Frequency bands of negative refraction in finite one-dimensional photonic crystals

We have discussed theoretically the negative refraction in finite one-dimensional (1D) photonic crystals (PCs) composed of alternative layers with high index contrast. The frequency bands of negative refraction are obtained with the help of the photonic band structure, the group velocity and the power transmittance, which are all obtained in analytical expression. There shows negative transverse position shift at the endface when negative refraction occurs, which is analysed in detail.     

Study on optical switching effect of photonic crystals with negative effective index of refraction

Based on transmission spectra, optical switching effect of equivalent negative refractive photonic crystals (PCs) composed of a triangular array of air cylinders in a GaAs matrix is studied by the finite-difference time-domain (FDTD) method in this paper. The mechanism of wave resonance is probed and the propagation of optical waves in the PCs is described in terms of effective refraction index and Bloch waves. Our numerical results show that the probability of spontaneous radiation would be enhanced extremely under the influence of Bloch resonance waves, stimulated emission and photon tunnel effect, resulting in the optical waves being localized greatly in the PCs at particular frequencies. In addition, we found that the position of transmission peaks, with values much greater than unit, can be controlled by tuning the central frequency of the waveguide source. It means that photon current in the PCs can also be controlled to optimize transmission properties of PCs, so as to meet the requirements of novel optical devices based on PCs, such as all-optical switches.     

二维光子晶体负折射现象条件及特性研究

结合光子晶体带隙图和等频率线图分析了二维光子晶体中出现负折射现象的条件,得出了负折射现象出现的频率范围.采用有限时域差分法模拟了光在光子晶体界面和内部的传输行为,验证了以上理论所给出的负折射出现的频段,观察到了明显的负折射现象.比较了不同介质、不同晶格结构光子晶体中不同频率的负折射行为.提出一种新结构的六角型二维三角晶格光子晶体分光镜的模型.     

Negative refraction in two-dimensional photonic crystals

We present some of our recent results for negative refraction in photonic crystals. The concept of negative refraction in photonic crystals is firstly introduced. Then, the propagation of electromagnetic waves in photonic crystals is systematically studied. By the layer Korringa–Kohn–Rostoker method, the coupling efficiency between external plane waves and the Bloch waves in photonic crystals is investigated. It is found that the coupling coefficient is highly angular dependent even for an interface between air with n=1 and a photonic crystal with effective index n_eff=-1. It is also shown that, for point imaging by a photonic crystal slab, owing to the negative refraction, the influence of the surface termination on the transmission and the imaging quality is significant. Finally, we present results experimentally demonstrating negative refraction in a two-dimensional photonic crystal at optical communication wavelengths. PACS 42.70.Qs; 41.85.Ct; 42.30.Va     

Efficient tunable negative refraction photonic crystal achieved by an elliptic rod lattice with a nematic liquid crystal

Photonic crystals (PCs) have many potential applications because of their ability to control light-wave propagation. We have investigated the electromagnetic wave propagation inside an elliptic rod PC slab by means of finite-difference time-domain simulations. The band structure of the PC composed of elliptic rod in the square and triangular lattices is studied by solving Maxwell's equations using the plane wave expansion method. Numerical simulations show that the refractive angle can be tuned greatly by rotating the directors of elliptic rod in the PC slab. Furthermore, an optical switch based on elliptic rod PC structures with nematic liquid crystals was proposed. In the on/off switching system, the partial band gap can be controlled when the normalized operation frequency is 0.28. The modulation induced by liquid crystals created a sharp switching in the photonic devices. Such a mechanism of negative refraction PCs should open up a new application for designing components in photonic integrated circuits.     

Negative refraction in one-dimensional plasma photonic crystals

We have theoretically explored the negative refraction (NR) in one-dimensional plasma photonic crystals (PCs) consisting of plasma and dielectric materials. By using the transfer matrix method and Bloch theorem, we have studied the group velocity and we have obtained the NR in plasma PCs with the help of the group velocity. The results show that plasma PCs can also exhibit the NR although they have a periodically modulated positive permittivity ? and permeability μ. It is also shown that the NR in plasma PCs exhibits difference behaviour in different frequency regions, ω < ω_p and ω > ω_p, respectively. The parameter dependence of the effects is also examined and discussed.     

