Equivalent Waveguide Research Articles

Higher-order fractal transverse modes observed in microlasers

Two classes of higher-order, fractal spatial eigenmodes have been predicted computationally and observed experimentally in microlasers. The equatorial plane of a close-packed array of microspheres, lying on one mirror within a Fabry-Pérot resonator and immersed in the laser gain medium, acts as a refractive slit array in a plane transverse to the optical axis. Edge diffraction from the slit array generates the high spatial frequencies (>104 cm−1) required for the formation of high-order laser fractal modes, and fractal transverse modes are generated, amplified, and evolve within the active medium. With a quasi-rectangular (4-microsphere) aperture, the fundamental mode and several higher-order eigenmodes (m = 2,4,5) are observed in experiments, whereas only the m = 1,2 modes are observed experimentally for the higher-loss resonators defined by triangular (3-microsphere) apertures. The fundamental and 2nd-order modes (m = 1,2) for the 4-sphere aperture are calculated to have qualitatively similar intensity profiles and nearly degenerate resonant frequencies that differ by less than <0.1% of the free-spectral range (375 GHz) but exhibit even and odd parity, respectively. For all of the observed fractal modes, the fractal dimension (D) rises rapidly beyond the intracavity aperture array as a result of the high spatial frequencies introduced into the mode profile. Elsewhere, D varies gradually along the resonator axis and 2.2 < D < 2.5. Generating fractal laser modes in an equivalent optical waveguide is expected to allow the realization of new optical devices and imaging protocols based on the spatial frequencies and variable D values available.

Analysis and simulation of X-band high-power microwave generation based on T-shaped four-period slow-wave structure

In this study, a T-shaped, four-period resonant slow-wave structure is optimally designed, and its high-frequency performance is comprehensively analyzed in theory. By using the image theory, the T-shaped waveguide unit is transformed into an equivalent ridge waveguide configuration. The high-frequency characteristics of the equivalent ridge waveguide, such as resonant frequency and structure of the T-shaped waveguide are analyzed by using equivalent circuit theory. The analysis has confirmed that in the ridge waveguide, starting from the second-highest order mode, the frequency points of the even-order modes are very consistent with those of the T-shaped waveguide; however, the odd-order modes have no such corresponding mode in the T-shaped waveguide, for they do not fulfill the electric boundary conditions required by the image method. On this basis, a T-shaped four-period resonant slow-wave structure is constructed, and its dispersion characteristics are analyzed to determine the resonant modes and frequencies, as well as the range of mode synchronization voltages. Simulations are subsequently performed to validate the effectiveness of the relativistic extended interaction radiation source, which includes the novel T-shaped periodic resonant slow-wave structure. Advanced three-dimensional particle simulations, in conjunction with optimization techniques show that a high-power microwave output at a frequency of 9.8 GHz, is achieved, which can delivers an average power of 71.4 MW. This output is attained under the conditions of a 448 kV beam voltage, 400 A beam current, and a 0.4 T uniform axial magnetic field, with an electron efficiency reaching 39.8%. This structure, characterized by the T-shaped waveguide, is demonstrated to be capable of producing high-efficiency, high-power microwaves with fewer periods, presenting a compact and efficient solution for generating high-power microwaves in advanced scientific applications.

A Semi-Analytical Method for the S-Parameter Calculations of an N × M Multimode Interference Coupler

A semi-analytical method for the S-parameter calculations of an N×M multimode interference coupler (MMI coupler) is presented. The proposed semi-analytical method is based on the mode decomposition and utilizes an effective index method to approximate the channel waveguide using an equivalent slab waveguide whose modes are described by exact analytic expressions. In comparison to the commonly used beam propagation method (BPM) and finite difference time domain method, which require significant time and computational resources, the proposed method accelerates the design process of photonic integrated circuits and basic building blocks such as an MMI coupler. The simulation results obtained using the developed method and the BPM were compared and showed very similar outcomes for different topologies of the MMI coupler. The key advantage of the proposed semi-analytical method over other analytical models is its ability to accurately simulate MMI couplers with an arbitrary position and number of input and output waveguides. In addition, this method can be extended using the theory of local coupled modes by taking into account the reflections from the end face of the MMI box.

Quantifying bound and leaky states of resonant optical lattices by Rytov-equivalent homogeneous waveguides.

