Stabilizing solutions at thresholds of the continuous spectrum and anomalous transmission of waves
A problem of scattering by a resonator connecting two 2D waveguides is studied. The incident wave is one of the waveguide modes taken at the spectral parameter close to a threshold of the continuous spectrum. It is shown that in the general case the reflection coefficient for such a mode is close to...
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| Veröffentlicht in: | Zeitschrift für angewandte Mathematik und Mechanik 2016-10, Vol.96 (10), p.1245-1260 |
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| container_title | Zeitschrift für angewandte Mathematik und Mechanik |
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| creator | Korolkov, A. I. Nazarov, Sergei A. Shanin, A. V. |
| description | A problem of scattering by a resonator connecting two 2D waveguides is studied. The incident wave is one of the waveguide modes taken at the spectral parameter close to a threshold of the continuous spectrum. It is shown that in the general case the reflection coefficient for such a mode is close to ‐1 (this case corresponds to an almost perfect reflection). Also it is shown that in some special cases the reflection coefficient is close to 0, and an almost perfect transmission is observed. The behavior of scattering at near‐threshold frequencies is determined by solutions corresponding to the threshold spectral parameter and crucially depends on whether stabilizing solutions do exist or not. Anomalous transmission is observed when there exist only solutions growing at infinity.
A problem of scattering by a resonator connecting two 2D waveguides is studied. The incident wave is one of the waveguide modes taken at the spectral parameter close to a threshold of the continuous spectrum. It is shown that in the general case the reflection coefficient for such a mode is close to ‐1 (this case corresponds to an almost perfect reflection). Also it is shown that in some special cases the reflection coefficient is close to 0, and an almost perfect transmission is observed. The behavior of scattering at near‐threshold frequencies is determined by solutions corresponding to the threshold spectral parameter and crucially depends on whether stabilizing solutions do exist or not. Anomalous transmission is observed when there exist only solutions growing at infinity. |
| doi_str_mv | 10.1002/zamm.201500016 |
| format | Article |
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A problem of scattering by a resonator connecting two 2D waveguides is studied. The incident wave is one of the waveguide modes taken at the spectral parameter close to a threshold of the continuous spectrum. It is shown that in the general case the reflection coefficient for such a mode is close to ‐1 (this case corresponds to an almost perfect reflection). Also it is shown that in some special cases the reflection coefficient is close to 0, and an almost perfect transmission is observed. The behavior of scattering at near‐threshold frequencies is determined by solutions corresponding to the threshold spectral parameter and crucially depends on whether stabilizing solutions do exist or not. Anomalous transmission is observed when there exist only solutions growing at infinity.</description><identifier>ISSN: 0044-2267</identifier><identifier>EISSN: 1521-4001</identifier><identifier>DOI: 10.1002/zamm.201500016</identifier><language>eng</language><publisher>Weinheim: Blackwell Publishing Ltd</publisher><subject>Incident waves ; Parameters ; Reflectance ; Reflection ; Scattering ; Scattering in waveguides ; scattering matrix ; Spectra ; threshold behavior ; Thresholds ; waveguide modes ; Waveguides</subject><ispartof>Zeitschrift für angewandte Mathematik und Mechanik, 2016-10, Vol.96 (10), p.1245-1260</ispartof><rights>2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim</rights><rights>Copyright © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c3886-5d54947bf7278cefb03cad4f111c70aedb2a193ed692149348939c4ab77d13a83</citedby><cites>FETCH-LOGICAL-c3886-5d54947bf7278cefb03cad4f111c70aedb2a193ed692149348939c4ab77d13a83</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1002%2Fzamm.201500016$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2Fzamm.201500016$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,777,781,1412,27905,27906,45555,45556</link.rule.ids></links><search><creatorcontrib>Korolkov, A. I.</creatorcontrib><creatorcontrib>Nazarov, Sergei A.</creatorcontrib><creatorcontrib>Shanin, A. V.</creatorcontrib><title>Stabilizing solutions at thresholds of the continuous spectrum and anomalous transmission of waves</title><title>Zeitschrift für angewandte Mathematik und Mechanik</title><addtitle>Z. Angew. Math. Mech</addtitle><description>A problem of scattering by a resonator connecting two 2D waveguides is studied. The incident wave is one of the waveguide modes taken at the spectral parameter close to a threshold of the continuous spectrum. It is shown that in the general case the reflection coefficient for such a mode is close to ‐1 (this case corresponds to an almost perfect reflection). Also it is shown that in some special cases the reflection coefficient is close to 0, and an almost perfect transmission is observed. The behavior of scattering at near‐threshold frequencies is determined by solutions corresponding to the threshold spectral parameter and crucially depends on whether stabilizing solutions do exist or not. Anomalous transmission is observed when there exist only solutions growing at infinity.
