Millimeter Wave Luneburg Lens Antenna Fabricated by Polymer Jetting
Rapid Prototyping
Kokou Gbele1, Min Liang1, Wei-Ren Ng1, Michael E. Gehm2 and Hao Xin1
1
University of Arizona, Tucson, AZ, 85721 USA
2
Duke University, Durham, NC 227708, USA
Abstract— In this paper, the design, fabrication and
characterization of a 3D printed Luneburg lens antenna working
at Ka and Q band are proposed. Gradient index control of the
lens is based on the mixing ratio of air voids and polymer. The
effective dielectric constant of the unit cell was estimated using
effective medium theory and extracted from full-wave finiteelement simulation results. The diameter of the lens was 7 cm. A
3D polymer jetting rapid prototyping technique was employed to
fabricate the lens antenna. In the measurement, the fabricated
lens antenna was fed by Ka and Q band waveguides and the
measured radiation pattern showed this 3D printed lens works
well as a high gain antenna.
L
lens radius to insure a correct gradient index [1]. The
measured dielectric properties of the printing material used in
this design are İr =2.7 and tanįe =0.01. The permittivity of 2.7
allowed the dielectric-air filling ratio to create the required
gradient index per (1) through the volume of the lens. Finiteelement simulation software Ansoft HFSS was applied here to
obtain the relationship between the dielectric rod size and the
effective permittivity of unit cell.
I. INTRODUCTION
uneburg lens is an attractive gradient index component
which can be used as antenna for wide angle scanning
because of its broadband behavior, high gain and the ability to
form multiple beams. Every point on the surface of an ideal
Luneburg lens is the focal point of a plane wave incident from
the opposite side. For a Luneburg lens made of non-magnetic
material, the dielectric constant distribution of the lens is
given by:
(1)
ε r (r ) = 2 − (r / R ) 2
where εr is the dielectric constant, R is the radius of the lens
and r is the distance from a point within the lens to the center
of the lens.
Traditionally, the fabrication of Luneburg lens is realized by
dividing the inhomogeneous lens into finite number of
concentric shells, each shell is fabricated using homogeneous
material with different permittivity and then all the shells are
assembled together. Other methods for building the Luneburg
lens such as drilling holes and changing the thickness of the
shells [2], utilizing metamaterials [3] and adjusting the pattern
on a printed circuit board [4] have also been reported.
However, these methods are mostly used for fabricating 2D
lenses because of their intrinsic or fabrication limitations.
Moreover, the conventional method of fabricating a Luneburg
lens is time consuming and prone to accuracy issue because
each layer needs to be fabricated separately and assembled
carefully.
In this work a Luneburg lens antenna operating at mmW
frequency was designed and fabricated using 3D printing
technique. The lens antenna was tested and highly directional
patterns have been obtained. Compared to other methods, this
3D printed Luneburg lens can be fabricated conveniently at a
lower cost and time.
II. DESIGN, FABRICATION AND MEASUREMENT SETUP
The Luneburg lens is designed with a unit cell periodicity of
2 × 2 × 2 mm3. As shown in Fig. 1, the unit cell is a dielectric
rod with its cross section size varied according to (1) along the
Fig. 1. Cubic unit cell design of the Luneburg lens with an overall dimension
of 2 mm × 2mm × 2mm.
The designed Luneburg lens was fabricated using a polymer
jetting rapid prototyping technique which allows fast
fabrication of 3D polymer components with arbitrary shapes
and complexity. The fabricated Luneburg lens is shown in Fig.
2. Figure 2 (a) shows the cross section at the center of the
Luneburg lens; one can see that the dielectric rod size is larger
at the center of the lens and gradually decreases to a smaller
size at the edge of the lens. Figure 2 (b) shows the entire lens
fed by a Q-band waveguide on the surface of the lens.
The radiation pattern of the lens antenna was measured
using a vector network analyzer (Agilent E8361A) and
preliminary results show a highly directional beam for both Ka
and Q band waveguide feeding. These results indicate the
fabricated Luneburg lens works well as a high direction
antenna in Ka and Q band.
(a)
(b)
Fig. 2. (a) Cross section at the center of the fabricated Luneburg lens. (b)
Feeding the Luneburg lens antenna using a Q band waveguide.
REFERENCES
[1]. R. K. Luneburg, Mathematical Theory of Optics. Los Angeles, CA: Univ.
California Press, 1964.
[2]. L. Xue and V.F. Fusco, “24 GHz automotive radar planar Luneburg lens,”
IET Microw. Antennas Propag., vol. 1, no. 3, pp. 624–628, 2007
[3]. Q. Cheng, H. F. Ma, and T. J. Cui, “Broadband planar Luneburg lens
based on complementary metamaterials,” Appl. Phys. Lett., vol. 95, pp.
181901 - 181901-3, 2009
[4]. C. Pfeiffer and A. Grbic, “A Printed, Broadband Luneburg Lens
Antenna,” IEEE Trans. Antennas & Propagation, vol. 58, no. 9, pp. 30553059, September 2010.