<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD Journal Publishing DTD v2.3 20070202//EN" "journalpublishing.dtd">
<article article-type="research-article" dtd-version="2.3" xml:lang="EN" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">
<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Phys.</journal-id>
<journal-title>Frontiers in Physics</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Phys.</abbrev-journal-title>
<issn pub-type="epub">2296-424X</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="publisher-id">851150</article-id>
<article-id pub-id-type="doi">10.3389/fphy.2022.851150</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Physics</subject>
<subj-group>
<subject>Original Research</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>Unequal Bandpass Filtering Power Divider Based on Hybrid HMSIW-SSPP Modes</article-title>
<alt-title alt-title-type="left-running-head">Pan et&#x20;al.</alt-title>
<alt-title alt-title-type="right-running-head">Unequal Bandpass Filtering Power Divider</alt-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname>Pan</surname>
<given-names>Bai Cao</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/915712/overview"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Yu</surname>
<given-names>Ping</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/1628436/overview"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Guo</surname>
<given-names>Ben Jian</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Qian</surname>
<given-names>Ya Hui</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Luo</surname>
<given-names>Guo Qing</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
</contrib>
</contrib-group>
<aff id="aff1">
<sup>1</sup>
<institution>Key Laboratory of RF Circuits and System Ministry of Education</institution>, <institution>School of Electronics and Information</institution>, <institution>Hangzhou Dianzi University</institution>, <addr-line>Hangzhou</addr-line>, <country>China</country>
</aff>
<aff id="aff2">
<sup>2</sup>
<institution>State Key Laboratory of Millimeter Waves</institution>, <institution>Southeast University</institution>, <addr-line>Nanjing</addr-line>, <country>China</country>
</aff>
<author-notes>
<fn fn-type="edited-by">
<p>
<bold>Edited by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1186480/overview">Kai-Da Xu</ext-link>, Xi&#x2019;an Jiaotong University, China</p>
</fn>
<fn fn-type="edited-by">
<p>
<bold>Reviewed by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1257191/overview">Cheng Zhang</ext-link>, Wuhan University of Technology, China</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1632937/overview">Jia-Yuan Yin</ext-link>, Xidian University, China</p>
</fn>
<corresp id="c001">&#x2a;Correspondence: Guo Qing Luo, <email>luoguoqing@hdu.edu.cn</email>
</corresp>
<fn fn-type="other">
<p>This article was submitted to Optics and Photonics, a section of the journal Frontiers in Physics</p>
</fn>
</author-notes>
<pub-date pub-type="epub">
<day>17</day>
<month>02</month>
<year>2022</year>
</pub-date>
<pub-date pub-type="collection">
<year>2022</year>
</pub-date>
<volume>10</volume>
<elocation-id>851150</elocation-id>
<history>
<date date-type="received">
<day>09</day>
<month>01</month>
<year>2022</year>
</date>
<date date-type="accepted">
<day>24</day>
<month>01</month>
<year>2022</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2022 Pan, Yu, Guo, Qian and Luo.</copyright-statement>
<copyright-year>2022</copyright-year>
<copyright-holder>Pan, Yu, Guo, Qian and Luo</copyright-holder>
<license xlink:href="http://creativecommons.org/licenses/by/4.0/">
<p>This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these&#x20;terms.</p>
</license>
</permissions>
<abstract>
<p>This letter presents a novel unequal bandpass filtering power divider based on hybrid-mode of half mode substrate integrated waveguide (HMSIW) and spoof surface plasmon polaritons (SSPPs). Bandpass response is achieved by combining the transmission properties of HMSIW and SSPPs simultaneously. The operating bandwidth can be designed in a wide range by simply optimizing the dimensions of HMSIW and SSPPs. In addition, defected ground structures (DGSs) are etched on the bottom of the substrate to improve out-of-band suppression. The power division ratio of the proposed unequal power divider is finally optimized to 1:3. The measured results agree with the simulated one. Such design provides a stable power division within wide frequency range from 6.5 to 9.5&#xa0;GHz.</p>
</abstract>
<kwd-group>
<kwd>unequal power divider</kwd>
<kwd>bandpass filtering</kwd>
<kwd>SSPPs</kwd>
<kwd>HMSIW</kwd>
<kwd>wide band</kwd>
</kwd-group>
<contract-num rid="cn001">K202221</contract-num>
<contract-num rid="cn002">LQ19F010010</contract-num>
