This paper deals with a new formulation for the diffraction of a plane wave by a periodic grating. As a simple example, the diffraction of a transverse magnetic wave by a perfectly conductive periodic array of rectangular grooves is discussed. On the basis of a shadow hypothesis such that no diffraction takes place and only the reflection occurs with the reflection coefficient -1 at a low grazing limit of incident angle, this paper proposes the scattering factor as a new concept. In terms of the scattering factor, several new formulas on the diffraction amplitude, the diffraction efficiency and the optical theorem are obtained. It is newly found that the scattering factor is an even function due to the reciprocity. The diffraction efficiency is defined for a propagating incident wave as well as an evanescent incident wave. Then, it is theoretically found that the 0th order diffraction efficiency becomes unity and any other order diffraction efficiencies vanish when a real angle of incidence becomes low grazing. Numerical examples of the scattering factor and diffraction efficiency are illustrated in figures.

We report effects of washing rubbed polyimide film on the near surface. Especially we focused dependence of solvent. Rubbed polyimide films have been used as liquid crystal alignment films in Liquid crystal displays (LCDs), and in actual LCD panel fabrication washing on film surfaces after rubbing is essential process to remove dust and pollution. We investigated the effects of washing by grazing incidence X-ray diffraction (GIXD) measurements. In GIXD, the X-ray penetration into the polymer was changed from 8 nm (suface sensitive) to 4 nm (bulk sensitive) by variation of the X-ray incidence angle. It was found that crystallization near the surface induced by soaking was considerably dependent on solvent. However, in-plane distribution of the surface polymer chains of polyimide film was not found to be dependent on the solvents.

Rubbed polyimide films have been widely used as liquid crystal alignment films for liquid crystal displays. Washing after rubbing is essential to fabricate liquid crystal displays, and should affect alignment of liquid crystal as well as rubbing. We investigated the effects of rubbing condition and soaking in acetone on polyimide films by grazing incidence X-ray diffraction. It was found that soaking in acetone promoted crystallization of surface aligned polymers, and that the crystallization by acetone was dependent on the initial polymer alignment. The larger initial crystalline phase was, the more newly crystallization occurred by soaking. It was also revealed that the crystallization by soaking in acetone was completed within 1 min.

A transverse magnetic (TM) plane wave is diffracted by a periodic surface into discrete directions. However, only the reflection and no diffraction take place when the angle of incidence becomes a low grazing limit. On the other hand, the scattering occurs even at such a limit, if the periodic surface is finite in extent. To solve such contradiction, this paper deals with the scattering from a perfectly conductive sinusoidal surface with finite extent. By the undersampling approximation introduced previously, the total scattering cross section is numerically calculated against the angle of incidence for several corrugation widths up to more than 104 times of wavelength. It is then found that the total scattering cross section is linearly proportional to the corrugation width in general. But an exception takes place at a low grazing limit of incidence, where the total scattering cross section increases almost proportional to the square root of the corrugation width. This suggests that, when the corrugation width goes to infinity, the total scattering cross section diverges and the total scattering cross section per unit surface vanishes at a low grazing limit of incidence. Then, it is concluded that, at a low grazing limit of incidence, no diffraction takes place by a periodic surface with infinite extent and the scattering occurs from a periodic surface with finite extent.

We have derived the novel extended UTD (Uniform Geometrical Theory of Diffraction) solution and the novel modified UTD solution for the back scattering of an incident whispering gallery (WG) mode on the edge of a cylindrically curved conducting sheet. By comparing with the reference solution obtained from the integral representation of the scattered field by integrating numerically along the integration path, we have confirmed the validity and the utility of the novel asymptotic solutions proposed in the present study. It is shown that the extended UTD solution can be connected smoothly to the modified UTD solution on the geometrical boundary separating the edge-diffracted ray and the surface-diffracted ray.

Rubbed polyimide films have been widely used as liquid crystal alignment films for liquid crystal displays (LCDs). We investigated the effect of rubbing on the surface molecules of polyimide films by using grazing incidence X-ray diffraction (GIXD) and reflection ellipsometry. We found that rubbing not only caused the polymer chains to align in the direction of rubbing but also to elongate near the film surface. However, the in-plane distribution of surface polymer chains of polyimide film was not found to be dependent on the rubbing conditions.

