Synthesis and characterization of porous silicon layers for 1D photonic crystal application

In this paper, we studied the optical and physical properties of electrochemically prepared porous silicon layers. The atomic force microscopy analysis showed that the etching depth, pore diameter and surface roughness increase as the etching time increased from 30 to 50 mA/cm². By tuning two current densities J₁ = 50 mA/cm² and J₂ = 30 mA/cm², two samples of 1D porous silicon photonic crystals were fabricated. The layered structure of 1D photonic crystals has been confirmed by scanning electron microscopy measurement which showed white and black strips of two distinct refractive index layers. Finally, the measured reflectance spectra of 1D porous silicon photonic crystals were compared with simulated results.     

Omnidirectional reflection from the one-dimensional photonic crystal containing anisotropic left-handed material

We study the transmission properties in the one-dimensional photonic crystal containing alternate anisotropic left-handed material (LHM) layers and regular isotropic right-handed material (RHM) layers. For such an anisotropic case, the dispersion relation from the Bloch theorem is derived and the Bragg gaps of the periodic structure are observed. It is found that in the m=0 Bragg gap, there is an omnidirectionally reflectional (ODR) region, which is also invariant with a change of scale length, similar with the [`(n)]=0\bar{n}=0 gap in isotropic one-dimensional photonic crystal. With the aid of effective medium theory (EMT), the analytic expressions of all six elements of the effective electric permittivity tensor and magnetic permeability tensor are obtained. By using these results, we investigate the ODR region in the m=0 Bragg gap in all the possible cases of both TE and TM modes. We find that with different choices of parameters, the m=0 Bragg gap has different transmission properties, and the ODR region in it changes, consequently. The edges of the ODR region are given out in these cases. To one's interest, these results predict a complete reflection region in the m=0 Bragg gap, which is able to omnidirectionally reflect waves in both TE and TM modes.     

非长波极限下二维光子晶体中横电模的等效介质理论

基于Mie散射理论, 推导、建立了适用于非长波极限的二维光子晶体中横电模的等效介质理论. 随后利用该理论探讨了二维光子晶体中横电模的负折射特性和零折射特性, 计算结果与相应的能带结构相符合, 验证了该理论在非长波极限条件下的适用性. 更进一步的是, 使用该理论能得到从能带结构中无法获取的额外信息.     

Near-infrared tunable narrow filter properties in a 1D photonic crystal containing semiconductor metamaterial photonic quantum-well defect

The near-infrared (NIR) narrow filter properties in the transmission spectra of a one-dimensional photonic crystal doped with semiconductor metamaterial photonic quantum-well defect (PQW) were theoretically studied. The behavior of the defect mode as a function of the stack number of the PQW defect structure, the filling factor of semiconductor metamaterial layer, the polarization and the angle of incidence were investigated for Al-doped ZnO (AZO) and ZnO as the semiconductor metamaterial layer. It is found that the frequency of the defect mode can be tuned by variation of the period of the defect structure, polarization, incidence angle, and the filling factor of the semiconductor metamaterial layer. It is also shown that the number of the defect mode is independent of the period of the PQW defect structure and is in sharp contrast with the case where a common dielectric or metamaterial defect are used. The results also show that for both polarizations the defect mode is red-shifted as the number of the defect period and filling factor increase. An opposite trend is observed as the angle of incidence increases. The proposed structure could provide useful information for designing new types of tuneable narrowband filters at NIR region.     

Traveling of light through a 1D photonic crystal containing a defect layer with resonant dispersion

Spectral properties of a 1D photonic crystal that is comprised of two multilayered dielectric mirrors and a nanocomposite layer between them as a structural defect are studied. The nanocomposite consists of silver nanoballs dispersed in a transparent matrix and is characterized by an effective resonant permittivity. The spectral manifestation of the defect mode splitting for the s-polarized waves is studied as a function of the angle of incidence and concentration of nanoballs. Specific features of the transmission spectra for the s- and p-polarized waves are established for the angle of incidence equal to the Brewster angle of the seeding photonic crystal. It is shown, in particular, that, in the region of the continuous transmission spectrum of the spolarized waves, there arises an additional bandgap caused by mixing of the resonant mode with photonic modes.     

