Electromagnetic Field Simulation of Dielectric Lens Antenna
Keiichi Itoh1, Katsumasa Miyata1, and Hajime Igarashi2
1

Akita National College of Technology, Japan
Graduate School of Information Science and Technology, Hokkaido University, Japan

2

Introduction

22.1

Simulation of Dielectric Lens Antenna

Simulation ModelFig.1 shows the operation of the waveguide slot antenna andthe image of its radiation patterns both with and without thedielectric lens. The slot which is cut in the wall of thewaveguide becomes the radiator, since the slot intercepts thecurrent flow on the wall. The radiation power from the slot
increases as the offset from the center of the waveguide
increases [3][4]. When the dielectric lens is loaded over the slot
aperture, the beam width of the radiation patterns becomesnarrower, and the radiation power in the far-field is enhanced.
In this paper, the analysis condition of the waveguide slot
antenna is set as follows: (1) the waveguide inner size a×b is
22.90×10.2 mm, (2) the waveguide is excited by TE10 mode, and(3) the target frequency is 12 GHz. Next, the proposed dielectriclens is defined as follows: (1) the diameter of the dielectric lens
 is 20 mm which is smaller than the wavelength = 25 mm, (2)the relative permittivity r and the loss tangent tan are 2.2 and10-4, respectively. In the FDTD modeling of the dielectric lens,
the sphere shape is approximately divided into the rectangularparallelepiped cells whose size is 0.5 mm. Hence, because theratio / is very small (/ =0.025), the proposed lens consistsof adequate number of the cells. The dielectric loss of theproposed lens is assumed to be negligible. Substitution of thecondition in Fig.1 into the equation (1) yields theconductivity=1.469×10-4 S/m.
(1)
   r  0 tan Fig. 1. Operation of the waveguide slot antenna and theimage of the radiation patterns with the dielectric lens.

(a) Without lens(b) With lensFig. 2. Visualization of the radio wave propagation from thewaveguide slot antenna by the FDTD method (500 time steps).
40

40

y [mm]

Generally, the larger an antenna aperture size, the higher thegain of the antenna becomes. However, by loading a dielectriclens on the antenna aperture, the antenna gain is expected to beimproved even for the small aperture antenna; which is called adielectric lens antenna. The problem of a dielectric lens antenna
is bulky, because the diameter of a lens  is usually larger than
the wavelength ; for example,  is one to five times as large as [1]. To develop a small planer antenna system, we load small
spherical dielectric lens over the slot aperture of the waveguideslot antenna [2]. The features of the proposed lens include; (1)the diameter is smaller than the wavelength, (2) the shape is not
the ordinary extended hemisphere but sphere. The small
spherical lens has the advantage that the miniaturization of theantenna becomes easy in comparison with the conventional lens.
To evaluate the performance of the antenna with theproposed lenses, we calculate the electromagnetic field of thewaveguide slot antenna by using finite-difference time-domain(FDTD) method [2]. As the FDTD method is a powerful tool forthe transient analysis, it is possible to analyze the radio wave
propagation from the antenna numerically and to visualize it.
This paper describes the FDTD modeling of the dielectric lensand the convergence effect of the proposed lens.
Next, we apply the FDTD method to the design of the
waveguide slot antenna. It would be difficult to apply theoretical
approaches to the analysis and design of the dielectric lensantennas. However, the FDTD method allows us to design evennovel antennas loaded by dielectric lenses. This paper reports
the usefulness of the design by the FDTD method for a 10-slot
waveguide slot array antenna.

y [mm]

1200−200x [mm]20200−200x [mm]20(a) Without lens(b) With lensFig. 3. The calculation results of the ray which is radiatedfrom the point source by using the ray tracing method.
2.2

