¹Graduate School of Natural and Applied Sciences, Eskişehir Osmangazi University,
Meşelik Kampüsü, Odunpazarı 26040, Eskişehir, Türkiye
E-mail: dr.ahmetyalcin@gmail.com
²Faculty of Science, Eskişehir Osmangazi University, Eskişehir, Türkiye,
Meşelik Kampüsü, Odunpazarı 26040, Eskişehir, Türkiye
E-mail: acetin@ogu.edu.tr

Abstract. The evolution equation for guided transverse electrical modes in a slab waveguide having a double negative core is derived for the electrical field. Special solutions of the dispersion equation for the case with double positive symmetric cladding are searched for. Relevant eigenmodes are formulated in terms of characteristic frequencies as a new method, and these frequencies corresponding to the oscillating guided modes are found for different wave numbers and core widths assuming the lossless Drude model can be used for the core medium with a Kerr-type nonlinearity. Results show that normalized characteristic frequencies increase with increasing wave numbers and mode numbers.

Keywords: slab waveguide, transverse modes, characteristic frequencies, Kerr-type nonlinearity, metamaterials.

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