This paper deals with the singular behavior of the diffraction of transverse magnetic (TM) waves by a perfectly conductive triangular periodic surface at a low grazing limit of incidence. The wave field above the highest excursion of the surface is represented as a sum of Floquet modes with modified diffraction amplitudes, whereas the wave field inside a triangular groove is written as a sum of guided modes with unknown mode amplitudes. Then, two sets of equations are derived for such amplitudes. From the equation sets, all the amplitudes are analytically shown to vanish at a low grazing limit of incidence. From this fact, it is concluded analytically that no diffraction takes place and only reflection occurs at a low grazing limit of incidence for any period length and any triangle height. This theoretical result is verified by a numerical example.

When a cylindrically curved concave conducting surface is terminated abruptly at the edge, the whispering gallery (WG) mode propagating toward the edge direction is radiated into the free space from the aperture plane at the edge. In this paper, by applying the new analysis method, we shall derive a uniform geometrical theory of diffraction solution (UTD) for the electric-type WG mode radiation field applicable in the transition region near the geometrical boundaries produced by the incident modal ray on the edge of the curved surface. The UTD is represented by the summation of the solution for the geometrical ray converted from the modal ray of the WG mode and the solution for the uniform edge diffracted ray scattered at the cylindrically curved edge. By comparing with the reference solution obtained numerically from the integral representation of the radiation field, we will confirm the validity and the utility of the UTD proposed in this paper.

The diffraction of a transverse magnetic (TM) plane wave by a perfectly conductive surface made up of a periodic array of rectangular grooves is studied by the modal expansion method. It is found theoretically that the reflection coefficient approaches -1 but no diffraction takes place when the angle of incidence reaches a low grazing limit. Such singular behavior is shown analytically to hold for any finite values of the period, groove depth and groove width and is then demonstrated by numerical examples.

This paper deals with the diffraction of TM plane wave by a perfectly conductive periodic surface. Applying the Rayleigh hypothesis, a linear equation system determining the diffraction amplitudes is derived. The linear equation is formally solved by Cramer's formula. It is then found that, when the angle of incidence becomes a low grazing limit, the amplitude of the specular reflection becomes -1 and any other diffraction amplitudes vanish for any perfectly conductive periodic surfaces with small roughness and gentle slope.

In this paper, the previously introduced periodic Fourier transform concept is extended to a two-dimensional case. The relations between the periodic Fourier transform, harmonic series representation and Fourier integral representation are also discussed. As a simple application of the periodic Fourier transform, the scattering of a scalar wave from a finite periodic surface with weight is studied. It is shown that the scattered wave may have an extended Floquet form, which is physically considered as the sum of diffraction beams. By the small perturbation method, the first order solution is given explicitly and the scattering cross section is calculated.

In the road-to-vehicle communication (RVC) on intelligent transport systems (ITS), the frequent occurrence of shadowing caused by other vehicles deteriorates wireless transmission quality because of a small sized zone. However, a diffraction wave generated at the edge of vehicle can be utilized in applying adaptive modulation method with decreased modulation level. Therefore, it can be expected to keep communication only with a diffraction wave under shadowing. Hence this paper proposes an application of adaptive modulation for RVC system. This paper first reveals its improved effect in shadowing duration by computer simulation considering practical traffic flow, radio reflection and diffraction, and then shows that applying adaptive modulation can increase throughput performance largely.

This paper is concerned with the application of ray tracing method (RTM) to field analysis in bended and branched tunnels. On the line of sight, direct wave from a source and reflected waves at the tunnel walls are dominant compared with diffracted waves, but off the line of sight, diffraction can not be ignored especially beyond an abrupt bending. As a result, a detailed attention should be focused on the RTM analysis when dealing with propagation in the region off the line of sight. In this paper, we take into account of the diffraction rays which are originally reflection rays, next diffracted at a bending edge, and again converted to reflection rays. It is shown that numerical results are in good agreement with the experimental data.

