GIPO News Letters

　　In recent years, photonic crystals (PhC) have attracted a lot of attention due to their exotic properties. By applying the properties, many applications have been proposed, such as filters, waveguides, cavities, beam splitter, etc. To design those devices, an effective numerical method is required. The plane wave expansion method (PWEM) based on Fourier series expansion is frequently adopted. However, it can only be applied to devices made by lossless and dispersionless materials. In addition, it can not analyze the leakage due to finite-size structures. However, in reality, devices cannot be made infinitely, and guided waves may suffer from significant leakage due to finite periodic structures.

We have derived a modified finite-difference method from Maxwell’s equations to calculate wavevectors corresponding to a certain given frequency. The above-mentioned limitations with conventional PWEM are overcome. We apply the developed method to analyze the propagation phenomena of finite-size photonic waveguides. Finite-difference method combined with perfect match layers (PML) are adopted in the analysis.

Fig. 1 shows the calculation domain. Fig. 2 shows the mode patterns of PhC waveguides with (a) one unit cell and (b) three unit cells beside the line defects. It can be seen that the decay is significantly reduced as more unit cells are added beside the line defects.


Fig. 1 Representation of calculation domain.	Fig. 2 Mode pattern of PhC waveguides with (a) one unit cell and (b) three unit cells beside the line defects.

The decay rate and the number of unit cells beside the line defects is linear in semi-logarithmic diagram as shown in Fig. 3, where k is the calculated propagation constant.

ZnS/Silica Nanocable Field Effect Transistor as Biological and Chemical Nanosensors

Sensing using planar field effect transistor (FET) has been demonstrated for decades but lower sensitivity has limited its applications. Compared to the surface region of a planar device, due to the ultrahigh surface-to-volume ratio, NWs and carbon nanotubes (CNTs) are ideal choices for sensors due to the introduced depletion/accumulation of charges near the surface as a result of surface binding/adsorption of foreign molecules and species. The NWs that have been extensively developed for sensing are silicon because of the massive knowledge that has existed for the chemical modification of native Si oxide surfaces. The FET of ZnS/silica core/shell nanostructures are attractive to biological and chemical sensors due to (i) its excellent and reproducible electronic characteristics of ZnS, (ii) the self-assembled silica shell as natural insulator on the surface of ZnS NW that serve as the protection layer against oxidation, and (iii) the massive existing knowledge about the chemical modification of silica surfaces.

Compound semiconductor/isolator (ZnS/silica) core/shell nanocables have been used to fabricate single nanowire based field effect transistors, which have been used for label-free, real-time, and sensitive detection of biological species. After chemical modification, amine- and oxide-functionalized nanocables exhibit linear pH-dependent conductance, which could be elucidated in terms of the change of surface charge during protonation and deprotonation.

Advanced Numerical Modelling for Photonic-Crystal and Optical-Waveguide Structures

A novel analysis method based on a multidomain pseudospectral method is proposed for calculating the band diagrams of two-dimensional photonic crystals and is shown to possess excellent numerical convergence behavior and accuracy. The proposed scheme utilizes the multidomain Chebyshev collocation method. By applying Chebyshev-Lagrange interpolating polynomials to the approximation of spatial derivatives at collocation points, the Helmholtz equation is converted into a matrix eigenvalue equation which is then solved for the eigen frequencies by the shift inverse power method. Suitable multidomain division of the computational domain is performed to deal with general curved interfaces of the permittivity profile and field continuity conditions are carefully imposed across the dielectric interfaces. The proposed method shows uniformly excellent convergence characteristics for both the transverse-electric and transverse-magnetic waves in the analysis of different structures. The analysis of a mini band gap is also shown to demonstrate the extremely high accuracy of the proposed method. (Physical Review E, vol. 75, pp. 026703-1–026703-14, 20 February 2007.)

New full-vectorial optical waveguide eigenmode solvers using pseudospectral frequency-domain (PSFD) formulations for optical waveguides with arbitrary step-index profile are presented. Both Legendre and Chebyshev collocation methods are considered in the formulation. By applying Legendre-Lagrange or Chebyshev-Lagrange interpolating polynomials to the approximation of spatial derivatives at collocation points, the Helmholtz equations for the transverse-electric or transverse-magnetic components are converted into a matrix eigenvalue equation which is then solved for the eigenmodes by the shift inverse power method. Suitable multidomain division of the computational domain is arranged to deal with general curved interfaces of the refractive-index profile together with a curvilinear mapping technique for each subdomain so that field continuity conditions can be carefully imposed across the dielectric interfaces, which is essential in achieving high numerical accuracy. The solver is applied to the optical fiber for the assessment of its numerical performance, to the classical benchmark rib waveguide for comparing with existing high-accuracy results, and to the fused fiber structure for demonstrating its robustness in calculating the form birefingence. (IEEE Journal of Quantum Electronics, vol. 44, no. 1, pp. 56–66, January 2008.)

