Propagation of transverse magnetic mode in a non-integer dimensional dielectric slab waveguide

In present paper, solutions for the transverse magnetic modes propagating in a non-integer dimensional (NID) dielectric slab waveguide have been derived. Medium within the slab is NID in direction normal to the dielectric interfaces of the slab. Transcendental equations in terms of non-integer order Hankel functions have been derived. The order of non-integer order Hankel functions depends on parameter describing dimension of the NID space. Using graphical treatment, it has been shown that behavior of propagating mode changes substantially when value of the parameter describing dimension of the NID space changes. It has also been noted that NID parameter significantly effects the value of propagation constant, attenuation constant and cutoff frequency. The classical results have also been recovered when dimension of the NID slab has been taken equal to the dimension of the medium surrounding the slab.