Convergence Effect of Dielectric Lens
We confirm both validity of the FDTD modeling of thedielectric sphere and convergence effect by visualizing theradiation from the slot. The perfectly matched layers (PML) areused as the absorbing boundary conditions. The calculation time
step is 9.623×10-13 s. As shown in Fig.2, the radiation with the3.1

Design of Resonant Array Antenna
We apply the FDTD method to the waveguide slot array
antenna design. Fig.4 shows a 10-slot waveguide slot array
antenna which has the short terminator with distance g/4 fromthe last slot, because the target antenna is operated as theresonant array. The design parameter is the slot length, the slot
spacing, and the slot offset. To simplify the design, the slot
length and the slot spacing are fixed to the resonant length asshown in Table 1, where the slot length with the dielectric lensbecomes shorter than the half wavelength [5]. Consequently,
the antenna design in this section is equivalent to determining
the slot offset value. Therefore, by varying the slot offset value,
we find the optimal slot offset value by using the FDTD method.
Table 1. Antenna Design Parameter
Parameters

With lensWithout lensSlot length L

10.5 mm (</2)

12.5 mm (=/2)

Slot spacing d

15 mm (=g/2)

3.2

Design Results
Fig.5 shows the calculation result of the radiation power andthe voltage standing wave ratio (VSWR). The radiation power isdefined as the maximum value of the radiation patterns. The
radiation power with the dielectric lens increases monotonously
as the slot offset increases. In contrast, the radiation power
without the lens has the peak value at x=3.5 mm. Usually, theslot offset is chosen to minimize VSWR [4][5]. The slot offset
which minimizes VSWR shows different value between with andwithout the dielectric lenses.
Fig.6 shows the calculated radiation patterns of the designed
antennas whose offset value is chosen from Fig.5. The
electromagnetic field simulation by using the FDTD method
demonstrates good performance for the resonant array design,
since the side-lobe level of both antennas becomes about 13 dB.
Also, the enhancement of the radiation power by loading theproposed lens is confirmed.
4Conclusion

We have applied the FDTD method to demonstrate thefeatures of the proposed dielectric lens on the waveguide slot
antenna. By visualizing the radiation from the slot, theconvergence effect of the proposed lens has confirmed. Also, we
have demonstrated the usefulness of the design method based on
the FDTD method as an example of the dielectric lens antenna.
The present design method is simpler and more convenient thanthe conventional design method [3][4] and is useful to develop
novel antennas.
Additionally, to design the electromagnetic devices, theevolutional design method by combining the FDTD method andthe genetic algorithm (GA) is proposed [6][7]. The evolutional
design of the non-resonant waveguide array antenna with theproposed lens has been reported in [7]. The establishment of theFig. 4. The design parameter and analysis model of 10-slot
waveguide slot array antenna with dielectric lenses.
−25

7With lensWithout lens

−30

6−35

5−40

4−45

3−50

2−55

4VSWR

Antenna Design

Radiation power [dB]

3antenna design method by the electromagnetic field simulationis the subject in future.

11068Slot offset x [mm]Fig. 5. The radiation power and VSWR versus the slot offset.
−30
Radiation power [dB]dielectric lens is found to be focused in the center comparedwith that without the lens. To evaluate the lens convergence, wecalculate the radiation from the slot by using another simulation
method. Fig.3 shows the calculation results by the ray tracing
method assuming the point wave source. It is demonstrated thatthe ray with the proposed lens converges in the center as well as
the results by the FDTD method.
Even though the diameter of the dielectric lens is smaller
than the wavelength, we confirm that the radiation converges inthe center. Additionally, it is thought that the FDTD modellingof the dielectric sphere is valid.

With lens−40 (Slot offset=7.5[mm])Without lens(Slot offset=4.0[mm])−50−60−70−80−90−60−30030Angle [deg]6090Fig. 6. The comparison of the radiation patterns of thedesigned antennas.
Acknowledgements
The work is partly supported by the collaborative
research program 2011, information initiative center,
Hokkaido University, Sapporo, Japan.
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