3D metal printed slot antenna array with high gain and enhanced bandwidth using triple-mode sine corrugated cavity resonator

This letter proposes a class of sine corrugated cavity resonators (SCCR). The SCCR can present slow ‐ wave features and provide dual ‐ mode (TE 104 and TE 105 ) wideband responses with reasonable sine period and depth. Based on it, a compact high ‐ gain bandwidth ‐ enhanced SCCR slot antenna array is designed. The high gain is obtained with seven radiation slots and the wideband is achieved due to three modes being utilised. The three modes include the modes of TE 104 and TE 105 of the SCCR and one feed slot mode. Compared with published works, the desired TE 104 and TE 105 can be obtained straightforwardly based on SCCR. The standard WR62 waveguide is utilised to feed the antenna. For validation, direct metal 3D printing technology is used to fabricate it with aluminium and copper powders as a comparison. Both measured results were discussed and showed a good agreement with the simulated ones.


| INTRODUCTION
Metal slot antennas have been widely employed in modern wireless communication applications requiring high gains, power-handling, and radiation efficiencies, such as base stations and satellite communication systems [1,2].However, two major issues of slot antennas will challenge the miniaturisation and wideband requirements of modern radio frequency (RF) systems.One is the bulky size and the other is the narrow bandwidth due to the waveguide resonators' high-quality factor and single-mode resonance.To overcome this, multi-mode waveguide resonators were proposed and studied to design compact wide bandwidth slot antennas in the past decades [3][4][5][6][7][8][9][10].
The classical works of bandwidth-enhanced slot antennas were reported based on dual-mode, triple-mode, and quadmode substrate integrated waveguide (SIW) resonators in refs.[3][4][5][6].The fractional bandwidth (FBW) improved highly from 1.4% to 17% compared with the single-mode-based slot antenna.However, the dielectric loss and the weak power handling of the SIW limited their applications.Then the metal multiple mode resonators started being studied to design the wideband slot antennas recently [7][8][9][10].In ref. [7], a triplemode resonator, consisting of a dual-mode resonator and a feeding slot mode, was proposed to design a wideband antenna.The designed slot antenna achieved more than 20% FBW without enlarging the device's sizes.The only drawback is the efficiency needs to be improved.In refs.[8][9][10], the mode perturbation technology was adopted to achieve multi-mode resonators.Metal posts were necessary to adjust the modes' frequencies or produce extra modes for achieving wideband radiation performances.However, the introduced metal posts increased the design and fabrication complexity.
On the other hand, using the periodical slow-wave structures is another effective method to reduce the size and extend the bandwidth for the designed passive components like the slot antenna.The sine corrugated waveguides (SCW) could present outstanding slow-wave features and high power capacity, which have been used to design travelling wave tubes in refs.[11][12][13].Hence, it is intuitive to imagine that the SCW is also suitable for designing compact wideband millimetre-wave antennas, but the related reports are rarely few [14].Moreover, the SCW can suffer larger fabrication tolerances in terms of its periodical shapes.Although the SCW is hard to fabricate using conventional computerised numerical control (CNC) technology, it is a less challenging task for direct metal 3D printing technology [15][16][17][18].
This paper describes the latest development of a 3D printed fully-metal slot antenna array based on the proposed sine corrugated cavity resonator (SCCR) as shown in Figures 1  and 2, resulting in attractive features such as high gain, high efficiency, wideband and compact size.Further to a more recent investigation [18], the analysis detail of the slow-wave effects of the SCCR is given in Part 2. The design process of the dual-mode-based wideband slot antenna array is described in Part 3. Compared with published works, the designed antenna avoided introducing metal posts, making the physical structure pretty simple.The designed antenna was fabricated using 3D metal printing technology with both aluminium and copper powders.The printing detail was given in Paer 4. The measured results based on both powders, for the first time to the author's knowledge, are also presented and discussed in Part 4 before the conclusion of this paper.

