A simple implementation of plane wave method is presented for modeling photonic crystals with arbitrary shaped 'atoms'. The Fourier transform for a single 'atom' is first calculated either by analytical Fourier transform or numerical FFT, then the shift property is used to obtain the Fourier transform for any arbitrary supercell consisting of a finite number of 'atoms'. To ensure accurate results, generally, two iterating processes including the plane wave iteration and grid resolution iteration must converge. Analysis shows that using analytical Fourier transform when available can improve accuracy and avoid the grid resolution iteration. It converges to the accurate results quickly using a small number of plane waves. Coordinate conversion is used to treat non-orthogonal unit cell with non-regular 'atom' and then is treated by standard numerical FFT. MATLAB source code for the implementation requires about less than 150 statements, and is freely available at http://www.lions.odu.edu/~sguox002.

The dispersion and loss in microstructured fibers are studied using a full-vectorial compact-2D finite-difference method in frequency-domain. This method solves a standard eigen-value problem from the Maxwell's equations directly and obtains complex propagation constants of the modes using anisotropic perfectly matched layers. A dielectric constant averaging technique using Ampere's law across the curved media interface is presented. Both the real and the imaginary parts of the complex propagation constant can be obtained with a high accuracy and fast convergence. Material loss, dispersion and spurious modes are also discussed.

Two numerical techniques for analysis of defect modes in photonic crystals are presented. Based on the finite-difference time-domain method (FDTD), we use plane wave incidences and point sources for excitation and analysis. Using a total-field/scattered-field scheme, an idealplane wave incident at different angles is implemented; defect modes are selectively excited and mode symmetries are probed. All modes can be excited by an incident plane wave along a non-symmetric direction of the crystal. Degenerate modes can also be differentiated using this method. A proper arrangement of point sources with positive and negative amplitudes in the cavity flexibly excites any chosen modes. Numerical simulations have verified these claims. Evolution of each defect mode is studied using spectral filtering. The quality factor of the defect mode is estimated based on the field decay. The far-field patterns are calculated and the Q values are shown to affect strongly the sharpness of these patterns. Animations of the near-fields of the defect modes are presented to give an intuitive image of their oscillating features.

Cladded multimode fiber optic tapers are proposed as chemical sensors using evanescent wave absorption. There is no need to strip the cladding; therefore, fabrication is easy and the taper is mechanically stronger than the taper without cladding. The transmission property and evanescent wave absorption are modeled using ray theory and wave theory, respectively. Effects of some parameters on the absorption sensitivity are analyzed numerically. Due to the presence of the cladding, the taper core is not in direct contact with the external medium, leading to some significant differences from the uncladded one, especially when the index of the external medium approaches the index of cladding or core. Tapers are fabricated and absorption experiments are conducted to show the feasibility of such a chemical sensor.

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In this paper, we compare three analysis methods for Bragg fibers, viz. the transfer matrix method, the asymptotic method and the Galerkin method. We also show that with minor modifications, the transfer matrix method is able to calculate exactly the leakage loss of Bragg fibers due to a finite number of H/L layers. This approach is more straightforward than the commonly used Chew's method. It is shown that the asymptotic approximation condition should be satisfied in order to get accurate results. The TE and TM modes, and the band gap structures are analyzed using Galerkin method.

A finite-difference frequency-domain (FDFD) method is applied for photonic band gap calculations. The Maxwell's equations under generalized coordinates are solved for both orthogonal and non-orthogonal lattice geometries. Complete and accurate band gap information is obtained by using this FDFD approach. Numerical results for 2D TE/TM modes in square and triangular lattices are in excellent agreements with results from plane wave method (PWM). The accuracy, convergence and computation time of this method are also discussed.

The X-ray diffractions of cobalt nanoparticles synthesized by a microfluidic reactor process at low temperature suggest glasslike phases with only one broad peak. An X-ray absorption fine-structure (XAFS) technique is used to investigate fine crystal phase transition or changes in atomic arrangement and interatom spacing, during the Co nanoparticle formation by the microfluidic reactor process. The results indicate that the dynamic energy and retention time in microfluidic channels, and Ostwald ripening and quenching processes will affect the atom arrangement and the interatom spacing significantly. The hierarchies of surface energies for the main cut planes in different Co crystal structures can be used to elaborate these effects very well. The atom rearrangement and the interatom spacing shift during the nanoparticle formation are very important in the control of the nanoparticle properties via microfluidic processes, particularly for those sensitive to their fine crystal structures, such as magnetic and optical properties.