Stepped Waveguide Research Articles

The novel impedance matching device realized by the structure of air-gap ring based on the doping method at microwave frequency

The doping method enabled the epsilon-near-zero (ENZ) medium to adjust its permeability effectively. In this study, we theoretically analyze that the gap ring structure formed by the ENZ medium doped with perfect electrical conductor (PEC) can be equivalent to the controllable series reactance. Based on this concept, a universal matching network that can match any complex impedance load by adjusting the gap ring spacing is constructed. We used the above universal matching network to carry out theoretical and simulation calculations on the matching effect of a random-sized stepped waveguide and horn antenna, and the results show that the impedance-matching technology has a good matching effect for different loads. Finally, experimental verification is carried out. Compared with traditional impedance-matching networks, the proposed structure has the characteristics of simplicity, reliability, low loss, high carrying power, low preparation requirements, and good application prospects. This work is a good example of the practicality of ENZ media and also provides a very meaningful idea for the development of new electromagnetic matching devices.

A Sub-THz Waveguide Magic-T With Coplanar Ports for Power Combination Applications

In this article, a compact waveguide magic-T (WMT) with four coplanar ports is presented for sub-THz power combination applications. In the WMT, simple and robust geometries, i.e. trapezoidal irises, cuboid-shaped ridge, and waveguide step, are employed to ease manufacturing difficulties at sub-THz frequencies. Thereinto, the trapezoidal irises replace the traditional multiple steps or long chamfers to simplify the waveguide transformer and shorten the path, the waveguide step widens the available bandwidth, and the cuboid-shaped ridge reduces the difference-port reflection and acts as a coupling probe for the sum-port to improve isolation. Moreover, a bed of nails is applied to the waveguide splitting-plane for electromagnetic (EM) leakage suppression and assembly convenience. To verify this WMT, a WR-4 band (170-260 GHz) prototype is fabricated and measured, showing an average combination efficiency of 92.2% within 175-255 GHz (37.2%-bandwidth). Then, the WMT is applied to a two-way combined solid-state power amplifier (SSPA) module. Thereinto, a contactless E-plane waveguide transition with unprecedented L-shaped chock grooves (LSCGs) is presented for waveguide system interconnection. In power measurement, the power combined module produces a maximum power output of 76.6-mW @ 216-GHz.

Three-dimensional acoustic asymmetric focusing by mode-conversion structure

Acoustic asymmetric focusing (AAF) has attracted widespread attention owing to its great potential in medical ultrasound. The recent development of acoustic metamaterials and metasurfaces has provided various concepts to achieve AAF systems. Generally, the previously demonstrated AAF lenses were limited to one-dimensional structures, leading to difficulties in practical applications. The realization of AAF in three-dimensional (3D) space based on a two-dimensional (2D) device still remains a challenge. Here, we experimentally and numerically study a 2D AAF lens based on mode converters composed of two pairs of phased unit cells I and II and a step waveguide. Based on the phase profile of sound focusing and the step waveguide of mode converters, we experimentally design and demonstrate a type of 2D AAF lens and observe acoustic focusing and asymmetric transmission simultaneously in 3D space under the excitation of the zero-order wave. Both the phenomena arise from the phase modulation of the lens and the cutoff frequency of the first-order wave for the step waveguide, respectively. The fractional bandwidth (the ratio of the bandwidth to the center frequency) of the lens can reach about 0.14. The proposed 2D AAF lens, as well as its associated mode converter, paves the way for the asymmetric manipulation of sound in 3D space that has potential applications in practical sound devices.

