\documentclass[10pt]{article}

\usepackage{fullpage}
\usepackage{setspace}
\usepackage{parskip}
\usepackage{titlesec}
\usepackage[section]{placeins}
\usepackage{xcolor}
\usepackage{breakcites}
\usepackage{lineno}
\usepackage{hyphenat}





\PassOptionsToPackage{hyphens}{url}
\usepackage[colorlinks = true,
            linkcolor = blue,
            urlcolor  = blue,
            citecolor = blue,
            anchorcolor = blue]{hyperref}
\usepackage{etoolbox}
\makeatletter
\patchcmd\@combinedblfloats{\box\@outputbox}{\unvbox\@outputbox}{}{%
  \errmessage{\noexpand\@combinedblfloats could not be patched}%
}%
\makeatother


\usepackage{natbib}




\renewenvironment{abstract}
  {{\bfseries\noindent{\abstractname}\par\nobreak}\footnotesize}
  {\bigskip}

\titlespacing{\section}{0pt}{*3}{*1}
\titlespacing{\subsection}{0pt}{*2}{*0.5}
\titlespacing{\subsubsection}{0pt}{*1.5}{0pt}


\usepackage{authblk}


\usepackage{graphicx}
\usepackage[space]{grffile}
\usepackage{latexsym}
\usepackage{textcomp}
\usepackage{longtable}
\usepackage{tabulary}
\usepackage{booktabs,array,multirow}
\usepackage{amsfonts,amsmath,amssymb}
\providecommand\citet{\cite}
\providecommand\citep{\cite}
\providecommand\citealt{\cite}
% You can conditionalize code for latexml or normal latex using this.
\newif\iflatexml\latexmlfalse
\providecommand{\tightlist}{\setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}%

\AtBeginDocument{\DeclareGraphicsExtensions{.pdf,.PDF,.eps,.EPS,.png,.PNG,.tif,.TIF,.jpg,.JPG,.jpeg,.JPEG}}

\usepackage[utf8]{inputenc}
\usepackage[ngerman,greek,english]{babel}



\usepackage{float}








\begin{document}

\title{An Only Metal, Compact, and Circular Polarizer Designed with Helical
Array Rods}



\author[1]{Seyed Jalil Hosseini}%
\affil[1]{Iran University of Science and Technology}%


\vspace{-1em}



  
  \date{June 16, 2024}


\begingroup
\let\center\flushleft
\let\endcenter\endflushleft
\maketitle
\endgroup





\selectlanguage{english}
\begin{abstract}
This paper presents a simple method to realize a circular polarizer by
inserting rods arranged helically in the cylindrical waveguide. In the
proposed polarizer, the rods are installed to excite the electric fields
on the perpendicular axis to the input field. In addition, the rod
locations create a 900 \selectlanguage{english}phase difference between two perpendicular axes
to convert the polarization from linear to circular. In the proposed
structure, the axial ratio is smaller than 0.4 dB and the phase
difference is about 900 \selectlanguage{english}at 10 GHz frequency. In addition, the reflection
coefficients are better than -14 dB for both E\_x and E\_y polarizations
at the same frequency. Also, this structure is very compact compared to
similar structures. Furthermore, this is made only of metal. Therefore,
there is no dielectric loss and it has high endurance. The validation
results have a good agreement with the simulation.%
\end{abstract}%



\sloppy


\section*{Introduction}

{\label{introduction}}

Waveguide polarizers are frequently used to increase the system's
attractiveness, and are mostly used in aperture antennas. The circular
polarizer waveguides (CPWs) convert a field with linear polarization
(LP) into a circular one. For the goal, the electric field should be
excited in two axes that are perpendicular to each other {[}1{]}.