<contract-num rid="cn003">61901143</contract-num>
<contract-sponsor id="cn001">State Key Laboratory of Millimeter Waves<named-content content-type="fundref-id">10.13039/501100011421</named-content>
</contract-sponsor>
<contract-sponsor id="cn002">Natural Science Foundation of Zhejiang Province<named-content content-type="fundref-id">10.13039/501100004731</named-content>
</contract-sponsor>
<contract-sponsor id="cn003">National Natural Science Foundation of China<named-content content-type="fundref-id">10.13039/501100001809</named-content>
</contract-sponsor>
</article-meta>
</front>
<body>
<sec id="s1">
<title>Introduction</title>
<p>The rapid development of wireless communication systems proposes more and more requirements for functional devices. In order to meet the market demands, different kinds of well-performed functional devices have been widely studied. In the past decade, substrate integrated waveguide (SIW) has become one of the hotspots in researches [<xref ref-type="bibr" rid="B1">1</xref>]. Considering its perfect high-pass transmission with low-loss, high-efficient properties, functional devices such as filter [<xref ref-type="bibr" rid="B2">2</xref>], power divider [<xref ref-type="bibr" rid="B3">3</xref>&#x2013;<xref ref-type="bibr" rid="B6">6</xref>] and coupler [<xref ref-type="bibr" rid="B7">7</xref>] have been proposed. Half-mode SIW (HMSIW) consists of only half of SIW structures, while keeping the same performance as SIW [<xref ref-type="bibr" rid="B8">8</xref>, <xref ref-type="bibr" rid="B9">9</xref>]. Miniaturization can be realized. Spoof surface plasmon polaritons (SSPPs) are guiding surface modes along periodic metamaterial structures. Such modes have also received wide attention for its unique properties of perfect low-pass transmission and near-field confinement [<xref ref-type="bibr" rid="B10">10</xref>, <xref ref-type="bibr" rid="B11">11</xref>]. SSPPs have been studies in field of different high-efficient designs such as bandpass filter [<xref ref-type="bibr" rid="B12">12</xref>, <xref ref-type="bibr" rid="B13">13</xref>], power divider [<xref ref-type="bibr" rid="B14">14</xref>, <xref ref-type="bibr" rid="B15">15</xref>], coupler [<xref ref-type="bibr" rid="B16">16</xref>], radiator&#x20;[<xref ref-type="bibr" rid="B17">17</xref>].</p>
<p>Filters and power dividers are the most commonly-used functional devices in wireless communication systems. In certain applications, both kinds of devices are required to be integrated with each other to reduce the occupied space. And their performances are crucial for systems stability. In recent years, a series of filters and power dividers based SIW and SSPPs have been reported [<xref ref-type="bibr" rid="B18">18</xref>, <xref ref-type="bibr" rid="B19">19</xref>]. In order to improve the integration and operating properties, parasitic structures like resonators [<xref ref-type="bibr" rid="B20">20</xref>], interdigital structures (ISs) [<xref ref-type="bibr" rid="B21">21</xref>], defected ground structures (DGSs) [<xref ref-type="bibr" rid="B22">22</xref>, <xref ref-type="bibr" rid="B23">23</xref>] have also been studied. The combination of SIW and SSPP provides a new solution for the miniaturization designs, since the power dividers of SIW are usually narrow-band and those of SSPP have limits of bulky dimensions.</p>
<p>In this letter, we proposed a novel unequal bandpass filtering power divider based on the hybrid HMSIW-SSPP modes, which shows compact size and power division ratio of 1:3. The hybrid unit can be compatible with the functional techniques of both HMSIW and SSPPs. The lower and upper edges of the passband can be controlled independently by changing the dimensions of HMSIW and SSPPs. Defected ground structure is also loaded aiming for improving out-of-band suppression.</p>
<sec id="s1-1">
<title>Design of Unequal Power Divider</title>
<p>The schematic configuration of the proposed unequal filtering power divider is shown in <xref ref-type="fig" rid="F1">Figure&#x20;1</xref> with dimensions labelled. As it can be seen in the figure, periodic corrugated slots are etched on the top layer of HMSIW. Two slots with gradient groove depths of h1 and h2 are used to achieve broadband excitation of SSPP modes. Optimizing grooves&#x2019; depths can help to improvement of the transmission efficiency. Two uniformed grooves of SSPP with depth of h3 are set as the transmission part. They collaborate with the HMSIW structures to provide the hybrid HMSIW-SSPP modes with unique transmission properties. The periodic interval of the SSPP units is p. At the output terminals, a SSPP channel of three unit matching structures with gradient grooves&#x2019; depths and tapered edges are designed for momentum matching of SSPP at port 2. Meanwhile, another HMSIW channel is paralleled connected between the hybrid unit and the SSPP channel. The widths of both HMSIW structures are L and L1, respectively.</p>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption>
