Simple generation of orbital angular momentum modes with azimuthally deformed cassegrain subreflector

1. 1
Simple generation of orbital angular
momentum (OAM) modes with azimuthally
deformed Cassegrain subreflector
W.J. Byun, Y.S. Lee, B.S. Kim, K.S. Kim, M.S. Kang, and
Y.H. Cho
A parabolic reflector antenna with an azimuthally deformed Cassegrain
subreflector is proposed to effectively generate arbitrary orbital angular
momentum (OAM) modes. The Cassegrain dual-reflector antenna was
fabricated for 18 GHz and measured in near-field range. Near-field to
far-field transformed radiation phase around full azimuth shows that the
proposed antenna generates fields with the 1=l OAM mode.
Simulated and measured feed reflection coefficients are below -10 dB
for 15.1 to 21.2 GHz, even though distance between a horn feed and a
deformed subreflector is 15.6 mm, thus expecting that our structure can
be used for a broadband low-profile antenna.
Introduction: Various researches based on orbital angular momentum
(OAM) modes have been extensively studied in optics [1]. Recently,
communication systems analogous to optical one were demonstrated in
radio frequency [2]-[4]. To utilize OAM characteristics for radio
communications, generating and detecting arbitrary OAM modes is
essential. In [2], a helicoidally parabolic reflector, which is similar to
[5], is used as a main reflector to transmit electromagnetic waves with
fundamental OAM mode ( 1=l ). In view of reflector antenna design,
fabricating the main parabolic surface as a helicoid [2], [5] is expensive
and inefficient, because ordinary main reflectors should be modified for
the generation of non-zero OAM modes. Therefore, we need a simple
and efficient method to generate arbitrary OAM modes with keeping the
main reflector unchanged. In this Work, we propose an alternative
structure [6] in which a Cassegrain subreflector is azimuthally deformed
instead of a main parabolic reflector. A parabolic reflector antenna with
an azimuthally deformed Cassegrain subreflector enables us to process
small area of a subreflector without modifying a large main reflector.
Because of this merit, we can adopt a variety of ordinary main reflectors
for the efficient generation of arbitrary OAM modes. In addition, the
proposed antenna has very good reflection characteristics due to the fact
that a deformed subreflector radiates higher-order OAM modes which
cannot be received by a normal feed horn.
Deformed Subreflector: A dual-reflector antenna is usually designed
with well-established standard procedures, for instance, depicted in [7].
In order to generate the specific OAM mode, the azimuthally deformed
surface of a subreflector defz is formulated by
)(),(subdef fn
lyxfz Φ−= , (1)
where ),(sub yxf is one of ordinary subreflector profiles including
Cassegrain, Gregorian [7], or axially displaced ellipse (ADE) types, l is
the number of OAM mode,
1
10
for
24
)( +
+
<≤




 +
−=Φ nn
nnn
l
l
fff
ff
f
π
l
f (2)
1,,1,0for
2
−== ln
l
n
n 
π
f , (3)
0λ is free-space wavelength, and )/(tan 1
xy−
=φ . When 0=l , (1)
reduces to common subreflector surface, ),(subdef yxfz = . It is noted
that the design formula similar to (1) has been already proposed for a
main parabolic reflector [5]. Based on (1) and [7], we designed a
parabolic reflector antenna with a deformed Cassegrain subreflector to
form fundamental OAM mode ( 1=l ). The antenna parameters defined
in [7] for a Cassegrain dual-reflector are as follows: main parabolic
reflector diameter ( mD ) = 237 mm, Cassegrain subreflector diameter
( sD ) = 35.6 mm, DF / = 0.4, and horn feed aperture = 26×19.5 mm2
,
10dB feed beamwidth ( cθ ) =

