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

In this paper, solution for the transverse electric (TEz) mode propagating in a non-integer dimensional (NID) dielectric slab waveguide has been derived. For region occupied by the slab, the medium is assumed to be NID along the direction normal to interfaces of the slab. Transcendental equations yield solution in form of non-integer order Hankel functions. The order of the Hankel functions depends on parameter describing the dimension of the NID space. Graphical results has been used to depict that the behavior of modes changes substantially with respect to NID parameter. It also affects the value of propagation constant, attenuation constant and cutoff frequency. The classical result is reproduced taking NID parameter equal to two. It is observed that the value of propagation constant for TM modes is higher than the value of propagation constant for TE modes. Moreover, the value of attenuation constant for TE modes is higher than the value of attenuation constant for TM modes.