The proposed CPW is compared to the previous ones as follows. C. Chang
et al. present a rectangular bending waveguide that converts an LP field
into a circular polarization (CP) field. Because the dominant mode is
the TE\textsubscript{10}, in the rectangular waveguides, the CPW can
convert the LP-TE\textsubscript{10} mode to the CP-TE\textsubscript{10}.
The major disadvantage of the structure is the misalignment of the inlet
and outlet. Hence, the CPW is not suitable for many applications
{[}2{]}. In Ref. {[}3{]}, a K-band CPW is investigated. A pair of
rectangular waveguides has been converted into a circular waveguide.
Also, a stepped blade is used inside the polarizer. The first problem of
the CPW is to be very long (about 5\(\lambda_{0}\)). Therefore, a
rectangular or circular waveguide cannot be used to convert a linear
field into a circular one. Rather, a rectangle-to-circle waveguide
converter should be used, which increases the complexity of the CPW.
Ref. {[}4{]} proposes a CPW that can transduce an LP field to CP one by
a dielectric septum. By using dielectric in the structure, the loss is
increased, dramatically. Therefore, electrical breakdown increases due
to the increase in the possibility of electrical creep. Hence, the
structure is unsuitable for high-power microwave (HPM) applications. The
CPW proposed in Ref. {[}5{]}, is a mode converter. The mode converters
installed to the outlet of the electromagnetics sources to convert a
donut-shaped pattern to a directive one are the waveguides that
transduce a TM\textsubscript{01} or TEM mode to a
TE\textsubscript{11}mode and or to a TE\textsubscript{10} mode, in the
circular and rectangular waveguide, respectively {[}6-16{]}. The CPW
introduced in Ref. {[}5{]}, is a mode converter that converts an
LP-TM\textsubscript{01} mode to a CP-TE\textsubscript{11} one. Due to
the excitation of TM\textsubscript{01} mode in the CPW input, its
applications are limited. Ref. {[}17{]} introduces a pair of grooves on
the wall of a waveguide installed on the length of the CPW. The use of
grooves has caused complexity in the CPW structure. In addition, a
simple circular waveguide cannot be used as a CPW. Also, due to the
increase in the external volume of the system, its compactness has
decreased, dramatically.

In this paper, we tried to resolve the limitations of the previous
structures. In the compact CPW proposed, we have used only a metal
structure to achieve a simple method to transduce an LP to a CP field in
a simple circular waveguide. Using only metal increases efficiency and
eliminates dielectric losses, completely. The only metal structure aim
is the ease of implementation and reduction of complexity. Also, the
proposed CPW is designed such that it does not occupy any volume outside
the circular waveguide. Hence the proposed CPW compactness is increased,
dramatically.

This paper is organized as follows. Sec. 2 presents the structure and
design of the proposed CPW. Sec. 3 reports some numerical studies on the
CPW features. Finally, in Sec. 4, the conclusion is presented.

\section*{Design Principle and
Structure}

{\label{design-principle-and-structure}}

The proposed polarizer consists of a circular metallic waveguide and a
few metal rods. The input field is in the form of the
LP-TE\textsubscript{11} mode of a circular waveguide. In a circular
waveguide, TE\textsubscript{11} mode is the dominant or fundamental
mode. Also, the output mode is CP-TE\textsubscript{11} of a circular
waveguide {[}18-22{]}. In the structure, inside the simple circular
waveguide, several metal rods are placed. These rods are arranged with
different lengths, helically. Because to generate a CP field, it must be
equally excited in two perpendicular axes (for example, X and Y). This
issue alone will not enough to generate a CP field, but the phase
difference between the two excited fields in the X and Y direction must
be 90\selectlanguage{ngerman}° {[}23-26{]}. If the phase difference is zero degrees, the
polarization will be slant. Furthermore, If the excited field in two
perpendicular axes is not equal or the phase difference is not zero or
90°, the field polarization is elliptical. The lengths of the rods have
been calculated and optimized to excite the equal electric fields in two
perpendicular axes with a phase difference of 90°, in the circular
waveguide outlet. In Fig. 1, the proposed CPW is shown.

Fig. 1. The proposed CPW structure, (a) top view, (b) side view

The proposed CPW is simulated and optimized with CST Microwave Studio.
Also, the results are validated by Ansys HFSS software. In the
structure, the operation frequency is selected at 10 GHz. To prevent the
excitation of higher modes, the diameter of the circular waveguide is 20
mm. In Table 1, the dimensions of the CPW are presented.

Fig. 2. The dimensions of the proposed CPW

The dimensions indicated in Fig. 2 are listed in Table 1.

Table 1. The proposed CPW dimensions.\selectlanguage{english}
\begin{longtable}[]{@{}llll@{}}
\toprule
\textbf{Dimension} & \textbf{Value (mm)} & \textbf{Dimension} &
\textbf{Value (mm)}\tabularnewline
\midrule
\endhead
d\textsubscript{w} & 20.00 & L\textsubscript{7} & 2.78\tabularnewline
L\textsubscript{w} & 55.12 & L\textsubscript{8} & 3.43\tabularnewline
s & 4.37 & L\textsubscript{9} & 1.83\tabularnewline
d & 2.50 & L\textsubscript{10} & 4.75\tabularnewline
d\textsubscript{r} & 1.24 & L\textsubscript{11} & 5.33\tabularnewline
t & 1.00 & L\textsubscript{12} & 0.71\tabularnewline
L\textsubscript{1} & 3.74 & L\textsubscript{13} & 3.88\tabularnewline
L\textsubscript{2} & 3.27 & L\textsubscript{14} & 1.73\tabularnewline
L\textsubscript{3} & 4.12 & L\textsubscript{15} & 2.15\tabularnewline
L\textsubscript{4} & 0.68 & L\textsubscript{16} & 1.30\tabularnewline
L\textsubscript{5} & 0.84 & L\textsubscript{17} & 2.67\tabularnewline
L\textsubscript{6} & 1.62 & L\textsubscript{18} & 5.27\tabularnewline
\bottomrule
\end{longtable}