METHODS OF CONTROLLING BOUNDARY TRANSPARENCY IN NON-HOMOGENOUS ELASTIC WAVEGUIDES

The work is devoted to the development of methods for controlling the efficiency of energy transfer in a composite elastic waveguide. Based on the analysis of the scattered field at the boundary of the stepped waveguide, formed by the rigid contact of two half-layers with the same mechanical characteristics, but with the different thicknesses, the main factors that affect the transparency of the interface were established. Harmonic oscillations generated by the first normal wave propagating from infinity in the narrower half-layer were considered. Mathematical difficulties of the posed boundary problem are due to the presence of a local singularity in the stresses at the point of change of the boundary conditions at the boundary of the two hemispheres. The solution is built by the superposition method, which allows taking into account the local singularity due to the asymptotic features of the unknowns. The quality criterion of the obtained solution was the control of the accuracy of the fulfillment of the conjugation conditions at the boundary of the two half-layers. The main attention in the work is focused on establishing the conditions for changing the transparency of the boundary depending on the frequencies, the symmetry of the oscillations, and the ratio of the half-layer widths. It was shown in the work that for both symmetric and antisymmetric oscillations of a stepped waveguide, there are frequency ranges in which the transparency of the boundary changes significantly. For both types of symmetry, in the frequency range up to the critical frequency for the third propagating normal wave, there are two frequency ranges in which the transparency of the boundary increases rather sharply. The frequencies at which local energy maxima are observed in the reflected field are different for symmetric and anti-symmetric oscillations. For symmetric oscillations, the first energy maximum in the reflected field is observed at the frequency when only one wave can propagate in both half-layers. This effect is due to the increase in the role of inhomogeneous waves in the transmitted field. The second energy maximum in the reflected field is due to the transformation of the energy of the incident wave into propagating waves of higher orders. In the case of antisymmetric oscillations, both maxima are due to the energy features of propagating waves of higher orders. The quality of energy resonance in the reflected field depends significantly on the symmetry of the oscillations. The established features of the scattered field make it possible to develop recommendations for controlling the transparency of the boundary in a stepped waveguide.

An X-band compact rectangular waveguide TE10-circular waveguide TE01 mode converter

This paper proposed an X-band compact efficient rectangular waveguide TE10-circular waveguide TE01 mode converter and conducted its structure design, theoretical analysis, numerical simulation, and experimental research. This mode converter is composed of a rectangular waveguide TE10–TE20 mode converter and a rectangular waveguide TE20-circular waveguide TE01 mode converter. In the design of the rectangular waveguide TE20-circular waveguide TE01 mode converter, a rectangular waveguide step is used to counteract the microwave reflection due to the discontinuity of the rectangular–circular waveguide connection, and two choke slots are involved to suppress the TE21 mode in the circular waveguide by cutting off the axial component of its surface current on the waveguide wall, so as to improve the TE01 mode conversion efficiency. The simulation results show that the reflection coefficient of the mode converter is less than 5% and the TE01 mode conversion efficiency is about 98.4% at the operation frequency of 9.3 GHz. The bandwidth with a transmission coefficient greater than 98% is about 200 MHz. The back-to-back experimental system is demonstrated, and the experimental results show that the measured TE01 mode conversion efficiency is about 98.2%, which is consistent with the simulation result.

Wideband and low‐loss transition from low‐temperature co‐fired ceramic laminated waveguide to subminiature coaxial connector for millimetre‐wave applications

This letter presents a novel transition scheme from laminated waveguide (LWG) to subminiature coaxial connector with wideband and low-loss performance. The laminated waveguide is achieved using multilayer low-temperature co-fired ceramic (LTCC) technology. In the conventional transition scheme, a length of grounded coplanar waveguide (GCPW) is used to connect the LWG and coaxial connector to obtain a wide bandwidth, which increase the transition size and radiation loss, especially in millimetre-wave (MMW) band. To realize a compact and low-loss LWG-to-coaxial connector transition, the GCPW line is removed and the whole LTCC transition structure is designed underneath the coaxial connector. Moreover, two stages of waveguide step are introduced to constrain the electromagnetic field in the transition for lower radiation loss, which also contributes to the wideband impedance matching. The back-to-back transition is designed and fabricated with LTCC technology to validate the proposed transition scheme. A measured bandwidth of 44% from 27.3 to 42.9 GHz is achieved under |S11| < −15 dB and the insertion loss of single transition is about 0.4 dB.

