Fresnel Zone Plate and Ordinary Lens Antennas: Comparative Study at

Microwave and Terahertz Frequencies

J. M. Rodríguez, Hristo D. Hristov, and Walter Grote

Departamento de Electrónica, Universidad Técnica Federico Santa María

Av. España 1680, Valparaíso, Chile
hristo.hristov@usm.cl

Abstract
Several realistic FZP lens antennas have been studied numericaly in the 38-GHz microwave and 625-GHz
low-terahertz frequency bands, and have been contrasted to the same in aperture, focal length and feed-horn
ordinary lens antenna. Both types of antennas have (i) close realized gains, (ii) similar bandwidths, (iii) comparable
cross-polar isolations and (iv) input mismatch qualities. It is found that for eight FZP phase-correction levels the
microwave FZP antenna give way to the ordinary lens antenna by 0.8 dB only. Shifting from the microwave to
terahertz band diminishes gain efficiency about 0.5 dB and 10 %, respectively, for both 8-step FZP and ordinary lens
antennas. As a reward, however, the FZP lenses are very much smaller and ligher, simpler for fabrication and have
superior technology tolerance.

1. Introduction

The diffractive in nature Fresnel zone plate (FZP) lenses and based on them lens or reflector antennas have
already have become elements in various microwave and millimeter-wave electronic systems [1-3]. Compared to the
ordinary refractive lenses the FZP lenses are preferred whenever thinner, lighter and easier for production focusing
tools are required. Despite of the fact that the FZP lenses and antennas are quite well examined theoretically their
practical value is still miscalculated. This is partly due to the lack of precise comparative knowledge on similar in
design and size diffractive and refractive (or reflective) devices, lenses or antennas. With the present publication the
authors pretend to fill up in some extent the gaps regarding the FZP lens antennas in two distinct frequency bands:
microwave and terahertz. For each band several designs of ordinary and FZP lens antennas comprising different
dielectric lenses but having the same feed-horn design, aperture and focal dimensions are examined and contrasted
by use of accurate electromagnetic solver [4].

2. FZP vs. Ordinary Lens Antennas

2.1 Dielectric FZP and Ordinary (Refractive) Lenses

The refractive plane-hyperbolic (Fig. 1(a)) dielectric lens has been chosen as a basic ordinary lens [5-6]. It
smoothly transforms by refraction the plane wave into a spherical (focused) one and vise versa, or acts like lens
antennas if designed properly. Parallel to the plane-hyperbolic lens several phase-corrected FZP lenses with
reasonable radiation efficiency are selected [2-3]: two single-dielectric lenses with 4-step (Fig. 1(b)) and 8-step
(Fig. 1(c)) profiles, respectively, and one planar multi-dielectric lens (Fig. 1(d)). The FZP lens makes a stepwise
wave transformation by means of diffraction with a maximum allowed phase error in each wave zone equal to 2π/p
, where usually p = 2, 4, 8 or 16. For p   the Fresnel zone plate is converted to the well known zoned lens.
Ordinary and FZP lenses have been designed for antenna operation at microwave frequency f mw =38 GHz (or
wavelength mw =7.89 mm) and low-terahertz (THz) frequency f thz =625 GHz (or thz =0.48 mm). Each
microwave lens antenna has a focal length Fmm =180 mm (or Fmm  mm =22.8). The lens/antenna aperture diameter
for all lenses is the same, Dmw =190.7 mm ( Dmw  mw =24.15). Thus, the lens aspect ratio Fmw Dmw is equal to
0.94. The single-dielectric FZP lenses (Fig. 1(a-e)) are made of low-loss dielectric material (Rexolite) with a relative
permittivity  =2.53 and a loss factor tan  mw = 0.0003 at 38 GHz. The planar four-dielectric phase-corrected lens

978-1-4244-5118-0/11/$26.00 ©2011 IEEE

 (a) (b) (c) (d)
Figure 1 Dielectric lenses: (a) plane-hyperbolic, Figure 2 Lens antenna with 4-step FZP and
(b) 4-step FZP, (c) 8-step FZP, and corrugated feed-horn
(d) four-dielectric FZP

