Optical Waves in Planar Waveguides with Left-handed Materials

In this thesis, optical waveguide with the left-handed material (LHM) is investigated. Maxwell’s equations and translation matrix method (TMM) are used to develop the waveguide theory for optical waveguide with left-handed materials. Then the characteristics of three-layer planar waveguides with left-handed materials are studied. Consequently, some different characteristics in optical waveguides between left-handed materials and conventional materials are compared. Furthermore, in the part of periodic structures, Bloch theory and translation matrix method are used to develop the band-edge equations and the relations of band structures, and then discuss the characteristics of band structures by changing the parameters of periodic structures. The analytical results show some characteristics of guided mode and surface mode in left-handed materials which is different in conventional materials. In guided modes, the fundamental mode disappears in any case, and the first order mode may appear in some particular parameters. In surface modes, mode degeneracy appears in a symmetric structure, and the energy of electromagnetic wave is focused on the interface. In two-layer periodic structure, the Brewster line is controllable, and the band structures are more complicated in left-handed materials than conventional materials.