Complete mode spectrum of a grounded dielectric slab with double negative metamaterials

The properties of a grounded dielectric slab with double negative (DNG) metamaterials are investigated in this paper. Dramatically different dispersion curves of evanescent surface modes (electromagnetic fields exponentially decay both in air and inside the slab) are observed. They are highly dependent on the medium parameters. As the counterpart of the improper complex leaky modes in a double positive (DPS) medium, the complex modes in a DNG medium are proved to be exclusively proper. They have exponentially decaying fields in the air region and are termed complex surface modes. It is found that there are an infinite number of complex surface modes and they cannot be suppressed. The Poynting vectors of complex surface modes are studied and it is proved that their integrals along the transverse direction are simply zero. The complete mode spectrum of the dielectric slab for both DPS and DNG media are tabled and compared. Surface wave suppression is discussed and its necessary and sufficient conditions are presented.