74 , mL = 62.6 mm, sL = 21 mm, and
a = 4.9 mm [7].
Fig. 1 Geometry of parabolic reflector antenna with azimuthally
deformed Cassegrain subreflector in near-field measurement facility
Fig. 2 Measured near-field phase distributions of parabolic reflector
antenna with deformed Cassegrain subreflector with f = 18 GHz
Measurement and Discussions: In order to verify feasibility of a
newly proposed antenna structure, we manufactured a main parabolic
reflector and an azimuthally deformed Cassegrain subreflector, and
performed near-field antenna measurement at f = 18 GHz illustrated
in Fig. 1. The subreflector surface was modified to form an azimuthally
deformed Cassegrain profile according to (1). Note that the deformed
profile (1) inevitably results in abrupt step at 0=φ shown in Fig. 1.
Main strong point of the proposed design is that a small area of a
subreflector, compared to a large main reflector, is processed to obtain
the 1=l OAM mode, and the main reflector can be chosen by
conventional ones such as a parabolic reflector or a reflectarray. This
property gives the flexibility of selection of main reflectors. Fig. 2
shows measured near-field phase distributions for the antenna in Fig. 1.
We can observe that near-field phase varies linearly around azimuth
( φ ), even though linear phase variation becomes deteriorated near
0=φ due to the abrupt step formed at 0=φ in Fig. 1. It is shown in
Fig. 3 that the proposed antenna has excellent reflection characteristics
for 15.1 to 21.2 GHz, both simulation and measurement. Even though
distance between a horn feed and a deformed subreflector in Fig. 1 is
very short, approximately 15.6 mm, feed reflection level is below -10
dB. This is because directly reflected wave from the subreflector has

2. 2
helical phase behaviour ( 1=l ) and it can be hardly received into a
normal horn feed with 0=l mode. As for a conventional Cassegrain
subreflector, direct reflection from near subreflector surface is severe
and it deteriorates overall gain behaviour. In terms of reflection
coefficient and antenna profile, our antenna in Fig. 1 is superior to the
previous parabolic reflector antenna in [5].
Fig. 3 Behaviour of reflection coefficients against frequency for
parabolic antenna with deformed Cassegrain subreflector in Fig. 1
Fig. 4 presents the far-field radiation patterns obtained by
transforming measured near-field distributions in Fig. 2. The simulated
and measured antenna gains are 25.3 dBi and 23.3 dBi, respectively.
Corresponding aperture efficiencies are 17% and 11%. Since E- and H-
plane directivity patterns in Fig. 4 have null at 0=θ , we assure that
the antenna in Fig. 1 generates non-zero OAM mode. Using the near-
field patterns in Fig. 2, transformed far-field co-polarization phase
around full azimuth ( φ ) is subsequently given in Fig. 5, thus
confirming that our antenna radiates the 1=l OAM mode.
Fig. 4 Near-field to far-field transformed directivity against observation
angle θ with near-field distributions in Fig. 2
-·-·-·-·- CST simulation ( 
0=φ )
——— measurement ( 
0=φ )
………. CST simulation ( 
90=φ )
--------- measurement ( 
90=φ )
Conclusion: A parabolic reflector antenna with an azimuthally
deformed Cassegrain subreflector was designed and fabricated to
confirm that the proposed antenna can generate the 1=l OAM mode
and feed reflection coefficient is below -10 dB, both simulation and
measurement. Near-field antenna measurement was performed and its
transformed far-field patterns clearly show that far-field radiation phase
varies linearly against azimuthal angle. Our proposed antenna structure
for OAM mode generation can be applied to other high gain antenna
including various subreflector or reflectarray types.
Fig. 5 Near-field to far-field transformed co-polarization phase against
azimuthal angle φ with near-field distributions in Fig. 2 and fixed polar
angle 
3=θ
Acknowledgments: This work was supported by Institute for
Information & communications Technology Promotion (IITP) grant
funded by the Korea government (MSIP) (No. B0101-15-222,
Development of core technologies to improve spectral efficiency for
mobile big-bang).
W.J. Byun, Y.S. Lee, B.S. Kim, K.S. Kim and M.S. Kang (Microwave
Technology Research Section, Electronics and Telecommunications
Research Institute (ETRI), Gajeong-ro 218, Yuseong-gu, Daejeon, 305-
700, Korea)
Y.H. Cho (School of Information & Communication Convergence
Engineering, Mokwon University, Doanbuk-ro 88, Seo-gu, Daejeon,
35349, Korea)
E-mail: yongheuicho@gmail.com
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