{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T17:54:19Z","timestamp":1785434059001,"version":"3.56.0"},"reference-count":33,"publisher":"Optica Publishing Group","issue":"2","license":[{"start":{"date-parts":[[2026,1,14]],"date-time":"2026-01-14T00:00:00Z","timestamp":1768348800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/doi.org\/10.1364\/OA_License_v2#VOR"},{"start":{"date-parts":[[2026,1,14]],"date-time":"2026-01-14T00:00:00Z","timestamp":1768348800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/opg.optica.org\/policies\/opg-tdm-policy.json"}],"funder":[{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"publisher","award":["NRF2020R1F1A1074015"],"award-info":[{"award-number":["NRF2020R1F1A1074015"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["opg.optica.org"],"crossmark-restriction":false},"short-container-title":["Opt. Lett."],"published-print":{"date-parts":[[2026,1,15]]},"abstract":"<jats:p>\n                    We investigate the emergence of specific modes in finite periodic (FP) parity-time (\n                    <jats:italic>P<\/jats:italic>\n                    <jats:italic>T<\/jats:italic>\n                    ) symmetric photonic structures using the transfer matrix (T-matrix) formalism. Three distinct resonant states are identified\u2014the coherent perfect absorber\u2013laser (\n                    <jats:italic>M<\/jats:italic>\n                    <jats:sub>\n                      <jats:italic>C<\/jats:italic>\n                      <jats:italic>L<\/jats:italic>\n                    <\/jats:sub>\n                    ), the unidirectional invisibility (\n                    <jats:italic>M<\/jats:italic>\n                    <jats:sub>\n                      <jats:italic>U<\/jats:italic>\n                      <jats:italic>I<\/jats:italic>\n                    <\/jats:sub>\n                    ), and the anti-reflection (\n                    <jats:italic>M<\/jats:italic>\n                    <jats:sub>\n                      <jats:italic>A<\/jats:italic>\n                      <jats:italic>R<\/jats:italic>\n                    <\/jats:sub>\n                    ) modes. We show that, unlike in a single-period\n                    <jats:italic>P<\/jats:italic>\n                    <jats:italic>T<\/jats:italic>\n                    bilayer\u2014where the\n                    <jats:italic>M<\/jats:italic>\n                    <jats:sub>\n                      <jats:italic>C<\/jats:italic>\n                      <jats:italic>L<\/jats:italic>\n                    <\/jats:sub>\n                    mode arises only once\u2014FP structures support recurring\n                    <jats:italic>M<\/jats:italic>\n                    <jats:sub>\n                      <jats:italic>C<\/jats:italic>\n                      <jats:italic>L<\/jats:italic>\n                    <\/jats:sub>\n                    modes as the number of periods increases.\n                    <jats:italic>M<\/jats:italic>\n                    <jats:sub>\n                      <jats:italic>A<\/jats:italic>\n                      <jats:italic>R<\/jats:italic>\n                    <\/jats:sub>\n                    modes appear between successive\n                    <jats:italic>M<\/jats:italic>\n                    <jats:sub>\n                      <jats:italic>C<\/jats:italic>\n                      <jats:italic>L<\/jats:italic>\n                    <\/jats:sub>\n                    modes. The required imaginary part of the refractive index (\n                    <jats:italic>n<\/jats:italic>\n                    <jats:sup>\n                      <jats:italic>\u2032<\/jats:italic>\n                      <jats:italic>\u2032<\/jats:italic>\n                    <\/jats:sup>\n                    ) for the emergence of each mode is determined by the ratio\n                    <jats:italic>l<\/jats:italic>\n                    \/\n                    <jats:italic>N<\/jats:italic>\n                    , where\n                    <jats:italic>l<\/jats:italic>\n                    is the mode order and\n                    <jats:italic>N<\/jats:italic>\n                    the number of periods. For small\n                    <jats:italic>l<\/jats:italic>\n                    \/\n                    <jats:italic>N<\/jats:italic>\n                    ,\n                    <jats:italic>n<\/jats:italic>\n                    <jats:sup>\n                      <jats:italic>\u2032<\/jats:italic>\n                      <jats:italic>\u2032<\/jats:italic>\n                    <\/jats:sup>\n                    increases linearly, whereas for large\n                    <jats:italic>l<\/jats:italic>\n                    \/\n                    <jats:italic>N<\/jats:italic>\n                    ,\n                    <jats:italic>n<\/jats:italic>\n                    <jats:sup>\n                      <jats:italic>\u2032<\/jats:italic>\n                      <jats:italic>\u2032<\/jats:italic>\n                    <\/jats:sup>\n                    approaches the\n                    <jats:italic>P<\/jats:italic>\n                    <jats:italic>T<\/jats:italic>\n                    critical point. Furthermore, the phase diagram shows that\n                    <jats:italic>M<\/jats:italic>\n                    <jats:sub>\n                      <jats:italic>C<\/jats:italic>\n                      <jats:italic>L<\/jats:italic>\n                    <\/jats:sub>\n                    modes exist solely in the\n                    <jats:italic>P<\/jats:italic>\n                    <jats:italic>T<\/jats:italic>\n                    -broken phase, while\n                    <jats:italic>M<\/jats:italic>\n                    <jats:sub>\n                      <jats:italic>A<\/jats:italic>\n                      <jats:italic>R<\/jats:italic>\n                    <\/jats:sub>\n                    modes remain confined to the\n                    <jats:italic>P<\/jats:italic>\n                    <jats:italic>T<\/jats:italic>\n                    -symmetric phase. These findings are validated using photonic nanobeam simulations, demonstrating the systematic realization of the three modes in FP\n                    <jats:italic>P<\/jats:italic>\n                    <jats:italic>T<\/jats:italic>\n                    -symmetric photonic systems.\n                  <\/jats:p>","DOI":"10.1364\/ol.581991","type":"journal-article","created":{"date-parts":[[2025,12,22]],"date-time":"2025-12-22T20:00:10Z","timestamp":1766433610000},"page":"464","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Universal appearance tendency of modes at the finite periodic\n                    <i>P<\/i>\n                    <i>T<\/i>\n                    -symmetric structure"],"prefix":"10.1364","volume":"51","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1883-0147","authenticated-orcid":true,"given":"Jihoon","family":"Choi","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/0049erg63","id-type":"ROR","asserted-by":"publisher"}]},{"name":"Research Institute of Natural Science, Gyeongsang National University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Young Ki","family":"Hong","sequence":"additional","affiliation":[{"name":"Research Institute of Natural Science, Gyeongsang National University"},{"name":"Gyeongsang National University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6086-9109","authenticated-orcid":true,"given":"Heeso","family":"Noh","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/0049erg63","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"285","published-online":{"date-parts":[[2026,1,14]]},"reference":[{"key":"ol-51-2-464-R1","doi-asserted-by":"publisher","first-page":"5243","DOI":"10.1103\/PhysRevLett.80.5243","type":"journal-article","volume":"80","author":"Bender","year":"1998","journal-title":"Phys. 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