(Fig. 1(d)) has been employed in addition, where the quarter-wave subzone relative permittivities are in the
following order: 1  1 (air subzone),  2  6.25 ,  3  4 and  4  2.25 . All dielectrics are supposed with a loss
factor equal to that of the Rexolite. The main physical data (depth, volume and weight) of the ordinary plane-
hyperbolic lens, two single-dielectric FZP with 4 and 8 phase correction steps in each wavelength zone,
correspondingly, and one four-dielectric planar FZP are listed in Table 1. The antennas based on the lenses
described above are fed by one and the same feed horn with aperture diameter of 24.9 mm (or mw ) and
axial length of 16.5 mm (or mw ). The feed horn is supposed to be golden with an electric conductivity of
 mw  5·107 S/m. Fig. 2 is a sketch of the lens antenna with 4-step conical corrugated horn with a phase center
at the FZP focal point.

Table 1 Physical data for 38-GHz FZP and

Depth Volume Weight ordinary lenses
Lens
(mm) (cm3) (kg)
Pl.-Hyper. 34.3 457.5 0.48

4-step FZP 11.03 170.4 0.18

8-step FZP 12.7 194.2 0.20

4-diel. FZP 3.9 115.0 -

The 625-GHz terahertz lens antennas are reduced copies of the 38-GHz microwave antennas scaled down by
the linear scale factor s = thz /mw = 0.0608 . Thus, the terahertz lens antenna diameter and focal length are
Dthz  sDmw  11.59 mm and Fthz  sFmw  10.94 mm, respectively. Scaled copies are also the terahertz feed horn
and its metal waveguide. The terahertz lens antennas are made also of Rexolite and golden metal, and both materials
behave much differently at terahertz frequencies [8]. The dielectric permittivities roughly preserve their microwave
values while the loss tangent is much bigger ( tan  thz  0.0045). The electric conductivity of terahertz feed-horn also
different ( thz  4.1·107 S/m). Thus, the electromagnetic characteristics of terahertz and microwave lens antennas
should differ only due to the distinct material loss.

2.2 Physical and Electromagnetic Comparative Results for Microwave and THz
bands
 The study is aimed on contrasting numerically the refractive (ordinary) and diffractive FZP lenses antennas in
two very distinct frequency bands: 38-GHz microwave band and 625-GHz terahertz band. One ordinary lens and
several FZP lenses, and the corresponding lens antennas have been designed, simulated and compared depending on
their diverse configurations and loss influence on the antenna characteristics in the above frequency bands. As a
configuration example a lens antenna having a diffractive 4-step FZP lens is sketched in Fig. 2.

Figs. 3(a) and 3(b) illustrate respectively the gain co-polar (solid lines) and cross-polar (dash lines)
radiation patterns of plane-hyperbolic lens antenna and 8-level phase-corrected FZP lens antenna simulated at the
diagonal cut plane   450 for the design microwave frequency of 38 GHz.
0 0

-10 -10

-20 -20
Gain Pattern (dB)

Gain Pattern (dB)

-30 -30

-40 -40

-50 -50

-60 -60

-70 -70

-80 -80
-150 -100 -50 0 50 100 150 -150 -100 -50 0 50 100 150
Angle (deg) Angle (deg)

(a) (b)
Figure 3 Gain co-polar (solid line) and cross-polar (dot line) radiation patterns of (a) plane-hyperbolic lens antenna
and (b) 8-step FZP lens antenna.

In Fig. 4 are given the realized antenna gain vs. frequency graphs in the (a) 38-GHz band (~30-50 GHz) for
2-step, 4-step, and 8-step FZP lenses, and plane-hyperbolic lens, and (b) 625-GHz band (~500-850 GHz) for 8-step
FZP lens and plane-hyperbolic lens only as these lenses suffer bigger influence by the material loss change.
38 38

36 36

34 34

32 32
Gain (dB)

Gain (dB)

30 30

28 28

26 26

24 24

22 22

20 20
30 35 40 45 50 500 550 600 650 700 750 800 850
Frequency (GHz) Frequency (GHz)

(a) (b)
Figure 4 Realized gain graphs vs. frequency in the: (a) microwave band for plane-hyperbolic lens (solid line), and,
8-step (dash-dot line) and 4-step (dash line) and 2-step (dot line) FZP lenses and (b) terahertz frequency band, for 8-
step (dot line) plane-hyperbolic lens (solid line),