The dimensions of the circular waveguides are determined according to
the operation frequency. But the dimensions and location of the rods
have been achieved by the numerical methods of optimization. The number
of rods is calculated according to the distance between the rods so that
the helical array of the rods can rotate 360\selectlanguage{ngerman}°. Hence, the overall size
of the CPW in the length, and radius is 55.12 and 20 mm, respectively,
which is equivalent to 1.84 \selectlanguage{greek}λ\selectlanguage{english}\textsubscript{0} and 0.67
\selectlanguage{greek}λ\selectlanguage{english}\textsubscript{0}, respectively.

The principle of the CPW working is as the following. To study the
proposed CPW working, changes in electric field intensity in the
presence of a conductor rod inside a circular waveguide must be
investigated. Fig. 3 indicates the electric vectors around a metal rod
inside a circular waveguide.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image3/image3}

\end{center}
\end{figure}

Fig. 3. The electric vectors around a metal rod inside a circular
waveguide.

According to the boundary conditions of electric fields, as expected,
and shown in Fig. 3, electric fields must always be perpendicular to a
conductor surface, also, a conductor rod inside the circular waveguide
change the direction of the electric field vectors. This brings us
closer to our goal, which is to convert an LP into a CP field. Using a
helical array along the length of the circular waveguide can generalize
this issue to all waveguide aperture. Optimizing makes it possible to
create an equal field intensity with a phase difference of 900 \selectlanguage{english}in two
axes perpendicular to each other, on the CPW aperture.

\section*{Numerical results}

{\label{numerical-results}}

Fig. 4 indicates the axial ratio, that is, the ratio of the vertical and
horizontal TE\textsubscript{11} modes, and the phase difference of these
modes. Note, to achieve circular polarization, we create electric fields
in two perpendicular directions with a phase difference of 900. \selectlanguage{english}In
addition to proving the electric field purity at the output of the
waveguide, the second and third components of the electric field are
shown in Fig. 5.

\textbf{Hosted file}

\verb`image4.emf`  available at \url{https://authorea.com/users/502151/articles/582308-an-only-metal-compact-and-circular-polarizer-designed-with-helical-array-rods}

Fig. 4. The axial ratio (AR) and the phase difference (PD) simulated by
CST Microwave Studio and validated by Ansys HFSS. The blue solid line
indicates the ideal results of the axial ratio and phase difference.

\textbf{Hosted file}

\verb`image5.emf`  available at \url{https://authorea.com/users/502151/articles/582308-an-only-metal-compact-and-circular-polarizer-designed-with-helical-array-rods}

Fig. 5. The other components of the electric field on the CPW aperture
simulated by CST Microwave Studio. The
TE\textsubscript{21}\textsuperscript{1} and
TE\textsubscript{21}\textsuperscript{2} are degenerate modes.

The other major result of the proposed CPW is the reflection
coefficient. The reflection coefficient that is under the acceptable
range (i.e., -10 dB) is shown in Fig. 6.

\textbf{Hosted file}

\verb`image6.emf`  available at \url{https://authorea.com/users/502151/articles/582308-an-only-metal-compact-and-circular-polarizer-designed-with-helical-array-rods}

Fig. 6. The reflection coefficient of the proposed CPW simulated by CST
Microwave Studio and validated by Ansys HFSS.

\section*{Conclusion}

{\label{conclusion}}

In this paper, we present a compact CPW, only metal, and easy to
manufacture, at the 10 GHz frequency. The overall size of the CPW in the
length and radius is 55.12 and 20 mm, respectively, which is equivalent
to 1.84 \selectlanguage{greek}λ\selectlanguage{english}\textsubscript{0} and 0.67 \selectlanguage{greek}λ\selectlanguage{english}\textsubscript{0}, respectively.
The axial ratio and phase difference of the polarizer are is smaller
than 0.4 dB and about 900, \selectlanguage{english}respectively, at the operating frequency. The
validation results validate the simulated ones, as well. Due to the
compact size, the proposed polarizer can be used in a wide range of
applications, including detectors and electromagnetic sources.