Stepped waveguide metamaterials as low-loss effective replica of surface plasmon polaritons

Abstract Surface plasmon polaritons (SPPs) have attracted intensive attention for the unprecedented developments of light–matter interactions in optics and photonics, providing a feasible method for light confinement and transmission at a subwavelength scale. However, SPPs traditionally suffer from large losses due to the intrinsic dissipations and absorptions, which hinder further development and applications of SPPs. Here, we theoretically and experimentally investigate the concept of stepped waveguide metamaterials behaving as low-loss effective replicas of SPPs. The proposed structure without natural plasmonic material maintains the identical field configuration to that in regular SPP but avoids the inherent losses, outperforming regular low-loss SPP design with natural plasmonic materials on SPP propagation lengths. Furthermore, stepped waveguide metamaterial exhibits excellent compatibility in direct interconnections with arbitrary regular SPP and potentially represents a feasible route toward new SPP devices with low-loss advantages.

Ultra-Wideband 90° Waveguide Twist for THz Applications

We report on the design, fabrication, and characterization of a novel 90° waveguide step twist with 56% fractional bandwidth. The proposed twist provides 90° field rotation in the frequency range 210–375 GHz. The experimental results are in good agreement with the electromagnetic simulations showing an insertion loss below 0.3 dB and a return loss better than 20 dB over most of the band. The ultra-wideband performance, tolerance to fabrication inaccuracies, and compactness makes the proposed design attractive for various mm and submillimeter applications. The twist geometry is optimized for simple fabrication through direct milling. Furthermore, the design remains highly compact since both steps are fabricated on a single washer.

Compact Shared-Aperture Dual-Band Dual-Circularly-Polarized Waveguide Antenna Array Operating at K/Ka-Band

In this article, a compact shared-aperture dual-band dual-circularly polarized waveguide antenna array is presented to achieve high gain and wide bandwidth in full-duplex satellite communication at K/Ka-band. The designed antenna array can simultaneously operate at 20 GHz band with right-hand circular polarization (RHCP) radiation and 30 GHz band with left-hand circular polarization (LHCP) radiation. The array is composed of circular polarization (CP) waveguide antenna elements and full-corporate feed networks. The ridged spectrum polarizer is inserted in the square waveguide to form CP radiation in a stepped waveguide antenna element. The sequential rotation technique is adopted in feed networks to further improve CP axial ratio (AR) performance and bandwidth. The prototype of the proposed 4 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times4$ </tex-math></inline-formula> antenna array is fabricated and measured for demonstration. Experimental results show that the overlapped bandwidth in terms of reflection coefficients less than −10 dB and AR lower than 2 dB is 18–22 GHz for RHCP radiation in K-band, and the corresponding bandwidth for LHCP radiation in Ka-band is 28–32 GHz. The measured cross-polarization levels are better than 25.82 dB at 20 GHz and 20.25 dB at 30 GHz, and the measured peak gains at K/Ka-band are 23.94 and 26.87 dBic, respectively.

Millimeter‐wave frequency reconfigurable antenna using simple VO 2 ‐based paired metasurface

In this article, a millimeter-wave frequency-reconfigurable metasurface antenna by electrically controlling vanadium dioxide (VO2) is proposed and studied. As a phase change material, VO2 is an insulator at room temperature but can turn into high conductivity metallic state when activated by continuous direct current (DC) voltage. By integrating the VO2 film between two simple rectangle metasurface cells, a frequency-reconfigurable paired metasurface structure (FRPMS) is achieved. The FRPMS can be considered as one unit when VO2 film is activated to metallic state while as two independent cells when VO2 film is in insulating state. In this way, the FRPMS can operate, respectively at 28 and 38 GHz with independent tunability. Moreover, a coplanar and staggered DC bias circuit with little effect on radiation is designed to switch the operating modes of VO2 easily. The antenna is fed by a stepped waveguide with ridges through a loop slot, which is suitable for dual-band feeding with large frequency ratio. One prototype is fabricated and measured for demonstration. When the VO2 film is in metallic state, the measured working band covers from 28.5 to 29.6 GHz with the maximum gain of about 7.1 dBi. When cooled down to insulating state, the antenna can work in a higher band from 36.7 to 38.3 GHz with the maximum gain of about 7.9 dBi. Due to the advantages of simple structure, high gain and easy tuning, the antenna can be expected to use in mmW wireless communication.

