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.

This paper deals with reflection and transmission of a TE plane wave from a one-dimensional random slab with slanted fluctuation by means of the stochastic functional approach. By starting with a generalized representation of the random wavefield from a two-dimensional random slab, and by using a manner for slanted anisotropic fluctuation, the corresponding random wavefield representation and its statistical quantities for one-dimensional cases are newly derived. The first-order incoherent scattering cross section is numerically calculated and illustrated in figures.

This paper deals with the scattering of transverse magnetic (TM) plane wave by a perfectly conductive surface made up of a periodic array of finite number of rectangular grooves. By the modal expansion method, the total scattering cross section pc is numerically calculated for several different numbers of grooves. It is then found that, when the groove depth is less than wavelenght, the total scattering cross section pc increases linearly proportional to the corrugation width W. But an exception takes place at a low grazing angle of incidence, where pc is proportional to Wα and the exponent α is less than 1. From these facts, it is concluded that the total scattering cross section pc must diverge but pc/W the total scattering cross section per unit surface must vanish at a low grazing limit when the number of grooves goes to infinity.

This paper deals with an integral method analyzing the diffraction of a transverse electric (TE) wave by a perfectly conductive periodic surface. The conventional integral method fails to work for a critical angle of incidence. To overcome such a drawback, this paper applies the method of image Green's function. We newly obtain an image integral equation for the basic surface current in the TE case. The integral equation is solved numerically for a very rough sinusoidal surface. Then, it is found that a reliable solution can be obtained for any real angle of incidence including a critical angle.

This paper deals with the diffraction of a transverse magnetic (TM) plane wave by a perfectly conductive periodic surface by an integral method. However, it is known that a conventional integral method does not work for a critical angle of incidence, because of divergence of a periodic Green's function (integral kernel). To overcome such a divergence difficulty, we introduce an image Green's function which is physically defined as a field radiated from an infinite phased array of dipoles. By use of the image Green's function, it is newly shown that the diffracted field is represented as a sum of radiation from the periodic surface and its image surface. Then, this paper obtains a new image integral equation for the basic surface current, which is solved numerically. A numerical result is illustrated for a very rough sinusoidal surface. Then, it is concluded that the method of image Green's function works practically even at a critical angle of incidence.

As a new idea for analyzing the wave scattering and diffraction from a finite periodic surface, this paper proposes the periodic Fourier transform. By the periodic Fourier transform, the scattered wave is transformed into a periodic function which is further expanded into Fourier series. In terms of the inverse transformation, the scattered wave is shown to have an extended Floquet form, which is a 'Fourier series' with 'Fourier coefficients' given by band-limited Fourier integrals of amplitude functions. In case of the TE plane wave incident, an integral equation for the amplitude functions is obtained from the the boundary condition on the finite periodic surface. When the surface corrugation is small, in amplitude, compared with the wavelength, the integral equation is approximately solved by iteration to obtain the scattering cross section. Several properties and examples of the periodic Fourier transform are summarized in Appendix.

By use of the shadow theory developed recently, this paper deals with the transverse electric (TE) wave diffraction by a perfectly conductive periodic array of rectangular grooves. A set of equations for scattering factors and mode factors are derived and solved numerically. In terms of the scattering factors, diffraction amplitudes and diffraction efficiencies are calculated and shown in figures. It is demonstrated that diffraction efficiencies become discontinuous at an incident wave number where the incident wave is switched from a propagating wave to an evanescent one, whereas scattering factors and diffraction amplitudes are continuous even at such an incident wave number.

This paper describes an open question in a mathematical formulation of the guided complex wave supported by a slightly random surface. In case of the TM wave propagating over a randomly reactive plane surface, a formal wave solution is obtained and is shown to have an equivalent network representation. It is pointed out, however, that such a formal solution has no physical significance, because the effective surface impedance in the transverse resonance condition determining the complex propagation constant is not an analytic function on the complex wavenumber plane and because the formal solution gives a diverging variance of the guided complex wave. It is concluded that it is still an open problem to have a correct mathematical formulation for the guided wave over a random surface. Finally suggestions are given for obtaining a correct mathematical formulation.

