Hung-chun Chang

Improved three-point formulas considering the interface conditions in the finite-difference analysis of step-index optical devices

A general relation, considering the interface conditions, between a sampled point and its nearby points is derived. Making use of the derived relation and the generalized Douglas scheme, the three point formulas in the finite-difference modeling of step-index optical devices are extended to fourth order accuracy irrespective of the existence of the step-index interfaces. With numerical analysis and numerical assessment, several frequently used formulas are investigated.

Low-index terahertz pipe waveguides

We propose and demonstrate a simple leaky structure for terahertz (THz) waveguiding. Different from previously reported air-core THz waveguides, in which a high-reflection-coated cladding layer is designed, the proposed structure here is a simple pipe with a large air core and a thin dielectric layer with uniform but low index. Using commercially available Teflon air pipes, we experimentally confirm that THz waves can be successfully guided in the central air core of 3-m-long pipes with excellent mode qualities, high coupling efficiencies, low attenuation constants, and controllable passband width.

Modal characteristics of antiresonant reflecting pipe waveguides for terahertz waveguiding

Modal characteristics of the THz pipe waveguide, which is a thin pipe consisting of a large air core and a thin dielectric layer with uniform but low index, are investigated. Modal indices and attenuation constants are calculated for various core diameters, cladding thicknesses, and cladding refractive indices. Numerical results reveal that the guiding mechanism of the leaky core modes, which transmit most of the power in the air-core region, is that of the antiresonant reflecting guiding. Moreover, modal patterns including modal intensity distributions and electric field vector distributions are shown for the fundamental and higher order modes. Experiments using time-domain spectroscopy with PMMA pipes also confirm the antiresonant reflecting guiding mechanism.

Yee-mesh-based finite difference eigenmode solver with PML absorbing boundary conditions for optical waveguides and photonic crystal fibers

Eigenvalue equations for solving full-vector modes of optical waveguides are formulated using Yee-mesh-based finite difference algorithms and incorporated with perfectly matched layer absorbing boundary conditions. The established method is thus able to calculate the complex propagation constants and the confinement losses of leaky waveguide modes. Proper matching of dielectric interface conditions through the Taylor series expansion of the fields is adopted in the formulation to achieve high numerical accuracy. The method is applied to the study of the holey fiber with triangular lattice, the two-core holey fiber, and the air-guiding photonic crystal fiber.

Compact finite-difference frequency-domain method for the analysis of two-dimensional photonic crystals

A finite-difference frequency-domain method based on the Yees cell is utilized to analyze the band diagrams of two-dimensional photonic crystals with square or triangular lattice. The differential operator is replaced by the compact scheme and the index average scheme is introduced to deal with the curved dielectric interfaces in the unit cell. For the triangular lattice, the hexagonal unit cell is converted into a rectangular one for easier mesh generation. The band diagrams for both square and triangular lattices are obtained and the numerical convergence of computed eigen frequencies is examined and compared with other methods.

Improved full-vectorial finite-difference mode solver for optical waveguides with step-index profiles

A general relation considering an interface condition between a sampled point and its nearby points in the finite-difference analysis of optical waveguides, is derived. Our formulation is a full-vectorial one, and the interface can be oblique to the global coordinate axes or even can have curvature. Using the derived formulation, optical waveguide structures with arbitrary step-index profiles can be dealt with. The validity of the proposed method is examined by comparing the numerical calculation with the analytical solution of a step-index optical fiber. The method is also applied to the analysis of fused fiber-optic couplers and compared with prior analysis using the surface integral equation method.

Three-dimensional noniterative full-vectorial beam propagation method based on the alternating direction implicit method

The alternating direction implicit (ADI) method is adopted in the full-vectorial beam propagation formulation, which was discretized in the longitudinal direction via the standard Crank-Nicholson scheme. Through proper operator decomposition, operator inversions for the cross coupling terms existing in the full-vectorial formulation are avoided and second order accuracy along the propagation direction is achieved in the proposed algorithm. With the aid of the ADI method, our full-vectorial algorithm also has good performance in efficiency. This implicit scheme can theoretically be shown to be numerically unconditionally stable. Several numerical simulations have been performed and compared with those obtained by the finite difference mode solving scheme based on the shifted inverse power method (SIPM) in order to examine the accuracy of our algorithm.

Design of optical path for wide-angle gradient-index antireflection coatings

What we believe to be a new principle is introduced for the design and selection of gradient-index antireflection profiles that are effective over a wide range of incident angles as well as wavelengths at a given physical film thickness. It is shown that at oblique incidence the smoothness of the optical path of incident light inside a gradient-index film has a crucial effect on the overall reflection. Thus the smoothness of variations in refractive angle (rather than that of the index profile itself) needs to be maximized for wide-angle operation. As an example, the performance of Gaussian and Quintic profiles at large incident angles are considered in light of this point of view.

Plasmonic optical properties of a single gold nano-rod

Polarization-contrast microscopy coupled with an atomic force microscope is utilized to attain far-field optical images of the multipolar surface plasmon resonance (SPR) modes of single gold nano-rod. Modulated standing modes resulted from the interference of longitudinal SPR modes and incident light are observed and studied. By counting the average distance of adjacent beats on this single gold nano-rod, the wave vector of longitudinal SPR modes can be obtained. We found a linear relationship between the wave vectors of the incident light and the induced SPR modes. Experimental results demonstrate a feasible way on acquiring plasmonic optical properties from an individual single gold nano-rod.

A novel fabrication method for all-fiber, weakly fused, polarization beamsplitters

A simple method for fabricating single-mode fused couplers for polarization beamsplitting is presented. The coupler is extremely weakly fused such that the first polarization modulation waist in its power transfer characteristic is clearly extended. Due to such a feature, the coupler drawing process may accurately be stopped at the waist point by simply monitoring the power variations of the output ports. We have achieved an average extinction ratio of -23.7 dB at the throughput port and -23.8 dB at the coupled port at the designated wavelength. The polarization bandwidth obtained is 38 nm. >