Degenerate Modes Research Articles

In-Band Full-Duplex Filtering Antenna Arrays Using High-Order Mode Cavity Resonators

In this article, a series of narrowband and wideband in-band full-duplex (IBFD) filtering antenna arrays (FAAs) using cavity-based high-order modes are investigated. It is found that the pairs of degenerate high-order modes in a single cavity resonator, TM <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$_{1n0}$ </tex-math></inline-formula> and TM <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$_{n10}$ </tex-math></inline-formula> ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> is even), are suitable for the IBFD FAA designs due to their advantages: 1) in-phase and same amplitude for each magnetic loop, which helps to enhance the gain, and 2) the modal orthogonality, which guarantees the isolation and cross-polarization level between two channels. The higher order response can be achieved by cascading more high-order mode resonators with the required external quality factor ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q_{e}$ </tex-math></inline-formula> ) and coupling coefficient ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> ). For proof of concept, two types of full-duplex waveguide arrays are implemented and tested. First, a second-order IBFD FAA with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$6\times $ </tex-math></inline-formula> 5 elements, using a pair of degenerate modes TM610 and TM160, is designed with 1% overlapped 10-dB bandwidth and 18.4-dBi realized gain within the passband. The method to improve realized gain and isolation level without increasing any circuit volume is also presented. Second, a fifth-order IBFD FAA using TM410 and TM140 modes is implemented with an overlapped 10-dB bandwidth of 15.6% and a realized gain of 12.5 dBi. The measured isolation between the two channels is better than 40.4 dB. An excellent agreement between simulated and measured results verifies that the proposed design methodology is feasible for designing high-order mode IBFD FAA.

Study of Parallel-Plate Waveguides Bordered by Reactive Huygens Metasurfaces

Huygens metasurfaces (HMSs) are 2-D structures exhibiting both electric and magnetic responses. In this article, the properties of a parallel-plate waveguide (PPW) formed by two dispersive reactive HMSs are investigated analytically by deriving the dispersion relations for supported surface waves. In particular, the PPWs formed by nondispersive HMSs are studied thoroughly and it is shown that they can support a maximum of four modes with a variety of transverse electric (TE) and transverse magnetic (TM) degenerate modes, modes with the same cutoff frequencies, and modes with constant phase and group velocities. Such explored PPWs offer degenerate modes with orthogonal polarizations with potential applications in leaky wave antennas and holographs. Moreover, PPWs with either nondispersive or dispersive borders support modes with subluminal phase velocities which find applications in device miniaturization. The proposed analytical derivations are verified by full-wave numerical simulations.

Coherent Control of Topological States in an Integrated Waveguide Lattice.

Topological photonics holds the promise for enhanced robustness of light localization and propagation enabled by the global symmetries of the system. While traditional designs of topological structures rely on lattice symmetries, there is an alternative strategy based on accidentally degenerate modes of the individual meta-atoms. Using this concept, we experimentally realize topological edge state in an array of silicon nanostructured waveguides, each hosting a pair of degenerate modes at telecom wavelengths. Exploiting the hybrid nature of the topological mode, we implement its coherent control by adjusting the phase between the degenerate modes and demonstrating selective excitation of bulk or edge states. The resulting field distribution is imaged via third harmonic generation showing the localization of topological modes as a function of the relative phase of the excitations. Our results highlight the impact of engineered accidental degeneracies on the formation of topological phases, extending the opportunities stemming from topological nanophotonic systems.

Speckle-learned convolutional neural network for the recognition of intensity degenerate orbital angular momentum modes

Intensity degenerate orbital angular momentum (OAM) modes are impossible to recognize by direct visual inspection even using available machine learning techniques. We are reporting speckle-learned convolutional neural network (CNN) for the recognition of intensity degenerate Laguerre–Gaussian (LGp , l) modes, intensity degenerate LG superposition modes, and intensity degenerate perfect optical vortices. The CNN is trained on the simulated one-dimensional far-field intensity speckle patterns of the corresponding intensity degenerate OAM modes. The trained CNN recognizes intensity degenerate OAM modes with an accuracy >99 % . Speckle-learned CNNs are also capable of recognizing intensity degenerate OAM modes even under the presence of high Gaussian white noise and atmospheric turbulence with an accuracy >97 % .

