Abstract—Although morphology-dependent resonances (MDRs) have been studied for decades, it is interesting to note that TM resonances have not been as widely investigated as those of the TE mode. Nevertheless, the formers are also worthy of additional study. Even though the TE and TM mode resonances can be generated using the same technique, their properties (such as the additional sharp peak in the source function at the particle surface) are quite distinct. We present the derivation of the resonance formulations for TM mode for both increasing and decreasing piecewise-constant refractive index profiles in a two-layer model of a sphere embedded in a uniform medium of different refractive index. Numerical and graphical results are also provided.

Index Terms—Electromagnetic, resonance, transverse magnetic, stratified medium.

Umaporn Nuntaplook is with Department of Mathematics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand. She is also with Department of Mathematics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand (email: ununtaplook@gmail.com).
John A. Adam is with Department of Mathematics and Statistics, Old Dominion University, Norfolk, VA 23529, USA.

Cite: Umaporn Nuntaplook, John A. Adam, "Shape Resonances of the Transverse Magnetic Mode in a Spherically Stratified Medium," International Journal of Applied Physics and Mathematics vol. 8, no. 3, pp. 18-30, 2018.