Parametric Analysis of Negative and Positive Refractive Index Lens Antenna by ANSYS HFSS

Lens antennas with multibeam, high gain, and low sidelobe level are potential candidates for base station antennas in 5G mobile communication. In this paper, the authors perform simulation and parametric analysis of a lens antenna with positive and negative refractive indexes (NRI) using the modern electromagnetic ﬁeld simulation software ANSYS HFSS. The simulation results of structures and theoretical calculations are analyzed and compared. The simulation results show the eﬀectiveness of using negative refractive index lens antennas to minimize the dimension. The lens thickness with a negative refractive index decreased from 24.5mm to 6.1 mm compared to the positive refractive index lens’s thickness. The results also indicate the similarities in gain, sidelobe level, amplitude, and electric ﬁeld distribution on the aperture plane of the negative and positive refractive indexes (PRI) lens antennas compared to the theoretical calculation. In addition, the authors simulate a lens structure with additional quarter wavelength matching layers (MLs) to estimate the antireﬂection performance.


Introduction
e fifth generation mobile system is now under development in the world [1][2][3]. e features of 5G in radio wave technology are millimeter wave frequency, small-size cells, and multiple input and multiple output (MIMO) systems [4,5]. e new technology will allow a 5G antenna to low latency, low path loss, multibeam, beam scanning ability, broadband, and stable radiation pattern. In the massive MIMO, the base station antenna should assign one access line corresponding to one radio beam to one user [5,6].
us, the base station antenna requires a multibeam radiation pattern like Figure 1. By using millimeter wave, the size of the base station antenna is reduced to about 30 cm; hence, types of antennas such as reflector, phased arrays, and dielectric lens antennas are proposed. As for a reflector antenna, a bifocal dual reflector and a reflectarray are proposed for multibeam application [7][8][9]. A phased array antenna is combined with a metasurface lens for extending the angular scan range, broadband, and multibeam [10][11][12][13][14][15][16][17]. As for a dielectric lens antenna, it has better multibeam radiation patterns than those of a dual reflector antenna, and this type of antenna also has structural features such as no blockage and having the same size beam forming surfaces of the front and rear surfaces, and stable radiation pattern [18][19][20][21][22]. However, on the downside, the thickness of dielectric lens antenna becomes larger. Meanwhile, when the refractive index is changed from the plus value to the minus value, the lens thickness can be remarkably reduced [23,24]. In the study [25], the authors have designed simulated electromagnetic fields and measured the structure of shaped dielectric lens antennas with refractive index n � ��� � 1.96 √ (Teflon) operating at 60 GHz using FEKO software. e results demonstrate very good agreements between the simulation results and the measured results.
However, there have been no studies of the simulation and comparison of negative and positive refractive index lens antennas in the electromagnetic environment. erefore, in this paper, the authors research and simulate negative and positive refractive index lens antennas using ANSYS HFSS electromagnetic simulator. e value of the positive refractive index (n � � 2 √ ) is approximately equal to that of Teflon refractive index (n � ��� � 1.96 √ ), which is studied and experimented in reference [25]. e comparison and analysis of lens size, gain, sidelobe level, and electric field distribution on the antenna planes and the effects of multiple reflections are performed. Also, the results are compared with the theoretical calculation of lens antennas. is paper consists of 5 sections. Section 2 shows the structures of lens antennas with negative and positive refractive indexes and fundamental expressions in determining the curve surface and the theoretical calculation of the lens antennas. Simulation conditions, parameters, and the matching layers structure are presented in section 3. Section 4 illustrates the simulation results, the comparison, and the discussion. Finally, the conclusions are summarized in section 5.

Lens Antenna Features and Structures.
e geometries of the negative and positive refractive index lens antennas are shown in Figure 2. e lenses are rotationally symmetric around the Z-axis. e conical horn antenna is used as a feed. e lens materials have the refractive indexes of n � − � 2 √ and n � � 2 √ . e lens has a basic structure, and its inner surface is curved and the outer surface is planar. e inner surface is generated by [20,26,27] where r is the distance from the focal point to the curve lens surface. e focal point is located at the origin of the coordinates axis. F is the distance between the focal point and the lens vertex. θ is the angle from the focal point to the inner lens surface and the Z-axis. n is a refractive index. ε r is relative permittivity. μ r is relative permeability. θ i and θ r indicate an incident angle and a refracted angle at a curve lens surface, respectively. ese angles satisfy Snell's law.
e distance from the origin to the lens vertex and the diameter of the lens are F � D � 100 mm. T indicates the lens thickness. e rays from the feed horn are refracted at the curve lens surface, which makes outgoing rays parallel to the Z-axis.
For a symmetrical axis lens with a feed horn at focal point, in Figure 2, E 2 p (θ)dθ is the power radiated per unit length by the feed horn between the angles θ and θ + dθ. en, if E 2 d (x) is the power per unit length in the corresponding aperture interval between x and x + dx, where x is the distance (x � r sin θ) from a point on the aperture plane to the oz axis, from equation (1), x distance is given by the following equation: Reflection from the lens surface is neglected. For the hyperbolic surface, the relationship between the electric field distribution on the aperture plane and the electric field of the feed horn is given by [27] From equations (5) and (6), the electric field distribution on the aperture plane is determined by: Applying equation (1) to determine the points on the upper curve lens surface on the xz plane with the negative and positive refractive indexes is shown in Table 1.