The properties of periodic optical lattices are generally investigated with rigorous numerical methods. For physical insight and understanding of the complex processes underlying observed spectra, simple analytical models are needed. Accordingly, we show that by applying full Rytov effective-medium formalisms, the bound and leaky states of resonant photonic lattices can be quantified with high precision. Thus, all key properties are embodied in Rytov-equivalent homogeneous waveguides. The symmetric effective-medium theory (EMT) model quantifies rigorously computed guided-mode resonance (GMR) reflectance loci defining the leaky states. The asymmetric EMT formula similarly quantifies the bound state in the continuum (BIC) loci. Even with the period and wavelength on similar scales, the analytical EMT refractive index solutions agree exactly with rigorous solutions. We apply the Rytov formulas to explain the resonant leaky band structure including appearance of GMR and BIC states as well as band transitions and band closure points. The wavenumbers of the equivalent waveguides represent the BIC embedded eigenvalues as quantified here.

Refractive index profile renormalization for a silicon waveguide bend

An index profile renormalization method is proposed to study the effective refraction index increase in a high-index contrast waveguide bend such as a silicon waveguide bend. This method transforms a waveguide bend to an equivalent straight waveguide (ESW). The simulation results show that the ESW method can calculate the effective refraction index increase in a three-dimensional (3D) bend, costing much less time than the traditional finite difference time domain method and the index profile renormalization (IPR) method developed for small radius cases. In addition, the field center shift is studied. The relationships are established between the effective refraction index increase and field center shift from the bend axis along the radial direction for estimations based on the approximated IPR method. These results can lead to great convenience in estimating the effective refraction index increase in 3D bend, which could be used in conditions requiring critical phase control.

Transformation-optics modeling of 3D-printed freeform waveguides.

Multi-photon lithography allows us to complement planar photonic integrated circuits (PIC) by in-situ 3D-printed freeform waveguide structures. However, design and optimization of such freeform waveguides using time-domain Maxwell's equations solvers often requires comparatively large computational volumes, within which the structure of interest only occupies a small fraction, thus leading to poor computational efficiency. In this paper, we present a solver-independent transformation-optics-(TO-) based technique that allows to greatly reduce the computational effort related to modeling of 3D freeform waveguides. The concept relies on transforming freeform waveguides with curved trajectories into equivalent waveguide structures with modified material properties but geometrically straight trajectories, that can be efficiently fit into rather small cuboid-shaped computational volumes. We demonstrate the viability of the technique and benchmark its performance using a series of different freeform waveguides, achieving a reduction of the simulation time by a factor of 3-6 with a significant potential for further improvement. We also fabricate and experimentally test the simulated waveguides by 3D-printing on a silicon photonic chip, and we find good agreement between the simulated and the measured transmission at λ = 1550 nm.

Mode Size Converter Based on Periodically Segmented Liquid Crystal Core Waveguide

We report the numerical and experimental study of a liquid crystal (LC) core periodically segmented waveguide (PSW) based mode size converter, fabricated on an ITO coated glass substrate. The effective index and mode size of the proposed device can be dynamically tuned by changing the applied voltage. The 5CB (4-cyano-4′-pentylbiphenyl) nematic LC has been used as the guiding layer, surrounded by the cladding of negative photoresist AZ15nXT. An equivalent waveguide model has been used to determine the waveguide characteristics, and we have shown that the effective index and mode size of the guided modes change with the duty cycle and the applied voltage. For a fixed duty cycle, we have experimentally demonstrated that the size of the fundamental mode can be tuned by the applied voltage. The advantage of using LC-PSW for mode size transformation is that the effective index and mode size in the fabricated waveguide can be varied by an externally applied electric field. It has also been experimentally demonstrated that the coupling efficiency between the LC-PSW and a single mode fiber can be maximized by appropriate choice of the applied voltage. The proposed mode size converter can be used in LC photonic lightwave circuits to couple the light between optical devices with maximum efficiency.

All-metallic high-efficiency generalized Pancharatnam–Berry phase metasurface with chiral meta-atoms

Abstract Metasurfaces based on the Pancharatnam–Berry (PB) phase have attracted significant attention in the domains of subwavelength optics and electromagnetics. Conventional theory predicts that the PB phase is exactly twice the rotation angle of the anisotropic meta-atoms. Differently, a recent advance has demonstrated that the generalized PB phase representing multiple times of the rotation angle could be obtained with high-fold rotational symmetry meta-atoms, but it suffers from the low cross-polarization conversion efficiency (the theoretical upper limit of 25%) that impedes its further applications, especially for meta-atoms with rotational symmetry ≥3. Here, we verify that the chiral meta-atoms with high-fold rotational symmetries could produce the generalized PB phase. Besides, the all-metallic configuration is utilized to design C2, C3, and C5 chiral catenary meta-atoms to improve their efficiency and bandwidth. The equivalent air waveguide with low loss between two adjacent meta-atoms is formed to analyse the higher performances of the all-metallic scheme for the realization of the generalized PB phase compared with the metal–insulator–metal and all-dielectric C3 meta-atoms. As a proof of concept, four metadevices including two spin-Hall metadevices and two holograms are experimentally demonstrated and their maximum efficiency could exceed 83% in simulation. This work could provide a high-efficiency platform for the study of the generalized PB phase in linear and nonlinear optics.