Broadband Bidirectional and Multi-Channel Unidirectional Acoustic Insulation by Mode-Conversion Phased Units

The technique of sound insulation has a wide range of potential applications in environment noise control and architectural acoustics. The rapid development of acoustic artificial materials has provided alternative solutions to design sound insulation structures. However, the realization of single-layer planar structures with bidirectional acoustic insulation (BAI) and unidirectional acoustic insulation (UAI) still poses a challenge. Here, we report the theoretical and experimental realization of two types of single-layer phased array lenses which presents the characteristics of broadband BAI and multi-channel UAI. Both types of lenses consist of 12 mode-conversion phased units which are composed of two types of unit cells (I and II) with an opposite phase and a step waveguide. Based on the phase regulation, the designed phased unit can realize the mode conversion between the zero-order and first-order waves and asymmetric sound manipulation, which enables multi-functional sound insulations. Based on the desired theoretical phase profiles, two types of lenses with BAI and UAI are realized for the incidence of the zero-order wave, and their fractional bandwidths can reach about 0.28 and 0.37, respectively. More interestingly, the UAI effect can be reversed for the incidence of the first-order wave. The proposed lenses based on the mode-conversion phased units have the advantages of single-layer planar structure, multi-functional sound insulation, and broad bandwidth, which have wide application prospect.

Creation of multi-frequency terahertz waves by optimized cascaded difference frequency generation

A new scheme which generates multi-frequency terahertz (THz) waves from planar waveguide by the optimized cascaded difference frequency generation (OCDFG) is proposed. A THz wave with frequency ω T1 is generated by the OCDFG with two infrared pump waves, and simultaneously a series of cascaded optical waves with a frequency interval ω T1 is generated. The THz wave with a frequency of M-times ω T1 is generated by mixing the m-th-order and the (m + M)-th-order cascaded optical wave. The phase mismatch distributions of cascaded difference frequency generation (CDFG) are modulated by changing the thickness of planar waveguide step by step, thereby satisfying the phase-matching condition from first-order to high-order cascaded Stokes process step by step. As a result, the intensity of THz wave can be enhanced and modulated by controlling the cascading order of OCDFG.

Demonstration of a Polymer-Based Single Step Waveguide by 3D Printing Digital Light Processing Technology for Isopropanol Alcohol-Concentration Sensor

A polymer based horizontal single step waveguide for the sensing of alcohol is developed and analyzed. The waveguide is fabricated by 3-dimensional (3D) printing digital light processing (DLP) technology using monocure 3D rapid ultraviolet (UV) clear resin with a refractive index of n = 1.50. The fabricated waveguide is a one-piece tower shaped ridge structure. It is designed to achieve the maximum light confinement at the core by reducing the effective refractive index around the cladding region. With the surface roughness generated from the 3D printing DLP technology, various waveguides with different gap sizes are printed. Comparison is done for the different gap waveguides to achieve the minimum feature gap size utilizing the light re-coupling principle and polymer swelling effect. This effect occurs due to the polymer-alcohol interaction that results in the diffusion of alcohol molecules inside the core of the waveguide, thus changing the waveguide from the leaky type (without alcohol) to the guided type (with alcohol). Using this principle, the analysis of alcohol concentration performing as a larger increase in the transmitted light intensity can be measured. In this work, the sensitivity of the system is also compared and analyzed for different waveguide gap sizes with different concentrations of isopropanol alcohol (IPA). A waveguide gap size of 300 µm gives the highest increase in the transmitted optical power of 65% when tested with 10 µL (500 ppm) concentration of IPA. Compared with all other gaps, it also displays faster response time (t = 5 seconds) for the optical power to change right after depositing IPA in the chamber. The measured limit of detection (LOD) achieved for 300 µm is 0.366 µL. In addition, the fabricated waveguide gap of 300 µm successfully demonstrates the sensing limit of IPA concentration below 400 ppm which is considered as an exposure limit by “National Institute for Occupational Safety and Health”. All the mechanical mount and the alignments are done by 3D printing fused deposition method (FDM).