Optical Modes in Elliptical Microcavities for Single-Photon Sources

A theory of optical modes in an elliptical microcavity has been developed using Mathieu functions in elliptical coordinates. A key difference from the circular case is the splitting of doubly degenerate modes. Split optical modes have been numerically calculated and their symmetry has been determined. A method has been proposed to choose the parameters of a cavity for a certain wavelength. The difference between the energies of optical modes in the cavity with metallic walls and in the dielectric cavity is no more than ~20%. The dispersion relations of optical modes show the possibility of degeneracy of modes with different symmetries, which allows the spectral and polarization filtering of radiation of single-photon sources and the fabrication of sources of multiply entangled states.

Vortex-frequency-comb generation assisted by PT -symmetric ring resonators

We study propagation of optical vortices (OVs) in coupled parity-time ($\mathcal{P}\mathcal{T}$) symmetric multimode fibers with equal gain and loss. We show that this system has two second-order exceptional points (EPs) of spectral branches confluence where the degenerate modes are odd and even Laguerre-Gaussian (LG) modes. We study the evolution of an arbitrary incoming superposition of LG modes with the same orbital index in such a coupler. We prove that if the loss parameter exceeds its value in the lowest-lying EP, in the limit of the large coupler's length the outcoming field tends to the same attractor state depicted on the orbital Poincar\'e sphere (PS) by the orbital ``black hole.'' We show that localization of such a ``black hole'' on the PS does not change with variations of loss parameter beyond its value at the lowest EP, which can be called the pinning of the orbital ``black hole.'' We also demonstrate that the fiber ring resonator based on such a coupler can generate an optical vortex frequency comb (FC) far from the EP. The mechanism of such generation is not connected with any nonlinearity in the system. We determine the coupler's parameters under which such generation is feasible. This property can be useful for optimizing fiber-based orbital angular momentum communications.

Trapped degenerate modes in an embedded-core flat circular plate

Vibrational energy trapping and environmental perturbations reduction are of growing interest in high-precision acoustic sensing applications, but combining these two features in a single structure imposes higher demands on conventional resonators. In this paper, we design an 'embedded-core' circular elastic resonator, of which mode shapes are characterized by cyclic symmetry, stable energy trapping, and modal degeneracy. An embedded inner plate consisting of material with a wave velocity lower than that of its outer plate can trap in-plane vibrations in a flat structure layout, while conventional mono-material substrate design always adopts plate thickness variations as a common configuration. A set of two-dimensional equations of motion of the plate, governing cyclic symmetric vibrations with two different circumferential order numbers nθ, is developed and derived via variational equations and modified trigonometric series expansion. It is found that the mode shapes for both torsional modes (nθ=0) and one of the degenerate modes (nθ=2), shows excellent trapping behavior, where the displacement amplitudes decay exponentially outside the inner-outer plate boundary, in agreement with the results of finite element analysis. In detailed analysis of the degenerate mode, appropriate modifications based on material combinations and geometric parameters of the embedded-core plate are proven to not only determine the modal eigenfrequencies, but enhance the acoustic energy trapping efficiency within the inner plate region, which provides effective guides for the optimal design of this unique resonator.

Self-chaotic microlasers for random bit generation

Semiconductor lasers with optical feedback can produce plentiful non-linear dynamics, including periodic and chaotic oscillations, which are usually applied to microwave signals and physical random number generation, respectively. Chaotic semiconductor lasers are especially successful in generating random numbers compared with pseudorandom numbers generated by a computing process. We report a self-chaotic microlaser based on the internal mode interaction of nearly degenerate modes. A special resonator is designed and demonstrated with the two modes’ frequency intervals on the order of GHz. These modes with strong mode beating result in chaos, and physical random bits are obtained from the laser output power at 10 Gb/s. Our proposals provide a novel scheme to generate laser chaos for high-speed random number generation.

Low-modal-crosstalk orthogonal combine reception for degenerate modes in IM/DD MDM transmission.

Weakly-coupled mode division multiplexing (MDM) techniques supporting intensity modulation and direct detection (IM/DD) transmission is a promising candidate to enhance the capacity of short-reach applications such as optical interconnections, in which low-modal-crosstalk mode multiplexers/demultiplexers (MMUX/MDEMUX) are highly desired. In this paper, we firstly propose an all-fiber low-modal-crosstalk orthogonal combine reception scheme for degenerate linearly-polarized (LP) modes, in which signals in both degenerate modes are firstly demultiplexed into the LP01 mode of single-mode fibers, and then are multiplexed into mutually orthogonal LP01 and LP11 modes of a two-mode fiber for simultaneous detection. Then a pair of 4-LP-mode MMUX/MDEMUX consisting of cascaded mode-selective couplers and orthogonal combiners are fabricated with side-polishing processing, which achieve low back-to-back modal crosstalk of lower than -18.51 dB and insertion loss of lower than 3.81 dB for all the 4 modes. Finally, a stable real-time 4 modes × 4λ × 10 Gb/s MDM-wavelength division multiplexing (WDM) transmission over 20-km few-mode fiber is experimentally demonstrated. The proposed scheme is scalable to support more modes and can pave the way to practical implementation of IM/DD MDM transmission applications.

