Localization and channeling of light in defect modes of two-dimensional photonic crystals

The spatial distribution of the electromagnetic field in a two-dimensional photonic crystal with a lattice defect is investigated. It is shown that in such a structure the field can be localized in a region smaller than one wavelength in size. The dependence of the spectrum of defect modes on the parameters of a two-dimensional photonic crystal is investigated. The light field at the exit of the photonic crystal possesses properties of a nonradiative mode, making it possible to achieve spatial resolution in the near-field much higher than the radiation wavelength. The possibilities of using this phenomenon in optical near-field microscopy to produce optical memory devices and to increase the efficiency of nonlinear optical interactions are discussed. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 5, 323–328 (10 September 1999)     

Optical defect modes at an active defect layer in photonic liquid crystals

An analytic approach to the theory of the optical defect modes in photonic liquid crystals in the case of an active defect layer is developed. The analytic study is facilitated by the choice of the problem parameters related to the dielectric properties of the studied structures. The chosen models allow eliminating polarization mixing at the external surfaces of the studied structures. The dispersion equations determining the relation of the defect mode (DM) frequency to the dielectric characteristics of an isotropic, birefringent and absorbing (amplifying) defect layer and its thickness are obtained. Analytic expressions for the transmission and reflection coefficients of the defect mode structure (DMS) (photonic liquid crystal-active defect layer-photonic liquid crystal) are presented and analyzed. The effect of anomalously strong light absorption at the defect mode frequency for an absorbing defect layer is discussed. It is shown that in a distributed feed-back lasing at the DMS with an amplifying defect layer, adjusting the lasing frequency to the DM frequency results in a significant decrease in the lasing threshold and the threshold gain decreases as the defect layer thickness increases. It is found that, generally speaking, the layer birefringence and dielectric jumps at the interfaces of the defect layer and photonic liquid crystal reduce the DM lifetime in comparison with the DMS with an isotropic defect layer without dielectric jumps at the interfaces. Correspondingly, generally speaking, the effect of anomalously strong light absorption at the defect mode frequency and the decrease in the lasing threshold are not so pronounced as in the case of the DMS with an isotropic defect layer without dielectric jumps at the interfaces. The case of a DMS with a low defect layer birefringence and sufficiently large dielectric jumps are studied in detail. The options of effectively influencing the DM parameters by changing the defect layer dielectric properties, and the birefringence in particular, are discussed.     

Magnetic surface plasmon-induced tunable photonic bandgaps in two-dimensional magnetic photonic crystals

We experimentally studied magnetically controllable photonic band gaps (PBGs) in two-dimensional magnetic photonic crystals consisting of ferrite rods. Besides the conventional PBG that relates to Bragg scattering, two other types of PBG, resulting from magnetic surface plasmon (MSP) resonance and spin-wave resonance, respectively, are observed. The PBG due to MSP resonance is particularly interesting because of its analogy to surface plasmon in metal; furthermore, it is shown to be completely tunable by an external static magnetic field from both an experimental and a theoretical point of view.     

Localized photonic modes in photonic crystal heterostructures

In this work, interface modes of two-dimensional photonic crystal heterostructures have been investigated by usage of the supercell method. The photonic crystal heterostructure is made of two photonic crystals with square symmetry in which one of them is composed of circular dielectric rods in air background and the other one is constructed by drilled square holes in dielectric. It is shown that using of a proper supercell plays an important role in obtaining the correct interface modes. We have also showed that the guided interface modes and single mode which is different from those reported in some published works are nearly dispersionless.     

Properties of defect modes in one-dimensional symmetric defective photonic crystals

We theoretically investigate the properties of defect modes in one-dimensional symmetric defective photonic crystals. We consider three defective photonic crystal structures, air/[(AB)^NsA^α(BA)^Ns]^Np/air, air/[(AB)^NsAB^βA(BA)^Ns]^Np/air, and air/{[(AB)^NsAB^βA(BA)^Ns]B^γ}^Np−1[(AB)^NsAB^βA(BA)^Ns]/air, where A and B are respectively taken to be the high- and low-index dielectric materials. The first has a defect layer of A^α, the second has a composite defect, AB^βA, and the third has a interleaving defect B^γ. The effect of thickness on the defect mode is studied by varying the parameters α, β, and γ, respectively, for the above model structures. It is found that the positions and the number of defect modes can be significantly changed due to the change in the defect thickness. In addition, by increasing the repeated number N_p, we can have multiple defect modes, leading to a possible design of tunable multichannel filter.     

Electromagnetic unidirectionality and frozen modes in magnetic photonic crystals

Magnetic photonic crystals are periodic arrays of lossless materials, at least one of which being magnetically polarized. Magnetization, either spontaneous or induced, is associated with nonreciprocal effects, such as Faraday rotation. Magnetic photonic crystals of certain configuration can also display strong spectral asymmetry, implying that light propagates in one direction much faster or slower than in the opposite direction. This essentially nonreciprocal phenomenon can result in electromagnetic unidirectionality. A unidirectional medium, being perfectly transmissive for electromagnetic waves of certain frequency, freezes the radiation of the same frequency propagating in the opposite direction. The frozen mode has zero group velocity and drastically enhanced amplitude. The focus of our investigation is the frozen mode regime. Particular attention is given to the case of weak nonreciprocity, related to the infrared and optical frequencies. It appears that even if the nonreciprocal effects become vanishingly small, there is still a viable alternative to the frozen mode regime that can be very attractive for a variety of practical applications.     