<p>Schematic of the proposed unequal filtering power divider.</p>
</caption>
<graphic xlink:href="fphy-10-851150-g001.tif"/>
</fig>
<p>
<xref ref-type="fig" rid="F2">Figure&#x20;2</xref> show the dispersion curves of the hybrid HMSIW-SSPP unit. And its structure is shown in the inset of <xref ref-type="fig" rid="F2">Figure&#x20;2</xref>. It can be observed from the figure that the cutoff frequency of HMSIW modes is lower than that of SSPP modes. Thus, bandpass response can be obtained. The hybrid unit provides bandpass property from 6.1 to 10.5&#xa0;GHz. As is introduced in literatures, the cutoff frequencies of SIW and SSPP modes can be controlled by changing the width of SIW and the depth of SSPP grooves. For the proposed design, reduction of L or h leads to upper shifting of the lower or upper cutoff frequencies, respectively. Limited by the space allocation, SSPP grooves are always smaller than HMSIW. So the cutoff frequencies of SIW are always lower than those of SSPPs.</p>
<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption>
<p>The dispersion curves of the hybrid HMSIW-SSPP unit. Inset: the structure of the hybrid HMSIW-SSPP&#x20;unit.</p>
</caption>
<graphic xlink:href="fphy-10-851150-g002.tif"/>
</fig>
<p>The dispersion properties of the hybrid HMSIW-SSPP unit under different parameters are compared in <xref ref-type="fig" rid="F3">Figure&#x20;3</xref>. The unit with dimensions of h &#x3d; 3.5&#xa0;mm, L &#x3d; 7&#xa0;mm, w &#x3d; 0.5&#xa0;mm and p &#x3d; 6&#xa0;mm is used as reference and shown as the red dashed lines in the figure. Then each dimension is optimized and compared. In <xref ref-type="fig" rid="F3">Figure&#x20;3A</xref>, the groove&#x2019;s depth in HMSIW unit is examined. When the depth h3 increases from 3 to 4&#xa0;mm, the upper cutoff frequencies shift from 11.2 to 9.4&#xa0;GHz, while the lower cutoff frequencies keep at 6.1&#xa0;GHz. Similarly, from <xref ref-type="fig" rid="F3">Figure&#x20;3B</xref> it can be seen that when width L increases from 6 to 8&#xa0;mm, the lower cutoff frequencies of the hybrid unit reduce from 6.8 GH to 5.5&#xa0;GHz. Meanwhile, small range fluctuation between 10.1 and 10.3&#xa0;GHz of the upper cutoff frequencies is observed. The width of the groove w and its interval p can also be used for the modulation of operating band (shown in <xref ref-type="fig" rid="F3">Figures 3C,D</xref>). The groove width w can change the upper cutoff frequencies in a small range. And the interval p has a significant impact on the upper cutoff frequencies. Since the increasing interval would lead to excessive length of the device, depth L is usually used in modulation of operating&#x20;band.</p>
<fig id="F3" position="float">
<label>FIGURE 3</label>
<caption>
<p>The dispersion properties of the hybrid unit under different parameters of <bold>(A)</bold> depth of SSPP grooves h, <bold>(B)</bold> width of HMSIW L, <bold>(C)</bold> width of SSPP grooves w, and <bold>(D)</bold> interval of SSPPs p.</p>
</caption>
<graphic xlink:href="fphy-10-851150-g003.tif"/>
</fig>
<p>The simulated transmissions at port 3 of the unequal filtering power divider are illustrated in <xref ref-type="fig" rid="F4">Figure&#x20;4</xref> to testify the bandwidth modulation of the hybrid unit. As is compared in <xref ref-type="fig" rid="F4">Figures 4A,B</xref>, upper cutoff frequencies or lower cutoff frequencies of <inline-formula id="inf1">
<mml:math id="m1">
<mml:mrow>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mrow>
<mml:mn>31</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> shift to lower frequency band independently without apparently mutual influence. Based on the above analysis, a high-efficient passband from 6.5 to 9.5&#xa0;GHz of unequal filtering power divider can be designed. The simulated S parameters are shown in <xref ref-type="fig" rid="F5">Figure&#x20;5</xref>. In the whole passband, the reflection coefficient <inline-formula id="inf2">
<mml:math id="m2">
<mml:mrow>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mrow>
<mml:mn>11</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> keeps below &#x2212;10&#xa0;dB, while the transmission coefficient <inline-formula id="inf3">
<mml:math id="m3">
<mml:mrow>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mrow>
<mml:mn>21</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf4">
<mml:math id="m4">
<mml:mrow>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mrow>
<mml:mn>31</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> are around &#x2212;2.2&#xa0;dB and &#x2212;7&#xa0;dB.</p>