CPW-fed printed tapered slot antenna loaded by a wideband stacked artificial magnetic conductor with a progressed performance

AbstractA low profile printed slot antenna (PSA) backed by broadband stacked artificial magnetic conductor (AMC) is introduced in this study. First, a suggested PSA with the radiating tapered slots excited by coplanar-waveguide (CPW) is used to expand the bandwidth in the measured range of 9.05–10.95 GHz (S11 ≤ −10 dB). Then, the suggested stacked AMC surface as the ground plane of the antenna is inserted into the PSA to gain improved radiation efficiency. The realized result from the PSA with the 11 × 17 stacked AMC array exhibits −10 dB measured impedance bandwidth from 6.97 to 13.34 GHz (62.73%). The suggested PSA with AMC compared to the PSA without AMC exhibits a size reduction of 52%, enhanced bandwidth of almost 44%, and excellent impedance matching with uni-directional radiation patterns. The novel AMC unit cell is realized based on the recognized method of stacked elements. The stacked AMC design operates at 10.63 GHz with an AMC bandwidth of 8–12.84 GHz (45.8%) for X-band operation. Besides, by introducing a specific method based on the reflection results of the equivalent waveguide feed, the number of AMC unit cells is investigated to obtain an optimal AMC array. In this approach, an equivalent waveguide feed corresponding to the center operating frequency is considered to choose the number of AMC array reflector.

Leaky-Wave Antenna Arrays for Flexible Dual-Beam Switching

Two novel types of dual-beam switching leaky-wave antenna (LWA) arrays based on substrate-integrated waveguides (SIWs) are proposed. The two antenna arrays consist of five SIW LWAs that work on the fundamental wave and −1st spatial harmonic wave simultaneously, so the arrays can realize fixed-frequency or frequency controlled dual-beam switching properties. The LWAs in one of the arrays have the same equivalent waveguide width and different slot periods, defined as the asymmetric dual-beam switching (ADBS) array. The LWAs in the other array have the same slot period and different equivalent waveguide widths, which is defined as the hybrid dual-beam switching (HDBS) array. The open stopbands of the arrays are suppressed by a simple structure. Using voltage-driven radio frequency chip switches (CSW-RFs) to change the excitation port, the arrays can realize the function of dual-beam switching at a fixed frequency. The measured results show that the forward beam of the ADBS array can switch from 13° to 80° while its backward beam switches from −75° to −10°, and the forward beam of the HDBS array is fixed at 45° while its backward beam switches from −10° to −80° when working at 28 GHz. Furthermore, the LWAs themselves can realize frequency-controlled ADBS in each excitation state. Therefore, the proposed arrays exhibit excellent performance in flexible dual-beam switching, which can be used in millimeter-wave applications where fixed-frequency beam switching or frequency-controlled beam switching is required.

Electromagnetic absorption of copper fiber oriented composite using 3D printing

Electromagnetic wave (EMW) pollution negatively impacts information, equipment security, and the human body. However, neither powder phase absorbent nor ferrite fiber using traditional casting methodology cannot form electromagnetic superstructure to flexibly enhance EMW absorbing capacity. Thereby, ferrite fiber absorbent in well-oriented manner by 3D printing can be a feasible solution in EMW absorption due to its structural EMW anisotropy property. In this study, the influence of EMW superstructures using 3D-printed oriented copper fiber upon microwave reflectivity is investigated, and an equivalent waveguide attenuator model is proposed. First, an EMW-absorbing composite containing 6 wt% copper powder and 25 wt% copper slag is prepared. In copper slag cementitious composite, copper fiber (CF) and steel fiber (SF) are incorporated at 0.5 wt% separately. In each group, EMW-absorbing elements are manufactured through casting, laminar parallel printing, and cross printing. The superstructure anisotropy and EMW absorption performance are investigated through a network analyzer. The cross superstructure is outstanding in low-frequency absorption, while the parallel superstructure demonstrates desirable reflectivity at a high-frequency range. The copper fiber-reinforced element produced through crossed printing is determined as the optimized configuration, reaching a −20.43 dB reflectivity peak with an 11.79 GHz bandwidth. Lastly, an equivalent waveguide attenuator model is proposed to explain the superposition enhancement of the dielectric property, space impedance matching, and multiple scattering.