Properties of defect modes in one-dimensional photonic crystals containing a graded defect layer

The properties of defect modes in one-dimensional photonic crystals (PCs) containing a graded defect layer are studied theoretically. The relative permittivity and magnetic permeability of the graded defect layer vary continuously along the direction perpendicular to the surface of the layer. The effect of the linear gradation profiles of the relative permittivity and permeability are studied in detail. It is shown that the defect modes appear inside the forbidden band gaps in its transmission spectra and the gradation profiles of the relative permittivity and permeability affect the defect modes significantly. By changing the gradation parameters, the intensity and position of the defect modes can be tuned. Therefore, introducing a graded defect layer in one-dimensional PCs provides possible mechanism for tuning the defect modes. This may be useful in the design of channeled filters.     

Characterization for defect modes of one-dimensional photonic crystals containing metamaterials

Transmission studies for one-dimensional photonic crystals(1DPCs)containing single-negative(SNG)materials inserted with multiple defects are presented.The numbers and positions of the defect modes inside zero-phase(zero-φeff)gap are found to be well characterized by effective medium theory.     

Defect modes of chiral photonic crystals with an isotropic defect

Specific features of the defect modes of cholesteric liquid crystals (CLCs) with an isotropic defect, as well as their photonic density of states, Q factor, and emission, have been investigated. The effect of the thicknesses of the defect layer and the system as a whole, the position of the defect layer, and the dielectric boundaries on the features of the defect modes have been analyzed. It is shown that when the CLC layer is thin the density of states and emission intensity are maximum for the defect mode, whereas when the CLC layer is thick, these peaks are observed at the edges of the photonic band gap. Similarly, when the gain is low, the density of states and emission intensity are maximum for the defect mode, whereas at high gains these peaks are also observed at the edges of the photonic band gap. The possibilities of low-threshold lasing and obtaining high-Q microcavities have been investigated.     

二维磁振子晶体中点缺陷模的耦合性质研究

在超原胞近似下, 利用平面波展开法数值计算了多点缺陷的二维磁振子晶体带结构及其部分缺 陷模的磁化强度场分布. 研究结果表明, 点缺陷模间的能量发生了耦合, 使自旋波沿着缺陷方向传播. 利用该性质可将含多点缺陷体的二维磁 振子晶体作为自旋波导波器件的制作材料.     

Localized modes in optics of photonic liquid crystals with local anisotropy of absorption

The localized optical modes in spiral photonic liquid crystals are theoretically studied for the certainty at the example of chiral liquid crystals (CLCs) for the case of CLC with an anisotropic local absorption. The model adopted here (absence of dielectric interfaces in the structures under investigation) makes it possible to get rid of mixing of polarizations on the surfaces of the CLC layer and of the defect structure and to reduce the corresponding equations to only the equations for light with polarization diffracting in the CLC. The dispersion equations determining connection of the edge mode (EM) and defect mode (DM) frequencies with the CLC layer parameters (anisotropy of local absorption, CLC order parameter) and other parameters of the DMS are obtained. Analytic expressions for the transmission and reflection coefficients of CLC layer and DMS for the case of CLC with an anisotropic local absorption are presented and analyzed. It is shown that the CLC layers with locally anisotropic absorption reduce the EM and DM lifetimes (and increase the lasing threshold) in the way different from the case of CLC with an isotropic local absorption. Due to the Borrmann effect revealing of which is different at the opposite stop-band edges in the case of CLC layers with an anisotropic local absorption the EM life-times for the EM frequencies at the opposite stop-bands edges may be significantly different. The options of experimental observations of the theoretically revealed phenomena are briefly discussed.     

二维正方格子磁性光子晶体的带隙结构

采用平面波展开的方法计算了正方格子二维磁性光子晶体(MPC)的光子带隙结构.散射子的形状分别为：长方形，正方形，六角形和圆形.通过调节磁导率，填充率和散射子的旋转角度，找到了MPC各种结构的最大的绝对带隙宽高比ω_R.研究发现：随着磁导率的增加，MPC绝对带隙中心频率ω_g单调减小，绝对带隙宽度Δω和其宽高比ω_R可能不同时达到最大值.而随着填充率或者散射子旋转角的增加，基本不改变ω_g的大小，各种结构的Δω和ω_R同时达到最大值. 关键词： 磁性光子晶体 光子带隙结构     

二维正方格子磁性光子晶体的界面传导模

采用平面波展开加超元胞方法计算了二维正方格子磁性光子晶体的光子带隙结构，其中散射子的形状分别为长方形，正方形，六角形和圆形.结果表明绝对带隙宽度和其宽高比远大于同种结构的非磁性光子晶体.在此基础上，构成了混合型异质结，并计算了相应的传导模，发现了理想的界面传导模，而且当磁性散射子为长方形、圆形、六角形散射子时产生传导模都不需要晶格畸变，这也是磁性光子晶体异质结所具备的优点. 关键词： 光子晶体 光子带隙结构 传导模     