Millimeter-Wave Frequency-Reconfigurable Metasurface Antenna Based on Vanadium Dioxide Films

A novel frequency-reconfigurable method using vanadium dioxide (VO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ) is proposed. VO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> is one kind of phase change material (PCM) which can be electrically switched between the states of insulator and metal. By integrating the VO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> film into a uniplanar compact photonic-bandgap (UC-PBG) structure, a frequency-reconfigurable metasurface (FRMS) structure with frequency ratio of 1.78 is constructed accordingly. Moreover, the active VO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -based FRMS is used as radiation element to design a high-gain millimeter-wave frequency-reconfigurable metasurface antenna (FRMSA), which is excited by a stepped waveguide through two slots of different lengths. In order to electrically activate the VO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> films of the antenna, a simple dc bias co-planarly localized with the FRMS is well designed. Benefiting from the convenient connection of the UC-PBG, only simple connection with two sides of the antenna is required for the dc bias, thus causing little impact on radiation due to far from the radiation region. One prototype is fabricated and measured for demonstration. When the VO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> film is activated to insulating state, the measured results show that the proposed FRMSA can operate in 23.25-24.3 GHz with the maximum gain of ~8.7 dBi, while it can work in 37-39.8 GHz with a peak gain of ~7.6 dBi when driven to metallic state. The ratio of two frequencies is about 1:1.61. Compared with other reported VO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -based antennas, the proposed antenna exhibits a larger frequency ratio and higher gain in millimeter-wave bands.

О роли анизотропии и нелинейных диффузионных эффектов при формировании волноводов в кристалле ниобата лития

Direct numerical simulation of a process of hydrogen diffusive intrusion into the lithium niobate monocrystal is fulfilled with reference to the manufacturing two-channel system of waveguides. The calculations were carried out according to the technology of waveguides production, taking into account the presence of several stages, which at first include the material saturation with the protons by treating the working surface with the melt of benzoic acid, and then annealing the sample. The contribution of the nonlinear diffusion to the process of the waveguide shaping is analyzed. It is shown that the formation of a stepped waveguide boundary is significantly influenced by the procedure of monocrystal annealing. Heretofore, the annealing stage was not quantitatively investigated. It can be emphasized that the attention has not been paid to the possible role of the annealing on formation of the sharper boundary between the waveguide and its mother substrate. A theoretical model of anisotropic diffusion in a solid material is constructed on the basis of experimental data, which indicate the presence of a transitional surface layer with pronounced regular mesostructural directions in the polished lithium niobate monocrystal. Based on the derived equations, the waveguides shape in a cross-section was simulated numerically for different values of inclination angle of the main axes with respect to the cut lines of the crystal. It is demonstrated that in the region of the waveguide bifurcation, when at the stage of protons intrusion the interaction of diffusive fluxes is possible, the diffusion anisotropy can lead to a breakdown of the waveguides symmetry, which can affect their optical properties.

Multimode Equivalent Networks for Shielded Microwave Circuits With Thick Metallizations

In this article, we show how the multimode equivalent network (MEN) technique can be extended to the analysis of multilayer boxed planar microwave circuits that are built using a thick metallization. This analysis is carried out considering the thick metallic circuit as a length of the uniform waveguide. The problem is then divided into two waveguide steps (or junctions). We first obtain the equivalent network of the two junctions. Then, we cascade them to obtain the MEN of the complete circuit, thereby including the effect of finite thickness rigorously. A key aspect of the formulation that we propose is that it includes ports in the transverse plane of the circuit. In addition to theory, several shielded microwave filters using a thick metallization are also analyzed. An in-depth study of the numerical convergence is also performed for two practical examples. Simulation results are shown to be in good agreement with both commercial simulation tools and measurements, thereby fully validating our theoretical formulation.

Design of 1178 nm diode laser with step waveguide layers for reduced voltage and low vertical divergence

A 1178 nm diode laser with step waveguide layers (SWGLs) into the optical cavity is designed for frequency doubling. It is found that the mode field of the fundamental mode can be modulated easily for this kind of diode laser. A strong confinement for the fundamental mode can also be achieved by adopting a low Al content in the optical cavity. Diode lasers with SWGLs can deliver a high output power. Compared with diode lasers based on the conventional large optical cavity, the low Al content results in a reduced voltage, which is helpful to improve the electro-optical conversion efficiency. Based on an asymmetric large optical cavity with SWGLs, a beam divergence of 15.5° in the vertical direction is obtained for the designed diode laser.

