Scaling Rules for TM Modes in Thin–Film Optical Waveguides

Three-media planar dielectric nonmagnetic optical waveguides represent basic structures employed in integrated optics and sensing. The previously published scaling rules for transverse electric (TE) and transverse magnetic (TM) modes in these structures were characterized with different sets of parameters for TE and TM cases. The latter case which is more involved received less attention. The present work suggests an alternative approach where both TE and TM modes are characterized by the same set of three parameters, that is, normalized frequency or film thickness, normalized guide index, and asymmetry measure. A complete specification of the TM modes requires an additional parameter, that is, the ratio of the index of refraction in the film to that in the substrate. The TE and TM solutions for the normalized guide index and the normalized guide thickness are displayed in common charts as functions of normalized frequency. This provides an improved insight into the differences between the TE and TM guided modes. Received: 16 October 2025 | Revised: 24 February 2026 | Accepted: 28 April 2026 Conflicts of Interest The author declares that he has no conflicts of interest to this work. Data Availability Statement Data sharing is not applicable to this article as no new data were created or analyzed in this study. Author Contribution Statement Štefan Višˇnovský: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Writing - original draft, Writing - review & editing, Visualization, Supervision, Project administration.