Tunable band gaps in electro-optical photonic bi-oriented crystals

Electrically induced birefringence is studied in photonic bi-oriented crystals in terms of molding lightflow in optical devices. In photonic bi-oriented crystals, misorientation of dielectric anisotropic grains results in a dielectric contrast at the grain boundaries. The translational periodicity of the optical constants depends upon a regular network of twisted dielectrics. Due to the anisotropy of the bicrystalline structure the direction of light propagation determines the dielectric contrast at the grain boundaries. In a specific crystallographic arrangement the optical properties of the bi-oriented crystal can be tuned by the electro-optical effect: the periodic dielectric contrast is electrically induced and photonic bandgaps are generated by applying external electric fields. The geometrical requirements for tunable photonic bicrystals are evaluated based on materials employed for electro-optical applications. Tunable photonic bi-oriented crystals may be candidates for fast optical switches, modulators and multiplexers in the optical communication network. Received: 5 July 2001 / Revised version: 3 August 2001 / Published online: 15 October 2001     

Three-dimensional photonic crystals containing designed defects achieved with two-photon photopolymerization

Two-photon photopolymerization （TPP） with femtosecond laser is a promising method to fabricate threedimensional （3D） photonic crystals （PCs）. Based on the TPP principle, the micro-fabrication system has been built. The 3D woodpile PCs with rod space of 2000 nm are fabricated easily and different defects are introduced in order to form the cross-waveguide and the micro-laser structure PCs. Simulation results of the optical field intensity distributions using finite-difference time domain （FDTD） method are given, which support the designs and implementation of the PC of two types in theory.     

Extended plane-wave-based transfer-matrix approach to simulating dispersive photonic crystals

It has been difficult to compute the band structures and transmission spectra for photonic crystals (PCs) with dispersive components included in the periodic units. Here we show that by using an extended plane-wave-based transfer-matrix method, we are able to formulate the problem for computing optical properties of dispersive PCs, including magnetic and left-handed PCs. This approach is very general, since it can treat PCs with arbitrary Bravais lattice composed of materials with arbitrary dielectric permittivities and magnetic permeabilities. Combined with the supercell method, this method can further simulate defective PCs such as PC-based waveguides and microcavities.     

Negative optical refraction in crystals with strong birefringence

The possibility of negative optical refraction of the extraordinary ray in crystals with strong birefringence is demonstrated.     

Physics and applications of photonic crystals

In this article, we investigate how the photonic band gaps and the variety of band dispersions of photonic crystals can be utilized for various applications and how they further give rise to completely novel optical phenomena. The enhancement of spontaneous emission through coupled cavity waveguides in a one-dimensional silicon nitride photonic microcrystal is investigated. We then present the highly directive radiation from sources embedded in two-dimensional photonic crystals. The manifestation of novel and intriguing optical properties of photonic crystals are exemplified experimentally by the negative refraction and the focusing of electromagnetic waves through a photonic crystal slab with subwavelength resolution.     

Manipulating light flow with one-dimensional photonic crystals of an electromagnetically induced transparency medium

The band structures and equifrequency contours of one-dimensional photonic crystals (PCs), which consist of an electromagnetically induced transparency (EIT) medium and a common dielectric medium, can be dramatically changed by tuning the coupling field intensity (or coupling Rabi frequency, CRF) of the EIT medium. It is found that for a probe light at a fixed frequency, either positive or negative refraction in the EIT PC can be realized with a proper CRF. The behavior of a Gaussian beam (probe light) obliquely incident on such an EIT PC slab is simulated numerically. The probe light beam transmitted from the slab can be shifted transversely in a large range, and negative refraction enhances this effect. The present scenario can be applied in some areas such as quantum optical and photonic device designs.     

Optical properties of one-dimensional photonic crystals fabricated by photo-electrochemical etching of silicon

The optical properties of one-dimensional photonic crystals (1D PCs), fabricated by electrochemical etching of periodic wall arrays on n-type (100) Si substrates, are investigated in this study. Several 1D PCs were fabricated with lattice periods varying from 4 to 7 μm and with trench depths in the range 160–210 μm. In-plane reflection spectra of the photonic structures at different depths were registered over a wide spectral range of 1.5–15 μm using Fourier Transform Infra-Red (FTIR) micro-spectroscopy. Some of the features observed in the reflection spectra of the structures investigated are believed to be as a result of interface roughness. A corrugated side-wall surface, an artifact of the fabrication technique, results in the degradation of optical reflection characteristics, principally mainly in the near IR spectral range, and the emergence of optical anisotropy. As a result of the periodicity, modulation of the reflection spectra, that is, the difference between the maxima and minima of the interference fringes, reached a value of 95% in the mid-infrared. The optical properties of the structures investigated indicate that they show promise for microphotonics applications.     

Intensity depending on object distance in a two-dimensional photonic crystal

The propagation of electromagnetic (EM) waves in two-dimensional triangular-lattice photonic crystals (PCs) is investigated through dispersion characteristics analysis and numerical simulation of field pattern. The designed PC structure can exhibit all angle negative refraction in the second band. A flat superlens formed from such a PC has been designed and its imaging properties have been investigated systematically. Good-quality images and focusing, with relative refractive index of ?1, have been observed in this system for TE mode waves. In contrast to the images in near-field region for the lowest valence band, non-near-field images, explicitly following the well-known wave-beam negative refraction law, have been demonstrated. The relation between the intensity of the image and the object distance has also been discussed in this paper. The extensive applications of such a phenomenon to optical devices are anticipated.     