Properties of defect modes in one-dimensional photonic crystals containing two nonlinear defects

Transmission properties of one-dimensional photonic crystal with two nonlinear defects were investigated based on the nonlinear transfer matrix method. From the inspection of the optical bistabilities around different defect modes, it was found that the threshold of bistability for the bonding mode is always lower than that for the anti-bonding mode. When intensity of the incident wave increases bistability could happen at any wavelength larger than the resonance wavelength of the linear anti-bonding mode in the gap. The threshold of bistability increases initially with the wavelength, then decreases sharply in reaching the resonance wavelength of the linear bonding mode. The coupling behavior of the two defects was also discussed, and it was found that the threshold of bistability increases with the distance between the two defects. A flat spectrum similar to that formed in the photonic crystal molecules was obtained under certain incident intensity.     

Phase response of omnidirectional reflection one-dimensional photonic crystals and defect modes

In this paper, we investigate the phase properties of light reflected from one-dimensional omnidirectional reflection photonic crystal. We observe that the phase changes drastically at large incident angles. This asymmetrical phase change should be considered at oblique incidence, and various phase compensators and retarders can be designed by this nonlinear curved surface of phase shift. Furthermore, for the coupled defect 1D PC, the phase change depends mainly on the top of the sharp peak of the weak undulation within the rectangular defect band, because the top of the peak of the undulation is very sharp, i.e. large phase change look like within almost a single frequency. This drastic phase change can be used to design phase controllers.     

Electro- and magneto-optical switching of defect modes in one- dimensional photonic crystals

The transmission spectra of polarized light waves in a photonic crystal/liquid crystal (PC/LC) cell placed between crossed polarizers and controlled by an electric or magnetic field have been studied experimentally and theoretically. Electro- and magneto-optical switching based on the interference of polarized defect modes has been demonstrated. The transmission spectra of the PC/LC cell have been calculated as a function of the voltage applied to the LC layer and the magnetic field strength. The results of the calculations agree well with the experimental data.     

二维磁振子晶体中线缺陷模的性质及其应用

在超原胞近似下, 利用平面波展开法数值计算了含线缺陷结构的二维磁振子晶体带结构及缺陷模的磁化强度场分布. 研究结果表明, 线缺陷结构的引入会在禁带中产生一个小范围的通带, 即产生线缺陷模. 该模式的存在可使自旋波沿着线缺陷结构的方向传播, 利用此性质含线缺陷结构的二维磁振子晶体材料可作为自旋波导波器件的制作材料. 关键词： 磁振子晶体 线缺陷 波导     

Extraordinary resonance transmission of two-dimensional terahertz metallic photonic crystals without defect

In this paper, we have demonstrated a kind of extraordinary transmission in the photonic first pass band of two-dimensional terahertz metallic photonic crystals: in the regime of low-middle metal filling radio, resonances among the metallic cylinders lead to sharp and high resonance peaks of Lorentz type, layer dependency of the peak numbers. The effect of positional disorders of metallic cylinders has been investigated as well. Based on a simple model proposed in this paper, we can intuitively understand the extraordinary transmission and roughly estimate resonance frequencies. Our results agree qualitatively with the experimental data reported in Appl. Phys. Lett. 65, 645.     

Photonic-band-gap structures and guide modes in two-dimensional magnetic photonic crystal heterostructures

We first investigate the band gap structures of two-dimensional magnetic photonic crystals (MPC) composed of rectangular (square) magnetic cylinders embedded in a host dielectric material in the rectangular (square) lattice, and we then study guide modes at interface of MPC heterostructures (MPCHs) by use of plane wave expansion method in combination with supercell technique. We find that both the mirror-symmetric MPCHs and the mixed-type MPCHs composed of square cylinders in a square lattice can produce the TM guide modes even without any lattice distortions. This feature is quite different from that of the non-magnetic PC heterostructures, in which the occurrence of the guide modes requires the relatively longitudinal gliding or transverse displacement of lattices. It may provide a new way to generate guide modes and apply to the device of light wave guides.Received: 26 August 2003, Published online: 2 April 2004PACS: 42.70.Qs Photonic bandgap materials - 78.67.-n Optical properties of low-dimensional, mesoscopic, and nanoscale materials and structures - 63.20.Pw Localized modes - 42.79.Gn Optical waveguides and couplers     

Enhanced second-harmonic generation for multiple wavelengths by defect modes in one-dimensional photonic crystals

We present an effective design of aperiodically stacked layers of nonlinear material and air, sandwiched by two truncated photonic crystals, in terms of the simulation annealing method. The constructed structure can achieve multiple-wavelength second-harmonic generation (SHG) at the preassigned wavelengths. We derive a general solution of SHG in 1D inhomogeneous systems and apply it to evaluate the SHG conversion efficiency. Numerical simulations show that the conversion efficiency of SHG can be significantly enhanced when the fundamental wave frequencies are assigned to the designed defect states.