\section*{References}

{\label{references}}

\begin{enumerate}
\tightlist
\item
  P. Naseri, J. R. Costa, S. A. Matos, C. A. Fernandes, and S. V. Hum,
  ``Equivalent Circuit Modeling to Design a Dual-Band Dual
  Linear-to-Circular Polarizer Surface,'' \emph{IEEE Transactions on
  Antennas and Propagation} , vol. 68, no. 7, pp. 5730--5735, Jul. 2020,
  Doi:\emph{10.1109/TAP.2020.2963949}.
\item
  C. Chang, S. Church, S. Tantawi, P. Larkoski, M. Sieth, and and K.
  Devaraj, ``Theory and Experiment of a Compact Waveguide Dual Circular
  Polarizer,'' \emph{Progress In Electromagnetics Research} , vol. 131,
  pp. 211--225, 2012, Doi:\emph{10.2528/PIER12072601}.
\item
  N. Nikolic, A. Weily, I. Kekic, S. L. Smith, and K. W. Smart, ``A
  Septum Polarizer with Integrated Square to Circular Tapered Waveguide
  Transition,'' in \emph{2018 IEEE International Symposium on Antennas
  and Propagation \& USNC/URSI National Radio Science Meeting} , Jul.
  2018, pp. 725--726. Doi:\emph{10.1109/APUSNCURSINRSM.2018.8608909}.
\item
  S.-W. Wang, C.-H. Chien, C.-L. Wang, and R.-B. Wu, ``A circular
  polarizer designed with a dielectric septum loading,'' \emph{IEEE
  Transactions on Microwave Theory and Techniques} , vol. 52, no. 7, pp.
  1719--1723, Jul. 2004, Doi:\emph{10.1109/TMTT.2004.830487}.
\item
  A. Chittora and S. V. Yadav, ``A Compact Circular Waveguide Polarizer
  with Higher Order Mode Excitation,'' in \emph{2020 IEEE International
  Conference on Electronics, Computing and Communication Technologies
  (CONECCT)} , Jul. 2020, pp. 1--4.
  Doi:\emph{10.1109/CONECCT50063.2020.9198499}.
\item
  S. J. Hosseini, M. Dahmardeh, and M. Yousefian, ``A high power TEM to
  TE10 mode converter with 70\% bandwidth,'' \emph{Journal of
  Electromagnetic Waves and Applications} , vol. 35, no. 3, pp.
  389--399, Feb. 2021, Doi:\emph{10.1080/09205071.2020.1842255}.
\item
  S. J. Hosseini, R.-A. Sadeghzadeh, and H. Aliakbarian, ``A TEM-TE11
  mode-transducing sectoral antenna by using dual dielectric
  window,''\emph{International Journal of Electronics Letters} , vol. 6,
  no. 4, pp. 403--412, Oct. 2018,
  Doi:\emph{10.1080/21681724.2017.1381997}.
\item
  S. J. Hosseini and M. Khalaj-Amirhosseini, ``An Eight-Port Planar
  Antenna for 3-D Beam Steering,'' \emph{IEEE Transactions on Antennas
  and Propagation} , pp. 1--1, 2022,
  DOI:\emph{10.1109/TAP.2022.3184475}.
\item
  G. Addamo \emph{et al.} , ``3D Printing of a Monolithic K/Ka-Band
  Dual-Circular Polarization Antenna-Feeding Network,'' \emph{IEEE
  Access} , vol. 9, pp. 88243--88255, 2021,
  Doi:\emph{10.1109/ACCESS.2021.3089826}.
\item
  R. Liu \emph{et al.} , ``A Wideband Circular Polarization Implantable
  Antenna for Health Monitor Microsystem,'' \emph{IEEE Antennas and
  Wireless Propagation Letters} , vol. 20, no. 5, pp. 848--852, May
  2021, Doi:\emph{10.1109/LAWP.2021.3065445}.
\item
  M. Yousefian, S. J. Hosseini, and M. Dahmardeh, ``Compact broadband
  coaxial to rectangular waveguide transition,'' \emph{Journal of
  Electromagnetic Waves and Applications} , vol. 33, no. 9, pp.
  1239--1247, Jun. 2019, Doi:\emph{10.1080/09205071.2019.1606737}.
\item
  S. J. Hosseini and M. Dahmardeh, ``Compact smile-like mode converter
  antenna with high power capacity level,'' \emph{Electromagnetics} ,
  vol. 41, no. 3, pp. 222--238, Apr. 2021,
  Doi:\emph{10.1080/02726343.2021.1903216}.
\item
  S. J. Hosseini, ``Conversion Donut-Shaped Pattern to Directive Without
  Using Any Mode Converter,'' \emph{American Journal of Electromagnetics