Growth and characterization of pure and picric acid doped ADP single crystals

Ammonium dihydrogen phosphate (ADP) is a pioneer kind of nonlinear optical crystal. It can be used in various electro-optical, nonlinear optical applications. The pure and different weight percentage of Picric acid doped ADP single crystals are grown using the slow solvent evaporation technique at room temperature. The powder XRD study shows single phasic nature of all the grown crystals. The photoluminescence study suggests that the dopant causes defect in structure of ADP by virtue of vibration relaxation and self trapping exciton. The dielectric constant and the dielectric loss of all the grown crystals exhibited universal behaviour over frequency range considered. The Correlation Barrier Hopping and the Non Overlapping Small Polaron Tunnelling kind of conductivity mechanism are observed. The grain and grain boundary is indentified using the complex Impedance and the complex modulus spectroscopy. The third order nonlinear optical susceptibility is increased on doping the Picric acid in ADP crystals. The results are discussed here.     

Two-dimensional function photonic crystals

In this paper, we have studied two-dimensional function photonic crystals, in which the dielectric constants of medium columns are the functions of space coordinates , that can become true easily by electro-optical effect and optical kerr effect. We calculated the band gap structures of TE and TM waves, and found the TE (TM) wave band gaps of function photonic crystals are wider (narrower) than the conventional photonic crystals. For the two-dimensional function photonic crystals, when the dielectric constant functions change, the band gaps numbers, width and position should be changed, and the band gap structures of two-dimensional function photonic crystals can be adjusted flexibly, the needed band gap structures can be designed by the two-dimensional function photonic crystals, and it can be of help to design optical devices.     

Flat lenses constructed by graded negative index-based photonic crystals with tuned configurations

Flat lenses are designed by means of graded negative refractive index-based photonic crystals （PCs） constructed using air-holes tuned with different shapes. By gradually modifying the filling factor along the transverse direction, we obtain the graded negative index-based lenses for the purpose of focusing an incident plane wave. The finite-difference and timedomain （FDTD） algorithm is adopted for numerical calculation. Our calculation results indicate that these lenses can finely focus incident plane waves. Moreover, for the same size of air-holes, the focusing properties of the lens with rectangular air-holes are better than those with the other shaped air-holes. The graded negative index PCs lenses could possibly enable new applications in optoelectronic systems.     

Homogenization of magnetodielectric photonic crystals

We calculate the low-frequency index of refraction of a medium which is homogeneous along axis z and possesses a periodic dependence of the permittivity epsilon(r) and permeability micro(r) in the x-y plane (2D magnetodielectric photonic crystal). Exact analytical formulas for the effective index of refraction for two eigenmodes with vector E or H polarized along axis z are obtained. We show that, unlike nonmagnetic photonic crystals where the E mode is ordinary and the H mode is extraordinary, now both modes exhibit extraordinary behavior. Because of this distinction, the magnetodielectric photonic crystals exhibit optical properties that do not exist for natural crystals. We also discuss the limiting case of perfectly conducting cylinders and clarify the so-called problem of noncommuting limits, omega-->0 and epsilon--> infinity.     

反常色散材料光子晶体中光输运的光学控制

研究了光抽运对由铯原子蒸气构成的光子晶体的影响.研究发现,利用较弱光强的线抽运光即可显著地改变这种反常色散光子晶体的透射率.而利用圆偏振光抽运可以进一步降低抽运光的阈值,并在反常色散光子晶体中获得极大的法拉第旋转.反常色散光子晶体的这些特性为光控光开关的研究和制作提供了一条新途径.     

正方介质柱光子晶体中异常传输现象研究

研究了电磁波在二维正方介质柱光子晶体中的传输,发现处于第一频带部分带隙的电磁波在不同界面切割方向上不同角度入射时可分别产生全反射及复杂异常折射现象如自准直现象、负折射现象.首先利用平面波展开法从理论上研究正方介质柱正方晶格光子晶体的频带结构及等频线,然后通过时域有限差分法来仿真研究光子晶体在第一频带部分带隙的传输特性.当光子晶体的界面切割沿着ΓX方向时,由于光子晶体内无本征模能够被有效地激发,入射波束被完全反射,这与光子带隙导致的全反射具有本质的不同;当光子晶体的界面切割方向沿着ΓM时,归因于其扁平的等频线,一定角度范围内入射的波束在光子晶体内几乎沿同方向传输即产生自准直现象.