| SINE CORRUGATED CAVITY RESONATOR ANALYSIS
Figure 1a gives the three-dimensional view (3-D) of the one cell of the SCCR, where a and t are the depth and period of the sine shape grooves.And the w 1 and h are the widths and the height of the middle rectangular area.The proposed SCCR can be obtained by extending the one-cell structure periodically in the z-axis within a given length of l 1 , as shown in Figure 1b.As a result, the sine corrugated can be built at both the top and bottom walls of the SCCR effectively.The sine corrugated surface can be defined by Equation (1): where a and t have the same meaning as the one-cell unit.
Although the sine corrugated waveguide can present hybrid modes (fast-wave and slow-wave) as proven in ref. [13], the relationships between the fast-/slow-wave and the depth and period of the SCCR still need to be studied.The slow-wave properties can be obtained usually by analysing the one-cell unit of the SCCR (Figure 1a).With the setting of the boundary conditions of the perfect conductor in both x-and y-directions and periodical in the z-direction, the eigenmode solver of CST is relied on to obtain the phase constant (β) versus frequency graphs of both sine corrugated parameters, depth (a) and period (t).All other parameters are fixed and listed in Figure 1.The phase constant versus the wide frequency range is obtained as shown in Figure 3, where each parameter was given three values for comparison.The straight red line is the base phase constant (β 0 ) called light-line that is calculated by β 0 = 2π/λ, where λ is the vacuum wavelength.The ten black curved lines are the phase constants of the first ten modes inside the SCCR.According to ref. [13], when β > β 0 or the area above the light line, the SCCR presents slow-wave effects and vice-versa.
In detail, as the depth (a) increases, the slow-wave frequency range is gradually enlarging while the phase constant is -983 almost unchanged (referring to the y-axis).Hence, changing the depth can increase the electrical length effectively.While for the period, increasing t would cause a smaller slow-wave frequency range but the larger t will lower the phase constant highly.This means the electrical length of SCCR also can be extended, which is sensible considering the larger t means a longer physical length with a fixed depth.
For more validation, the whole structure (Figure 1b) was also simulated and the relationships between the different modes and depth/period were obtained as shown in Figure 4.It should be noted that although only four modes, fifth to eighth, were chosen for display, all other modes of the SCCR have the same trends.With the depth increasing, the frequencies of all four modes decreased.The parameter t showed a similar decreasing trend even though the frequencies fluctuated within a small range.This can be explained by Equation (2) which is the cavity perturbation theory.
where ω and ω r are the angular resonant frequency after and before perturbation respectively.ω e , ω m are average electrical and magnetic energies of one specific mode of the cavity.The Δv represents the volume altered with a value of Δv < 0 when the cavity walls concaved and when Δv > 0 the cavity walls convexed.And W is the total average energy after perturbation.Assuming concaved perturbation loaded at the area where magnetic powers are less than electrical powers ( Δv < 0, ω e > ω m ), the resonant frequency of the resonator will be decreased because ω − ω r < 0. In this case, t increasing usually means the electrical length of the SCCR is increasing, which should decrease the resonant frequency.However, the sine valley groove can be regarded as the concaved cavity perturbation that will also impact the resonant frequency.When t is small (say t < 2.8 in this model), the frequency change caused by the perturbation is dominant.Since perturbation might happen randomly at the area where ω e < ω m or ω e > ω m , which will increase or decrease the mode frequency.When t is large enough, the increased electrical length is dominant which would cause the frequency with the pattern of the same modes to drop.For validation, Figure 5 gives the H-field distribution of the sixth and fifth modes of the SCCR with different values of t.As can be seen, When t is larger than 2.8, the sixth mode becomes the TE 202 mode while the TE 105 mode turned into the fifth mode due to the electrical length increasing.When t < 2.8, the frequencychanging trends are the same as stated before.Note that although only t = 2.5 was given, other values have the same modes of TE 105 .In general, it can be concluded that both the corrugated depth (a) and period (t) of the SCCR can miniaturise the resonator's size effectively.Meanwhile, it is necessary to mention that a larger period or depth would lead to a larger consumption of computer resources.

| ANTENNA LAYOUTS, MECHANISM, AND DESIGN
Following the above analysis, it can be known that the SCCR can provide slow-wave properties and disturb the field distribution characteristics, which is suitable for designing compact wideband slot antenna arrays.In this section, detailed design principles about the required slots antenna array will be given.

| Slot antenna array configuration
The initial configuration is shown in Figure 2, where the proposed slot antenna array has five radiation elements, unlike the typical antenna array with m � n radiation elements (both m and n are integers).The radiation elements are the same longitudinal slots etched on the top broad wall with width and length of w a and l a respectively.Then for introducing more radiation slots to improve the gain while maintaining the field distribution characteristics of the inside modes, two more extra rectangular bricks were added at the centre of the broadside wall as shown in Figure 6, where a total of seven radiation slots were etched.The space between the adjacent slots in the zdirection is denoted by d a1 while in the x-direction, is denoted by d a2 and d a3 .
In addition, the feed is the standard WR62 waveguide as given in Figure 2a, which is relatively simple due to the utilisation of the high-order mode technique [9].To achieve pure boresight radiation patterns and low side lobe, the feeding port is placed at the geometry centre of the antenna array.The radiation slots are also symmetrical to the centre for the same reason.The feeding can excite the TE 104 and TE 105 simultaneously through the feeding slot whose length and width are denoted by l p and w p respectively.It should be noted that except for controlling the impedance matching, the feed slot -985 2023, 13, Downloaded from https://ietresearch.onlinelibrary.wiley.com/doi/10.1049/mia2.12410 by Nes, Edinburgh Central Office, Wiley Online Library on [06/11/2023].See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions)on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License also worked as the third mode that can extend the bandwidth, which will be illustrated in the next subsection.

