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Abstract: The characteristics of the directional couplers based on the horizontal multiple-slotted waveguides with slanted sidewalls are analyzed in detail by using a mode solver based on the full-vectorial finite element method with perfectly matched layers absorbing boundary conditions. The coupling length of the directional coupler as functions of the structural parameters including waveguide spacing, sidewalls angle, the thickness and refractive index of the slot regions, both in quasi-TE and quasi-TM modes, is obtained. The effective indexes and the field distributions of the even and odd modes also are presented. The numerical results show that polarization-independent directional couplers can be realized by properly choosing structural and material parameters. [Copyright &y& Elsevier]

Abstract: A full-vectorial (FV) analysis of optical dielectric waveguide bends by using finite difference (FD) method in terms of magnetic field components is developed in a local cylindrical coordinate system. The perfectly matched layer absorbing boundary conditions via the complex coordinate stretching technique are incorporated into the FV wave equations for effectively demonstrating the leaky nature of waveguide bends, and a six-point FD scheme is constructed to approximate the cross-coupling terms for improving the convergent behavior. The leaky modes of a typical rib waveguide bend are calculated and the complex propagation constants and the field patterns for TE- and TM-like modes are obtained. Solutions are good agreement with those from the film mode matching method, which shows the validity and utility of the established method. [Copyright &y& Elsevier]

Abstract: A compact wavelength demultiplexer is designed for the operation at 1.30 and 1.55μm wavelengths using the three-dimensional semi-vectorial beam propagation method. The parabolically tapered multimode interference (MMI) coupler based on the deep-etched SiO2/SiON rib waveguide is introduced into the present demultiplexer for reducing the length. The numerical results show that a MMI section of 330.0μm in length, which is only 76% length of a straight MMI coupler, is achieved with the contrasts of 42.3 and 39.2dB in quasi-TE mode, and 38.4 and 37.8dB in quasi-TM mode at wavelengths 1.30 and 1.55μm, respectively and the insertion losses below 0.2dB. The modified finite difference scheme is applied to approximate the resulting equations along the transverse directions, in which the discontinuities of the derivatives of magnetic field components H y and H x along the vertical and horizontal interfaces, respectively, are involved. [Copyright &y& Elsevier]

Abstract: A modified full-vectorial finite-difference beam propagation method based on H-fields in solving the guided-modes for optical waveguides with step-index profiles is described. The propagation is split into two substeps. In the first substep, the field propagates in the absence of the cross-coupling terms, and then they are evaluated and double used in the second substep. An improved six-point finite-difference scheme is constructed to approximate the cross-coupling terms along the transverse directions. By using the imaginary-distance procedure, the field patterns and the normalized propagation constants of the fundamental modes for a buried rectangular waveguide and rib waveguide are presented, and the hybrid nature of the full-vectorial guided-modes is demonstrated. Solutions are in good agreement with the benchmark results from film mode matching method, which tests the validity and utility of the present method. [Copyright &y& Elsevier]

Abstract: The mapped Galerkin method in solving the full-vector and quasi-vector wave equations in terms of transverse magnetic fields (H-formulation) for optical waveguides with step-index profiles is described. By transforming the whole x–y space onto a unit square and using two-dimensional Fourier series expansion, the modal distributions and propagation constants for optical waveguides are obtained in the absence of boundary truncation. Results for step-index circular fiber, buried rectangular waveguide, and optical rib waveguide are presented. Solutions are good agreed with exact solutions and numerical results by using vector nonlinear iterative method, Fourier operator transform method, and vector beam propagation method. [Copyright &y& Elsevier]

• The rectangular grooves are shallowly etched on the MMI waveguide to introduce the refractive-index perturbations on the MMI waveguide eigenmodes, leading to an effective refractive-index manipulation of the eigenmodes. • The refractive-index perturbation scheme provides a simple and scalable method to manipulate the four beat lengths of the two wavelengths at TE- or TM-polarization in a single waveguide via self-imaging effect, leading to a compact footprint. • The present refractive-index perturbation scheme realizes, for the first time, NIR/MIR wavelength demultiplexing and polarization independence simultaneously in an individual device. • A compact and polarization-independent wavelength diplexer for 1.31/2 μm is also realized by flexibly changing the dimensions, showing the flexibility and extensibility of our refractive-index perturbation scheme. Faced with the rapid growth of internet traffic demand, which has posed a huge challenge to the current fiber-based communications systems, expanding the telecommunications bands from traditional near-infrared (NIR) region to mid-infrared (MIR) region is emerging as an attractive solution. And on-chip wavelength division multiplexing (WDM) application for NIR/MIR wavelengths is an essential element in future optical telecommunication systems. Here, we propose a compact silicon-based polarization-independent wavelength diplexer for the NIR/MIR wavelengths of 1.55/2 μm, where multiple rectangular grooves are shallowly etched on the silicon MMI waveguide for introducing the refractive-index perturbations on the MMI waveguide eigenmodes. And this refractive-index perturbation scheme provides a simple and scalable method to manipulate the four beat lengths of the two wavelengths at TE- or TM-polarization in a single waveguide via self-imaging effect, leading to a compact footprint. By optimizing the structural parameters, both NIR/MIR wavelength demultiplexing and polarization independence, for the first time, are obtained simultaneously in the present single device. From the results, the proposed diplexer is only 21.6 μm in length, and shows a wide bandwidth of ∼ 100/120 nm around the wavelength of 1.55/2 μm for insertion loss (IL) < 1 dB and extinction ratio (ER) > 15 dB. Moreover, we also realize a compact and polarization-independent wavelength diplexer for 1.31/2 μm by flexibly changing the dimensions, showing the flexibility and extensibility of our refractive-index perturbation scheme. Besides, fabrication tolerances are analyzed and mode propagation profiles are also demonstrated. [ABSTRACT FROM AUTHOR]