3D Printed Dielectric Fresnel Lens
Shiyu Zhang
School of Electronic, Electrical and Systems Engineering, Loughborough University, Loughborough, UK, LE11 3TU.
S.Zhang@lboro.ac.uk
Abstract— This paper presents the design and fabrication of
a zone plate Fresnel lens. 3D Printing is used for rapid
prototyping this low-cost and light-weight lens to operate at 10
GHz. This lens is comprised of four different 3D printed
dielectric zones to form phase compensation in a Fresnel lens.
The dielectric zones are fabricated with different infill
percentage to create tailored dielectric constants. The dielectric
lens offers 18 dBi directivity at 10 GHz when illuminated by a
waveguide source.
Index Terms— Fresnel lens, zone plate, flat lens, additive
manufacturing, 3D Printing
I. INTRODUCTION
Lens antennas have been widely studied due to the highly
directional radiation, wide angle scanning and formed beam.
The lenses are able to transform the spherical wave fronts into
plane wave fronts to enhance the directivity of the antennas
[1]–[5]. Fresnel lenses (FL) are relatively thin and flat, they
usually have smaller volumes and weighs compared with
conventional shaped lenses. They can be fabricated by using
inexpensive dielectric materials, which makes them suitable
for consumer applications [6]–[9].
The traditional fabrication approaches for dielectric lenses
are dominated by using mechanical machining. The lens
surface can be grooved to lead the wave have higher phase
velocity by travelling through the grooved zones. Another
method to accomplish the phase correction is to divide the lens
into several concentric zones with different dielectric
constants. This approach can be either realised by several
tightly fitted concentric dielectric rings with various dielectric
constants, or using uniform dielectric material that is
perforated to create different dielectric zones [10], [11]. The
FL that fabricated using the dielectric zones method generally
has uniform thickness with flat surface, however the precisely
machining is involved in which increases manufacturing
complexity. Moreover, the machining technique removes or
shapes parts of the raw materials which generates material
waste.
The three-dimensional (3D) Printing technology constructs
objects as successive layers. It is one-step process and able to
generate complex internal structures. It significantly simplifies
the manufacture process and reduces material waste.
Furthermore, 3D Printing can create perforated structures that
are difficult to be realised by machining due to the mechanical
strength of material.
The dielectric materials can be custom-made by using 3D
Printing [12]. By adjusting the infill percentage of the 3D
material, it can create materials with bespoke structures with
customised dielectric constant values. The 3D Printed
dielectric materials which are cost efficient and can be rapidly
prototyped. This gives engineers more freedom in antenna
design.
This paper presents a novel dielectric FL that fabricated by
using 3D Printing. In this work, an ABS based 3D Printing
filament PREPERM
®
TP20280 was used. The dielectric
constant of this 3D filament was characterised as 4.4 and loss
tangent was 0.004. This material could be both injection
moulded or extruded to form a designed shape. A fused
deposition modelling (FDM) Makerbot® Replicator™ 2X 3D-
printer was used to fabricate the FL. The extrusion temperature
was 230°C with the 110°C heated platform. The lens geometry
was designed with radially varied infill percentages. Then the
dielectrics were printed as non-solid which leads air voids into
the lens and therefore the dielectric constants of the zones in
the FL were tailor-fabricated. The entire FL was fabricated in
one-step process.
II. P
ROTOTYPE DESIGN
The design of the FL was carried out at 10 GHz and the
lens had a uniform thickness. The radii (Ri) for each dielectric
zone can be determined using:
=
2
+ (
)
i = 2, 3, …, P (1)
Where P is the phase correcting index, λ
o
is the design
wavelength and F is focal length. In this work the lens was
designed for quarter wave phase correction. An F/D = 0.3 was
chosen, to obtain a short focal length. The diagram of the FL
is shown in Fig. 1. The focal length F was 30 mm.
The thickness of the lens t is related to the dielectric
constants of two adjacent Fresnel zones and it can be obtained
using:
=
(
)
s = 2, 3, …, P (2)
1
2
3
4
45.0
67.0
86.2
104.0 mm
Fig. 1. Dielectric Fresnel lens design
In this design, the highest dielectric constant value was 4.4
which was realised by using 100% infill 3D material. In order
to reduce the thickness and the weight, the centre ring with the
minimum dielectric constant was equal to 1 which was air.
Therefore the lens was made of three dielectric rings and one
air ring per full-wave zone. By substituting P = 4,
t = 20.5 mm,
Ɛ
max
= 4.4, Ɛ
min
= 1 and λ
o
= 30 mm into (2), the
dielectric constant value for each ring could be obtained. The
values with the corresponding infill percentages for the
Fresnel zone radii are given in Table I.
TABLE I FRESNEL ZONE RADII AND CORRESPOIND DIELECTRIC CONSTANTS
i Ɛ
r
R
i
in mm Infill percentage in %
1
1.0
22.5
0
2
4.4
33.5
100
3
3.0
43.1
58.8
4
1.9
52.0
25.6
III. R
ESULTS
A simulation was carried out using CST MICROWAVE
STUDIO. The 3D modelling of this dielectric FL is shown in
Fig. 2. The innermost ring was empty which had equivalent
dielectric constant = 1. The empty centre significantly reduced
the weight of the lens. A rectangular waveguide source with
dimension of 22.86 mm × 10.16 mm was located at the focal
point on the lens axis.
Fig. 2. The dielectric FL is illuminated by a rectangular waveguide source
located on the axis
The simulated electric field in the XoZ plane of the
dielectric FL with the waveguide source is shown in Fig. 3. It
shows that FL reduced the width of the main radiation lobe of
the source, which would enhance the directivity and led to an
increased gain. The far field patterns of the dielectric FL at the
frequency 10 GHz is shown in Fig. 4. This dielectric FL
antenna had directivity 18.2 dBi. The directivity was
significantly increased at boresight (theta = 0°). The -3dB
angular width was approximately 16°. Since this dielectric FL
had a small focal length, the short distance between FL and
waveguide reduced the side lobe level.
Fig. 3 Simulated electric field in XoZ plane of the dielectric FL with the
waveguide source at 10 GHz
Dielectric FL
Waveguide
source
Fig. 4. Simulated Far field pattern of dielectric FL in XoZ plane at 10 GHz
IV. CONCLUSION
This paper has presented a low-profile and light-weight
dielectric Fresnel lens. The 10 cm diameter prototype lens
with 90° phase correction was comprised of three dielectric
rings and one empty ring at the centre. The dielectric FL
antenna offered directivity enhancement and suitable for
various antenna applications.
The rapid prototyping 3D Printing technique was used for
fabrication this dielectric lens to give bespoke dielectric
constants for each ring. The dielectric rings were printed as
non-solid internal structures with specific material infill
percentage. The entire lens could be 3D printed in a single-
step process without machining or assembling, which
significantly simplified the manufacturing process.
ACKNOWLEDGMENT
The authors would like to thank the Premix for providing
the 3D Printing filament.
R
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-20
-10
0
10
20
-90 -60 -30 0 30 60 90
Directivity (dBi)
Theta / Degree
