Zi Hua Wang

Multichannel switchable system for spatial solitons

We consider a model of a nonlinear planar waveguide with a sinusoidal modulation of the refractive index in the transverse direction, which gives rise to a system of parallel troughs that may serve as channels that trap solitary beams (spatial solitons). The model can also be considered as an asymptotic one describing a dense planar array of parallel nonlinear optical fibers, with the modulation representing the corresponding effective Peierls–Nabarro potential. By means of the variational approximation and by direct simulations we demonstrate that the one-soliton state trapped in a channel has no existence threshold and is always stable. In contrast with this a stationary state of two beams trapped in two adjacent troughs has an existence border, which is found numerically. Depending on the values of the parameters, the two-soliton states are found to be dynamically stable over an indefinitely long or a finite but large distance. We consider the possibility of switching the beam from a channel where it was trapped into an adjacent one by a localized spot attracting the beam through the cross-phase modulation. The spot can be created between the troughs by a focused laser beam shone transversely to the waveguide. By means of the perturbation theory and numerical method we demonstrate that the switching is possible, provided that the spot’s strength exceeds a certain threshold value.

Coupling efficiency of butt-joined planar waveguides with simultaneous tilt and transverse offset

An efficient method has been proposed for evaluating the junction loss between two nonidentical arbitrarily graded-index planar optical waveguides caused by simultaneous transverse and angular misalignments. The salient feature of the method is an exact representation of the modal. Fields which is particularly adapted to loss evaluation at imperfect junctions. The power transmission coefficient at the junction is expressed via the overlap integral method as a weighted sum of simple Laguerre-Gaussian functions, the weight factors being determined by solving a linear matrix eigenvalue problem. The present formulation has a very broad scope of validity and can be used for the modal analysis of integrated optical planar components such as waveguide lenses and to estimate the coupling efficiency of more practical fiber-to-channel butt-joints. The method can also he used to test the accuracies of other approximate methods such as those based on the Gaussian approximation of the lowest order planar waveguide mode.

Improved Rouard's method for fiber and waveguide gratings

Abstract An improvement has been made to Rouards method for the analysis of fiber and waveguide gratings. The real reflectivity of each interface is used instead of an approximate value obtained by coupled-mode theory. The improved Rouards method becomes a complete Rouards method and an exact method. It is simple and independent on coupled-mode theory for no calculation of coupling coefficient required. Numerical examples of uniform and nonuniform gratings have been given.

Free-space mode approximation for radiation modes of a slab waveguide and its application

Taking the symmetric slab waveguide as an example,we show that radiation modes of a weakly guiding planar optical waveguide can be approximated by the free space modes,their field expression and normalization constants are simple and understandable physically and can be obtained directly without any calculation.By applying this approximation,the far field and radiation loss calculations caused by random wall imperfections have been significantly simplified.

APPLICATION OF THE COUPLED MODE THEORY TO EIGENVALUE PROBLEMS OF GRADED-INDEX OPTICAL FIBERS

The propagation constant and the modal field distribution for guided modes of an arbitrary graded-index optical fiber have been calculated with the use of the coupled mode theory. The infinitely extended parabolic profile fiber is taken as an ideal waveguide, and an arbitrary radially inhomogeneous optical fiber can be viewed as a perturbation. Its modal field can be expanded in terms of a complete set of ideal waveguide modes. Eigenvalues and modal fields are then obtained from coupled mode equations that have been transformed into a set of linear equations. Numerical results have been presented and compared with exact values.