Beam-Scanning Orbital Angular Momentum Circular Leaky-Wave Antenna With a Half-Mode Corrugated Substrate Integrated Waveguide

This letter presents a novel circular leaky-wave antenna (CLWA) on a half-mode inter-digitated capacitor based corrugated substrate integrated waveguide (HM-IDC-CSIW) to produce a beam-scanning orbital angular momentum (OAM) wave. Longitudinal radiating slots in a conventional LWA have been translated into an arc-shaped slot for this CLWA. An array of arc-shaped slots is then used to produce OAM mode 1 from 17 to 21 GHz, while producing a beam-scanning of ± 30° in the azimuth plane. The measured results of the antenna confirm a gain of 12–14.2 dBi throughout the frequency band while maintaining an efficiency >70% and a high OAM mode purity. Such OAM-based antennas with frequency-controlled beam-scanning can be used for secure communications and to create imaging systems that can sense in different directions simultaneously.

Abstract-This letter presents a novel circular leaky-wave antenna (CLWA) on a half-mode inter-digitated capacitor based corrugated substrate integrated waveguide (HM-IDC-CSIW) to produce a beam-scanning orbital angular momentum (OAM) wave.Longitudinal radiating slots in a conventional LWA have been translated into an arc-shaped slot for this CLWA.An array of arc-shaped slots is then used to produce OAM mode 1 from 17 to 21 GHz, while producing a beam-scanning of ± 30°in the azimuth plane.The measured results of the antenna confirm a gain of 12-14.2dBi throughout the frequency band while maintaining an efficiency >70% and a high OAM mode purity.Such OAM-based antennas with frequency-controlled beam-scanning can be used for secure communications and to create imaging systems that can sense in different directions simultaneously.

I. INTRODUCTION
O RBITAL angular momentum (OAM) waves or vortex beams have been a subject of interest because of their potential capability to produce an additional degrees of freedom besides with frequency and polarization with a theoretically infinite number of modes, allowing for high-resolution imaging [1], [2], [3].It can also be used to detect multiple targets simultaneously [1], [4] as well as angular velocity, radius, and tilt angle of rotating objects [5], [6], [7].It can also increase the channel capacity within a communication network with a theoretically infinite number of channels based on different OAM modes [8], [9].
An OAM beam produces a vortex-shaped field (hence, also known as vortex beam) with helical transversal phase distribution consisting of an azimuthal phase term e −jlϕ , where l is the topological charge or OAM mode number, and ϕ is the azimuthal angle around the propagation axis [10], [11].Several methods have been presented in the literature to achieve a vortex beam by creating a periodic phase delay across the azimuthal plane.Some of the most popular techniques include uniform circular arrays [12], [13], spiral phase plates [14], parabolic reflectors [15], and The authors are with the Wolfson School of Mechanical, Electrical, and Manufacturing Engineering, Loughborough University, LE11 3TU Loughborough, U.K. (e-mail: a.bansal@lboro.ac.uk; w.g.whittow@lboro.ac.uk).
Digital Object Identifier 10.1109/LAWP.2023.3316789metasurfaces [16], [17], [18], [19], [20].Leaky-wave antennas (LWA) [21], [22], [23] can be used to create a controlled phase delay among radiating elements in a sequential array, producing a helical phase front and hence, generating an OAM beam [24], [25], [26].This letter demonstrates a circularly bent half-mode IDCbased corrugated substrate integrated waveguide (HM-IDC-CSIW) loaded with a periodic slot array to produce a beamscanning OAM wave of Mode 1.The letter is divided as follows.Section II describes the half-mode interdigitated capacitor-based corrugated substrate integrated waveguide (HM-IDC-CSIW) layout and its working followed by the design of the proposed circular leaky-wave antenna (CLWA) in Section III.Section IV discusses the measured results of the antenna and demonstrates its beam-scanning capabilities, followed by a conclusion in Section V.

