Analytical expression of transmission for the orbital angular momentum (OAM) communication using loop antenna arrays and paraboloids is derived to achieve a communication distance of 100 m. With the field distribution of the single “transformed OAM mode” radiated by a loop antenna, the collimated field by the transmitting paraboloid and its diffracted field are analytically derived. Effects of frequencies, sizes of paraboloids, and shifts of transmitting and receiving arrays from the focal planes are included. With the diffracted field distribution on the focal plane of the receiving paraboloid, transmission between the transmitting and receiving loop antennas is analytically estimated. It is shown that the transmission between the antennas with different OAM modes is null, but the transmission between the antennas with the same mode can be reduced. To clarify the mechanism of the reduction, factors of the reduction are quantitatively defined, and the explicit formulae are derived. Based on the analytical results, numerical estimation for a communication distance of 100 m is demonstrated, where the frequency, the focal length, and the size of the paraboloid are 150 GHz, 50 cm and 100 cm, respectively. Where both arrays are located on each focal plane, the transmission for the signal is more than -7.78 dB for eight kinds of OAM modes. The transmission is the least for the highest-order mode. The transmission loss is shown to be mitigated by optimizing the shifts of transmitting and receiving arrays from their focal planes. The loss is made almost even by exploiting the tradeoff of the improvement for the mode orders. The transmission is improved by 5.98 dB, to be more than -1.80 dB, by optimizing the shifts of the arrays.

In this study, the edge diffraction of a TM-polarized electromagnetic plane wave by two-dimensional dielectric wedges has been analyzed. An asymptotic solution for the radiation field has been derived from equivalent electric and magnetic currents which can be determined by the geometrical optics (GO) rays. This method may be regarded as an extended version of physical optics (PO). The diffracted field has been represented in terms of cotangent functions whose singularity behaviors are closely related to GO shadow boundaries. Numerical calculations are performed to compare the results with those by other reference solutions, such as the hidden rays of diffraction (HRD) and a numerical finite-difference time-domain (FDTD) simulation. Comparisons of the diffraction effect among these results have been made to propose additional lateral waves in the denser media.

This paper details the design of a plate that controls the beam direction in an aperture array excited by a waveguide 2-plane hybrid coupler. The beam direction can be controlled in the range of ±15-32deg. in the quasi H-plane, and ±26-54deg. in the quasi E-plane at the design frequency of 66.425GHz. Inductive irises are introduced into tapered waveguides in the plate and the reflection is suppressed by narrow apertures. A plate that has a larger tilt angle in the quasi E-plane and another plate with conventional rectangular waveguide ports as a reference are fabricated and measured. The measured values agree well with the simulation results.

In this study, edge diffraction of an electromagnetic plane wave by two-dimensional conducting wedges has been analyzed by the physical optics (PO) method for both E and H polarizations. Non-uniform and uniform asymptotic solutions of diffracted fields have been derived. A unified edge diffraction coefficient has also been derived with four cotangent functions from the conventional angle-dependent coefficients. Numerical calculations have been made to compare the results with those by other methods, such as the exact solution and the uniform geometrical theory of diffraction (UTD). A good agreement has been observed to confirm the validity of our method.

In this study, the electromagnetic scatterings from conducting bodies have been investigated via a surface equivalence theorem. When one formulates equivalent electric and magnetic currents from geometrical optics (GO) reflected field in the illuminated surface and GO incident field in the shadowed surface, it has been found that the asymptotically derived radiation fields are found to be the same as those formulated from physical optics (PO) approximation.

This paper newly proposes a fast computation technique on the method of image Green's function for p-characteristic calculations, when a plane wave with the transverse wavenumber p is incident on a periodic rough surface having perfect conductivity. In the computation of p-characteristics, based on a spectral domain periodicity of the periodic image Green's function, the image integral equation for a given incidence p maintains the same form for other particular incidences except for the excitation term. By means of a quadrature method, such image integral equations lead to matrix equations. Once the first given matrix equation is performed by a solution procedure as calculations of its matrix elements and its inverse matrix, the other matrix equations for other particular incidences no longer need such a solution procedure. Thus, the total CPU time for the computation of p-characteristics is largely reduced in complex shaped surface cases, huge roughness cases or large period cases.