Radiation Characteristics of Cranial Leaky Lamb Waves.

We numerically and experimentally investigate the dispersion properties of leaky Lamb waves in the cranial bone. Cranial Lamb waves leak energy from the skull into the brain when propagating at speeds higher than the speed of sound in the surrounding fluid. The understanding of their radiation mechanism is significantly complicated by the geometric and mechanical characteristics of the cortical tables and the trabecular bone (diploë). Toward such understanding, we here analyze the sub-1.0 MHz radiation angle dispersion spectrum of porous bone phantoms and parietal bone geometries obtained from μ CT scans. Our numerical results show that, when diploic pores are physically modeled, leakage angles computed from time transient finite-element analyses correspond to those predicted by an equivalent three-layered fluid-loaded waveguide model. For the bone geometries analyzed, two main leaky branches are observed in the near-field dispersion spectrum: a fast wave radiated at small angles, which is related to the fastest fundamental Lamb mode supported by the cranial bone, and a slower wave radiated at larger angles. This observation is also confirmed by experimental tests carried out on an immersed parietal bone.

Experimentally realization of dual nonlinear dielectric resonance and electromagnetic characteristics of Manganese-doped ZnO NPs in X-Band

In this paper, the electromagnetic details of Manganese-doped Zinc Oxide (Mn–ZnO) nanoparticles (NPs) were measured using the waveguide measurement method in the frequency range 8–12.5 GHz. The evaluations have been utilized by the Nicolson-Ross-Weir method for electromagnetic properties such as permittivity and permeability. The results indicate, dual nonlinear dielectric resonance in X-band at 9.446 and 10.47 GHz. The equivalent circuit and simulated waveguide structure are inserted to explain and verify the dual dielectric resonance. Consequently, Inductance-Capacitance properties are detected by the obtained impedance regarding the reaction of the NPs to the electromagnetic waves and, the outgoing power for the simulated waveguide has a sharp drop at around the two main resonance domains. The evaluated magnetic susceptibility quantity affirms that the Mn–ZnO NPs act as ferro and paramagnetic material at less and above than 10.39 GHz.

Static Schwinger-Level Electric Field Nonlinearities and Their Significance to Photons and Photon Entanglement

In this work, we postulate that Schwinger’s threshold for a dynamic electric field intensity to induce spatial nonlinearity is a special case and, more generally, it is the threshold field for both static and dynamic electric fields. Fields of this magnitude induce negative-energy charges to adapt positive energy attributes; within an atom, they also support interstate energy transfers and intrastate chaotic mixing of time-varying fields. Nonlinearity-induced chaos forms the basis for the probabilistic nature of photon creation. Answers to physical problems at atomic and lower scales continuously evolve because chaotic-like electron movements change their configurations on a time scale of 10 zs. Within atoms, frequency mixing that creates an optical frequency field occurs in the nonlinear region surrounding the nucleus. On a probabilistic basis, a ring of vacuum charge can be induced that forms into an equivalent waveguide, which confines the energy as it travels permanently away from the atom. The propagating relativistically augmented fields losslessly induce charges that bind and protect the energy-carrying fields. The photon charge-field ensemble is a closed system and possesses all first-order photon properties, including zero rest mass and permanent stability. For near-neighbor photons traveling at a speed approaching c, we find a small constant force between them that is dependent upon their relative spin orientations. Our model shows that the radius of a photon is ≈10 am and that photon wavelength information is coded by energy.

Dual-Band Shared-Aperture High-Efficiency Reflectarray Antenna Based on Structure-Reuse Technique

A millimeter-wave dual-band shared-aperture high-efficiency reflectarray antenna (RA) based on the structure-reuse technique is proposed in this letter, which consists of two sets of elements with full 360° phase compensation ranges. The oblique dipole element excited by the substrate integrated waveguide (SIW) is employed for the lower frequency band. The equivalent metallic waveguide element with the unchanged periodic grid and transverse size is selected for the higher frequency band. To make full use of the radiating aperture and, then, improve the aperture efficiency of the dual-band RA, the SIW-fed dipole cells are used to replace a pair of symmetry walls of the metallic waveguide cell in the x -polarization direction. The measured gains of the proposed RA are 28.7 dBi with the aperture efficiency of 43.59% at 18 GHz and 35.8 dBi with the efficiency of 50.12% at 38 GHz. The simulated and measured results successfully validate the effectiveness of the proposed method in the design of a millimeter-wave dual-band shared-aperture RA.