Conical Horn Antenna Structures.
e structure, fundamental dimensions, and the electric field of the conical horn antenna are illustrated in Figure 3(a). e feed horn is  used to illuminate a wide angle for the lens. e radiation pattern of the conical horn antenna is shown in Figure 3

Designing Matching Layers.
A lens antenna with highdensity dielectric material allows improving the energy transmission efficiency. However, using a lens whose material is a dielectric causes the worsening, which affects the International Journal of Antennas and Propagation 3 radiation properties of the antenna. ese effects are due to multiple reflections on the curve surface and inside the lens. is can be overcome by covering the lens with matching layers. Matching layers thickness is limited to a quarter wavelength [28][29][30][31][32]. e designed lens structure with a quarter wavelength matching layers at the front and the rear of the lens and some layers parameters are shown in Figure 4, where ε r is relative permittivity of the lens. ε ML indicates permittivity of the matching layers (ε ML � �� ε r √ ). D ML is the matching layer thickness (D ML � λ g /4). λ g is the internal MLs wavelength.

Simulation Conditions and Parameters.
e simulation parameters and the personal computer configurations are indicated in Table 2.
e ANSYS HFSS and FEKO electromagnetic simulators are used to calculate the electrical field on the planes and the electric field distribution on the aperture plane based on designed structures. e Multilevel Fast Multipole Method (MLFMM) is applied simultaneously in order to optimize the calculation ability, save the computer memory, and minimize the calculation time. e lenses are set with the relative permeability μ r � 1 and μ r � −1 and the relative permittivity ε r � 2 and ε r � −2 corresponding to the refractive index of n � � 2 √ and n � − � 2 √ , respectively. For the lenses with matching layers, the parameters are set: and D ML ≈ 2.25 . e distance between the focal point and lens vertex equals the diameter of the lens aperture (F � D � 100 mm). e survey frequency is 28 GHz.

4.1.
e Electric Field Distribution on the yz Plane. Electric field distributions of a lens antenna with the refractive indexes of n � � 2 √ and n � − � 2 √ are shown in Figure 5. It is clearly observed that the radiation rays from the conical horn antenna are spherical waves, which are refracted and reformed when reaching the curve inner lens surface, and the waveforms at the outer surface are planar.
is is correct in both cases of n � , and this meets the theoretical conditions of the lens antennas. In order to ensure the simulation accuracy of HFSS software, a comparison with FEKO software is performed. In the study [25], the authors have made the design and simulation using FEKO and conducted experimental measurements of the shaped dielectric lens antenna structure with a positive refractive index (n � ���� 1.96 √ ) operating on 60 GHz. e results in the study [25] show a similarity between simulation by FEKO and measured results. is demonstrates the simulation calculation accuracy of the FEKO software. Figure 5 is proves the precision in constructing the structure and setting the methods and parameter calculations.