Bandwidth-Enhanced Circularly Polarized Slot Antenna and Array Under Two Pairs of Degenerate Modes in a Single Resonant Cavity

A novel design concept of bandwidth-enhanced full-metal circularly polarized (CP) cavity-backed slot antenna and array based on two pairs of degenerate modes in a single cavity is proposed in this paper. Conventional CP antenna based on one pair of degenerate modes only has one axial-ratio (AR) minima and causes a narrow AR bandwidth. Two pairs of degenerate modes in a proposed multimode cavity resonator can initially produce two separate CP operating bands. Then, a pair of metal prisms is introduced to allocate the two bands in proximity to each other, thus obtaining a wide operating bandwidth with two AR minima. As the radiation slots are directly fed by the electric field of the cavity modes, 2 × 2 cross slots are placed on the top wall so as to comprise a CP array. As such, a very simple wideband CP antenna array is realized by virtue of a single multiple-mode resonator without needing extra power dividers. Finally, the 2 × 2 wideband CP antenna array is fabricated and measured. Measurement shows that the proposed antenna array can achieve 15% bandwidth, a peak gain of 11.8 dBic, and a peak total efficiency of 96%.

Reconfigurable Full-Metal Circularly-Polarized Cavity-Backed Slot Antenna and Array With Frequency and Polarization Agility

In this brief, reconfigurable circularly-polarized (CP) cavity-backed slot antenna (CBSA) and antenna array with frequency and polarization agility are proposed. Two degenerate modes TE101 and TE011 are respectively perturbed by the metal posts along y-axis (named as MP-1) and x-axis (named as MP-2), and independent frequency tuning is obtained. Then, two crossed slots are placed on the top wall to radiate the electromagnetic energy of TE101 and TE011 modes, respectively. In this context, circular polarization can be realized by setting different lengths of MP-1 and MP-2. Besides, reconfigurable polarization between left-hand and right-hand circular polarization can be realized by exchanging the lengths of MP-1 and MP-2. Meanwhile, reconfigurable operating frequency can be realized by simultaneously increasing or decreasing the lengths of MP-1 and MP-2. In addition, a reconfigurable <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$4{\times }4$ </tex-math></inline-formula> CP array without introducing power dividers and without increasing the number of tuning metal posts is further investigated. Finally, the reconfigurable <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$4{\times }4$ </tex-math></inline-formula> CP array is fabricated and tested. Reconfigurable frequency, reconfigurable polarization, high total efficiency, and stable radiation pattern are simultaneously obtained. Good agreement between measured and simulated results well validates the proposed design concept.

Spinful Topological Phases in Acoustic Crystals with Projective PT Symmetry.

For the classification of topological phases of matter, an important consideration is whether a system is spinless or spinful, as these two classes have distinct symmetry algebra that gives rise to fundamentally different topological phases. However, only recently has it been realized theoretically that in the presence of gauge symmetry, the algebraic structure of symmetries can be projectively represented, which possibly enables the switch between spinless and spinful topological phases. Here, we report the experimental demonstration of this idea by realizing spinful topological phases in "spinless" acoustic crystals with projective space-time inversion symmetry. In particular, we realize a one-dimensional topologically gapped phase characterized by a 2Z winding number, which features double-degenerate bands in the entire Brillouin zone and two pairs of degenerate topological boundary modes. Our Letter thus overcomes a fundamental constraint on topological phases by spin classes.

Additively Manufactured Dual Circularly Polarized Antennas With Bidirectional Same-Sense Radiation and Wide Bandwidth Characteristics

This communication presents two additively manufactured bidirectional circularly polarized (CP) antennas. Each antenna radiates the same-sense CP waves in opposite directions and has the capability of altering the CP state to either right-hand CP (RHCP) or left-hand CP (LHCP) by switching the feeding ports. They adopt the same scheme of combining a linearly polarized (LP) bidirectional source and two polarizers of the same type. Different polarizers, a single-slab dielectric polarizer (Ant 1) and a linearly tapered slot polarizer (Ant 2), are proposed and applied for them, respectively. The LP source adopts a circular waveguide-based structure. By altering the orthogonal degenerate modes in the waveguide, the CP states can be switched correspondingly. To validate the design ideas, prototypes of the two antennas are fabricated and tested. Experimental results show that the axial ratio bandwidth (ARBW) of Ant 1 and Ant 2 is 30.3% (4.9–6.66 GHz) and 17.9% (5.26–6.3 GHz), respectively. Within the ARBW, their gain is 8.4± 0.8 and 7.2± 1 dBic, respectively. These results demonstrate that both antennas exhibit the advantages of wide band, high gain, and ease of fabrication over the conventional designs.

