Junichi Nakayama

Synthesis of Hadamard transformers by use of multimode interference optical waveguides

We propose a synthesis method of optical Hadamard transformer using multimode interference (MMI) couplers. By using the signal transfer matrix of 2 x 2, 4 x 4, and 8 x 8 MMI couplers, we show that sum and difference units of input signals can be synthesized. An interchange unit of two signals can also be synthesized. One synthesis method of Hadamard transformers is a combination of only 2 x 2 units, and the other is a combination of N x N(N > or = 4) units as well as 2 x 2 units. The design examples of operation units are shown, and the size and the output power of Hadamard transformers are estimated.

Optical fiber fault locator by the step frequency method.

A step frequency method (SFM) is proposed as a new scheme for an optical fiber fault locator. The principle of operation and significant features of the method are described. The feasibility was demonstrated by detecting the discontinuities in a 10-km long multimode fiber using the 830-nm wavelength. The results demonstrate the feasibility of using the SFM in practical fiber optical networks.

Theory of light scattering from a random metal surface: Excitation of surface plasmons in a Ag film

The scattering of light by a silver film with a random rough surface and the excitation of surface plasmon modes at the metal surface are theoretically studied in detail by means of the new stochastic treatment. The silver film is assumed sandwiched between the air and a crystal and a plane wave is incident through the crystal to excite the surface‐plasmon mode. The stochastic formulation is developed for the stated problem and approximate solutions are obtained for the coherent and incoherent scattered waves involving the optical theorem. Details of the scattering characteristics are numerically calculated for various combinations of film thickness, surface roughness, and correlation length. The angular pattern of incoherent scattering into the crystal is shown to have two sharp resonant peaks due to the excitation of the surface plasmon, which are directly observable by an experiment.

Mass operator for wave scattering from a slightly random surface

Abstract This paper deals with the mass operator representing multiple-scattering effects in the theory of wave scattering from a slightly random surface. By means of the stochastic-functional approach, a recurrence equation for the mass operator is obtained in the form of an iterative integral. However, its solution oscillates in a non-physical manner against the number of iterations. Next, the recurrence equation may be regarded as a nonlinear integral equation, when the number of iterations goes to infinity. An analytical solution of the nonlinear integral equation is presented for a special case in which the roughness spectrum is the Dirac delta function. Then, the nonlinear integral equation is solved numerically for the Gaussian roughness spectrum by iteration, starting from such an analytical solution. It is shown that only a few iterations are required to obtain the mass operator, even when the correlation distance is small. Effects of the mass operators on the coherent reflection coefficient and ...

Diffraction Amplitudes from Periodic Neumann Surface: Low Grazing Limit of Incidence (II)

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.

Wave scattering from a periodic random surface generated by a stationary binary sequence

Abstract This paper studies the scattering of a TE plane wave from a periodic random surface generated by a stochastic binary sequence using a stochastic functional method. The scattered wave is first expressed as a product of an exponential phase factor and a periodic stationary process. The periodic stationary process is then expressed by a harmonic series representation, that is a ‘Fourier series’ with ‘Fourier coefficients’ given by mutually correlated stationary processes. These stationary processes are regarded as stochastic functionals of the binary sequence and they are represented by orthogonal binary functional expansions with band-limited binary kernels. The binary kernels are determined up to the second order from the boundary condition. Then, several statistical properties of the scattering are calculated numerically and illustrated in figures. It is found that, in the binary case, the second-order scattering cross section has a subtractive term and becomes much smaller than the first-order one.

SCATTERING OF A TM PLANE WAVE FROM PERIODIC RANDOM SURFACES

Abstract This paper deals with the scattering of a TM plane wave from conductive periodic random surfaces. By means of the stochastic functional approach, the scattered field is expressed in terms of a harmonic series representation, in which the coefficients are homogeneous random functions and are given by Wiener–Hermite expansions. An approximate solution for the Wiener kernels is obtained up to the second order. Several anomalies appear in the angular distribution of the incoherent scattering because of combinations of scattering due to surface randomness and diffraction due to surface periodicity. These are incoherent Woods anomalies associated with guided surface waves propagating along the surface, enhanced backscattering and diffracted backscattering enhancement. The physical reasons for these anomalies and numerical results are discussed.

