rectangular cavities, dual-mode resonators (DMRs) including even mode and odd mode are used to accomplish dual-bandpass response. Additionally, an efficient transition is presented and applied to achieve a good impedance matching from rectangular waveguide (RW) to GGW. To better demonstrate, a multilayer DBF with working center frequencies of 67.9 and 69.8 GHz is designed, fabricated and measured. Good consistency can be observed between the simulation result and the measurement result.

Spurious response suppression in wideband bandpass filters using chirality

A simple chiral medium is used to enhance the response of a conventional microstrip coupled line bandpass filter (BPF). The approach is applicable to both narrowband and wideband BPFs using the presented chiral topology. The topology is based on an ultra-subwavelength planar chiral particle that is utilized in the interface between two slabs of substrate. More specifically the medium realizes the suppression of the second spurious response of the filter at a large bandwidth, which enables its practical application in wideband coupled-line based BPFs. The effect of the chiral particles on the substrate's effective permittivity and on the phase velocities of the even and odd mode of two coupled transmission lines on top of the substrate structure is explicitly used in the design of the filter. The methodology is applicable to any coupled-line BPF order. Two wideband microstrip coupled-line prototype filters are designed, fabricated, and measured, one involving a substrate without particles and one involving the chiral substrate. Measurement results are in good agreement with the simulations. The chiral medium based filter results in a wide fractional bandwidth (FBW) of 81% for a 1 GHz center frequency and a measured suppression level of −60 dB.

Higher order mode conversion induced by discontinuities in waveguides

In this paper, we provide a theoretical prediction about the likelihood of producing high-order modes using, as far as we know, the simplest mode converter. The mode converter is a simple discontinuous waveguide for which reflection and transmission have recently been reported. As a result of the scattering of the fundamental guided mode (TE0), we have found that the high-order mode excitation is highly dependent on the position of the discontinuity. On the one hand, we discovered that in the presence of a discontinuity in the propagation direction, only even modes (TE0 and TE2) are excited, skipping the odd mode (TE1). When a lateral shift is considered, however, both even and odd higher-order modes (TE1 and TE2) are generated. Furthermore, after some lateral shifting, we found that only the pure TE2 mode is propagated.

Mode conversion and separation in magneto-optical photonic crystal waveguide.

We present mode conversion in different magneto-optical photonic crystal (MOPC) waveguides. An odd-mode waveguide (OMW) and an even-mode waveguide (EMW) are designed by adjusting the geometric parameters of the waveguide. These waveguides are constructed by adding a layer of yttrium-iron-garnet (YIG) rods with opposing magnetic fields between an MOPC and an Al2O3 photonic crystal (PC). Due to the coupling effect caused by the middle layer of YIG rods, the OMW (or EMW) only supports an odd (or even) mode within a single-mode frequency range. Simulation results demonstrate that they can convert other modes into odd or even modes, and there is almost no power loss during the conversion. Most importantly, they are robust against backscattering from perfect electric conductors (PECs) and point defects. Based on these properties, we propose a device that can efficiently separate the odd and even modes into different ports. These results offer a novel approach to controlling the transmission modes of waveguides, which facilitates the interconnection of diverse topological magneto-optical waveguides.

A Novel Compact, Wideband Four-Way Wilkinson Power Divider With an Improved Isolation Topology

This letter describes a novel lumped element circuit topology for the Wilkinson power divider (WPD) with compact and wideband performance using the bandpass matching network. The design method is inspired by even and odd modes analysis techniques, and the odd-mode circuit has the same grade as the even-mode one by an improved isolation network. The design equations for the proposed WPD are derived by analyzing the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Z$</tex-math> </inline-formula> parameter and the widest frequency response is obtained. The power divider is fabricated based on the GaAs-integrated passive device (IPD) technology that features a compact size of 1.5 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times$</tex-math> </inline-formula> 1.7 mm, with a relative bandwidth of 66.7%, good isolation greater than 20 dB, insertion loss (IL) less than 1.3 dB, and return loss (RL) better than 12.3 dB over a range of 1.3–2.6 GHz.

Nonreciprocal topological mode conversion by encircling an exceptional point in dynamic waveguides.