A Modified-square Slot Antenna with Circular Polarization Characteristics for Military Band Applications

In this work, the design and performance of a circularly polarized (CP) antenna designed using characteristic modal analysis (CMA) for military band application is presented. The substrate used is single-sided glass-reinforced epoxy and the antenna dimensions are 37×37×1.6 mm 3 . The antenna is compact, low-profile, circular polarized having an ARBW of around 500 MHz (center frequency 4.6 GHz). A coplanar waveguide (CPW) fed monopole antenna is used for excitation of the modified-square slot antenna that incorporates quarter section of circular symmetrical patches on the four corners. A stub orthogonal to the CPW fed monopole capacitively tunes the low Q mode as identified by CMA technique to shift to a lower frequency to create degenerate modes in military band for circular polarization generation. The 3-dB AR bandwidth of the antenna is in the frequency range 4.43- 4.9 GHz and measured value of impedance bandwidth is 3.33 GHz. The fractional ARBW and impedance BW are 10.07 % and 61.6 % respectively. The peak antenna gain in the CP frequency band is 3.75 dBic. The proposed antenna exhibits good polarization purity, the minimum axial ratio is 1.38 at 4.6 GHz. The broad circular polarized antenna is suited for military applications covering the frequency range 4.43-4.9 GHz.

A closed clockwork theory: ℤ2 parity and more

We develop a new class of clockwork theories with an augmented structure of the near-neighbour interactions along a one-dimensional closed chain. Such a topology leads to new and attractive features in addition to generating light states with hierarchical couplings via the usual clockwork mechanism. For one, there emerges a ℤ2 symmetry under the exchange of fields resulting in a physical spectrum consisting of states, respectively even and odd under the exchange parity with a two-fold degeneracy at each level. The lightest odd particle, being absolutely stable, could be envisaged as a potential dark matter candidate. The theory can also be obtained as a deconstruction of a five-dimensional theory embedded in a geometry generated by a linear dilaton theory on a S1/ℤ2 orbifold with three equidistant 3-branes. Analogous to the discrete picture, the ℤ2 symmetry in the bulk theory necessitates the existence of a KK spectrum of even and odd states, with doubly degenerate modes at each KK level when subject to certain boundary conditions.

The effect of spin–orbit coupling on the physical and superconducting properties of the Ir-rich cubic Laves superconductors AIr[formula omitted] (A = Y, Lu, and Th)

We have examined the impact of spin–orbit coupling (SOC) in cubic Laves superconductors AIr2 (A = Y, Lu, and Th) by realizing ab initio pseudopotential calculations of their physical and electron–phonon interaction properties. The inclusion of SOC removes the degeneracy of the electronic states and moderately influences the elastic and mechanical properties of all the compounds investigated. A critical examination of the elastic and mechanical properties reveals that all the compounds studied are soft (ductile) because of significant metallic bonding. The SOC effect on the phonon and electron–phonon interaction properties depends on the type of A element. This coupling has little influence on the phonon properties of YIr2. However, differently from YIr2, three optical phonon branches of LuIr2 and ThIr2 originating from the triply degenerate zone-center T2u mode are significantly affected by the inclusion of SOC. Although the effect of SOC on the electron–phonon interaction properties changes with the type of A atom, the presence of this coupling improves the agreement with experiment for the superconducting transition temperatures of all the cubic Laves superconductors investigated.