Enlargement of the omnidirectional reflectance gap in one-dimensional photonic crystal heterostructure containing double negative index material

In this paper, we investigate by theoretical analysis a way to enlarge the frequency range of band gap in one-dimensional heterostructure photonic crystal (PC) made of two PCs alternate stacked by conventional and double negative index material. The numerical results by scattering matrix method (SMM) show that, for the proposed PC with appropriate parameters, there is an omnidirectional photonic band gap (OBG), which is insensitive to incident angle and polarization. The thickness ratio of layers in the second PC is the inverse and identical of that in the first PC, respectively. Two PCs form the PC heterostructures. Moreover, we demonstrate the existence of OBG and notable enlargement of the frequency range of the OBG in proposed PC heterostructure. The reason is that the pass band of one of the two PCs falls into the forbidden band of another PC. Decreasing the thickness of layers but not changing the thickness ratio of layers in the second PC, the frequency range of OBG keeps invariant. However, with the increasing of thickness of layers, the frequency range of OBG gets narrow.     

Accurate radial basis function based neural network approach for analysis of photonic crystal fibers

In this paper, a new and an accurate artificial neural network approach (ANN) is presented for the analysis and design of photonic crystal fibers (PCFs). The new ANN approach is based on the radial basis functions which offer a very quick convergence and high efficiency during the ANN learning. The accuracy of the suggested approach is demonstrated via the excellent agreement between the results obtained using the presented approach and the results of the full vectorial finite difference method (FVFDM). In addition, a new design of highly birefringence PCF with low losses for the two polarized modes is presented using the proposed approach.     

Sensitivity improvement of broadband electro-optic polymer-based optical phase modulator using 1D and 2D photonic crystal structures

This Letter introduces the design and simulation of a microstrip-line-based electro-optic(EO) polymer optical phase modulator(PM) that is further enhanced by the addition of photonic crystal(PhC) structures that are in close proximity to the optical core. The slow-wave PhC structure is designed for two different material configurations and placed in the modulator as a superstrate to the optical core; simulation results are depicted for both1 D and 2D PhC structures. The PM characteristics are modeled using a combination of the finite element method and the optical beam propagation method in both the RF and optical domains, respectively.The phase-shift simulation results show a factor of 1.7 increase in an effective EO coefficient(120 pm/V) while maintaining a broadband bandwidth of 40 GHz.     

Influence of the group-velocity on the pulse propagation in 1D silicon photonic crystal waveguides

We present a detailed analysis of the influence of the group velocity (GV) on the dynamics of optical pulses upon their propagation in one-dimensional photonic crystal waveguides (PhCW). The theoretical model used in our analysis incorporates the linear optical properties of the PhCW (GV dispersion and optical losses), free-carrier (FC) effects (FC dispersion and FC-induced optical losses) and nonlinear optical effects (Kerr nonlinearity and two-photon absorption). Our analysis shows that, unlike the case of uniform waveguides, the GV of the pulse, dispersion coefficients, and the waveguide nonlinear coefficient are periodic functions with respect to the propagation distance. We also demonstrate that linear and nonlinear effects depend on the group velocity, v _g , as v_g^-1v_{g}^{-1} and v_g^-2v_{g}^{-2}, respectively.     

Design for 2D anisotropic photonic crystal with large absolute band gaps by using a genetic algorithm

A 2-state genetic algorithm (GA) approach is used to design a two-dimensional (2D) anisotropic photonic crystal of square lattice with a maximal absolute band gap. The unit cell is devided equally into many small squares, and each filling pattern of squares with two dielectric materials corresponds to a binary number. As a numerical example, the GA gives a 2D Te structure with a relative width of the absolute band gap of about . After a further optimization, a new structure is obtained with a relative width of the absolute band gap of about .Received: 1 November 2003, Published online: 9 April 2004PACS: 42.70.Qs Photonic bandgap materials - 78.20.Ci Optical constants (including refractive index, complex dielectric constant, absorption, reflection and transmission coefficients, emissivity) - 02.70.-c Computational techniques     