  and Applications} , vol. 9, no. 1, Art. no. 1, Mar. 2021,
  Doi:\emph{10.11648/j.ajea.20210901.11}.
\item
  S. J. Hosseini and M. Dahmardeh, ``Conversion of a donut-shaped
  pattern to a directive one using a wide frequency band hive-shaped
  pattern director antenna,'' \emph{Electromagnetics} , vol. 41, no. 8,
  pp. 557--569, Nov. 2021, Doi:\emph{10.1080/02726343.2022.2031156}.
\item
  S. J. Hosseini and H. Oraizi, ``TEM-TE11 mode converter antenna like a
  pelican beak,'' \emph{IET Microwaves, Antennas \& Propagation} , vol.
  14, no. 9, pp. 934--942, 2020, Doi:\emph{10.1049/iet-map.2020.0017}.
\item
  S. J. Hosseini and H. Oraizi, ``Wide-band conversion of donut-shaped
  pattern to directive one by square-shaped pattern director
  antenna,''\emph{International Journal of Microwave and Wireless
  Technologies} , pp. 1--8, Nov. 2021,
  Doi:\emph{10.1017/S1759078721001422}.
\item
  C. Shu, S. Hu, Y. Yao, Y. Alfadhl, and X. Chen, ``W-band grooved-wall
  circularly polarised horn antenna,'' \emph{IET Microwaves, Antennas \&
  Propagation} , vol. 14, no. 11, pp. 1171--1174, 2020,
  Doi:\emph{10.1049/iet-map.2020.0100}.
\item
  S. J. Hosseini, ``A circularly polarized TEM to TE11 mode converter
  antenna,'' \emph{The Journal of Engineering} , vol. 2022, no. 2, pp.
  216--222, 2022, Doi:\emph{10.1049/tje2.12110}.
\item
  S.-W. Wang, C.-H. Chien, C.-L. Wang, and R.-B. Wu, ``A circular
  polarizer designed with a dielectric septum loading,'' \emph{IEEE
  Transactions on Microwave Theory and Techniques} , vol. 52, no. 7, pp.
  1719--1723, Jul. 2004, Doi:\emph{10.1109/TMTT.2004.830487}.
\item
  S. V. Yadav and A. Chittora, ``Circularly polarized high-power antenna
  with higher-order mode excitation,'' \emph{International Journal of
  Microwave and Wireless Technologies} , vol. 14, no. 4, pp. 477--481,
  May 2022, Doi:\emph{10.1017/S1759078721000611}.
\item
  P. Naseri, J. R. Costa, S. A. Matos, C. A. Fernandes, and S. V. Hum,
  ``Equivalent Circuit Modeling to Design a Dual-Band Dual
  Linear-to-Circular Polarizer Surface,'' \emph{IEEE Transactions on
  Antennas and Propagation} , vol. 68, no. 7, pp. 5730--5735, Jul. 2020,
  Doi:\emph{10.1109/TAP.2020.2963949}.
\item
  P. Das and K. Mandal, ``Passive FSS based polarization converter
  integrated microstrip antenna,'' \emph{International Journal of RF and
  Microwave Computer-Aided Engineering} , vol. 32, no. 2, p. e22982,
  2022, Doi:\emph{10.1002/mmce.22982}.
\item
  C. Chang, S. Church, S. Tantawi, P. Larkoski, M. Sieth, and and K.
  Devaraj, ``Theory and Experiment of a Compact Waveguide Dual Circular
  Polarizer,'' \emph{Progress In Electromagnetics Research} , vol. 131,
  pp. 211--225, 2012, Doi:\emph{10.2528/PIER12072601}.
\item
  M. Rad, N. Nikkhah, B. Zakeri, and M. Yazdi, ``Wideband Dielectric
  Resonator Antenna With Dual Circular Polarization,'' \emph{IEEE
  Transactions on Antennas and Propagation} , vol. 70, no. 1, pp.
  714--719, Jan. 2022, Doi:\emph{10.1109/TAP.2021.3098516}.
\item
  M. A. Sofi, K. Saurav, and S. K. Koul, ``A linear to circular
  polarization reconfigurable converter based on frequency selective
  surface,'' \emph{Microwave and Optical Technology Letters} , vol. 63,
  no. 5, pp. 1425--1433, 2021, Doi:\emph{10.1002/mop.32779}.
\item
  S. J. Hosseini, ``A Compact CP Mode Converter
  Antenna,''\emph{Microwave Review} , vol. 28, no. 4, pp. 3--8, 2022.
\end{enumerate}

\selectlanguage{english}
\FloatBarrier
\end{document}

