Localized defect modes in finite magnetic two-dimensional photonic crystals

We present a detailed study of localized defect modes in finite two-dimensional magnetic photonic crystal consisting of cylindrical ferrite material in air background by using the scattering matrix method. It is shown that due to having positive and negative value of the effective magnetic permeability in interested photonic band gap, the defect modes present different behavior. Our results show that the modes appeared in positive permeability region have features similar to the modes supported by the dielectric photonic crystal while those created in the negative permeability region are strongly localized at the interface of defect ferrite rod with air background. Moreover, results indicate that defect modes occurred in the negative region are sharper than those appeared in the positive one which means the quality factor of former case is extremely high.     

Refraction of light in two-dimensional photonic crystals

Refraction of light at an interface between a homogeneous dielectric and a two-dimensional photonic crystal is studied. Using the isofrequency method, various cases of refraction, including a change in the magnitude and direction of the wave vector of the incident wave, in the refractive indices of the media, and in the mutual orientation of the interface and the translation vectors of the photonic crystal, are investigated. Different types of refraction and the possibilities for realizing negative and multiwave refraction are considered.     

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.     

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.     

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.     

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.     

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     

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.     

含负折射率材料1维光子晶体的偏振无关非全向的缺陷模

运用光学传输矩阵理论,研究了含负折射率材料1维光子晶体缺陷模的偏振特性。结果显示,零均折射率带隙中缺陷模对入射角和偏振有较强的依赖。通过对缺陷层参数的优化设计,得到了一系列的偏振无关非全向缺陷模,这是传统1维光子晶体中不能出现的。应用这些缺陷模,设计了低通、高通、带通空间滤波器。与传统光子晶体空间滤波器相比,这些空间滤波器具有偏振无关的优点。     

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.     

含负折射率材料1维光子晶体的偏振无关非全向的缺陷模

运用光学传输矩阵理论,研究了含负折射率材料1维光子晶体缺陷模的偏振特性。结果显示,零均折射率带隙中缺陷模对入射角和偏振有较强的依赖。通过对缺陷层参数的优化设计,得到了一系列的偏振无关非全向缺陷模,这是传统1维光子晶体中不能出现的。应用这些缺陷模,设计了低通、高通、带通空间滤波器。与传统光子晶体空间滤波器相比,这些空间滤波器具有偏振无关的优点。     

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.     

Two-dimensional photonic crystals with a lattice defect: Spectrum of defect modes, localization of light, and formation of evanescent waves

Properties of an electromagnetic field localized in the defect modes of two-dimensional photonic crystals are studied. The defect-mode spectrum of these structures is calculated, electromagnetic field localization and channeling effects are analyzed, and the properties of the field inside and beyond a photonic crystal with a lattice defect are also studied. The calculations show that the electromagnetic field is localized in the defect mode of a photonic crystal in a region smaller than the wavelength. The dependence of the defect-mode spectrum on the parameters of the photonic crystal is investigated and possibilities for controlling the spectrum of defect modes are indicated. It is shown that the optical field leaving a photonic crystal possesses the properties of a evanescent wave, which means that spatial resolution substantially greater than the wavelength of the radiation can be achieved in the near field and opens up possibilities for using photonic crystals with a lattice defect in near-field optical microscopy. The possibility of externally controlling an optical field localized in the defect modes of a photonic crystals is demonstrated.     

Beaming of light and enhanced transmission via surface modes of photonic crystals

We report beaming and enhanced transmission of electromagnetic waves by use of surface corrugated photonic crystals. The modes of a finite-size photonic crystal composed of dielectric rods in free space have been analyzed by the plane-wave expansion method. We show the existence of surface propagating modes when the surface of the finite-size photonic crystal is corrugated. We theoretically and experimentally demonstrate that the transmission through photonic crystal waveguides can be substantially increased by the existence of surface propagating modes at the input surface. In addition, the power emitted from the photonic crystal waveguide is confined to a narrow angular region when an appropriate surface corrugation is added to the output surface of the photonic crystal.     

条形耦合波导对光子晶体耦合缺陷模的影响

光子晶体的耦合缺陷模可以通过透射谱形状来表征,而透射谱形状则与连接缺陷的条形耦合波导相关.不同于直接耦合时信号相移只依赖于缺陷模的共振频率,当存在耦合波导时信号相移也决定于波导的长度和色散关系.随着波导长度的增加,透射谱形状发生从三峰到两峰,再到平项,最后又回到三峰的周期性变化.时间耦合模的分析表明,在缺陷模频率附近理论结果与时域有限差分法的计算结果完全一致,表明在此复杂情况下理论模型依然有效.     

Properties of single and multiple defect modes in one-dimensional photonic crystals containing left-handed metamaterials

Wave propagation is studied in structures consisting of alternate left- and right-handed layers.Bragg gap and zero-n gap appear in different frequency regions of the structure.The periodicity of the structure is broken by simply reversing the order of the layers in one half of the structure,resulting in defect modes located inside the zero-n gap and Bragg gap.These modes can be made very narrow by adding more layers in the structure.The defect mode located inside the zero-n gap is sensitive to the symmetry of the structure and insensitive to the angle of incidence of the incoming radiation.Multiple modes are also generated inside the gaps by repeating the structural pattern.Thus,a simple structure can be used for single and multiple modes that are important for different applications.     

Band gaps and nonlinear defect modes in one-dimensional photonic crystals with anisotropic single-negative metamaterials

We propose a one-dimensional photonic crystal (1DPC) with multilayered periodic structures containing dispersive anisotropic single-negative (ASNG) (permittivity- or permeability-negative) metamaterials. The influences of the ratio of d_A/d_B and their scale on ASNG gaps are discussed. Moreover, the effect of a nonlinear defect layer introduced into the proposed structure is also analyzed, and the results show that the defect mode has two peaks of electrical fields in the defect layer and its bistability property is also different from a defect mode in PCs with isotropic SNG gaps.