The power coupling coefficients between cores of waveguide systems with random geometrical imperfections along the fiber axis are determined by comparing numerical solutions of the coupled mode equations with numerical solutions of the coupled power equations and the dependence of the power coupling coefficient on the correlation length with respect to the propagation constants of modes is clarified. When the correlation length D is small the power coupling coefficient is proportional to κ 2 D where κ is the mean mode coupling coefficient and is independent of the fluctuation of the propagation constants. For sufficiently large D the power coupling coefficient dc decreases in proportion to D-1 with increasing D and when D , dc 0. Then the dependence of the power coupling coefficient on the mode coupling coefficient and the fluctuation of the propagation constants δ β is expressed as a function of a single variable κ /δ β .

The scattering of a plane wave from the end-face of a three-dimensional waveguide system composed of a large number of cores is treated by the volume integral equation for the electric field and the first order term of a perturbation solution for TE and TM wave incidence is analytically derived. The far scattered field does not almost depend on the polarization of an incident wave and the angle dependence is described as the Fourier transform of the incident field in the cross section of cores. To clarify the dependence of the scattering pattern on the arrangement of cores some numerical examples are shown.

In an image fiber containing a large number of cores, a certain class of crosstalk has been found to decrease with the distance along the fiber axis. This crosstalk is absolutely distinguished from the usual crosstalk that increases with the distance. A theoretical model is presented based on the power transfer between three groups of modes supported by each core. The process of power transfer is described by coupled power equations. Values of the coupling coefficients can be determined from the measurement of the crosstalk. The equations are solved numerically for the transmission of a point image. The results are in good agreement with measurement results.

One of coupling coefficients appearing in the coupled power equations describing the crosstalk in an image fiber is derived based on the coupled mode theory. Cores arranged in the cross-section of the fiber differ randomly to the degree of several percent in size and consequently modes propagating along the cores differ randomly. Random fluctuations of the propagation constants of modes cause the random transfer process of power between the cores, whereas contributions of the random fluctuations of the mode coupling coefficients to the statistical process can be neglected. The coupling coefficient is described as the ratio of the power transfer ratio to the coupling length for two cores with slightly different radii characterizing the random cores. The theoretical results are in good agreement with measurement results except near cutoff.

We deal with the scattering of a scalar plane wave by a half plane with a sinusoidally deformed edge from a straight edge by a physical optics approximation. The normal incidence of a plane wave to an edge is assumed. A contribution of an edge to the field integral is asymptotically evaluated and the basic properties of the scattering caused by the edge deformation is clarified. The scattering pattern has peaks at specific scattering angles, which agree with diffraction angles calculated by the well-known grating formula for normal incidence. Some numerical examples are shown and it is shown that the results are in good agreement with the results obtained by the GTD method for low angle incidence.

In the plane wave scattering from a periodic grating high order diffracted plane waves disappear at a low grazing angle limit of incidence. In this paper the scattering of a beam wave by the end-face of an ordered waveguide system composed of identical cores of equal space is treated by the perturbation method and the scattered field is analytically derived. The possibility that high order diffracted beam waves remain at a low grazing angle limit of incidence is shown.

An analysis of the E-type plane wave scattering by a dielectric cylinder based on the charge simulation method is given. Numerical examples show that it gives a very good result if the position of singularities of the approximate solution is fixed by making use of the conformal mapping.

Random fluctuations of the propagation constants of modes along the fiber axis are taken into consideration and the power coupling coefficient between cores of an image fiber is theoretically derived. For the fiber used for the measurement in the previous paper (A. Komiyama, IEICE, vol.E79-C, no.2, pp.243-248, 1996) it is verified that the coupling coefficient can be described in terms of statistical properties of the propagation constants in the cross-section of the fiber.

We deal with the scattering of a plane wave by the end-face of a waveguide system by the numerical method based on the sinc function and calculate the electric field on the end-face. It is shown that the results obtained analytically by the perturbation method are in relatively good agreement with the numerical results.

We deal with the scattering of a plane wave by the end-face of an ordered waveguide system composed of identical cores of equal space by the perturbation method and derive analytically the diffraction amplitude. It is shown that the results are in relatively good agreement with those obtained by the numerical method.

The coupled mode equation describing the propagation of light in a disordered waveguide system composed of randomly different cores in size is analytically solved by the perturbation method and the average amplitude of light is derived. In the summation of a perturbation series only successive scatterings from different cores are taken into account. The result obtained shows that the average amplitude behaves as if in an ordered waveguide system composed of identical cores at short distance and decreases exponentially with increasing distance at large distance. The result is compared with the result obtained by the coherent potential approximation and the both results are in good agreement with each other. The results are also compared with the results obtained by numerically solving the coupled mode equation.

Localization properties of mode waves in an off-diagonally disordered waveguide system are presented. The disorder is introduced by taking spacings between cores to be random variables. Coupled mode equations are transformed into a matrix eigenvalue problem and eigenvalues and eigenvectors are numerically obtained. Correspondences between the natures of modes and the modal density of states are discussed. The system is divided into several sections which behave effectively as isolated systems. Modes in the entire system are a superposition of modes associated with the sections. A section is divided into several elements, which do not only behave apparently as isolated systems but also couple with each other. When an element includes two cores coupled strongly with each other due to a narrow spacing, modes are strongly localized there. The extent of the modes is almost independent of the disorder of the system. In a system with small disorder strongly localized modes can exist. The modes appear outside the propagation constant band of the ordered system composed of identical cores of equal spacing. Modes near the center of the band are extended over a number of elements and have the relatively large extent. Many modes appear near the center of the band and the modal density of states has a sharp peak there.

Asymptotic expansions of the amplitudes of the direct and scattered waves in a waveguide system with an imperfection core are derived for large core number and the partial cancellation of the direct wave by the scattered wave is shown in detail. The total power of light in the cross section of a waveguide system is analytically derived and it is shown that the total power of the sum of the direct and scattered waves decreases from that of the direct wave because of the cancellation, the difference of the total power transfers to the localized wave and the total power of light is conserved.

An asymptotic expansion of the amplitude of the scattered wave by an imperfection core in a waveguide system is derived and it is shown that the scattered wave is partially canceled by the direct wave at large distance and a shadow takes place. For z→ ∞ where z is the distance along the waveguide axis the amplitudes of the direct and scattered waves decrease in proportion to z- and in the shadow region the amplitude of the sum of both waves decreases in proportion to z-. To supplement the analytical results some numerical examples are shown.

The asymptotic behaviour of the light power at large distance in a random waveguide system with a short correlation length and a mathematical mechanism of the asymptotic behaviour are clarified. The discussion is based on the coupled mode theory. First, for the light propagation in an ordered waveguide system a new description in terms of the light power is presented. A solution of the integro-differential equation describing the light power is expressed as a contour integral in the Laplace transform domain. Singularities of the integrand are branch points and the branch cut integral determines the asymptotic behaviour of the solution. The light power decreases in inverse proportion to the distance. Secondly the description is extended to the case of a random waveguide system. The differential equation of the recurrence type describing the incoherent power is reduced to the integro-differential equation and it is shown that the kernel is the product of the kernel for an ordered system and the damping term. The equation is solved by using the same procedure as that for an ordered system and a contour integral representation of the solution is obtained. Singularities of the integrand are poles and branch points. The poles arise from the damping term of the kernel and the residues of the poles determine the asymptotic behaviour of the solution. The incoherent power decreases in inverse proportion to the square root of the distance.