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We have applied the effective index method to reduce the two-dimensional (2-D) refractive index profile into the 1-D refractive index structure and modified the wave equations to obtain the paraxial wave equations. Then, transverse electric (TE) and transverse magnetic (TM) polarized fields in the curved single-mode planar waveguides are analyzed by using the scalar beam-propagation method (BPM) employing the finite-difference method with a slab structure. The bending loss in bent waveguides is analyzed for optical fields obtained from the BPM and comparisons are made between the loss for the waveguides with various radius of curvature and the refractive index difference. The outward shift of the optical field, which is generated at the connection between a straight and a bent waveguide, is obtained from the results of calculation of location of the maximum optical intensity. The transition loss can be reduced by introducing an optimized inward offset at a straight-to-bend junction. The birefringence for TE and TM polarized fields in bent waveguides is calculated from the phase difference of the optical fields. The wavelength shift due to the birefringence of TE and TM polarized fields in bent waveguides is also calculated.Index Terms-Beam-propagation method (BPM), bending loss, bent waveguide, birefringence, effective index method (EIM), optimized inward offset, transparent boundary condition, wavelength shift.

This paper proposes an architectural design of light-weight IPv6 (LWIPv6) for low-power wireless personal area networks (LoWPANs). The LoWPAN is a simple and lowcost wireless communication system, which allows wireless connectivity in a variety of applications with requirements of limited power and relaxed throughput. LoWPAN devices conform to the IEEE 802.15.4 standard specified by the IEEE Computer Society. This paper also suggests how to make IP and IPv6 networking benefits in LoWPANs. Consequently, this paper describes systems requirements analysis (SRA) of LoWPANs with regard to the Internet protocol (IP) layer, also proposes a design of the LWIPv6 architecture focused on LoWPAN, and finally simulates IP communications between LoWPAN devices in a viewpoint of performance analysis. The proposed architecture and protocol in LWIPv6 are substantially optimized for the IP stack, such as header compression, simplified neighbor discovery, and reduction of overhead in the Internet control message protocol (ICMP) functionality.Index Terms -Light-weighted Internet protocol version 6, low-power wireless personal area networks, LWIPv6, LoWPAN

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