Study On Propagation Characteristics Of Photonic Crystals Based On Single-negative Materials

Photonic crystal is a kind of artificial crystal which is composed of different medium arranged alternately.It is a new type of optical microstructure material with periodic changes of dielectric constant and permeability.Photonic crystals can be divided into one-dimensional photonic crystals,two-dimensional photonic crystals and three-dimensional photonic crystals according to the periodicity of their refractive index changes in space.Photonic band gap is an important characteristic of photonic crystal.The photonic band gap composed of positive index materials will change with the change of incident angle and polarization?A material in which either the dielectric constant or the permeability is negative is called a single-negative material in which electromagnetic waves cannot propagate.The introduction of single-negative materials into photonic crystal structures can generate zero-effective phase(zero-?_eff)photonic band gaps(PBG)independent of incident angle and polarization.Due to the high research value of these special photonic band gaps,they have become the research hotspots in recent years.In this paper,the optical properties of photonic crystals and heterostructures composed of single-negative materials are studied by using the transfer matrix method and MATLAB.The main contents are as follows:(1)We mainly study the photonic band gap and propagation characteristics of a tunable one-dimensional photonic crystal(ABCD)^N filter composed of four different single-negative materials.The results show that the number of resonant modes can be controlled by the period,and the band gap and formant,including frequency position and quality factor,can be controlled by adjusting the thickness,dielectric constant and permeability of the dielectric layer.The results show that the dielectric constant has a greater effect on the quality factor than the permeability.In addition,the angular response of the filter is also studied.The calculated results show that the transmission peak of one-dimensional photonic crystal structure(ABCD)^N is insensitive to the incident angle at frequencies below 1.1GHz.Therefore,the photonic crystal structure(ABCD)^N with tunable omnidirectional and angle-sensitive filter channels has great potential for multi-channel filter applications.(2)We have studied the filtering properties of photonic crystal heterostructure(ABA')^M(B'A'B)^N.When the thickness ratio x increases,the width of the zero effective phase band gap decreases,and the resonant mode frequency at both sides of the band gap moves to the tunneling-mode of the band gap center frequency.The number of resonant modes and the transmittance at the edge of the band gap remain unchanged,and the quality factor Q increases significantly as the thickness ratio x increases.The frequency position and number of tunneling modes in the zero effective phase band gap remain unchanged,the full width at half maximum(FWHM)becomes narrower,the quality factor Q increases,and the transmittance is almost constant and does not change with the angle.When M is equal to N,a tunneling mode appears in the zero effective phase band gap.The angular frequency position of the tunneling mode remains unchanged,but the transmittance of the tunneling mode decreases,the FWHM of the tunneling mode decreases,and the quality factor Q increases.The relationship between the number of resonance modes increased by s and the period value M,N at the edge of the zero effective phase band gap is s=2(N-2),and the resonance modes do not change with the angle.The FWHM and the transmittance of the tunneling mode decreases,but the quality factor Q increases.When M is less than N,The relationship between the number of resonance modes increased by s and the period value M,N at the edge of the zero effective phase band gap is s=2(N-M).The quality factor of resonance modes is basically unchanged,and the transmittance is reduced.When M is greater than N,the number of resonant modes on both sides of the tunneling mode located at the center frequency of the zero effective phase band gap remains unchanged,and the transmittance decreases,but less than when M is less than N,and the FWHM is almost unchanged.With the increase of d _A thickness,the transmission of the tunneling mode with 0.79577 GHz frequency decreases,the half-peak width decreases,and the quality factor Q increases.There are two resonant modes with frequencies located on both sides of the tunneling mode.The frequency positions shift to zero effective phase band gap center frequency with the increase of the thickness of d _A,the FWHM of the resonant mode becomes smaller,the quality factor Q increases,and the transmittance decreases.Compared with other types of heterostructures,we find that the heterostructure(ABA')^M(B'A'B)^N has a higher filter quality factor,is completely insensitive to angle,and has a simpler structure.