Radiation Patterns.
e radiation patterns of the conical horn antenna and the lens antennas with different refractive indexes are illustrated in Figure 6.
e green dashed dotted line shows the radiation pattern when n � � 2 √ , the blue dashed one represents the radiation pattern when n � − � 2 √ , and the black dashed squared line indicates the radiation pattern of conical horn antenna without lens. Clearly, the gain of the lens antenna when n � − � 2 √ reaches 27.34 dBi while that of the lens antenna when n � � 2 √ is 27.20 dBi, which are significantly higher than the gain of the conical horn antenna without lens, at 15.15 dBi.
is demonstrates the effectiveness in improving the ability of the radiation properties of the lens antenna. e red solid dotted line represents the PRI antenna's radiation pattern of the designed lens antenna with the same size, simulated by FEKO electromagnetic field software. e results show that the red solid dotted line and the green dashed dotted line are in good agreement. is shows the accuracy of the result in the simulation calculation using both software tools. Consequently, it can be concluded that the simulation results using HFSS software in the proposed model are accurate because the simulation process done by HFSS and FEKO software tools in the study [25] used the same calculation method, the multilevel fast multipole method (MLFMM). us, from the results of the electric field distribution, from Figures 5(a) and 5(c) and the radiation pattern of the lens antenna with a positive refractive index, we can see that the correlation results between the HFSS and FEKO software tools are done with the same calculation method to confirm the results' accuracy based on our proposed model. e simulation results are indicated in Table 3. e sidelobe level in H-plane reaches the lowest value of -21.80 dB for a positive refractive index lens n � � 2 √ , and −20.17 dB for a negative refractive index lens n � − � 2 √ , while the sidelobe level of the conical horn antenna just gets −18.00 dB. Besides, the half power beam-widths (HPBW) of negative and positive refractive index lens antennas are fairly similar, at 7.78°and 7.13°, respectively. By contrast, the HPBW of a conical horn antenna without lens is 30.50°. e dimension of the lens is determined based on equation (1) and the structure-constructing method of using the simulator. From equation (1), we can see that when the refractive index of the lens is a positive value (n � � 2 √ ), the inner curved surface structure of the lens is convex and directed towards the feed horn. e lens thickness at the center is a maximum, 24.5 mm. However, when the lens's refractive index has a negative value (n � − � 2 √ ), the inner curved surface structure of the lens is concave, and the lens dimension has the thickest at the    International Journal of Antennas and Propagation 5 lens edge and is equal to 6.1 mm, which is significantly thinner than that of positive refractive index lens. As a result, negative refractive index lens antennas for base stations could be designed with smaller sizes reducing outer impacts.

e Electric Field Amplitude Distribution on the Aperture
Plane. e electric field amplitude distributions on the aperture plane of the lens antennas for n � � 2 √ and n � − � 2 √ are shown in Figures 7 and 8. In Figure 7, it is obvious that electric field distributions in both cases are uniform and symmetric around the Z-axis. In addition, Figure 8 shows that the electric field amplitude distribution of the lens antenna is theoretically calculated according to equation (7) and simulated with positive and negative refraction indexes. us, electric field amplitudes on the aperture plane distributed along the lens diameter line are high and tend to decrease gradually to the sides. e simulation results and theoretical calculations are quite similar. is shows the accuracy in the design and theoretical calculations. e ripples on the amplitude distribution lines in case of the simulation occur due to the reflection from the lens surface.

e Effects of Matching Layers.
e comparisons of the radiation patterns of the different refractive index lens antennas with and without matching layers on the yz plane are illustrated in Figure 9. It can be observed that when utilizing quarter wavelength matching layers for the positive refractive index lens, the antenna gain increases by 0.60 dBi compared to the one without quarter wavelength matching layers, whereas the antenna gain is almost unchanged when using MLs for negative refractive index lens. e sidelobe   e investigation into the electric field distribution of lens antennas with and without quarter wavelength matching layers is presented in Figure 10. Spillover and diffraction occur more clearly at the lens edge for a positive refractive index. In Figure 11, the electric field amplitude distributions on the aperture planes between the antenna lens with and without the quarter wavelength matching layers are compared with each other. e results show that, in the case of the positive refractive index lens antennas, the black solid line, which illustrates the field amplitude distribution of the lens antenna with matching layers, is smoother and less jagged than the red dashed one presenting the case without matching layers. In contrast, the field amplitude distribution line of the negative refractive index   International Journal of Antennas and Propagation 7 lens antenna with matching layers is even more rugged than without MLs. is shows the more uniform electric field distribution on the aperture plane of the positive refractive index lens antennas when using the quarter wavelength matching layers. e authors use the ray tracing method to investigate the effects of multiple reflection from the curve lens surface, as shown in Figure 12. Accordingly, black solid lines are the incident rays that travel from the focal point to the inner surface of the lens where the refraction and reflection phenomena occur. Most of the parts of the incident ray power are refracted, which makes outgoing rays parallel to the Z-axis, the solid red lines, while the rest are reflected at the curve surface, the blue dashed lines. is phenomenon causes spillover and diffraction. As to the positive refractive index lens, the lens structure is convex. us, reflected rays from the curve lens surface tend towards diffraction at the lens edge. Meanwhile, reflected rays from negative refractive

Conclusions
Two types of antennas with the positive and negative refractive index lens are simulated by using the electromagnetic simulator ANSYS HFSS. e result accuracy is verified by comparing the obtained antenna parameters with the theoretical calculations. e findings show that when the negative refractive index material is used, the lens thickness is 6.1 mm, which is significantly smaller than that of the positive refractive index material, at 24.5 mm. Further, sidelobe levels are also maintained at a low level, as shown in Table 3. ose results show the effectiveness of using negative refractive index lens antennas in constructing base station antennas. In addition, when investigating the antenna structure, quarter wavelength matching layers are added to the lens to reduce reflection from the curve surface. e results show that the matching layers are an effective choice for improving the radiation properties of a positive refractive index lens antenna.

Data Availability
e data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that there are no conflicts of interest regarding the publication of this paper.