{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:53:40Z","timestamp":1760151220690,"version":"build-2065373602"},"reference-count":90,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2022,2,22]],"date-time":"2022-02-22T00:00:00Z","timestamp":1645488000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this work, we report the construction of different classes of complex-valued refractive index landscapes, with real spectra, in the framework of the factorization method. The particular case of guiding hyperbolic-type profiles is considered in the PT- and non-PT-symmetric configurations. In both schemes, the imaginary part of the refractive index satisfies the zero-total-area condition indicating that the total transverse optical power is preserved, allowing stable propagating modes to be obtained. The spectra and the guided modal field amplitudes are obtained and their orthogonality relations are established.<\/jats:p>","DOI":"10.3390\/sym14030432","type":"journal-article","created":{"date-parts":[[2022,2,22]],"date-time":"2022-02-22T22:35:00Z","timestamp":1645569300000},"page":"432","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Classes of Balanced Gain-and-Loss Waveguides as Non-Hermtian Potential Hierarchies"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5401-7778","authenticated-orcid":false,"given":"Ivan","family":"Bocanegra","sequence":"first","affiliation":[{"name":"Instituto Polit\u00e9cnico Nacional, UPIITA, Av. Instituto Polit\u00e9cnico Nacional 2580, Ciudad de M\u00e9xico 07340, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7133-0803","authenticated-orcid":false,"given":"Sara","family":"Cruz y Cruz","sequence":"additional","affiliation":[{"name":"Instituto Polit\u00e9cnico Nacional, UPIITA, Av. Instituto Polit\u00e9cnico Nacional 2580, Ciudad de M\u00e9xico 07340, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,2,22]]},"reference":[{"key":"ref_1","unstructured":"Okoshi, T. (1982). Optical Fibers, Academic Press."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Gomez-Reino, C., Perez, M.V., and Bao, C. (2002). Gradient-Index Optics. 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