A new broadband buffer circuit technique and its analytical design method are proposed for a high-speed decision circuit featuring both a higher input sensitivity and a larger phase margin. The buffer circuit characteristics are significantly improved by employing a series peaking source follower (SPSF), where a peaking inductor is inserted between the first and second source follower stages. Optimization of the peaking inductance successfully enhances the 3-dB bandwidth of the data-input buffer and the clock buffer by 7 GHz for both, over conventional double-stage source follower SCFL buffers. The proposed circuit technique and design method are applied to a 10-Gbit/s decision circuit by the use of production-level 0. 5 µm GaAs MESFETs. The fabricated decision circuit achieves a data input sensitivity of 43 mVp-p and a phase margin of 240 both at 10-Gbit/s: a 230 mVp-p smaller input sensitivity and a 35 larger phase margin than those of conventional non-peaking inductor types.

As a new method to generate a homogeneous, random, binary image with a rational power spectrum, this paper proposes a discrete-valued auto-regressive equation, of which random coefficients and white noise excitation are all discrete-valued. The average and spectrum of the binary image are explicitly obtained in terms of the random coefficients. Some computer results are illustrated in figures.

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.

This paper deals with an orthogonal functional expansion of a non-linear stochastic functional of a stationary binary sequence taking 1 with unequal probability. Several mathematical formulas, such as multivariate orthogonal polynomials, recurrence formula and generating function, are given in explicit form. A formula of an orthogonal functional expansion for a stochastic functional is presented; the completeness of expansion is discussed in Appendix.

A new formula on the Hermite expansion is presented in an explicit form. An application of the formula is given to a random boundary value problem: a plane wave reflection from a flat plane, of which position is randomly distributed in the normal direction, is presented. Several numerical results are given for a verification of the formula and for a discussion of the exact behavior of the fluctuation part of the reflection power.

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.

This paper gives a systematic approach to generate a Markov chain by a discrete-valued auto-regressive equation, which is a a nonlinear auto-regressive equation having a discrete-valued solution. The power spectrum, the correlation function and the transition probability are explicitly obtained in terms of the discrete-valued auto-regressive equation. Some computer results are illustrated in figures.

The generation and design of a stationary Markov signal are discussed as an inverse problem, in which one looks for a transition probability when a stationary probability distribution is given. This paper presents a new solution to the inverse problem, which makes it possible to design and generate a Markov random signal with arbitrary probability distribution and an exponential correlation function. Several computer results are illustrated in figures.

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.

Reverse-recovery modeling for p-i-n diodes in the high current-density conditions are discussed. With the dynamic carrier-distribution-based modeling approach, the reverse recovery behaviors are explained in the high current-density conditions, where the nonquasi-static (NQS) behavior of carriers in the drift region is considered. In addition, a specific feature under the high current-density condition is discussed. The proposed model is implemented into a commercial circuit simulator in the Verilog-A language and its reverse recovery modeling ability is verified with a two-dimensional (2D) device simulator, in comparison to the conventional lumped-charge modeling technique.

This paper deals with the scattering of a TM plane wave from a perfectly conductive sinusoidal surface with finite extent. For comparison, however, we briefly discuss the diffraction by the sinusoidal surface with infinite extent, where we use the concept of the total diffraction cross section per unit surface introduced previously. To solve a case where the sinusoidal corrugation width is much wider than wave length, we propose an undersampling approximation as a new numerical technique. For a small rough case, the total scattering cross section is calculated against the angle of incidence for several different corrugation widths. Then we find remarkable results, which are roughly summarized as follows. When the angle of incidence is apparently different from critical angles and diffraction beams are all scattered into non-grazing directions, the total scattering cross section increases proportional to the corrugation width and hence the total scattering cross section per unit surface (the ratio of the total scattering cross section to the corrugation width) becomes almost constant, which is nearly equal to the total diffraction cross section per unit surface in case of the sinusoidal surface with infinite extent. When the angle of incidence is critical and one of the diffraction beams is scattered into a grazing direction, the total scattering cross section per unit surface strongly depends on the corrugation width and approximately approaches to the total diffraction cross section per unit surface as the corrugation width gets wide.

This paper deals with a TE plane wave reflection and transmission from a one-dimensional random slab by means of the stochastic functional approach. The relative permittivity of the random slab is written by a Gaussian random field in the vertical direction with finite thickness, and is uniform in the horizontal direction with infinite extent. An explicit form of the random wavefield is obtained in terms of a Wiener-Hermite expansion with approximate expansion coefficients (Wiener kernels) under a small fluctuation case. By using the first three terms of the random wavefield representation, the optical theorem is illustrated in figures for several physical parameters. It is then found that the optical theorem holds with good accuracy.