A finite element method based eigenvalue algorithm is developed for the analysis of band structures of two-dimensional non-diagonal anisotropic photonic crystals under the in-plane wave propagation. The characteristics of band structures for the square and triangular lattices consisting of anisotropic materials are examined in detail and the intrinsic effect of anisotropy on the construction of band structures is investigated. We discover some interesting relationships of band structures for certain directions of the wave vector in the first Brillouin zone and present a theoretical explanation for this phenomenon. The complete band structures can be conveniently constructed by means of this concept. (Optics Express, vol. 15, no. 9, pp. 5416–5430, 30 April 2007.)

A full-vectorial finite element method based eigenvalue algorithm is developed to analyze the band structures of two-dimensional (2D) photonic crystals (PCs) with arbitray 3D anisotropy for in-plane wave propagations, in which the simple transverse-electric (TE) or transverse-magnetic (TM) modes may not be clearly defined. By taking all the field components into consideration simultaneously without decoupling of the wave modes in 2D PCs into TE and TM modes, a full-vectorial matrix eigenvalue equation, with the square of the wavenumber as the eigenvalue, is derived. We examine the convergence behaviors of this algorithm and analyze 2D PCs with arbitrary anisotropy using this algorithm to demonstrate its correctness and usefulness by explaining the numerical results theoretically. (Optics Express, vol. 15, no. 24, pp. 15797–15811, 26 November 2007.)

White-light light-emitting device based on surface plasmon-enhanced CdSe/ZnS nano-crystal wavelength conversion on a blue/green two-color light-emitting diode

　 We demonstrate the implementation of a white-light device by spin-coating CdSe/ZnS nano-crystals (NCs) on the top of a blue/green two-color InGaN/GaN quantum-well light-emitting diode for converting blue and green emissions into red light through the absorption/reemission process. Meanwhile, Au nano-particles (NPs) are mixed with CdSe/ZnS NCs for generating localized surface plasmon (LSP) modes to couple with the CdSe/ZnS NCs. The LSP modes can absorb green emission and effectively transfer the energy into the CdSe/ZnS NCs through the coupling process for enhancing red emission. With the LSP coupling process, the conversion efficiency from the blue/green range into red light can be increased by around 30 %. The conversion quantum efficiency can reach 52.8 %.

by K.Y. Lo, Y.J. Huang, J.Y. Huang, Z.C. Feng, W.E. Fenwick, M. Pan and I.T. Ferguson

The structures of the Zn–O bonding in ZnO (0002) thin films prepared by metal organic chemical vapor deposition (MOCVD) have been studied by reflective second harmonic generation (RSHG). The polar Zn–O bond on the top layer is not canceled out and presents 3 mm symmetrical structures on the well-grown ZnO (0002) surface. The average polar strength of the Zn–O bond is correlated with the quality of the ZnO (0002) thin film. The mirror symmetry is caused by the nonvanished polar of twin boundary due to the mismatch between the ZnO film and sapphire substrate and analyzed using s-polarized RSHG with s-polarized fundamental light irradiation. These results demonstrate that the Zn–O heteropolar bonds on the smooth ZnO surface contribute to the SHG intensity.

　 A photonic crystal generally consists of two or more materials with different dielectric constants. These different materials are arranged periodically with a period on a length scale of optical wavelength. Analogous to semiconductor crystals, the periodic refractive index of photonic crystals can cause the destructive or constructive interference. This provides some ranges of frequency called photonic band gaps in which light cannot propagate in the crystal. With photonic crystals, one can manipulate the optical wave in a wavelength scale, leading to many applications such as waveguides, micro-cavities, filters, etc. If a line defect is properly introduced in a photonic crystal slab, one can obtain a photonic crystal slab line-defect waveguide with certain desired spectral property. In other words, it is possible to manipulate the band structure or dispersion relation of the waveguide by properly designing the spatial structure of the photonic crystal. For example, flattening the dispersion relation of some wave mode can result in the reduction of group velocity. This may lead to the realization of slow light with the application of delay devices. This kind of research can be formulated as an inverse problem for synthesizing a photonic crystal structure subject to some specific conditions of band diagram. In this research, the simulated annealing algorithms together with the plane wave expansion method and the effective index method are used to synthesize the photonic crystal slab line-defect waveguides with various values of group velocity.