Enhanced scattering from a thin film with one-dimensional disorder

This paper deals with a TE plane wave scattering from a thin film with one-dimensional disorder by means of the stochastic functional approach. The thin film is one-dimensionally inhomogeneous in the horizontal direction with infinite extent, and is homogeneous in the vertical direction with finite thickness. Based on an approximate wavefield representation in terms of a Wiener–Hermite expansion in a preceding paper (Tamura et al., 2004, Waves in Random Media, 14, 435–465), the first- and second-order incoherent scattering cross-sections are presented in explicit forms and scattering properties are discussed. The scattering properties vary entirely with the film thickness. In a case where the thickness is smaller than a few wavelengths in the thin film, enhanced scattering and associated enhanced scattering may appear as sharp peaks or dips on the second-order incoherent scattering distribution if the thin film has guided wave modes. When the thickness becomes sufficiently larger than the wavelength inside the film, a new enhanced scattering phenomenon appears as gentle peaks on the second-order incoherent scattering distribution in four special directions. Such four directions are the directions of forward scattering, specular reflection, backscattering, and the symmetrical direction of forward scattering with respect to the normal of the film surface.The first-order incoherent scattering occurs distinctly in four such directions. Such enhanced scattering is independent of the existence of the guided wave modes inside the thin film, and deeply relates to the structure of the thin film with one-dimensional disorder that has infinite correlation in the vertical direction. For SiC and glass thin films having one-dimensional disorder with a Gaussian correlation and three types of exponential correlation, the first- and second-order incoherent scattering cross-sections are illustrated in figures. The narrow enhanced scattering peaks appear for the glass film in a thin case. The gentle enhanced peaks turn up for both the SiC and glass films in a thick case. Furthermore, the optical theorem is calculated for several cases. It is then found that the error of the optical theorem decreases and the performance of the wavefield is improved by taking into account the second-order incoherent scattering.

Wave reflection and transmission from a thin film with one-dimensional disorder

Abstract This paper deals with a TE plane wave reflection and transmission from a thin film with one-dimensional disorder by means of the stochastic functional approach. The relative permittivity of the thin film is written by a Gaussian random field in the horizontal direction with infinite extent, and is uniform in the vertical direction with finite thickness. Arandomwavefield is obtained in terms of a Wiener–Hermite expansion representation with approximate expansion coefficients (Wiener kernels) under a small fluctuation case. For a SiC thin film and a glass thin film having one-dimensional disorder with Gaussian correlation or an exponential correlation, numerical examples of the first-order incoherent scattering cross section and the optical theorem are illustrated in the figures. It is then found that ripples and four major peaks appear in angular distributions of the incoherent scattering. Such four peaks may occur in the directions of forward scattering, specular reflection, backscattering and in the symmetrical direction of forward scattering with respect to the normal to surface of the thin film. Physical processes that yield such ripples and peaks are discussed.

Scattering of a plane wave from a periodic random surface: a probabilistic approach

Abstract This paper deals with a probabilistic formulation of the wave scattering from a periodic random surface. When a plane wave is incident on a random surface described by a periodic stationary stochastic process, it is shown by a group-theoretic consideration that the scattered wave may have a stochastic Floquet form, i.e. a product of a periodic stationary random function and an exponential phase factor. Such a periodic stationary random function is then written by a harmonic series representation similar to a Fourier series, where Fourier coefficients are mutually correlated stationary processes instead of constants. The mutually correlated stationary processes are represented by Wiener - Hermite functional series with unknown coefficient functions called Wiener kernels. In case of a slightly rough surface and TE wave incidence, low-order Wiener kernels are determined from the boundary condition. Several statistical properties of the scattering are calculated and illustrated in figures.