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.

We have proposed the novel optical model for layer structure film to precisely control light diffusion angle range. By introducing structure characteristics to the phase grating model, we successfully constructed the novel optical model. In addition, we clarified that difference of refractive indices of layer structure and layer width are important factors for precisely control of light diffusion angle range.

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.

This paper deals with the diffraction of a monochromatic plane wave by a periodic grating. We discuss a problem how to obtain a numerical diffraction efficiency (NDE) satisfying the reciprocity theorem for diffraction efficiencies, because diffraction efficiencies are the subject of the diffraction theories. First, this paper introduces a new formula that decomposes an NDE into two components: the even component and the odd one. The former satisfies the reciprocity theorem for diffraction efficiencies, but the latter does not. Therefore, the even component of an NDE becomes an answer to our problem. On the other hand, the odd component of an NDE represents an unwanted error. Using such the decomposition formula, we then obtain another new formula that decomposes the conventional energy error into two components. One is the energy error made by even components of NDE's. The other is the energy error constructed by unwanted odd ones and it may be used as a reciprocity criterion of a numerical solution. This decomposition formula shows a drawback of the conventional energy balance. The total energy error is newly introduced as a more strict condition for a desirable solution. We point out theoretically that the reciprocal wave solution, an approximate solution satisfying the reciprocity for wave fields, gives another solution to our problem. Numerical examples are given for the diffraction of a TM plane wave by a very rough periodic surface with perfect conductivity. In the case of a numerical solution by the image integral equation of the second kind, we found that the energy error is much reduced by use of the even component of an NDE as an approximate diffraction efficiency or by use of a reciprocal wave solution.

A numerical investigation revealed the relation between the groove randomness of actual-size diffraction gratings and the diffraction efficiencies. The diffraction gratings we treat in this study have around 10000 grooves. When the illumination wavelength is 600 nm, the entire grating size becomes 16.2 mm. The simulation was performed using the difference-field boundary element method (DFBEM). The DFBEM treats the vectorial field with a small amount of memory resources as independent of the grating size. We firstly describe the applicability of DFBEM to a considerably large-sized structure; regularly aligned grooves and a random shallow-groove structure are calculated by DFBEM and compared with the results given by standard BEM and scalar-wave approximation, respectively. Finally we show the relation between the degree of randomness and the diffraction efficiencies for two orthogonal linear polarizations. The relation provides information for determining the tolerance of fabrication errors in the groove structure and measuring the structural randomness by acquiring the irradiance of the diffracted waves.

This paper proposes a novel image integral equation of the first type (IIE-1) for a TE plane wave scattering from periodic rough surfaces with perfect conductivity by means of the method of image Green's function. Since such an IIE-1 is valid for any incident wavenumbers including the critical wavenumbers, the analytical properties of the scattered wavefield can be generally and rigorously discussed. This paper firstly points out that the branch point singularity of the bare propagator inevitably appears on the incident wavenumber characteristics of the scattered wavefield and its related quantities just at the critical wavenumbers. By applying a quadrature method, the IIE-1 becomes a matrix equation to be numerically solved. For a periodic rough surface, several properties of the scattering are shown in figures as functions of the incident wavenumbers. It is then confirmed that the branch point singularity clearly appears in the numerical solution. Moreover, it is shown that the proposed IIE-1 gives a numerical solution satisfying sufficiently the optical theorem even for the critical wavenumbers.