A problem of scattering by a resonator connecting two 2D waveguides is studied. The incident wave is one of the waveguide modes taken at the spectral parameter close to a threshold of the continuous spectrum. It is shown that in the general case the reflection coefficient for such a mode is close to ‐1 (this case corresponds to an almost perfect reflection). Also it is shown that in some special cases the reflection coefficient is close to 0, and an almost perfect transmission is observed. The behavior of scattering at near‐threshold frequencies is determined by solutions corresponding to the threshold spectral parameter and crucially depends on whether stabilizing solutions do exist or not. Anomalous transmission is observed when there exist only solutions growing at infinity.</description><subject>Incident waves</subject><subject>Parameters</subject><subject>Reflectance</subject><subject>Reflection</subject><subject>Scattering</subject><subject>Scattering in waveguides</subject><subject>scattering matrix</subject><subject>Spectra</subject><subject>threshold behavior</subject><subject>Thresholds</subject><subject>waveguide modes</subject><subject>Waveguides</subject><issn>0044-2267</issn><issn>1521-4001</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><recordid>eNqFkcFLHTEQh4O00NfXXnte8OJlXzNJdrM5iq1aUAu2pdBLyGazGt3dvGayWv3rm-WJSC89hDDh-2aGXwj5AHQDlLKPj2YcN4xCRSmFeo-soGJQily8IitKhSgZq-Ub8hbxZkEU8BVpvyXT-sE_-umqwDDMyYcJC5OKdB0dXoehwyL0uXKFDVPy0xxmLHDrbIrzWJipyyeMZlieUzQTjh4xN1mse3Pn8B153ZsB3fune01-HH_-fnRann09-XJ0eFZa3jR1WXWVUEK2vWSysa5vKbemEz0AWEmN61pmQHHX1YqBUFw0iisrTCtlB9w0fE0Odn23MfyeHSadN7FuGMzk8nIamqriSgBUGd3_B70Jc5zydplitVCM5glrstlRNgbE6Hq9jX408UED1UvkeolcP0eeBbUT7v3gHv5D61-H5-cv3XLnekzuz7Nr4q2uJZeV_nlxouETz396SfUl_wvGJ5WR</recordid><startdate>201610</startdate><enddate>201610</enddate><creator>Korolkov, A. I.</creator><creator>Nazarov, Sergei A.</creator><creator>Shanin, A. V.</creator><general>Blackwell Publishing Ltd</general><general>Wiley Subscription Services, Inc</general><scope>BSCLL</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>201610</creationdate><title>Stabilizing solutions at thresholds of the continuous spectrum and anomalous transmission of waves</title><author>Korolkov, A. I. ; Nazarov, Sergei A. ; Shanin, A. V.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c3886-5d54947bf7278cefb03cad4f111c70aedb2a193ed692149348939c4ab77d13a83</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Incident waves</topic><topic>Parameters</topic><topic>Reflectance</topic><topic>Reflection</topic><topic>Scattering</topic><topic>Scattering in waveguides</topic><topic>scattering matrix</topic><topic>Spectra</topic><topic>threshold behavior</topic><topic>Thresholds</topic><topic>waveguide modes</topic><topic>Waveguides</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Korolkov, A. I.</creatorcontrib><creatorcontrib>Nazarov, Sergei A.</creatorcontrib><creatorcontrib>Shanin, A. 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V.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Stabilizing solutions at thresholds of the continuous spectrum and anomalous transmission of waves</atitle><jtitle>Zeitschrift für angewandte Mathematik und Mechanik</jtitle><addtitle>Z. Angew. Math. Mech</addtitle><date>2016-10</date><risdate>2016</risdate><volume>96</volume><issue>10</issue><spage>1245</spage><epage>1260</epage><pages>1245-1260</pages><issn>0044-2267</issn><eissn>1521-4001</eissn><abstract>A problem of scattering by a resonator connecting two 2D waveguides is studied. The incident wave is one of the waveguide modes taken at the spectral parameter close to a threshold of the continuous spectrum. It is shown that in the general case the reflection coefficient for such a mode is close to ‐1 (this case corresponds to an almost perfect reflection). Also it is shown that in some special cases the reflection coefficient is close to 0, and an almost perfect transmission is observed. The behavior of scattering at near‐threshold frequencies is determined by solutions corresponding to the threshold spectral parameter and crucially depends on whether stabilizing solutions do exist or not. Anomalous transmission is observed when there exist only solutions growing at infinity.
A problem of scattering by a resonator connecting two 2D waveguides is studied. The incident wave is one of the waveguide modes taken at the spectral parameter close to a threshold of the continuous spectrum. It is shown that in the general case the reflection coefficient for such a mode is close to ‐1 (this case corresponds to an almost perfect reflection). Also it is shown that in some special cases the reflection coefficient is close to 0, and an almost perfect transmission is observed. The behavior of scattering at near‐threshold frequencies is determined by solutions corresponding to the threshold spectral parameter and crucially depends on whether stabilizing solutions do exist or not. Anomalous transmission is observed when there exist only solutions growing at infinity.</abstract><cop>Weinheim</cop><pub>Blackwell Publishing Ltd</pub><doi>10.1002/zamm.201500016</doi><tpages>16</tpages></addata></record> |
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| source | Wiley Online Library Journals Frontfile Complete |
| subjects | Incident waves Parameters Reflectance Reflection Scattering Scattering in waveguides scattering matrix Spectra threshold behavior Thresholds waveguide modes Waveguides |
| title | Stabilizing solutions at thresholds of the continuous spectrum and anomalous transmission of waves |
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