Inverse design of a single-step-etched ultracompact silicon polarization rotator.

We propose and experimentally demonstrate a novel ultracompact silicon polarization rotator based on equivalent asymmetric waveguide cross section in only single-step etching procedure for densely integrated on-chip mode-division multiplexing system. In the conventional mode hybridization scheme, the asymmetric waveguide cross section is employed to excite the hybridized modes to realize high performance polarization rotator with compact footprint and high polarization extinction ratio. However, the fabrication complexity severely restricts the potential application of asymmetric waveguide cross section. We use inverse-designed photonic-crystal-like subwavelength structure to realize an equivalent asymmetric waveguide cross section, which can be fabricated in only single-step etching process. Besides, a theory-assisted inverse design method based on a manually-set initial pattern is employed to optimize the device to improve design efficiency and device perform. The fabricated device exhibited high performance with a compact footprint of only 1.2 × 7.2 µm2, high extinction ratio (> 19 dB) and low insertion loss (< 0.7 dB) from 1530 to 1590 nm.

Multifunctional beam steering via switchable negative refraction, self-collimation, and zero refraction effects in conventional and annular photonic crystals.

Negative refraction (NR), self-collimation (SC), and zero refraction (ZR) effects of photonic crystals play an important role in beam steering. In this work, we report a multifunctional beam steering concept in photonic crystals, i.e., integrating two or three of the NR, SC, and ZR effects together at the same frequency. We find the square-lattice dielectric ring photonic crystal is an ideal candidate to realize the switchable function of ZR-SC while the square-lattice dielectric ring photonic crystal is more suitable for realizing the ZR-SC, ZR-NR, and ZR-SC-NR functions. The photonic band theory and an equivalent waveguide model are employed to explain these switchable functions in conventional and annular photonic crystals.

A new formula for the optimum width of Substrate Integrated Waveguide

A new formula for calculating the optimum width of a Substrate Integrated Waveguide (SIW) corresponding to the first mode is presented in this paper. Finite Difference Frequency Domain (FDFD) method is applied to analyze the waveguide structure where geometrical parameters of the SIW are iteratively varied in order to minimize the gap between cutoff frequencies of SIW structure and that of an equivalent conventional rectangular waveguide. Adequate parameters are used to derive the new formula. To verify the accuracy of the new formula, several waveguides are designed and analyzed using the commercial software HFSS. The calculated propagation constants are compared with experimental measurements from literature, a very good conformity is obtained.

A Compact Wideband SIW Bandpass Filter with Wide Stopband and High Selectivity

A novel method to design a wideband substrate integrated waveguide (SIW) bandpass filter (BPF) with compact size, wide stopband and high selectivity is presented. In this method some unique electromagnetic band-gap (EBG) cells are periodically etched on the top layer of SIW to realize a wide passband propagating below the equivalent waveguide cutoff frequency. By changing the configuration of EBG cells, undesired harmonics in upper stopband can be suppressed and a wideband BPF with wide stopband can be obtained. By symmetrically loading two complementary split ring resonators (CSRRs) on the tapered gradient lines of the input/output ports, a transmission zero near the passband can be introduced, and it makes the frequency selectivity of upper sideband improve significantly. As a verification, a wideband SIW BPF with a 3.02 GHz absolute bandwidth (ABW) and a 64.7% fractional bandwidth (FBW) centered at 4.67 GHz is designed, simulated, manufactured, and measured. The results of the experiment and simulation are in good agreement.

A new design of substrate integrated waveguide diplexer using complementary split ring resonators

Design method for achieving the acceptable electrical responses (isolation and impedance matching) of a mixer in two-close frequency with substrate integrated waveguide (SIW) is presented. SIW diplexer with complementary split ring resonators and an open stub is proposed. The SIW loaded diplexer is operated below the cutoff frequency of the equivalent waveguide for SIW; therefore, the size of the structure is compacted. Input and output ports matching are realized in the light of open microstrip stub. The diplexer with optimum dimensions is designed and fabricated. The measurement results verified the design procedures. They also show that operation frequencies are very close together, and also the proposed structure is suitable for long term evolution frequency bands.