<fig id="F4" position="float">
<label>FIGURE 4</label>
<caption>
<p>Simulated transmission coefficients (<inline-formula id="inf5">
<mml:math id="m5">
<mml:mrow>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mrow>
<mml:mn>31</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>) with different dimensions of <bold>(A)</bold> h3 and <bold>(B)</bold> L.</p>
</caption>
<graphic xlink:href="fphy-10-851150-g004.tif"/>
</fig>
<fig id="F5" position="float">
<label>FIGURE 5</label>
<caption>
<p>Simulated S parameters of unequal filtering power divider.</p>
</caption>
<graphic xlink:href="fphy-10-851150-g005.tif"/>
</fig>
</sec>
</sec>
<sec id="s2">
<title>Optimization and Measurement</title>
<p>The DGS can disturb the current distribution on the metallic ground and introduce an extra transmission zero. In the optimized model, a two-element array of inverted T-shaped DGSs is introduced. The DGSs are loaded on the bottom layer of the hybrid HMSIW-SSPP units to improve the upper stopband rejection. The structure of the DGS unit is shown in the inset of <xref ref-type="fig" rid="F6">Figure&#x20;6A</xref>, in which the red line represents the contour of the grooves on the top layer. The DGS is etched on the bottom layer and it is in the middle of two adjacent grooves. The dimensions of the DGS decide the frequency of its transmission zero. And the optimized dimensions are a1 &#x3d; 1.9&#xa0;mm, a2 &#x3d; 4.4&#xa0;mm, a3 &#x3d; 3.8&#xa0;m, t &#x3d; 0.6&#xa0;mm, s &#x3d; 0.45&#xa0;mm, g &#x3d; 0.25&#xa0;mm. The comparison of <inline-formula id="inf6">
<mml:math id="m6">
<mml:mrow>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mrow>
<mml:mn>21</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> of the design with and without the DGSs is shown in <xref ref-type="fig" rid="F6">Figure&#x20;6A</xref>. The transmission with two-element array of DGSs provides an extra transmission zero, providing better out-of-band suppression. The cut-off efficiency of transmission zero of DGS at 10&#xa0;GHz can be improved by increasing the number of DGSs used in the model. A small shift of the cutoff frequency of SSPPs is observed due to the coupling between DGSs and SSPPs. The transmission of the proposed design loaded with DGSs are shown in <xref ref-type="fig" rid="F6">Figure&#x20;6B</xref>. An unequal power divider with bandpass filtering effect is observed within band from 6.5 to 9.5&#xa0;GHz. The simulated <inline-formula id="inf7">
<mml:math id="m7">
<mml:mrow>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mrow>
<mml:mn>11</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is lower than &#x2212;20&#xa0;dB in the passband. <inline-formula id="inf8">
<mml:math id="m8">
<mml:mrow>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mrow>
<mml:mn>21</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf9">
<mml:math id="m9">
<mml:mrow>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mrow>
<mml:mn>31</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> are &#x2212;2.2&#xa0;dB and &#x2212;7&#xa0;dB, respectively. Within the whole operating band, S21 undulates between &#x2212;2.6&#xa0;dB and &#x2212;2.3&#xa0;dB, and S31 undulates between &#x2212;7.4&#xa0;dB and &#x2212;7&#xa0;dB. The simulations indicate a stable power division. The power division ratio of port 2 and port 3 is&#x20;3:1.</p>
<fig id="F6" position="float">
<label>FIGURE 6</label>
<caption>
<p>
<bold>(A)</bold> the comparison of <inline-formula id="inf10">
<mml:math id="m10">
<mml:mrow>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mrow>
<mml:mn>21</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> of the designs with and without DGSs. <bold>(B</bold>) Simulated S-parameters of the design with DGS.</p>
</caption>
<graphic xlink:href="fphy-10-851150-g006.tif"/>
</fig>
<p>A prototype of the proposed unequal filtering power divider is fabricated and measured. The substrate is F4B board with relative permittivity of 2.65 and thickness of 1&#xa0;mm. Photographs of the prototype are shown in <xref ref-type="fig" rid="F7">Figure&#x20;7</xref>. The total dimensions of the proposed design are 45&#xa0;mm &#xd7; 25&#xa0;mm &#xd7; 1&#xa0;mm. <xref ref-type="fig" rid="F8">Figure&#x20;8</xref> shows the compared of the simulated and measured S-parameters. The measured transmissions are about 1&#xa0;dB lower than the simulated ones, because of the machining accuracy of the sample and the unskilled welding of SMA connectors in the experiments. The operating bandwidth and power division effect keeps steady.</p>
<fig id="F7" position="float">
<label>FIGURE 7</label>
<caption>
<p>
<bold>(A)</bold> Top view and <bold>(B)</bold> back view of the prototype.</p>
</caption>
<graphic xlink:href="fphy-10-851150-g007.tif"/>
</fig>
