Theoretical Research On Surface Modes Of One-Dimensional Photonic Crystals

Surface mode on photonic crystals is nonradiation electromagnetic mode which localized on the surface of photonic crystals. When the ideal photnic crystal is truncated at the surface,its translational symmetry is broken,resulting in surface mode occurred in the band gap.It exists in the form of Bloch wave in the photonic crystal (PC) side and plane wave in the media side while both decay exponentially. Surface mode of one-dimensional photonic crystal (1DPC) has long been proved by theory and verified experimentally.It has also been widely studied and applied in the sensing field.But there is still a lack of reseach on the waveguide device which based on the surface wave of IDPC,especially the research of transmission characteristics and coupling property of Bloch wave.This paper firstly analyzes the band structure of IDPC,then study the property of surface mode on 1DPC and symmetrical semi-infinite 1DPC by the supercell method and direct match procedure.The main works and innovation are as follows:(1) By using the equivalent theory of symmetrical thin films,band structure of 1DPC is investigated in detail.We emphatically study the band overlap phenomenon of 1DPC and explain its physical mechanism. It is found that there are two reasons of band overlapping phenomenon:one is optical hole,regardless of the polarization of incident wave is TE or TM polarization,The electromagnetic wave will propagate through the PC with no reflections long as the phase thickness of each layer meet δ=mπ.The other is Brewster angle, It occurs only for TM polarization, and can be found in the first band gap,contrary to optical hole.(2) We use the supercell method and iterative fresnel equation to calculate the dispersion curves of surface mode and ATR reflection spectrum.We found surface mode could be flexibly controlled by change the thickness of outmost layer of 1DPC when the layer’s refractive index is higher and the difference of localization of electric filed of different positions in the band gap are obvious. The surface modes which far from the light line of vacuum and localized at the midgap will strongly confined on the PC side and in the air side.We excited the surface mode of 1DPC can by the Kreschmann configuration and the optical properties of tansmission medium can be predicted by the shape and position of resonance peak.(3) The coupling properties of surface mode in symmetrical semi-infinite one-dimensiondnal photonic crystals are studied by direct match procedure and iterative fresnel equation.We calculate the dispersion relation,splitting degree and coupling strength analytically.It is found that surface mode split into odd mode and even mode,the frequncy of odd mode is always higher than even mode.Reducing the thickness of the outermost layer of the PC and the gap refractive index results a large splitting degree when gap width is small and vice versa. Smaller gap width and closer distance between coupling modes and vacuum light line lead to greater coupling strength.ATR reflection spectrum of our structure shows that the exitation of coupled mode could be controlled by periodicity number of the bottom 1DPC.