II. HALF-MODE IDC-BASED CORRUGATED SIW
Substrate integrated waveguides (SIW) are generally loaded with vias to create a virtual wall in the H-plane to avoid leakage and, hence, produce a planar waveguide structure [27].Such waveguides, however, tend to be rigid and are costly to fabricate because of the number of vias on the structure.A corrugated substrate integrated waveguide (CSIW) uses inductive stubs as a replacement for vias and, hence, produces a similar virtual electric wall in the H-plane [28].Several CSIWs have been presented in the literature [29], [30].They operate at the TE10 mode and tend to have higher transmission losses than conventional SIWs.
A new SIW was proposed in [24] and [31] where inductive stub-based corrugations were replaced with integrated digitated capacitor (IDC) based corrugation to achieve better isolation and, hence, comparatively lower transmission losses.
Here, we break the IDC-CSIW from the center to produce a half-mode IDC-based corrugated SIW (HM-IDC-CSIW), as it offers a small form factor and is easy to bend for a circular LWA.The transition of conventional SIW to HM-IDC-SIW is shown in Fig. 1.The dimensions for the three waveguides are as follows: waveguide width w g = 6 mm, via diameter d v = 0.5 mm, pitch of vias p = 0.5 mm, stub length l s = 3 mm, stub width w s = 0.5 mm, and gap between stubs g = 0.5 mm.The three waveguides were designed on a Taconic TLY-5 substrate of relative permittivity, ε r = 2.2, loss tangent = 0.001, and height h = 0.787 mm.The guide width for the HM-IDC-CSIW is half of the IDC-CSIW.
HM-IDC-CSIW's performance as a planar waveguide is compared with simulated S-parameters and electric field plots,  as shown in Fig. 2. Both IDC-CSIWs have a cut-off freq. of 15 GHz and operate at the TE10 mode.The transmission loss for a 10 cm long IDC-CSIW and HM-IDC-CSIW is approx.0.77 dB and 1.12 dB averaged over the operating frequency.Further, the E-field plots of the HM-IDC-CSIW in Fig. 2(b) confirm its operation as a planar waveguide.
This HM-IDC-CSIW only has corrugations on one side and hence, can easily be bent to a circular shape.It can also be used as a host guiding structure for a leaky-wave antenna, as discussed in Section III.

III. CIRCULAR LEAKY-WAVE ANTENNA FOR OAM BEAM
The half-mode IDC-CSIW is bent to create a circular ring and is loaded with periodic arc-shaped slots to achieve a controlled phase delay that can produce a Mode 1 OAM beam.This section describes the antenna design in two parts: slot placement in Section III-A and antenna layout in Section III-B.

A. Slot Placement on HM-IDC-CSIW
For an easier understanding of the design, the cartesian coordinate system here is converted into a cylindrical coordinate system.Hence, a longitudinal slot in a Cartesian layout is converted into an arc-shaped slot in the cylindrical layout, as shown in Fig. 3. Here, l slot = 8.7 mm is the length of longitudinal slot, and w slot = 0.6 mm is the width of the slot, both calculated based on the operating frequency of 17-21 GHz.It is converted into an angular length of θ slot = 22°.The waveguide width w g and inductive stub dimensions are the same as Fig. 1.The waveguide is designed with a radius r in = 20.8mm to host ten slots of arc length 8 mm.
As the current distribution changes along the r-axis of the waveguide, the position of the arc-slot becomes a crucial parameter to attain optimum radiation characteristics.To achieve optimum radiation, the slot should demonstrate maximum admittance to the surface current.The slot offset r off was tested in simulations and the S-parameters were analyzed with the assumption of no material or conductor losses, and 1W power input was made.The amount of power radiated with a change in slot offset is shown in Fig. 3(c).Hence, for optimum results, slots are placed at a distance of (r in + r off ) = 22.9 mm from the center.

B. Circular Leaky-Wave Antenna Design
The circular LWA has a total radius of r sub = 30 mm and consists of ten periodic slots, as shown in Fig. 4. The waveguide was fed with coaxial feed pins of diameter d = 0.6 mm at two diagonally opposite ends.A hole of diameter, D = 1.8 mm, was created on the ground plane to match 50 Ω impedance with the connector feed.The slots were placed at a fixed arc length of 13 mm, which can be translated to an angular distance of θ g = 36°, this allows for a fixed phase delay over the arc length between each slot at 17-21 GHz.One of the two feeds   is activated, and the wave travels from the feed point to both sides of the circular array.The five slots on each side in ± r-axis produce a continuous helical phase front, leading to an OAM beam in the far field.

