An improved finite difference method in solving vector wave equations based on H fields for full-vectorial analysis of optical waveguides is described.A six-point finite difference scheme of high accuracy is constructed to approximate cross-coupling terms.It takes into account the discontinuities in derivatives of magnetic component at horizontal and vertical interfaces.Moreover,the scheme is independent of structure of waveguide due to explicit expressions.The guided-mode patterns and normalized propagation constants of a step-index fiber,a rectangular waveguide and a rib waveguide are presented.The hybrid nature of full-vectorial guided-modes is demonstrated.The results agree well with analytical solutions and the benchmark results of modal transverse resonance method.It demonstrates accuracy and convergence of the method.

Under a compulsive boundary condition,a simplified time-domain finite-difference beam propagation method (TD-FD-BPM) suitable for the analysis of fiber Bragg grating (FBG) is presented.In the alternating-direction implicit method (ADIM) and the generalized Douglas (GD) scheme, the time-domain beam propagation equation is discretized with a truncation error two orders lower than that of conventional finite-difference scheme.The compulsive boundary condition simplifies the boundary model,which is important in the numerical analysis of optical waveguides with open boundary conditions.We focused on the position of excitation,the shape of the pulse and its distribution in the radial direction,and the use of the one-way continuous-wave (CW) scheme.Using a modified sinusoidal pulse,a satisfactory reflective spectrum is obtained in a short symmetrical FBG through discrete Fourier transform.

A 3D trapered spot-size converter (3D-SSC) on a rib cross-sectional optical waveguide, one of the key components in photonic devices connecting with single mode optical fibers,is investigated through simulating lightwave transmission in this component based on 3D-FD beam propagation method.Geometry parameters,such as laterally boundaries,length,width of the large section,thickness and those of the transitional optical waveguide for connecting SMOF to 3D-SSC are discussed and analyzed.The simulation shows that the insert loss of 3D-SSC can be lower than 2 dB as the width in the area of 11.5 μm~13.5 μm and the thickness in the area of 4.5 μm~6.5 μm at the large end of the taper when the taper length is in the region of 200 μm~500 μm.The capability and the alignment tolerance of the 3D-SSC is better than those of the planar SSC,and the 3D-SSC with a nonlinear lateral boundary acquires lower insertion loss than that with a linear lateral boundary.It is found that the 3D-SSC converts gradually the guided modes from multi-mode to single mode finally.

Regular fractal has ideal scale-invariance.But the probability distribution curve and the range of scale-invariance of random fractal (for example thin film growth) are related to the calculation method.The scale-invariance is not good and the multifractal spectrum is not smooth when the probability is calculated by variance from average height.The range of scale-invariance can be extend to 3 orders of magnitude and the multifractal spectrum is smooth when the probability is calculated by height based on the bottom of the film.An extending method is here used to correct the deviation of gray level setting-up so as to improve the multifractal spectrum.The effect of the range of the moment order q is discussed as well.