Research On Characteristics And Application Of Dirac Localized Mode In Photonic Crystal

Photonic crystal is an artificial lens which is composed of periodic arrangement of different dielectric materials or metal material.photonic crystal attract a research fever in optical communication field.It has promoted the development of optical communication devices,which contains photonic crystal fibers?photonic crystal laser?photonic crystal waveguides and optics resonator.Optical cavities and waveguides are essential building blocks of many modern optical devices.They rely upon total internal reflections or photonic bandgaps,to achieve field confinement.This article illustrates a novel light trapping named Dirac mode,which is different from the traditional light confinement,in detail.This novel wave localization that is attributable to neither of the traditional light guiding mechanisms.By adopting the combination of theoretical analysis and numerical analysis method,we have been done detailed and in-depth research and stated the Dirac mode in two-dimensional photonic crystal about the theoretical foundation?numerical calculation and unique properties.This article has done these research contents as following:(1)A novel Dirac localized mode,which exists around the Dirac point of two-dimensional photonic crystal,has been discussed.Different from traditional light guiding mechanism,Dirac localized mode relies upon neither the total internal reflection nor photonic crystal band gap to achieve light control to achieve light confinement.It rely on the phenomena that density of the state at Dirac point is zero to achieve light trapping.Bloch states near the Dirac point own linear dispersion characteristics.In analogy with theory of Dirac point in the graphene,combine the massless Dirac equation with the Maxwell equation of the photonic crystal to describe the Dirac wave function c.(2)The Dirac localized mode has been found in two-dimensional triangular and honeycomb lattice photonic crystal.In addition to the special principle of light trapping,the Dirac localized model also has a different algebraic-decay feature,the envelope function of the state decay as as r-3/2 with the distance in the space rather than traditional localized mode decays exponentially.Dirac localized mode only exists at a specific Dirac frequency rather than a frequency range,which means this new localized mode owns feature of frequency selectivity.(3)Archimedean-like lattice photonic crystal was also been found has Dirac localized mode at another Dirac frequency fD = 0.2038c/a.In this structure,only the wave which frequency is the Dirac frequency fD = 0.2038 c/a,can be trapped.Meanwhile,the simulation result of the FDTD method confirmed the conclusion.From the figures of mode field distribution and quality factor,it is apparent that the most of mode field energy are confined around the defect in this photonic crystal structure,and reached harmonic oscillation with a high quality factor.Besides,the mode amplitude decays as power function r-3/2 at large distance,other than like common localized mode decays exponent(4)Besides,we also design a honeycomb-like lattice photonic crystal to achieve the Dirac localized mode.It has been found the Dirac frequency is fD = 0.1067c/a in this photonic crystal structure.When the cavity is simulated with a pulsed source whose frequency is Dirac frequency,the numeric simulation results by FDTD method is coincide with the dates obtained by PWE method,and conform with other properties of this novel localized mode such as algebraic field profile?high quality factor?phase profile?The phenomenon states when the frequency is set as the Dirac frequency,the wave would achieve harmonic oscillation in the photonic crystal cavity and be confined around the defect.(5)On the basis of the above research,the Dirac localized mode can be applied to photonic crystal fibers.Different from the traditional photonic crystal fibers,which rely upon photonic bandgaps or total internal reflections to achieve light-guide,the photonic crystal fiber based on the Dirac localized mode is more intriguing.The new Dirac mode has a unique characteristic that the amplitude of the mode decays as power function r-3/2 at large distance in the plane x-y.Comparing with the traditional localized mode in photonic crystal fiber whose amplitude decays exponentially,the wave package of Dirac localized mode can transmit further and it can enable long-range interaction between multiple cores.Besides,due to only the wave which frequency is the Dirac frequency can be confined,that makes this photonic crystal owns frequency selectivity.These properties will promote the development of the application of photonic crystal fibers and optical devices.