<fig id="F8" position="float">
<label>FIGURE 8</label>
<caption>
<p>Comparison of simulated and measured S-parameters.</p>
</caption>
<graphic xlink:href="fphy-10-851150-g008.tif"/>
</fig>
</sec>
<sec sec-type="conclusion" id="s3">
<title>Conclusion</title>
<p>In this paper, an unequal filtering power divider based on hybrid HMSIW-SSPP mode is proposed. The passband can be controlled independently by changing the dimensions of HMSIW and SSPPs. DGSs are introduced on the bottom layer of the device to improve the out-of-band suppression. A prototype working from 6.5 to 9.5&#xa0;GHz is designed and fabricated. And power division ratio of 1:3 is obtained. Such design provides solutions for miniaturized multi-functional devices, and could be used in wireless communication systems.</p>
</sec>
</body>
<back>
<sec id="s4">
<title>Data Availability Statement</title>
<p>The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding author.</p>
</sec>
<sec id="s5">
<title>Author Contributions</title>
<p>All authors listed have made a substantial, direct, and intellectual contribution to the work and approved it for publication.</p>
</sec>
<sec id="s6">
<title>Funding</title>
<p>This work is supported partly by Open Research Program of State Key Laboratory of Millimeter Wave under contract K202221, partly by Zhejiang Provincial Natural Science Foundation of China under contract LQ19F010010, and partly by National Natural Science Foundation of China under contract 61901143.</p>
</sec>
<sec sec-type="COI-statement" id="s7">
<title>Conflict of Interest</title>
<p>The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
</sec>
<sec sec-type="disclaimer" id="s8">
<title>Publisher&#x2019;s Note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.</p>
</sec>
<ref-list>
<title>References</title>
<ref id="B1">
<label>1.</label>
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Deslandes</surname>
<given-names>D</given-names>
</name>
<name>
<surname>Wu</surname>
<given-names>K</given-names>
</name>
</person-group>. <article-title>Integrated Microstrip and Rectangular Waveguide in Planar Form</article-title>. <source>IEEE Microw Wireless Compon Lett</source> (<year>2001</year>) <volume>11</volume>(<issue>2</issue>):<fpage>68</fpage>&#x2013;<lpage>70</lpage>. <pub-id pub-id-type="doi">10.1109/7260.914305</pub-id> </citation>
</ref>
<ref id="B2">
<label>2.</label>
<citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname>Nedelchev</surname>
<given-names>M</given-names>
</name>
<name>
<surname>Stosi&#x0107;</surname>
<given-names>B</given-names>
</name>
<name>
<surname>Iliev</surname>
<given-names>I</given-names>
</name>
<name>
<surname>Ilieva</surname>
<given-names>A</given-names>
</name>
<name>
<surname>Don&#x010D;ov</surname>
<given-names>N</given-names>
</name>
</person-group>. &#x201c;<article-title>Wave-based Digital Model of Substrate-IntegratedWaveguide (SIW) Filters for K Band</article-title>,&#x201d; In <conf-name>2020 43rd International Conference on Telecommunications and Signal Processing (TSP)</conf-name>; <publisher-loc>Milan, Italy</publisher-loc> (<year>2020</year>). p. <fpage>325</fpage>&#x2013;<lpage>8</lpage>. <pub-id pub-id-type="doi">10.1109/TSP49548.2020.9163541</pub-id> </citation>
</ref>
<ref id="B3">
<label>3.</label>
<citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname>Shreyus</surname>
<given-names>GS</given-names>
</name>
<name>
<surname>Khatwani</surname>
<given-names>H</given-names>
</name>
<name>
<surname>Shambavi</surname>
<given-names>K</given-names>
</name>
</person-group>. &#x201c;<article-title>Power Divider with Substrate Integrated Waveguide and CSRR for C Band Application</article-title>,&#x201d; In <conf-name>2017 Innovations in Power and Advanced Computing Technologies (i-PACT)</conf-name>; <conf-loc>Vellore, India</conf-loc> (<year>2017</year>). p. <fpage>1</fpage>&#x2013;<lpage>5</lpage>. <pub-id pub-id-type="doi">10.1109/IPACT.2017.8245019</pub-id> </citation>
</ref>
<ref id="B4">
<label>4.</label>
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Xu</surname>
<given-names>H-X</given-names>
</name>
<name>
<surname>Wang</surname>
<given-names>G-M</given-names>
</name>
<name>
<surname>Zhang</surname>
<given-names>C-X</given-names>
</name>
<name>
<surname>Yu</surname>
<given-names>Z-W</given-names>
</name>
<name>
<surname>Chen</surname>
<given-names>X</given-names>
</name>
</person-group>. <article-title>Composite Right/left-Handed Transmission Line Based on Complementary Single-Split Ring Resonator Pair and Compact Power Dividers Application Using Fractal Geometry</article-title>. <source>IET Microw Antennas Propag</source> (<year>2012</year>) <volume>6</volume>(<issue>9</issue>):<fpage>1017</fpage>&#x2013;<lpage>25</lpage>. <pub-id pub-id-type="doi">10.1049/iet-map.2011.0427</pub-id> </citation>