We propose an algorithm for the scattering analyses of gratings with various local defects based on the difference-field boundary-element method (DFBEM). In the algorithm, the defect in the grating is partitioned, and the DFBEM is sequentially applied for each defect section. We validate the proposed algorithm by demonstrating its flexibility for various defect topologies for a locally deformed grating.

In the scattering problem of dielectric gratings in conical mounting, we have considered and formulated scattering fields using transverse electric (TE) and transverse magnetic (TM) waves. This paper formulates scattering fields by superpositions of right-circularly (RC) and left-circularly (LC) polarized waves through the matrix eigenvalue method.

Thickness of crystalline layer induced by annealing after rubbing at surface of polyimide film for liquid crystal displays was estimated to be 3--5 nm by grazing-incidence X-ray diffractions with multi incident angles. Agreement of thickness of crystalline layer with that of initially oriented layer suggests polymer orientation induced by rubbing proceeds crystallization by annealing. Furthermore, no in-plane smectic ordering in bottom 20,nm region of polyimide film was suggested.

In the theory of periodic gratings, there is no method to make up a numerical solution that satisfies the reciprocity so far. On the basis of the shadow theory, however, this paper proposes a new method to obtain a numerical solution that satisfies the reciprocity. The shadow thoery states that, by the reciprocity, the $m$th order scattering factor is an even function with respect to a symmetrical axis depending on the order $m$ of diffraction. However, a scattering factor obtained numerically becomes an even function only approximately, but not accurately. It can be decomposed to even and odd components, where an odd component represents an error with respect to the reciprocity and can be removed by the average filter. Using even components, a numerical solution that satisfies the reciprocity is obtained. Numerical examples are given for the diffraction of a transverse magnetic (TM) plane wave by a very rough periodic surface with perfect conductivity. It is then found that, by use of the average filter, the energy error is much reduced in some case.

This paper is concerned with a method to reduce the computation time of the Discrete Ray Tracing Method (DRTM) which was proposed to numerically analyze electromagnetic fields above Random Rough Surfaces (RRSs). The essence of DRTM is firstly to search rays between source and receiver and secondly to compute electric fields based on the traced rays. In the DRTM, the method discretizes not only RRSs but also ray tracing procedure. In order to reduce computation time for ray searching, the authors propose to modify the conventional algorithm discretizing RRSs with equal intervals to a new one which discretizes them with unequal intervals according to their profiles. The authors also use an approximation of Fresnel function which enables us to reduce field computation time. The authors discuss the reduction rate for computation time of the DRTM from the numerical view points of ray searching and field computation. Finally, this paper shows how much computation time is reduced by the new method.

This paper deals with an integral equation method for analyzing the diffraction of a transverse magnetic (TM) plane wave by a perfectly conductive periodic surface. In the region below the periodic surface, the extinction theorem holds, and the total field vanishes if the field solution is determined exactly. For an approximate solution, the extinction theorem does not hold but an extinction error field appears. By use of an image Green's function, new formulae are given for the extinction error field and the mean square extinction error (MSEE), which may be useful as a validity criterion. Numerical examples are given to demonstrate that the formulae work practically even at a critical angle of incidence.

Current distributions induced on a circular disk of conductor are analyzed rigorously for an electric dipole incidence, when the source dipole is polarized parallel to the disk and located at an arbitrary position, and they are evaluated numerically. As the height of the dipole increases, the current distribution of the dipole approaches that of the plane wave incidence. Using a multiple precision arithmetic, numerical data for the current distribution are obtained for larger radii of a disk than the former approach.

In the theory of diffraction gratings, the conventional integral method is considered as a powerful tool of numerical analysis. But it fails to work at a critical angle of incidence, because a periodic Green's function (integral kernel) diverges. This problem was resolved by the image integral equation in a previous paper. Newly introducing the reflection extinction theorem, this paper derives the image extinction theorem and the image integral equation. Then, it is concluded that the image integral equation is made up of two physical processes: the image surface radiates a reflected plane wave, whereas the periodic surface radiates the diffracted wave.