Broadband integrative acoustic asymmetric focusing lens based on mode-conversion meta-atoms

Acoustic asymmetric focusing (AAF) has a great potential application in medical ultrasound imaging, focused ultrasound therapy, and nondestructive testing. The advancement of acoustic metamaterials and metasurfaces has provided various mechanisms to design AAF lenses. However, due to the existence of a certain difficulty in realizing sound focusing and asymmetric transmission simultaneously, the realization of the AAF lens with a broad bandwidth and an integrative planar structure still remains a challenge. Here, we theoretically propose and experimentally demonstrate an integrative planar AAF lens based on a type of mode-conversion meta-atom composed of two types of phased unit cells with a phase difference of π and a step waveguide. The meta-atom can realize the conversion between the zero-order and first-order waves and asymmetric sound transmission, which arises from the phase modulation and the cutoff frequency of the first-order wave, respectively. Based on the proposed mode-conversion meta-atoms, we design a broadband AAF lens with high performance, in which its fractional bandwidth can reach about 0.19 and the focus size is only about 0.38λ. The proposed mode-conversion meta-atom and its associated AAF lens provide diverse routes for designing asymmetric multi-functional sound devices with promising applications.

A $Ka$ -Band 3-D-Printed Wideband Stepped Waveguide-Fed Magnetoelectric Dipole Antenna Array

A novel millimeter-wave aperture-coupled magnetoelectric (ME) dipole antenna with a low-profile metallic geometry is proposed based on the 3-D printing technology. An impedance bandwidth of 53.7%, a gain up to 10.8 dBi, and stable unidirectional radiation patterns with the cross polarization of less than -38 dB are achieved by the antenna. Its operating mechanism and design process are studied in detail as well. In order to widen the bandwidth of the millimeter-wave fullcorporate H-plane air-filled waveguide feed network, a wideband H-plane stepped waveguide T-junction with a compact size is then investigated, which has a bandwidth of about 50% for the reflection coefficient of less than -20 dB. By combining the presented radiating element with the feed network, an 8 x 8 ME dipole array is designed, printed, and tested in the Ka-band. An enhanced bandwidth of 31%, symmetric radiation patterns with the cross polarization of less than -35 dB, and a gain varying from 25.5 to 28.5 dBi are experimentally obtained. The proposed design demonstrates the advantage of utilizing the 3-D printing method to improve the operating characteristics of the millimeter-wave antenna array and is attractive for the emerging wideband millimeter-wave wireless applications.

A Wideband High-Gain Planar Integrated Antenna Array for $E$ -Band Backhaul Applications

A novel wideband high-gain planar antenna array for $E$ -band backhaul applications is presented in this article. The antenna element is composed of a substrate integrated waveguide (SIW) cavity-backed patch and a stepped waveguide horn. The SIW cavity-backed patch is worked as wideband waveform and impedance transformer to excite the stepped waveguide horn on the upper layer. The stepped waveguide horn is employed to enhance the gain of the antenna element by increasing the radiation aperture. Based on the proposed antenna element, a $2 \times 2$ subarray with element spacing larger than a wavelength is designed. A groove, which works as secondary radiation source, is etched between the elements to improve the gain and suppress the high sidelobes of the $2 \times 2$ subarray. By taking the advantage of the groove, the $2 \times 2$ subarray achieves a maximum boresight gain of 17 dBi and an −10 dB impedance bandwidth of 21.8% from 70 to 87 GHz. For further enhancing the gain, a prototype including $16 \times 16$ elements is manufactured and measured. The experimental results confirm that the proposed antenna achieves the −10 dB impedance bandwidth of 22.4% from 71 to 88.5 GHz and a peak gain of 28.8–30.9 dBi. With the merits of a wider operating bandwidth, high gain, low profile, and low cross-polarization, the proposed antenna array is suitable for application in the $E$ -band wireless backhaul systems.