有效折射率微扰法研究单缺陷光子晶体平板微腔的性质

应用有效折射率微扰法结合二维/三维平面波方法研究了施主和受主缺陷型H1微腔的性质, 使用修正后的有效折射率可以准确地计算微腔的腔模频率, 与三维全矢量时域有限差分法的计算结果很相近. 对于施主型H1微腔, 以介质带边为匹配标准修正的有效折射率计算的微腔腔模频率误差最小, 而对于受主型H1微腔, 匹配标准则应设置为中间带. 有效折射率微扰法既可以将计算的维度从三维降到二维, 大大减少计算所需的计算机内存和时间, 又可以保持计算结果的准确性, 这对于光子晶体微腔的广泛应用具有非常重要的价值.     

Technique for determining the cell parameters of the confined one-dimensional photonic crystal,based on the Floquet-Bloch formalism

The technique for determining the cell structural parameters of the confined one-dimensional photonic crystal, based on the strict analytical representation of Floquet-Bloch waves in the form of inhomogeneous waves is proposed.     

Pressure, temperature and plasma frequency effects on the band structure of a 1D semiconductor photonic crystal

In this work using the transfer-matrix formalism we study pressure, temperature and plasma frequency effects on the band structure of a 1D semiconductor photonic crystal made of alternating layers of air and GaAs. We have found that the temperature dependence of the photonic band structure is negligible, however, its noticeable changes are due mainly to the variations of the width and the dielectric constant of the layers of GaAs, caused by the applied hydrostatic pressure. On the other hand, by using the Drude's model, we have studied the effects of the hydrostatic pressure by means of the variation of the effective mass and density of the carriers in n-doped GaAs, finding firstly that increasing the amount of n-dopants in GaAs, namely, increasing the plasma frequency, the photonic band structure is shifted to regions of higher frequencies, and secondly the appearance of two regimes of the photonic band structure: one above the plasma frequency with the presence of usual Bragg gaps, and the other, below this frequency, where there are no gaps regularly distributed, with their width diminishing with the increasing of the plasma frequency as well as with the appearance of more bands, but leaving a wide frequency range in the lowest part of the spectrum without accessible photon states. Also, we have found characteristic frequencies in which the dielectric constant equals for different applied pressures, and from which to higher or lower values the photonic band structure inverts its behavior, depending on the value of the applied hydrostatic pressure. We hope this work may be taken into account for the development of new perspectives in the design of new optical devices.     

Parameters of defect mode of 1D microwave waveguide photonic crystal with metal inclusions in the element that disturbs periodicity

Amplitude–frequency characteristics of the transmission coefficient of microwave waveguide photonic crystal with violation of periodicity are studied in the presence of a plane conducting small-size inclusion that occupies a part of the transverse cross section of the waveguide inside a disturbed layer located at different positions. The conducting small-size inclusion in the disturbed layer of photonic crystal causes the low-frequency shift of the defect mode in the band gap, and the maximum shift is observed when the metal inclusion is located at the interface or center of disturbance depending on the thickness of the disturbed layer.     

Effects of a constant electric field in the polariton spectrum of a 1D magnetic photonic crystal with antiferromagnetic interlayer exchange

The effect of a constant external electric field was analyzed and the contribution of the volume fractions of magnetic and nonmagnetic phases to the polariton dynamics of a one-dimensional easy-axial fer-romagnet-nonmagnetic dielectric photonic crystal with a magnetic compensation point was determined using the effective medium method.     

1 × 4 optical multiplexer based on the self-collimation effect of 2D photonic crystal

In this paper, a novel 1 × 4 optical multiplexer (OMUX) based on the two dimensional photonic crystal embed cascaded Mach–Zehnder interferometer (MZI) employing self-collimation effect was proposed and its performance were numerically demonstrated. The 1 × 4 OMUX consists of four beam splitters and five mirrors. Light propagates in the OMUX employing self-collimation effect. The theoretical transmission spectra at different output ports of OMUX were analyzed with the theory of light interference. Then they were investigated with the finite-difference time-domain (FDTD) simulation technique. The simulation results indicate the cascaded Mach–Zehnder interferometer can work as a 1 × 4 optical multiplexer by selecting path length in the structure properly. For the drop wavelength 1550 nm, the free spectral range of the OMUX is about 24 nm, which almost covers the whole optical communication C-band window. The presented device that has no only a compact size but also a high output efficiency, may have practical applications in photonic integrated circuits.     