High frequency (HF) diffraction is known as local phenomena, and only parts of the scatterer contribute to the field such as the edge, corner and specular reflection point etc. Many HF diffraction techniques such as Geometrical Theory of Diffraction (GTD), Uniform Theory of Diffraction (UTD) and Physical Theory of Diffraction (PTD) utilize these assumptions explicitly. Physical Optics (PO), on the other hand, expresses the diffraction in terms of radiation integral or the sum total of contributions from all the illuminated parts of scatterers, while the PO currents are locally defined at the point of integration. This paper presents PO-based visualization of the scattering and diffraction phenomena and tries to provide the intuitive understanding of local property of HF diffraction as well as the relations between PO and the ray techniques such as GTD, UTD etc. A weighting named "eye function" is introduced in PO radiation integrals to take into account of local cancellation between rapidly oscillating contributions from adjacent currents; this extracts important areas of current distribution, whose location moves not only with the source but also with the observation point. PO visualization illustrates both local property of HF scattering and defects associated with ray techniques. Furthermore, careful examination of visualized image reminds us of the error factor in PO as applied for curved surfaces, named fictitious penetrating rays. They have been scarcely recognized if not for visualization, though they disturb the geometrical shadow behind the opaque scatterer and can be the leading error factors of PO in shadow regions. Finally, visualization is extended to slot antennas with finite ground planes by hybrid use of modified edge representation (MER) to assess the significance of edge diffraction.

This study examines a slitted parallel plate waveguide (PPW) from the perspective of diffraction and equivalent circuit representation for a narrow slit and radiation, including the surface wave effect, from a wide slit. The fundamental differences between the diffraction and equivalent admittance properties of the slit discontinuities in typical microstrip and waveguide structures are considered by comparing how the waveguide heights of the PPW and dielectric constants filling the inside of the PPW correspond to those of the two structures, respectively.

A TlGaAs/GaAs multiple quantum-well (MQW) structure having four identical well layers was grown on a GaAs (001) substrate by low-temperature molecular-beam epitaxy (MBE) at 190. The (004) X-ray diffraction (XRD) curve of this sample showed satellite peaks up to the 3rd order at least. The measured XRD curve agreed well with the theoretically simulated one with a Tl content of x=7% and a width of 57 for the TlxGa1-xAs well layers. This result indicates that the grown MQW structure has good single-crystalline quality as well as flat and sharp interfaces.

This paper deals with the wave scattering from a periodic surface with finite extent. Modifying a spectral formalism, we find that the spectral amplitude of the scattered wave can be determined by the surface field on only the corrugated part of the surface. The surface field on such a corrugated part is then expanded into Fourier series with unknown Fourier coefficients. A matrix equation for the Fourier coefficients is obtained and is solved numerically for a sinusoidally corrugated surface. Then, the angular distribution of the scattering, the relative power of each diffraction beam and the optical theorem are calculated and illustrated in figures. Also, the relative powers of diffraction are calculated against the angle of incidence for a periodic surface with infinite extent. By comparing a finite periodic case with an infinite periodic case, it is pointed out that relative powers of diffraction beam are much similar in these of diffraction for the infinite periodic case.

This paper deals with a mathematical formulation of the scattering from a periodic surface with finite extent. In a previous paper the scattered wave was shown to be represented by an extended Floquet form by use of the periodic nature of the surface. This paper gives a new interpretation of the extended Floquet form, which is understood as a sum of diffraction beams with diffraction orders. Then, the power flow of each diffraction beam and the relative power of diffraction are introduced. Next, on the basis of a physical assumption such that the wave scattering takes place only from the corrugated part of the surface, the amplitude functions are represented by the sampling theorem with unknown sample sequence. From the Dirichlet boundary condition, an equation for the sample sequence is derived and solved numerically to calculate the scattering cross section and optical theorem. Discussions are given on a hypothesis such that the relative power of diffracted beam becomes almost independent of the width of surface corrugation.

A periodic approach introduced previously is applied to the TM wave scattering from a finite periodic surface. A mathematical relation is proposed to estimate the scattering amplitude from the diffraction amplitude for the periodic surface, where the periodic surface is defined as a superposition of surface profiles generated by displacing the finite periodic surface by every integer multiple of the period . From numerical examples, it is concluded that the scattering cross section for the finite periodic surface can be well estimated from the diffraction amplitude for a sufficiently large .

The present paper describes the finite difference time domain (FDTD) analysis of the light-beam diffraction from two- and three-dimensional (2-D and 3-D) magneto-optical (MO) disk structures. First, we show that the proposed new FDTD formulation is valid for MO disk medium and can avoid the divergence of fields encountered during the conventional FDTD calculations. Second, as the application of the present method to more complicated models, the main- and cross-polarized diffracted fields are numerically calculated for 2-D and 3-D four-layered MO disk models. The phase differences between two kinds of polarized components are shown. The results obtained here indicate that the proposed FDTD formulation can be applied to more complicated MO disk structures.