Fundamental wave phenomena on biased-ferrite planar slab waveguides in connection with singularity theory

Abstract

In this paper, characteristic dispersion phenomena and interactions of the discrete surface-and leaky-wave modes supported by a grounded biased-ferrite slab waveguide are analyzed using singularity and critical-point theory. Surface-and space-wave leaky modes are studied for different orientations of the applied magnetic bias field. As the bias field is rotated away from a coordinate axis, the modes become hybrid, and mode coupling or modal degeneracies may occur. Mode coupling, in general, is governed by a Morse critical point (MCP), and the behavior of the MCP is found to be useful in explaining and predicting modal behavior on this complicated waveguiding structure. In addition, leaky-wave dispersion behavior and leaky-wave cutoff associated with a fold singular point is studied by varying the orientation of the applied magnetic bias field.Index Terms-Critical points, ferrite slab, leaky waves, mode coupling, singularity theory, surface waves. Alexander B. Yakovlev

Modal Phenomena of Surface and Bulk Polaritons in Magnetic- Semiconductor Superlattices

“…These extreme states can be carefully identified and studied involving the approach based on the theory of the Morse critical points from the catastrophe theory [31][32][33][34][35][36]. This treatment has been originally applied to study open waveguides and resonators [31,32], and later it has been extended to more complex waveguide structures [33][34][35]. From viewpoint of this theory, the presence of the Morse critical points is generally defined by a set of nonlinear differential equations written in the form [33]:…”

“…ThetypeofeachextremestatedefinedbysetofEq. (25)canbeuniquelyidentifiedfromthe sign of the Hessian determinant [35]. For instance, when H < 0, the corresponding Morse critical point represents a saddle point, which occurs in the region of a modal coupling (the anti-crossing effect), whereas in the case of degeneracy, when H ¼ 0, it is a non-isolated critical point (the crossing effect).…”

“…The polaritons dispersion relations for these specific cases of magnetization can be obtained by using general results derived in Section 2 with applying appropriate boundary and initial conditions. Further in this study we are mainly interested in a manifestation of the crossing and anti-crossing effects which are considered involving a unified technique about the Morse critical points from the catastrophe theory (for details, see [35]- [40] and Appendix B).…”