| Triple-mode slot antenna array realisation
In the published works, multi-layer structures or metal posts were often needed to obtain the required multi-modes for constructing high gain wideband antennas [8][9][10], which increased the volumes or designing complexity.In our design, according to the design requirements, that is, larger than 20% FBW for K u -band application, the required modes (TE 104 and TE 105 ) can be obtained directly by adequately choosing the values of the period and depth of the SCCR using the CST eigenmode solver.The final dimensions are given in Figure 6.For designing the antenna array, the high-order mode method is used to determine the places of etched radiation slots.Hence, the H-field distributions of both desired modes are shown in Figure 7a,b firstly.It should be noted that there are also other modes existing between the two modes (Figure 7c,  d), but they cannot be excited as will be illustrated later.Referring to the H-field distribution of the TE 104 and TE 105 , each H-field loop is distributed over the cavity in the x-direction and has the same amplitude in phase.For obtaining the high gain, the radiation slots should be etched at the H-field loops in-phase of each mode, as denoted with black lines in Figure 7a,b.Although the etched slots are out-of-phase for both frequencies, this is sensible since the wideband response is equal to cascading two single-band antennas directly.In addition, to increase radiation elements for improving the gain, the longitudinal slots were divided into two and three, as shown in Figure 6.
The feeding slot is placed at the centre of the SCCR surface with its long side oriented along the x-axis, the same as the Hfield of the TE 104 and TE 105 , c.f. Figure 7a,b.In addition, the feed H-field is parallel to the broad side of the feed slot while the feed E-field is parallel to the narrow side of the slot.Thus, the TE 104 and TE 105 could be excited successfully [19].Then the TE 104 and TE 105 will excite the slot antenna modes and finally radiate the electromagnetic energy out to the air.On the other hand, the H-field pattern of the TE 203 and TE 303 modes has been altered much because of the sine corrugated shape, they still maintain the mode characteristics of TE 203 and TE 303 which are called quasi-TE 203 and quasi-TE 303 modes.As can be seen, both of them cannot be excited since their Hfields are either vertical to the feed slot or the field energy is empty related to the feeding place, which ensures the desired wideband can be constructed by the TE 104 and TE 105 effectively without interfering (i.e.transmission notch).
For validation, Figure 8 gives the feed slot parameters w p, refer to Figure 2, versus the bandwidth impendence matching curves or S 11 .As shown, as w p increases, the impendence bandwidth matched well over the entire passband ranges of the TE 105 and nTE 106 mode (13.18-16.52GHz), which enables us to achieve more than 20% FBW easily.In addition, three resonant poles appeared in the passband and one of them is attributed to the feed slot window.To prove this, Figure 8 also gives the E-field distributions at 15.72 GHz.As presented, the electric field is mainly distributed around the feeding slot which differs from the E-field distribution of the TE mode.
To this end, the design guidelines of the antenna array are given as follows: According to the requirements of the size and bandwidth, determine the modes of SCCR initially.Then determine the radiating width w a and length l a of the radiation slots, which initially can be selected to be w a = λ 0, 13.18GHz /5 and l a = λ 0, 13.18GHz /2.Also, the d a1 is set to be a little larger than λ 0, 13.18GHz /2, while the d a2 and d a3 should not be less than 1.5 mm for mechanical robustness consideration.The width and length of the feeding slot were chosen to be the same as the radiation slot initially.The final dimensions were obtained using CST to do the final optimisation with the goal of S 11 below −10 dB and the dynamic range of each parameter set to �10% away from the initial values.
The final simulated results of the antenna array are shown in Figure 9, where a wide bandwidth from 13.09 to 16.63 GHz with S 11 below −10 dB can be observed.It should mention that unless otherwise stated, the conductivity setting in this paper is σ = 3.0 � 10^7 S/m.The average gain across the passband is around 12 dBi, which is high considering the compact size.In addition, due to bypass coupling of the highorder modes, the upper stopband has the filtering function.The simulated transmission efficiency across the passband is more than 97% which is also higher than the normal waveguide slots antenna array.