</ref>
<ref id="B5">
<label>5.</label>
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Moznebi</surname>
<given-names>A-R</given-names>
</name>
<name>
<surname>Afrooz</surname>
<given-names>K</given-names>
</name>
</person-group>. <article-title>Compact Power Divider Based on Half Mode Substrate Integrated Waveguide (HMSIW) with Arbitrary Power Dividing Ratio</article-title>. <source>Int J&#x20;Microw Wireless Technol</source> (<year>2017</year>) <volume>9</volume>(<issue>3</issue>):<fpage>515</fpage>&#x2013;<lpage>21</lpage>. <pub-id pub-id-type="doi">10.1017/S1759078716000544</pub-id> </citation>
</ref>
<ref id="B6">
<label>6.</label>
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Xu</surname>
<given-names>H-X</given-names>
</name>
<name>
<surname>Liang</surname>
<given-names>J-G</given-names>
</name>
<name>
<surname>Wang</surname>
<given-names>G-M</given-names>
</name>
<name>
<surname>Wu</surname>
<given-names>F-T</given-names>
</name>
<name>
<surname>Zhang</surname>
<given-names>C-X</given-names>
</name>
</person-group>. <article-title>Modelling of Composite Right/left-Handed Transmission Line Based on Fractal Geometry with Application to Power Divider</article-title>. <source>Microwaves, Antennas &#x26; Propagation, IET</source> (<year>2012</year>) <volume>6</volume>:<fpage>1415</fpage>&#x2013;<lpage>21</lpage>. <pub-id pub-id-type="doi">10.1049/iet-map.2012.0137</pub-id> </citation>
</ref>
<ref id="B7">
<label>7.</label>
<citation citation-type="confproc">
<person-group person-group-type="author">
<name>
<surname>Pezhman</surname>
<given-names>M</given-names>
</name>
<name>
<surname>Heidari</surname>
<given-names>A</given-names>
</name>
</person-group>. <article-title>Design of Compact SIW-Based Multi-Aperture Coupler for Ku-Band Applications</article-title>. <conf-name>2019 27th Iranian Conference on Electrical Engineering (ICEE)</conf-name>. <conf-date>30&#x20;April-2 May 2019</conf-date>, <conf-loc>Yazd, Iran</conf-loc> (<publisher-name>IEEE</publisher-name>) <fpage>1338</fpage>&#x2013;<lpage>41</lpage>. (<year>2019</year>). <pub-id pub-id-type="doi">10.1109/iraniancee.2019.8786463</pub-id> </citation>
</ref>
<ref id="B8">
<label>8.</label>
<citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname>Hong</surname>
<given-names>W</given-names>
</name>
<name>
<surname>Liu</surname>
<given-names>B</given-names>
</name>
<name>
<surname>Wang</surname>
<given-names>Y</given-names>
</name>
<name>
<surname>Lai</surname>
<given-names>Q</given-names>
</name>
<name>
<surname>Tang</surname>
<given-names>H</given-names>
</name>
<name>
<surname>Yin</surname>
<given-names>XX</given-names>
</name>
<etal/>
</person-group> &#x201c;<article-title>Half Mode Substrate Integrated Waveguide: A New Guided Wave Structure for Microwave and Millimeter Wave Application</article-title>,&#x201d; In <conf-name>2006 Joint 31st International Conference on Infrared Millimeter Waves and 14th International Conference on Teraherz Electronics</conf-name>; <conf-loc>Shanghai, China</conf-loc> (<year>2006</year>). p. <fpage>219</fpage>. <pub-id pub-id-type="doi">10.1109/ICIMW.2006.368427</pub-id> </citation>
</ref>
<ref id="B9">
<label>9.</label>
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Cui</surname>
<given-names>Y</given-names>
</name>
<name>
<surname>Xu</surname>
<given-names>K-D</given-names>
</name>
<name>
<surname>Guo</surname>
<given-names>Y-J</given-names>
</name>
<name>
<surname>Chen</surname>
<given-names>Q</given-names>
</name>
</person-group>. <article-title>Half-mode Substrate Integrated Plasmonic Waveguide for Filter and Diplexer Designs</article-title>. <source>J&#x20;Phys D: Appl Phys</source> (<year>2022</year>) <volume>55</volume>:<fpage>125104</fpage>. <pub-id pub-id-type="doi">10.1088/1361-6463/ac44bf</pub-id> </citation>
</ref>
<ref id="B10">
<label>10.</label>
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Ma</surname>
<given-names>HF</given-names>
</name>
<name>
<surname>Shen</surname>
<given-names>X</given-names>
</name>
<name>
<surname>Cheng</surname>
<given-names>Q</given-names>
</name>
<name>
<surname>Jiang</surname>
<given-names>WX</given-names>
</name>
<name>
<surname>Cui</surname>
<given-names>TJ</given-names>
</name>
</person-group>. <article-title>Broadband and High-Efficiency Conversion from Guided Waves to Spoof Surface Plasmon Polaritons</article-title>. <source>Laser Photon Rev</source> (<year>2014</year>) <volume>8</volume>(<issue>1</issue>):<fpage>146</fpage>&#x2013;<lpage>51</lpage>. <pub-id pub-id-type="doi">10.1002/lpor.201300118</pub-id> </citation>
</ref>
<ref id="B11">
<label>11.</label>
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Garcia-Vidal</surname>
<given-names>FJ</given-names>
</name>
<name>
<surname>Mart&#xed;n-Moreno</surname>
