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TM-modes in a planar optical waveguide with a graded index of the symmetric Epstein type |
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| Institution: | 1. The University of Texas at Austin, McKetta Department of Chemical Engineering, 200 E. Dean Keeton St. Stop C0400, Austin, TX 78712-1589, USA;2. Nanoscience and Microsystems Engineering, University of New Mexico, Albuquerque, NM 87131-0001, USA;3. Advanced Materials Laboratory, Sandia National Laboratories, PO box 5800, Albuquerque, NM 87185, USA;4. Department of Chemical and Biological Engineering, University of New Mexico, Albuquerque, NM 87131-0001, USA |
| Abstract: | The eigenvalue problem for the TM-modes in a planar optical waveguide is rigorously solved by analytical and numerical methods in the case of a symmetric Epstein-type variation of the dielectric permittivity. It is shown that there exists a finite number of guided TM-modes. The TM-modal fields are expressed in terms of Heun functions and the corresponding eigenvalues (or propagation coefficients) are numerically determined from the minimal solution of a three-term recurrence relation. Upper and lower bounds are established for the difference between corresponding eigenvalues of the TE- and TM-modes. |
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