The topology of exceptional points (EPs) has been revealed by taking stationary or dynamical encircling around them, which induces eigenstate exchange or chiral mode conversion. However, the conversions are usually reciprocal obeying restricted transmittances. Here we propose the concept of nonreciprocal encircling of EPs in a dynamic waveguide under complex modulation. The waveguide allows direction-dependent EPs in their quasienergy spectra due to different phase-matching conditions for opposite propagation direction. We design a closed loop that will encircle the EP in the backward direction but not in the forward direction. In this way, a nonreciprocal topological conversion is achieved as the forward transmittance from the even to odd mode significantly exceeds the backward transmittance from the odd to even mode. As a result, the forward propagation produces two modes with equal strength while the backward propagation leads to a specific mode regardless of the input. The structure is promising for making robust optical isolators.

Polarization-selective modulation of meandered-line metamaterials with graphene surface plasmonics

Periodic metal lines are the first kind of metamaterials, which typically exhibit plasmonic resonances to the normally incident waves polarized perpendicularly to them, i.e., transverse magnetic (TM) waves. Meandered lines can obtain resonances for both TM and transverse electric (TE) incidences and have found important applications in chirality and polarization conversion. Recently, several stimuli have been investigated to dynamically modulate the optical properties of periodic lines, which simultaneously tune both TE and TM resonances and show little polarization dependence. In this work, metal-graphene hybrid meandered-line metamaterials are designed for polarization-selective modulation at terahertz frequencies for the first time. The periodic lines meandered in S-shape resonate at 103 GHz for TE waves and at 195 and 320 GHz for TM waves, respectively. Graphene strips are patterned in pairs right at the bending corners along the polarization direction of TE waves, which produce even plasmonic dipole mode for TE incidence. In contrast, they are asymmetric with respect to the TM waves and generate odd coupling mode under TM incidence. These modes with various field concentrations exhibit considerable modulation difference to the graphene conductivity variation. As the graphene chemical potential sweeps, TE transmittance is modulated from 0.7 to 0.47 at 100 GHz, and TM transmittance is modulated just from 0.4 to 0.39 at 190 GHz and from 0.57 to 0.52 at 289 GHz, respectively. The corresponding modulation axial ratio is as large as 23 and 4.6 under a low bias from -1.2 to 1.2 V. This work paves a new way to control terahertz waves polarization-selectively.

Compact Microstrip Bandstop Filter for UWB Application

In this paper, a novel Ultra-Wideband (UWB) Bandstop Filter (BSF) with five Transmission Zeros (TZ) and three Transmission Poles (TP) is presented. This filter is designed with a new type of resonator. Validation of the proposed filter with the lumped model is also investigated. Further, the transmission line circuit model of the filter is proposed, and consequently even and odd mode impedance is calculated analytically. Furthermore, a compact size of 16.8 mm × 14.98 mm (0.2λg × 0.18λg) is achieved by employing folded stubs. The proposed filter offers an Ultra-wide bandwidth of 7.5 GHz (2.9 –10.4 GHz) with a rejection depth of greater than 20 dB over the entire stopband. Moreover, the upper and lower skirt factors of 70 dB per GHz are achieved. A prototype of the proposed UWB BSF is fabricated and measured. Simulated and measured results are in good agreement, which validates the proposed design.

Multimode and Reconfigurable Phase Shifter of Spoof Surface Plasmons

Traditional phase shifters are mainly focused on phase performance and rarely consider the phase shift between different electromagnetic (EM) modes, limiting their widespread applications. Spoof surface plasmon polaritons (SSPPs) support EM waves with strong field confinements, giving rise to the time delay of signals. Due to the flexible dispersion behaviors, SSPPs can be engineered at will by designing the plasmonic structure parameters. Benefitting from these characteristics, here we propose a multi-mode and reconfigurable SSPP phase shifter loaded with varactor diodes. By controlling the dispersion behaviors, phase differences between different SSPP modes can be realized, and the phase shift of each mode can be reconfigured. Experimental results show that the proposed SSPP phase shifter can achieve about 240°, 241°, and 340° phase shifts among the fundamental (even) modes, the high-order (odd) modes, and the fundamental and high-order modes, respectively, by switching the bias voltages applied to the varactors. Additionally, the proposed SSPP phase shifter has the capability to continuously tune the phase difference in each mode. Simulations and measurements have a good consistency. This work lays the groundwork for SSPP applications in large-scale integrated circuits and wireless communication systems and has a promising application in Terahertz circuits.