激光全息法制作二、三维光子晶体的模拟计算及禁带分析

激光全息法制作二、三维光子晶体相比于传统半导体微加工及精密机械加工技术具有很多优势，比如通过一次光辐射就可以制作出大体积、均匀的周期性结构，且能更自由、更容易地控制光子晶体结构.提出一种多光束干涉模型，通过设计模型中光束的各项参数，计算分析出二、三维光子晶体的结构.基于平面波展开法，理论计算了fcc结构光子晶体的完全禁带随填充率和介电常数比变化的情况.以上计算结果为后期实验中采用激光全息法制作二、三维光子晶体结构提供了良好的指导方向和理论依据. 关键词： 光子晶体 激光全息 多光束干涉 完全禁带     

Assessment of the presumed mapping function approach for the stationary laminar flamelet modelling of reacting double scalar mixing layers

This paper assesses the Presumed Mapping Function (PMF) approach in the context of the Stationary Laminar Flamelet Modelling (SLFM) of a reacting Double Scalar Mixing Layer (DSML). Starting from a prescribed Gaussian reference field, the PMF approach provides a presumed Probability Density Function (PDF) for the mixture fraction that is subsequently employed to close the Conditional Scalar Dissipation Rate (CSDR) upon doubly-integrating the homogeneous PDF transport equation. The PMF approach is unique in its ability to yield PDF and CSDR distributions that capture the effect of multiple fuel injections of different composition. This distinct feature overcomes the shortcomings of the classical SLFM closures (the β-distribution for the PDF and the counterflow solution for the CSDR). The current study analyses the impact of the binary (two-stream) and trinary (three-stream) PMF approaches on the structure of laminar flamelets in a DSML formed by the mixing of a fuel stream and an oxidiser stream separated by a pilot. The conditions of a partially-premixed methane/air piloted jet flame are considered. A parametric assessment is performed by varying the local mixing statistics and the findings are compared to those of the classical SLFM approach. Further, the influence of the PMF approach on flamelet extinction and transport by means of differential diffusion is thoroughly investigated. It is shown that the trinary PMF approach captures the influence of the pilot stream as it is capable of yielding bimodal CSDR and trimodal PDF distributions. It is further demonstrated that, when the influence of the pilot is significant, flamelets generated using the trinary CSDR closure extinguish at higher strain levels compared to flamelets generated using the binary and counterflow closures. Lastly, it is shown that the trinary PMF approach can be critical for accurate SLFM computations of DSMLs when differential diffusion effects are important.     

Quantification of the lift height for magnetic force microscopy using 3D surface parameters

In this work, the quantitative conditions for the lift height for imaging of the magnetic field using magnetic force microscopy (MFM) were optimized. A thin cobalt film deposited on a monocrystalline silicon (1 0 0) substrate with a thickness of 55 nm and a thin nickel film deposited on a glass with a thickness of 600 nm were used as samples. The topography of the surface was acquired by tapping mode atomic force microscopy (AFM), while MFM imaging was performed in the lift mode for various lift heights. It was determined that the sensitivity of the measurements was about 10% higher for images obtained at a scan angle of 90° compared to a scan angle of 0°. Therefore, the three-dimensional surface texture parameters, i.e., average roughness, skewness, kurtosis and the bearing ratio, were determined in dependence on the lift height for a scan angle of 90°. The results of the analyses of the surface parameters showed that the influence of the substrate and its texture on the magnetic force image could be neglected for lift heights above 40 nm and that the upper lift height limit is 100 nm. It was determined that the optimal values of the lift heights were in the range from 60 to 80 nm, depending on the nature of the sample and on the type of the tip used.