Thermal-noise-resistant optomechanical entanglement via general dark-mode control

Quantum entanglement not only plays an important role in the study of the fundamentals of quantum theory, but also is considered as a crucial resource in quantum information science. The generation of macroscopic entanglement involving multiple optical and mechanical modes is a desired task in cavity optomechanics. However, the dark-mode effect is a critical obstacle against the generation of quantum entanglement in multimode optomechanical systems consisting of multiple degenerate or near-degenerate mechanical modes coupled to a common cavity mode. Here we propose an auxiliary-cavity-mode method to enhance optomechanical entanglement in a multimode optomechanical system by breaking the dark-mode effect. We find that the introduction of the auxiliary cavity mode not only assists the entanglement creation between the cavity mode and the mechanical modes, but also improves the immunity of the optomechanical entanglement to the thermal excitations by about three orders of magnitude. We also study the optomechanical entanglement in the network-coupled optomechanical system consisting of two mechanical modes and two cavity modes. By analyzing the correspondence between the optomechanical entanglement and the dark-mode effect, we find that optomechanical entanglement can be largely enhanced once the dark mode is broken. In addition, we study the mechanical entanglement and find that it is negligibly small. We also present some discussions on the experimental implementation with a microwave optomechanical setup, on the relationship between the dark-mode-breaking mechanism and the center-of-mass and relative coordinates, and on the explanation of the important role of the dark-mode breaking in the enhancement of optomechanical entanglement. Our results pave the way towards the preparation of entangled optomechanical networks and noise-resistant quantum resources.

Symmetry Breaking in an Experimental Annular Combustor Model With Deterministic Electroacoustic Feedback and Stochastic Forcing

AbstractIn this study, we use an annular combustor experimental model with electroacoustic feedback to investigate systematically the effect of stochastic forcing and nonuniform flame response distribution on azimuthal thermoacoustic modes. We break the symmetry of a nominally degenerate mode of azimuthal order m by imposing a nonzero 2m Fourier component of the flame gain, b2m, and of the time-delay, ε2m. Various orientations between the gain and the time-delay staging patterns are considered. In addition, stochastic forcing is introduced. First, all experiments are performed without noise, as well as at the maximum noise intensity. We observe that the mode nature that dominates in the presence of intense noise may be far from the one observed in noise-free conditions. To better understand the effect of noise in the presence of asymmetries, we repeat some of the experiments at various noise intensities. Although our results confirm that for the axisymmetric configuration and some asymmetric configurations pure spinning modes are never reached, we also observe some radically different behaviors. For a noise-free experiment leading to a purely standing mode, the introduction of a sufficient amount of noise can lead to beating. We also observe that, for a mode that is nearly standing in the absence of noise, an increase in the noise intensity leads to the predominance of mixed modes with a clearly favored spinning direction. We explain our experimental results with the aid of low-order models.

A Low-Cost SISL Differentially Fed Dual-Polarized Stacked Patch Antenna With Enhanced Common-Mode Suppression Using Characteristic Mode Analysis

A wideband differentially fed dual-polarized stacked patch antenna with high common-mode (CM) suppression is proposed in this article using the characteristic mode analysis (CMA) and the substrate integrated suspended line (SISL) technology. Based on the CMA, orthogonal slots are loaded within the stacked patch to enhance the directivity of the second-order degenerate modes and reallocate the resonating frequency of the fundamental degenerate modes. A crossed dipole is introduced within the driven patch to ensure polarization uniformity between the two paired degeneracies. The CM suppression level ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{S}_{\mathrm {CC}}11$ </tex-math></inline-formula> ) is enhanced from–10 to–1.30 dB within the frequency range of 4.0–7.0 GHz by embedding circular slots embedded within the stacked patch and controlling the slot radius. Measured results demonstrate a–10 dB differential impedance bandwidth of 28.4% (4.62–6.18 GHz) and high isolation of better than–39.5 dB between the differential ports. The antenna depicts stable measured radiation patterns with low cross-polarization (<–30 dB). The measured average antenna gain and efficiency are 9.55 dBi and 85.5% within the DM passband. In addition, a high <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{S}_{\mathrm {CC}}11$ </tex-math></inline-formula> better than–1.05 dB is measured within the desired DM band.

Global phase diagram of bound states in the continuum

Bound states in the continuum (BICs) in photonic-crystal slabs have been conventionally classified into three types: single-resonance parametric, symmetry-protected, and Friedrich–Wintgen BICs. Here, we show that the single-resonance parametric BICs come from the coupling between the guided resonance (GR) and Fabry–Perot (FP) modes, and the symmetry-protected BICs from the coupling between degenerate GR modes. Hence, the three types of BICs in photonic-crystal slabs can be classified by the three different Friedrich–Wintgen origins. Based on this universal classification, a global phase diagram of BICs can be obtained with each phase identified by the indices of the three different Friedrich–Wintgen-type BICs. When BICs are created or annihilated, a phase transition occurs and is experimentally observed, in which the FP modes play a significant role. Our work shows a clear physical picture on whether BICs exist and how sensitive they are to changes in the parameter space, and enables improvements in experiment design and applications.