| FABRICATION AND MEASUREMENT
The sine shape is challenging to fabricate using traditional CNC technology but is a straightforward job for direct metal 3D printing.In order to avoid using supports and to check the inside printing quality, the antenna array was split into two pieces for printing, as shown in Figures 10 and 11.The split pieces can offer the best surface finish for all surfaces, that is, there are no down skin surfaces.Also, it is beneficial for measuring and assessing inside surface roughness.The small circles are screw holes for assembling.The printing starts from the bottom surface, layer by layer, until the end of the top surface.The whole printing process avoids using supports since the safe angle of θ s is less than 55°[20] in the printing direction (z-axis).
The antenna array was fabricated using the Renishaw AM500Q printer with powders of aluminium (AlSi10 Mg) [21] and commercially pure copper (>99.5%)powder provided by Renishaw Plc.The AM500 system uses 480-W laser power to sinter the copper powder, which obtains a much higher conductivity of 88% International Annealed Copper Standard.Thus, the printed copper powder-based models have better electrical conductivity but are heavier than the aluminium ones.The fabricated pieces are shown in Figure 10, where Figure 10a,c are aluminium and copper powder pieces while Figure 10b is the aluminium-based assembled model.It can be seen that even with the sine corrugated periodical structures, the printed models are of good quality.Specifically, the -987 measured fabrication errors of both models were around þ0.05 mm in the printing directions.Also, the Profilometer is used to measure the roughness and the maximum value is around 15 μm for the aluminium model while for the copper model is 5 μm.It should be pointed out that the measured surface roughness excluded the corrugated surface because of the limitation of the profilometer.
Finally, the RF properties of both antenna arrays were tested, and the in-band response was plotted together with simulated ones, as shown in Figure 9.As presented, both models agree well with simulated results in lower frequency areas (less than 14.5 GHz).However, there is a slight frequency shifting at higher frequencies.This is caused by the rough surface and testing environments.In addition, both measured gains are very close to the simulated ones and the maximum value is 13.64 dBi that achieved by the copper model.The compared radiation patterns are given in Figure 12a-d, where frequency points across the passband were selected.Both printed antenna models exhibit similar radiation patterns across the In general, these printed models have relatively consistent results, which showed that the sine corrugated waveguide resonator combined with direct metal 3D printing technology could enable us to create novel features for millimetre-wave components applications.
The comparison with other reported wideband slot antennas is provided in Table 1.As can be observed, the proposed slot antenna (this work) has an attractive feature combination of high radiation efficiency, high gain, and wide bandwidth in terms of its compact size.

| CONCLUSION
This paper proposed a sine corrugated cavity resonator (SCCR) for K u -band applications.By controlling the depth and period of the SCCR, the resonator not only has slow-wave features but also re-shapes the field distribution characteristics for producing wideband dual-mode responses.This enables us to design advanced devices that normal shapes are not attainable.A compact slot antenna array with a simple feeding structure is proposed and designed based on the SCCR.The designed antenna exhibits a wide bandwidth as well as a high gain across the passband.Direct metal 3D printing with aluminium and copper powder was deployed for experimental validation.The tested results of both printed models showed a good agreement with the simulated models even without the post-polishing process.

Ref
The 3D view of the one-cell structure.(b) Configuration of the proposed SCCR.Dimensions are (unit: mm): h = 3.0, w 1 = 25, l 1 = 40, a = 0.8, t = 2.0.F I G U R E 2 Layouts of the initial slot antenna (a) Side view.(b) Top view of the radiation surface.(c) Top view of the feed surface.RAO ET AL.

F I R E 3
Simulated β of the first ten modes for different sine corrugated depth (a) and period (t): (a) Depth.(b) Period.984 -RAO ET AL.

I G U R E 4
Resonance frequencies versus different parameters: (a) Depth.(b) Period.F I G U R E 5 The H-field distribution of different values of t.(a) Mode 6.(b) Mode 5. F I G U R E 6 Top view of the radiation surface with seven slots.Dimensions are (unit: mm): l 2 = 8, w 2 = 8, l a = 10.6, w a = 5.0, lp = 11.2, w p = 4.6, d a1 = 15.5, d a2 = 2.4, d a3 = 2.0.RAO ET AL.

F I G U R E 9
The gain and the S 11 of the slot antenna array.F I G U R E 1 0 Status check under printing.F I G U R E 1 1 (a) Aluminium powder-based printed pieces.(b) Aluminium powder-based assembled antenna prototype.(c) Copper powder-based printed pieces.RAO ET AL.

F I G U R E 1 2
Compared radiation patterns.(a) 13.32 GHz at the xz plane.(b) 13.32 at the yz plane.(c) 15.5 GHz at the xz plane.(d) 15.5 GHz at the yz plane.

T A B L E 1
Comparison with other reported slot antenna.