We extend the continuity relations of field derivatives across an abrupt interface to arbitrary orders for transverse electric and magnetic waves in slab structures. Higher-order finite-difference formulation is then obtained by combining the systematically-obtained interface conditions with Taylor series expansion. Generalized Douglas scheme is also adopted to further enhance the convergence of truncation errors by two orders. We apply the derived finite-difference formulation, up to nine-points in this paper, to solve the guided modes in simple a slab waveguide and multiple quantum well waveguides. The results shows the truncation error is much higher, up to tenth order, as expected. Using those higher-order schemes, accurate results are obtained with much fewer sampled points, and hence with tremendously less computation time and memory.

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we propose and analyze a series of vertical directional couplers based on SOI-compatible hybrid plasmonic waveguides. We investigate two configurations: metal-insulator-metal (MIM) and insulator-metal-insulator (IMI). Both slab and threedimensional analyses show that MIM directional couplers have better coupling performance such as sub-micron coupling length and lower loss. To ensure the normalized power loss lower than 5%, the coupling length can be chosen as short as 0.492 μm (about one third of the wavelength 1.55 μm). The coupler size can be traded for even lower power loss. In one example, a lesscompact design yields 3% power loss, while maintains sub-micron coupling length. We further verified our design with beam propagation analysis. The analysis independently verifies the compact MIM design does show guided mode coupling length along vertical direction can be as short as 0.492 μm.Index Terms-Hybrid plasmonic waveguides, vertical directional coupler, waveguide mode analysis.

We propose a modified gain-guided index-antiguided (GGIAG) fiber structure for large mode area laser amplifiers, in which a thin dielectric layer is placed between the low-index core and the high-index cladding. The introduced dielectric layer functions as a Fabry-Perot etalon. By letting the resonant wavelength of the Fabry-Perot layer coincide with the signal wavelength, the signal is gain-guided in the fiber core. Moreover, the pump is confined in the low-index core owing to the antiresonant reflection originated from the Fabry-Perot layer. Numerical results indicate that the leakage loss of the pump can be minified over two orders of magnitude in the proposed structure, and thus the end-pumping efficiency could be enhanced significantly.

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