<given-names>L</given-names>
</name>
<name>
<surname>Pendry</surname>
<given-names>JB</given-names>
</name>
</person-group>. <article-title>Surfaces with Holes in Them: New Plasmonic Metamaterials</article-title>. <source>J&#x20;Opt A: Pure Appl Opt</source> (<year>2005</year>) <volume>7</volume>(<issue>2</issue>):<fpage>S97</fpage>&#x2013;<lpage>S101</lpage>. <pub-id pub-id-type="doi">10.1088/1464-4258/7/2/013</pub-id> </citation>
</ref>
<ref id="B12">
<label>12.</label>
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Jaiswal</surname>
<given-names>RK</given-names>
</name>
<name>
<surname>Pandit</surname>
<given-names>N</given-names>
</name>
<name>
<surname>Pathak</surname>
<given-names>NP</given-names>
</name>
</person-group>. <article-title>Spoof Surface Plasmon Polaritons Based Reconfigurable Band-Pass Filter</article-title>. <source>IEEE Photon Technol Lett</source> (<year>2019</year>) <volume>31</volume>(<issue>3</issue>):<fpage>218</fpage>&#x2013;<lpage>21</lpage>. <pub-id pub-id-type="doi">10.1109/LPT.2018.288900710.1109/lpt.2018.2889007</pub-id> </citation>
</ref>
<ref id="B13">
<label>13.</label>
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Xu</surname>
<given-names>K-D</given-names>
</name>
<name>
<surname>Lu</surname>
<given-names>S</given-names>
</name>
<name>
<surname>Guo</surname>
<given-names>Y-J</given-names>
</name>
<name>
<surname>Chen</surname>
<given-names>Q</given-names>
</name>
</person-group>. <article-title>High-order Mode of Spoof Surface Plasmon Polaritons and its Application in Bandpass Filters</article-title>. <source>IEEE Trans Plasma Sci</source> (<year>2021</year>) <volume>49</volume>(<issue>1</issue>):<fpage>269</fpage>&#x2013;<lpage>75</lpage>. <pub-id pub-id-type="doi">10.1109/tps.2020.3043889</pub-id> </citation>
</ref>
<ref id="B14">
<label>14.</label>
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Wu</surname>
<given-names>Y</given-names>
</name>
<name>
<surname>Li</surname>
<given-names>M</given-names>
</name>
<name>
<surname>Yan</surname>
<given-names>G</given-names>
</name>
<name>
<surname>Deng</surname>
<given-names>L</given-names>
</name>
<name>
<surname>Liu</surname>
<given-names>Y</given-names>
</name>
<name>
<surname>Ghassemlooy</surname>
<given-names>Z</given-names>
</name>
</person-group>. <article-title>Single-conductor Co-planar Quasi-Symmetry Unequal Power Divider Based on Spoof Surface Plasmon Polaritons of bow-tie Cells</article-title>. <source>AIP Adv</source> (<year>2016</year>) <volume>6</volume>(<issue>10</issue>):<fpage>105110</fpage>. <pub-id pub-id-type="doi">10.1063/1.4966051</pub-id> </citation>
</ref>
<ref id="B15">
<label>15.</label>
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Gao</surname>
<given-names>X</given-names>
</name>
<name>
<surname>Zhou</surname>
<given-names>L</given-names>
</name>
<name>
<surname>Yu</surname>
<given-names>XY</given-names>
</name>
<name>
<surname>Cao</surname>
<given-names>WP</given-names>
</name>
<name>
<surname>Li</surname>
<given-names>HO</given-names>
</name>
<name>
<surname>Ma</surname>
<given-names>HF</given-names>
</name>
<etal/>
</person-group> <article-title>Ultra-wideband Surface Plasmonic Y-Splitter</article-title>. <source>Opt Express</source> (<year>2015</year>) <volume>23</volume>(<issue>18</issue>):<fpage>23270</fpage>. <pub-id pub-id-type="doi">10.1364/OE.23.023270</pub-id> </citation>
</ref>
<ref id="B16">
<label>16.</label>
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Gao</surname>
<given-names>X</given-names>
</name>
<name>
<surname>Zhang</surname>
<given-names>HC</given-names>
</name>
<name>
<surname>He</surname>
<given-names>PH</given-names>
</name>
<name>
<surname>Wang</surname>
<given-names>ZX</given-names>
</name>
<name>
<surname>Lu</surname>
<given-names>J</given-names>
</name>
<name>
<surname>Yan</surname>
<given-names>RT</given-names>
</name>
<etal/>
</person-group> <article-title>Crosstalk Suppression Based on Mode Mismatch between Spoof SPP Transmission Line and Microstrip</article-title>. <source>IEEE Trans Compon., Packag Manufact Technol</source> (<year>2019</year>) <volume>9</volume>(<issue>11</issue>):<fpage>2267</fpage>&#x2013;<lpage>75</lpage>. <pub-id pub-id-type="doi">10.1109/TCPMT10.1109/tcpmt.2019.2931373</pub-id> </citation>
</ref>
<ref id="B17">
<label>17.</label>
<citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname>Tang</surname>
<given-names>X</given-names>
</name>
<name>
<surname>Zhang</surname>
<given-names>Q</given-names>
</name>
<name>
<surname>Hu</surname>
<given-names>S</given-names>
</name>
<name>
<surname>Chen</surname>
<given-names>Y</given-names>
</name>
