The two variational principles, the Maupertuis' and the Hamilton's principle, are discussed in conjunction with the Fermat's principle. These two principles are shown to describe two different aspects of waves, thus resulting in the different geometry of wave propagation, the treatment of which is thus called the stationary optics or the dynamical optics, respectively. Comparisons for the results obtained from these geometrical optics are given. Another new variational principle valid for the dynamical waves reflected/refracted at the inter-faces, which has not yet been discovered so far, is also derived.

We describe a geometrical optics approach for the analysis of dielectric tapered waveguides. The method is based on the ray-optical treatment for wave-normal rays defined newly to waves of light in open structures. Geometrical optics fields are represented in terms of two kinds of wave-normal rays: leaky rays and guided rays. Since the behavior of these rays is different in the two regions separated at critical incidence, the geometrical optics fields have certain classes of discontinuity in a transition region between leaky and guided regions. Guided wave solutions are given as a superposition of guided rays that zigzag along the guides, all of which are totally reflected upon the interfaces. By including some leaky rays adjacent to the guided rays, we obtain more accurate guided wave solutions. Calculated results are in excellent agreement with wave optics solutions.

Phase information on wave scattering is not unique and greatly depends on a choice of the origin of coordinates in the measurement system. The present paper argues that the center of scattering for polygonal cylinders should not be a geometrical center of the obstacle such as a center of gravity but be a position that acts as a balance to the electrostatic field effects from edge points. The position is exactly determined in terms of edge positions, edge parameters and lengths of side of polygons. A few examples are given to illustrate a difference from the center of geometry.

It is shown from the Hilberts theory that if the real function Π(θ) has no zeros over the interval [0, 2π], it can be factorized into a product of the factor π+(θ) and its complex conjugate π-(θ)(=). This factorization is tested to decompose a real far-zone field pattern having zeros. To this end, the factorized factors are described in terms of bicomplex mathematics. In our bicomplex mathematics, the temporal imaginary unit "j" is newly defined to distinguish from the spatial imaginary unit i, both of which satisfy i2=-1 and j2=-1.

Since semiconductor memory chip has been growing rapidly in its capacity, memory testing has become a crucial problem in RAMs. This paper proposes a new RAM test algorithm, called generalized marching test (GMT), which detects static and dynamic pattern sensitive faults (PSF) in RAM chips. The memory array with N cells is partitioned into B sets in which every two cells has a cell-distance of at least d. The proposed GMT performs the ordinary marching test in each set and finally detects PSF having cell-distance d. By changing the number of partitions B, the GMT includes the ordinary marching test for B1 and the walking test for BN. This paper demonstrates the practical GMT with B2, capable of detecting PSF, as well as other faults, such as cell stuck-at faults, coupling faults, and decoder faults with a short testing time.

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.

The mathematical theory of bicomplex electromagnetic waves in two-dimensional scattering and diffraction problems is developed. The Vekua's integral expression for the two-dimensional fields valid only in the closed source-free region is generalized into the radiating field. The boundary-value problems for scattering and diffraction are formulated in the bicomplex space. The complex function of a single variable, which obeys the Cauchy-Riemann relations and thus expresses low-frequency aspects of the near field at a wedge of the scatterer, is connected with the radiating field by an integral operator having a suitable kernel. The behaviors of this complex function in the whole space are discussed together with those of the far-zone field or the amplitude of angular spectrum. The Hilbert's factorization scheme is used to find out a linear transformation from the far-zone field to the bicomplex-valued function of a single variable. This transformation is shown to be unique. The new integral expression for the field scattered by a thin metallic strip is also obtained.

A numerical scheme for the analytic continuation of radiation patterns of the azimuthal coordinate θ into the whole space over the complex plane is given. The scattering data given over the real space [0, 2π] are extended into the complex plane by using the recurrence formulas. An example shows the validity of mathematically exact evaluation for the scattering from polygonal cylinders.

A bicomplex representation for time-harmonic electromagnetic fields appearing in scattering and diffraction problems is given using two imaginary units i and j. Fieldsolution integral-expressions obtained in the high-frequency and low-frequency limits are shown to provide the new relation between high-frequency diffraction and low-frequency scattering. Simple examples for direct scattering problems are illustrated. It may also be possible to characterize electric or magnetic currents induced on the obstacle in terms of geometrical optics far-fields. This paper outlines some algebraic rules of bicomplex mathematics for diffraction or scattering fields and describes mathematical evidence of the solutions. Major discussions on the relationship between high-frequency and low-frequency fields are relegated to the companion paper which will be published in another journal.

A method of calculating geometrical optics fields in dielectric tapered waveguides excited at the input ends by a monochromatic Gaussian beam light is presented. It is shown that field distributions expected at the output ends of waveguides can be determined without calculating fields at intermediate steps of propagation between the input and output ends. Examples of multimode propagation and monomode propagation in a linearly tapered waveguide are given.

Scattering of the two dimensional electromagnetic waves is studied by the infinite sequences of zeros arising on the complex plane, which just correspond to the null points of the far field pattern given as a function of the azimuthal angle θ. The convergent sequences of zeros around the point of infinity are evaluated when the scattering objects are assumed to be N-polygonal cylinders. Every edge condition can be satisfied if the locations of zeros are determined appropriately. The parameters, which allow us to calculate the exact positions of zeros, are given by the asymptotic analysis. It is also shown that there are N-directions of convergence, which tend to infinity. An illustrative example is presented.