Table 2 FZP and ordinary lens antenna parameters

for the microwave and terahertz bands
Greal Eff BW BnW Ixp S11
Lens/Antenna parameters
(dB) (%) (deg) (%) (dB) (dB)
1. 38-GHz 4-step FZP 34.2 45.7 2.85 34 31 -19.1
3. 38-GHz 4-diel. FZP 34.7 51.2 2.70 23 36 -16.6
4. 38-GHz 8-step FZP 34.9 53.7 2.75 33 31 -19.7
4.1 625-GHz 8-step FZP 34.4 47.9 2.90 32 29 -16.3
5. 38-GHz Pl-Hyp. lens 35.7 66.6 2.75  80 35 -14.7
5.1 625-GHz Pl-Hyp. lens 35.2 57.6 2.75  80 34 -15.3
 Table 2 summarizes the main electromagnetic parameters of 38-GHz antenna designs employing two single-
dielectric FZP lenses (no. 1 and no. 4) with four or eight phase-correction steps, one four-dielectric FZP lens (no.
3), and one plane-hyperbolic lens (no. 5). Two of the 38-GHz antennas are scaled down in size (no. 4.1 and no. 5.1)
to fit the 625-GHz band. The antenna parameters of interest are: (a) maximum realized co-polar gain Greal in
decibels and the corresponding antenna efficiency Eff in percent around the design frequency. Greal and Eff take
into account all a BnW in percents relative to the peak gain frequency, (b) minimum cross-polar isolation Ixp in
decibels, antenna losses (material, mismatch, polarization, etc.), (c) half-power main lobe beamwidth BW in
degrees; (d) 3-dB gain bandwidth calculated at the diagonal  = 450 -plane in the  -interval 1800  0    180 ,
and (e) input scattering (reflection) coefficient S11 in decibels.

3. Conclusion

Several realistic microwave and low-terahertz FZP lens antennas have been numerically studied in detail in
two frequency bands: microwave and terahertz. They are contrasted to the same in aperture, focal length and feed-
horn ordinary lens antenna with plane-hyperbolic lens. It is found that for four or more FZP phase-correction levels
(steps or different dielectrics) both antenna types, FZP and ordinary, have (i) close Greal values, (ii) similar
beamwidths, and (iii) comparable cross-polar isolations and mismatch qualities. In both 38-GHz and 625-GHz bands
the 8-step microwave FZP antenna give way before the ordinary lens antenna by 0.8 dB only. Our extra study has
shown that the 16-step FZP antenna is closer in gain to the ordinary lens but comes at the expense of the bigger size
and production complexity. Shifting from the microwave to terahertz band diminishes Greal and Eff by about 0.5
dB and 10 %, respectively, for both 8-step FZP and ordinary lens antennas.

Because the examined FZP lenses and antennas are much narrowbanded than the ordinary ones all these
parameter similarities are hold in a smaller bandwidth of about 20-30%.

As a reward, however, the FZP lenses are very much smaller in depth, volume and weight than the ordinary
lenses (Table 1), and this leads to a creation of significantly lighter lens antennas with a constrained frequency
bandwidth. Besides, the diffractive plane-step FZP lenses are simpler and easier for production compared to the
thick or zoned refractive antenna lenses. And finally, it is known that the diffractive lenses have better tolerance
superiority compared to the refractive ones, which in addition ease their fabrication.

A feasible application of FZP optics similar to the studied here is envisioned in a receiver for the Atacama
Large Millimeter Array (ALMA) radio telescope in Chile, for operation in the low-frequency mm-wave band
between 31 GHz and 45 GHz.

4. Acknowledgments
The authors acknowledge the support of the Chilean Conicyt Agency under the Fondecyt Research Project
1095012/09 executed at Departamento de Electrónica, Universidad Técnica Federico Santa María, Valparaíso.

5. References
[1] J. C. Wiltse, Editor, Microwave and millimeter-wave engineering for communications and radar , SPIE, vol.
CR54, Chapter 11, Nov. 1994, pp. 273-293.

[2] H. D, Hristov, Fresnel zones in wireless links, zone plate lenses and antennas, Artech House, 2000.

[3] I. V. Minin and O. V. Minin, Diffractional optics of millimeter waves, IoP, Bristol, UK, 2004.

[4] CST microwave studio, CST Computer simulation technology AG, 2010.

[5] Y. T. Lo, and S. W. Lee, Antenna handbook, Springer, 1993.

[6] P. F. Goldsmith, Quasioptical Systems, Wiley, 1998.