In this paper, from the viewpoint of wave optics, a computational method is proposed for the loss analysis of multimode fiber splice due to such multiple misalignment as end separation, axis displacement and angular misalignment.

In this paper, a new method based on the mode-matching method in the sense of least squares is presented for analyzing the two dimensional scattering problem of TE plane wave incidence to the infinite plane surface with an arbitrary imperfection of finite extent. The semi-infinite upper and lower regions of that surface are a vacuum and a perfect conductor, respectively. Therefore the discussion of this paper is developed about the Dirichlet boundary value problem. In this method, the approximate scattered wave is represented by the integral transform with band-limited spectrum of plane waves. The boundary values of those scattered waves are described by only abscissa z and Fourier spectra are obtained by applying the ordinary Fourier transform. Moreover, new approximate functions are made by inverse Fourier transform of band-limited those spectra. Consequently, the integral equations of Fredholm type of second kind for spectra of approximate scattered wave functions are derived by matching those new functions to exact boundary value in the sense of least squares. Then it is shown analytically and numerically that the sequence of boundary values of approximate wave functions converges to the exact boundary value, namely, the boundary value of the exact scattered wave in the sense of least squares when the profile of imperfection part is described by continuous and piecewise smooth function at least. Moreover, it is shown that this sequence uniformly converges to exact boundary value in arbitrary finite region of the boundary and the sequence of approximate wave functions uniformly converges to the exact scattered field in arbitrary subdomain in the upper vacuum domain of the boundary in wider sense when the uniqueness of the solution of the Helmholtz equation is satisfied with regard to the profile of the imperfection parts of the boundary.

In this paper, a method for analyzing the transmission, reflection and scattering of the thin-film waveguide with partial periodic structure is proposed. This method results in the Fredholm integral equation of the second kind. The results of analyses based on the first order approximate solutions are given.

In this paper, scattering problem of the directional coupler for the slab waveguides are analyzed by the mode-matching method in the sense of least squares for the lowest order even TE mode incidence. It is considered that the analysis of this coupler for the slab waveguides presents the fundamental data to design the directional coupler for the three dimensional waveguides. This directional coupler is composed of three parallel slabs which are placed at equal space in the dielectric medium. Respective slabs are core regions of three respective waveguides. The periodic groove structure of finite extent is formed on the both surfaces of core region of the central waveguide among them. The power of incident TE mode is coupled to other two waveguides through periodic groove structure. The coupled TE mode propagates in the other waveguides to the same or opposite direction for the direction of incident mode which propagates in the waveguide having periodic structure when the Bragg condition is selected appropriately. The scattered field of each region of this directional coupler is described by the superpositions of the plane waves with bandlimited spectra, respectively. These approximate wave functions are determined by the minimization of the mean-square boundary residual. This method results in the simultaneous Fredholm type integral equations of the second kind for these spectra. The first order approximate solutions of the integral equations are derived and the coupling efficiency and scattered fields are analyzed on the basis of those solutions in this paper.

A mode-matching method in the sense of least squares are proposed for analyzing grating coupler having a periodic groove structure of finite extent which is formed on the surface of the core region of the thin-film waveguide. The grating couplers are analyzed for the plane wave incidence when the Bragg condition is satisfied. The discussion is developed about the grating couplers formed on the asymmetric and symmetric waveguides. The approximate scattered fields of each region of the grating coupler are described by the superpositions of the plane waves with band-limited spectra, respectively. These approximate wave functions are determined by the minimization of the mean-square boundary residual. This method results in the simultaneous Fredholm type integral equations of the second kind for these spectra. Results of analyses based on the first order approximate solutions are presented. A comparison between our results and those of Green's function approach for grating couplers having rectangular, triangular and sinusoidal grooves of different depth is presented.

A mode-matching method in the sense of least squares is applied for analyzing grating couplers having various groove shapes. These couplers are formed on surfaces of core regions of the thin-film waveguides and their periodic parts extend finitely. The grating couplers are analyzed for the plane wave incidence when the Bragg condition is satisfied. The discussion is developed about the grating coupler which is formed on the asymmetric waveguide and has arbitrary triangular grooves. However various couplers, which have triangular, rectangular and sinusoidal grooves and are formed on asymmetric and symmetric waveguides, are analyzed and results for them are presented in this paper. The approximate scattered fields of each region of the coupler are described by the superpositions of the plane waves with band-limited spectra, respectively. These approximate wave functions are determined by the minimization of the mean-square boundary residual. This method results in the simultaneous Fredholm type integral equations of the second kind for these spectra. Results of analyses based on the first order approximate solutions are presented. The comparison between each coupling efficiency derived by the present method for couplers having sinusoidal, triangular and rectangular grooves is presented in this paper.

In this paper, scattering problem of the grating coupler is analyzed by the mode-matching method in the sense of least squares for the gaussian light beam incidence. This coupler has a periodic groove structure of finite extent, which is formed on the surface of the core layer of the symmetric thin-film waveguide. In the present method, the approximate scattered fields of each region of the grating coupler are described by the superpositions of the plane waves with band-limited spectra, respectively. These approximate wave functions are determined by the minimization of the mean-square boundary residual. This method results in the simultaneous Fredholm type integral equations of the second kind for these spectra. The first and second order approximate solutions of the integral equations are derived analytically and the coupling efficiency and scattered fields are analyzed on the basis of those solutions. A qualitative and physical consideration for the scattering problem of the grating coupler is presented with the fundamental data derived from approximate solutions in this paper.