</person-group>. &#x201c;<article-title>Spoof Surface Plasmon Polaritons (SSPP) for Endfire Radiation,</article-title>,&#x201d; In <conf-name>2018 IEEE Asia-Pacific Conference on Antennas and Propagation (APCAP)</conf-name>; <conf-loc>Auckland, New Zealand</conf-loc> (<year>2018</year>). p. <fpage>414</fpage>&#x2013;<lpage>5</lpage>. <pub-id pub-id-type="doi">10.1109/APCAP.2018.8538201</pub-id> </citation>
</ref>
<ref id="B18">
<label>18.</label>
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Zhang</surname>
<given-names>Q</given-names>
</name>
<name>
<surname>Zhang</surname>
<given-names>HC</given-names>
</name>
<name>
<surname>Wu</surname>
<given-names>H</given-names>
</name>
<name>
<surname>Cui</surname>
<given-names>TJ</given-names>
</name>
</person-group>. <article-title>A Hybrid Circuit for Spoof Surface Plasmons and Spatial Waveguide Modes to Reach Controllable Band-Pass Filters</article-title>. <source>Sci Rep</source> (<year>2015</year>) <volume>5</volume>:<fpage>16531</fpage>. <pub-id pub-id-type="doi">10.1038/srep16531</pub-id> </citation>
</ref>
<ref id="B19">
<label>19.</label>
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Guan</surname>
<given-names>D-F</given-names>
</name>
<name>
<surname>You</surname>
<given-names>P</given-names>
</name>
<name>
<surname>Zhang</surname>
<given-names>Q</given-names>
</name>
<name>
<surname>Xiao</surname>
<given-names>K</given-names>
</name>
</person-group> <article-title>Hybrid Spoof Surface Plasmon Polariton and Substrate Integrated Waveguide Transmission Line and its Application in Filter</article-title>. <source>IEEE Trans Microwave Theor Techn.</source> (<year>2017</year>) <volume>65</volume>(<issue>12</issue>):<fpage>4925</fpage>&#x2013;<lpage>32</lpage>. <pub-id pub-id-type="doi">10.1109/tmtt.2017.2727486</pub-id> </citation>
</ref>
<ref id="B20">
<label>20.</label>
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Li</surname>
<given-names>T</given-names>
</name>
<name>
<surname>Wang</surname>
<given-names>G-M</given-names>
</name>
<name>
<surname>Lu</surname>
<given-names>K</given-names>
</name>
<name>
<surname>Xu</surname>
<given-names>H-X</given-names>
</name>
<name>
<surname>Liao</surname>
<given-names>Z-H</given-names>
</name>
<name>
<surname>Zong</surname>
<given-names>B</given-names>
</name>
</person-group>. <article-title>Novel Bandpass Filter Based on Csrr Using Koch Fractal Curve</article-title>In <source>PIER Lett</source> (<year>2012</year>) <volume>28</volume>:<fpage>121</fpage>&#x2013;<lpage>8</lpage>. <pub-id pub-id-type="doi">10.2528/PIERL11082903</pub-id> </citation>
</ref>
<ref id="B21">
<label>21.</label>
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Pan</surname>
<given-names>BC</given-names>
</name>
<name>
<surname>Luo</surname>
<given-names>GQ</given-names>
</name>
<name>
<surname>Liao</surname>
<given-names>Z</given-names>
</name>
<name>
<surname>Cai</surname>
<given-names>JL</given-names>
</name>
<name>
<surname>Cai</surname>
<given-names>BG</given-names>
</name>
</person-group>. <article-title>Wideband Miniaturized Design of Complementary Spoof Surface Plasmon Polaritons Waveguide Based on Interdigital Structures</article-title>. <source>Sci Rep</source> (<year>2020</year>) <volume>10</volume>:<fpage>3258</fpage>. <pub-id pub-id-type="doi">10.1038/s41598-020-60244-7</pub-id> </citation>
</ref>
<ref id="B22">
<label>22.</label>
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Pan</surname>
<given-names>BC</given-names>
</name>
<name>
<surname>Yu</surname>
<given-names>P</given-names>
</name>
<name>
<surname>Liao</surname>
<given-names>Z</given-names>
</name>
<name>
<surname>Zhu</surname>
<given-names>F</given-names>
</name>
<name>
<surname>Luo</surname>
<given-names>GQ</given-names>
</name>
</person-group>. <article-title>A Compact Filtering Power Divider Based on Spoof Surface Plasmon Polaritons and Substrate Integrated Waveguide</article-title>. <source>IEEE Microw Wireless Compon Lett</source> (<year>2021</year>) <fpage>1</fpage>&#x2013;<lpage>4</lpage>. <pub-id pub-id-type="doi">10.1109/lmwc.2021.3116169</pub-id> </citation>
</ref>
<ref id="B23">
<label>23.</label>
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Han</surname>
<given-names>Y</given-names>
</name>
<name>
<surname>Liu</surname>
<given-names>Z</given-names>
</name>
<name>
<surname>Zhang</surname>
<given-names>C</given-names>
</name>
<name>
<surname>Mei</surname>
<given-names>C</given-names>
</name>
<name>
<surname>Chen</surname>
<given-names>Q</given-names>
</name>
<name>
<surname>Hu</surname>
<given-names>K</given-names>
</name>
<etal/>
</person-group> . <article-title>A Flexible Microstrip Low-Pass Filter Design Using Asymmetric Pi-Shaped DGS</article-title>. <source>Ieee Access</source> (<year>2019</year>) <volume>7</volume>:<fpage>49999</fpage>&#x2013;<lpage>50006</lpage>. <pub-id pub-id-type="doi">10.1109/access.2019.2910350</pub-id> </citation>
</ref>
</ref-list>
</back>
</article>