IV. MEASURED RESULTS
The fabricated CLWA was fed using a planar microstrip line to a coaxial pin feed converter and is shown in Fig. 5.The microstrip line is printed on a Rogers 5880 dielectric laminate of height, h 2 = 0.254 mm.The width of the microstrip line is w 50 = 0.8 mm to match the 50 Ω line impedance of the feed at the antenna as well as connector.The microstrip line width  is w 100 = 0.4 mm to avoid leakage and back lobes.A 2.4 mm connector is used to feed the antenna.
The simulated and measured S 11 of the CLWA are shown in Fig. 6.The measured S 11 and S 21 are found to have a slight shift in frequency compared to the simulated results.This is because of the height of the feed pins.However, the frequency bands are maintained and S 21 is less than −18 dB, confirming an operating 10 dB bandwidth of 17-21 GHz.The simulated absolute E-field at 18 GHz in Fig. 7 shows the flow of electric fields within the CLWA in two directions and can be correlated with the slot locations to demonstrate the phase change in EM-wave as it  arrives at each slot based on their relative location on the circular waveguide.
The circular flow of the E-field allows us to achieve a helical phase front leading to an OAM beam within the operating frequency.This is confirmed by the measured radiation patterns in the azimuth and elevation axes, as shown in Fig. 8.A null is observed in the center of the radiation pattern for each operating band.Note that the simulated and measured radiation patterns had very good agreement within 3°, however, only measured results are included in Fig. 8 to make the figure easier to read.The sidelobe levels (SLLs) are found to be approx.6-8 dB for all frequency bands.This is because of the fan-beam characteristics of an LWA and can be minimized by introducing metallic walls around the circular LWA and redirecting side lobes toward the main beam.
As the antenna is a curved LWA, the change in frequency leads to a phase shift, which, in turn, allows for frequency-controlled beam scanning.The proposed antenna demonstrates a ±30°b eam-scanning in the azimuthal plane.Please note that this beam-scanning angle is measured based on the position of the central null for each OAM radiation pattern, see Fig. 8(a).The mode 1 OAM beam is further confirmed with the holographic view of the measured phase-front at 19 GHz (where the central null is at an azimuthal and elevation angle of 0°) in Fig. 9.This holographic view was measured at a distance of 1 m from the antenna using the NSI2000 anechoic chamber, see Fig. 9.
The measured and simulated mode purity for OAM mode 1 for 17-21 GHz is calculated based on the method explained in [14] and is shown in Fig. 10.The antenna has a measured gain of 12-14.2dBi with an efficiency >70% throughout the freq.band and is shown in Fig. 11.The measured directivity of the antenna was found to be slightly shifted compared to simulations.Hence, even though the measured efficiency is less compared to simulations (by merely 0.3 dB), the measured gain is approximately the same as simulations.

V. CONCLUSION
This letter shows the operation of half-mode IDC-CSIW as a planar waveguide, which is then bent circularly to achieve an OAM beam with mode 1.The new circular LWA is shown to operate at a frequency band of 17-21 GHz.As the electric field travels in a circular path, the radiated beam generates a helical wavefront and, hence, an OAM beam.Furthermore, with the change in frequency, the phase shift within the leaky-wave changes, leading to a change in beam angle.Hence, a beamscanning OAM mode 1 has been presented in simulations and measurements.The measured antenna has a beam-scanning capability of ± 30°in the azimuth plane with a mode purity greater than 70% throughout the frequency band.The antenna has a measured gain of 12-14.5 dBi with an efficiency >70%.Such OAM-based antennas with frequency-controlled beam-scanning can be used for secure communications and to create imaging systems that can sense in different directions simultaneously.The work can be extended to create new OAM modes with either a change in spacing between the slots or with a change in frequency.Theoretically, if we double the frequency, it should generate an OAM mode 2. However, IDC-CSIW has the limitation of an upper cut-off frequency.This cannot be realized here.The proposed work offers a small form-factor antenna compared to the literature discussed in Section I while maintaining a high gain, high efficiency, and high mode purity.

Fig. 3 .
Fig. 3. (a) Straight HM-IDC-CSIW with longitudinal slot in Cartesian plane; (b) circular HM-IDC-CSIW with arc-slot with the cylindrical coordinate system; (c) simulated change in power radiated by one arc-slot with change in slot offset (inset: E-field plot for a waveguide with arc-slot at 20 GHz).

Fig. 4 .
Fig. 4. (a) Top and (b) bottom view of the circular LWA layout with a periodic array arc-slot.

Fig. 5 .
Fig. 5. (a) Top and (b) bottom view of the fabricated antenna design with a microstrip-line-based feeding.

Fig. 7 .
Fig. 7. Simulated E-field plot in z-axis at 20 GHz showing the flow of electric fields along the circumference of CLWA.

Fig. 8 .
Fig. 8. Measured radiation patterns in (a) azimuth and (b) elevation planes for the CLWA at 17-21 GHz; Inset: 3-D radiation pattern at 19 GHz, showing the azimuth and elevation planes.

Fig. 9 .
Fig. 9. (a) CLWA placed inside the anechoic chamber, and a representation of holographic measurement in 3-D space; (b) theoretically calculated ideal phase front for OAM mode 1; (c) measured phase front at 19 GHz (color bar describes the phase in degrees).

Fig. 10 .
Fig. 10.Simulated and measured mode purity for OAM mode 1 at different operating frequencies.

Fig. 11 .
Fig. 11.Simulated and measured gain (left axis) and total efficiency (right axis) of the CLWA.
Beam-Scanning Orbital Angular Momentum Circular Leaky-Wave Antenna With a Half-Mode Corrugated Substrate Integrated Waveguide Aakash Bansal , Member, IEEE, and William G. Whittow , Senior Member, IEEE