Study On The Characteristics Of A New Localized Mode Based On The Dirac Point In 2D Photonic Crystals

Photonic crystals can support localized modes as properties of resonators or waveguides.Many devices used in:integrated optics are derived from resonators or waveguides,including microlasers,optical fibres,couplers,filters,splitters and signal routers.These devices acquire their functionality through internal couplings between basic cavity/waveguide building blocks.Traditional optical resonators and waveguides rely on total internal reflection or a photonic bandgap to achieve their field confinement.Any couplings realized by these two trapping mechanisms are necessarily short-range because the tail of the localized mode,on which the interaction is based,decays exponentially with distance.Here we report a new trapping mechanism in photonic crystals by which long-range cavity/waveguide coupling is enabled.Dirac point can take the role of a photonic bandgap with the establishment of cavity modes.Such cavity modes are obtainable in the presence of neither a complete photonic bandgap nor total internal reflection.Because this trapping mechanism is fundamentally different from the two established mechanisms,the resulting modes are novel and exciting.The field profile of the Dirac mode is a standing wave and decays algebraically as l/r3/2away from its centre,thus enabling long-range coupling between resonators and waveguides.Dirac mode is a true bound state with a very high Q value.It degrades gradually as the resonant frequency of the corresponding cavity shifts away from the Dirac frequency.Leakage into the continuum of states imposes a finite frequency bandwidth on the Dirac mode for applications.The interactions between two resonators and between a resonator and a waveguide have been studied by numerical means.The coupling coefficient between two resonators is numerically found to decay as ? ?d-3/2 and that between a resolator and a waveguide is found to decay as ? ?d-1/2 with distance d between the two interacting blocks.In 2D anisotropic plasma photonic crystals,the complete band gap and the Dirac mode are studied.The complete band gaps are obtained by introducing tellurium dielectric rods using modified plane wave expansion method with a standard linearization technique.The complete band gap could be tuned by filling factor,plasma frequency and magnetic field,respectively.The effective tunable ranges of these parameters are given out.The results could be helpful in designing 2D anisotropic plasma photonic crystals with large complete band gaps.Dirac mode in 2D plasma photonic crystal has also been studied.It is a true bound state and decays algebraically as 1/r3/2away from its centre.As an advantage,the Dirac point could also be modulated by the filling factor,plasma frequency and plasma cyclotron frequency.When an external magnetic field parallel to the wave vector is applied,Dirac point for left circular polarizated waves and right circular polarizated waves could be produced separately.This property will bring about a new kind of applications in plasma photonic crystal systems,such as polarization splitter,circularly polarized laser.As the plasma acts as metamaterial in microwave region,this investigation will extend the possibilities of Dirac mode to more metamaterial photonic crystal devices.