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 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.

Among several optical devices in integrated optics, the fundamental characteristics of collinear optical switching devices have been studied about optical dielectric waveguides. Conventional waveguide-type acousto-optic (A-O) devices use collinear and longitudinal interactions with mode coupling based on the Bragg condition between optical waves and surface acoustic waves (SAW). Collinear A-O devices of the waveguide-type show sufficient performance for wavelength-selective switching with narrow bandwidths. However, in these collinear A-O devices, interaction time is several microseconds for 10 mm waveguide device length. In A-O devices of optical waveguides using transverse A-O interaction, where SAW propagates transversely to optical wave propagation direction, SAW propagation lengths needed for complete A-O interaction may become 10 µm and interaction time may be several nanoseconds. In this paper, fundamental characteristics of the transverse A-O interaction are studied as an electromagnetic boundary value problem. Refractive indices in optical waveguides induced by A-O effects with SAW are shown by sine functions. Wave field characteristics in periodic structures for transverse directions are analyzed by analytic method of Hill's equations for transverse spectral functions. Electromagnetic fields in regions with periodic structures are discussed by the Mathieu functions and the perturbation method. Dispersion characteristics of A-O eigen modes are studied for wavelengths of optical waves and SAW, with A-O coefficients.

We deal with the scattering of a plane wave by the end-face of a waveguide system by the numerical method based on the sinc function and calculate the electric field on the end-face. It is shown that the results obtained analytically by the perturbation method are in relatively good agreement with the numerical results.

This paper deals with a characteristic of the so-called effective boundary condition for a plane wave scattering from periodic surfaces with perfect conductivity. The perturbation solution with all orders is explicitly given under the effective boundary condition. It is newly found that such a perturbation solution satisfies the optical theorem under the exact boundary condition. A comparison between such a perturbation solution and a reference solution for the exact boundary condition by other methods is performed. Then, the validity of such a perturbation solution is concretely discussed.

The scattering of a plane wave from the end-face of a three-dimensional waveguide system composed of a large number of cores is treated by the volume integral equation for the electric field and the first order term of a perturbation solution for TE and TM wave incidence is analytically derived. The far scattered field does not almost depend on the polarization of an incident wave and the angle dependence is described as the Fourier transform of the incident field in the cross section of cores. To clarify the dependence of the scattering pattern on the arrangement of cores some numerical examples are shown.

The coupled mode equation describing the propagation of light in a disordered waveguide system composed of randomly different cores in size is analytically solved by the perturbation method and the average amplitude of light is derived. In the summation of a perturbation series only successive scatterings from different cores are taken into account. The result obtained shows that the average amplitude behaves as if in an ordered waveguide system composed of identical cores at short distance and decreases exponentially with increasing distance at large distance. The result is compared with the result obtained by the coherent potential approximation and the both results are in good agreement with each other. The results are also compared with the results obtained by numerically solving the coupled mode equation.

This paper studies scattering and diffraction of a TE plane wave from a periodic surface with semi-infinite extent. By use of a combination of the Wiener-Hopf technique and a perturbation method, a concrete representation of the wavefield is explicitly obtained in terms of a sum of two types of Fourier integrals. It is then found that effects of surface roughness mainly appear on the illuminated side, but weakly on the shadow side. Moreover, ripples on the angular distribution of the first-order scattering in the shadow side are newly found as interference between a cylindrical wave radiated from the edge and an inhomogeneous plane wave supported by the periodic surface.

In this paper, we propose a novel sound field reproduction system that uses the simultaneous perturbation (SP) method as well as two fast convergence techniques. Sound field reproduction systems that reproduce any desired signal at listener's ear generally use fixed preprocessing filters that are determined by the transfer functions from loudspeakers to control points in advance. However, control point movement results in severe localization errors. Our solution is a sound field reproduction system, based on the SP method, which uses only an error signal to update the filter coefficients. The SP method can track all control point movements but suffers from slow convergence. Hence, we also propose two methods that offer improved convergence speeds. One is a delay control method that compensates the delay caused by back-and-forth control point movements. The other is a compensation method that offsets the localization error caused by head rotation. Simulations demonstrate that the proposed methods can well track control point movements while offering reasonable convergence speeds.

In this paper, we propose the introduction of a frequency domain variable perturbation control and a leaky algorithm to the frequency domain time difference simultaneous perturbation (FDTDSP) method in order to improve the cancellation performance and the stability of the active noise control (ANC) system using the perturbation method. Since the ANC system using the perturbation method does not need the secondary path model, it has an advantage of being able to track the secondary path changes. However, the conventional perturbation method has the problem that the cancellation performance deteriorates over the entire frequency band when the frequency response of the secondary path has dips because the magnitude of the perturbation is controlled in the time domain. Moreover, the stability of this method also deteriorates in consequence of the dips. On the other hand, the proposed method can improve the cancellation performance by providing the appropriate magnitude of the perturbation over the entire frequency band and stabilizing the system operation. The effectiveness of the proposed method is demonstrated through simulation and experimental results.

This paper studies the scattering of a TM plane wave from a perfectly conductive sinusoidal surface with finite extent by the small perturbation method. We obtain the first and second order perturbed solutions explicitly, in terms of which the differential scattering cross section and the total scattering cross section per unit surface are calculated and are illustrated in figures. By comparison with results by a numerical method, it is concluded that the perturbed solution is reasonable even for a critical angle of incidence if the surface is small in roughness and gentle in slope and if the corrugation width is less than certain value. A brief discussion is given on multiple scattering effects.

An RF adaptive array antenna (RF-AAA) configured with variable capacitors is proposed. This antenna system can control the power combining ratio and phase value of received signals. In this paper, we focus on the diversity effects of RF-AAA. First, we show the design methodology of the combiner circuit to realize the effective combining. Second, the perturbation method and the steepest gradient method are compared for the optimization algorithms to provide fast convergence and suboptimum solutions among the variable circuit constants. Finally, in simulation, we show the RF-AAA can achieve diversity antenna gains of 7.7 dB, 10.9 dB and 12.6 dB for 2-branch, 3-branch and 4-branch configuration, respectively, which have higher performance than the selection combining.

Coupling between resonators are analyzed theoretically on basis of the coupled mode theory. New and basic equations for the coupling coefficient are derived and compared with those of waveguides. They should be useful for understanding the physical background of coupling and designing a new coupling scheme.

Nonlinear distortions in an anti-series varactor pair (ASVP) are analyzed by a perturbation method. To the authors' knowledge, this paper presents the first derivation of an analytical expression that explicitly shows intermodulation and harmonic distortions of the ASVP. In addition to canceling the expected even-order distortion, the third-order distortion can be suppressed simultaneously when a certain condition is satisfied. We also find that the second- and third-order distortions can be greatly suppressed without dependence on dc bias voltage if the varactors in the ASVP have an ideal abrupt p-n junction. These theoretical predictions are verified by measuring the second- and third-order harmonic distortions of an ASVP. The experimental results show that the second-order harmonic distortion is suppressed by approximately 20 dB. The third-order harmonic distortion is suppressed to the same extent in the theoretically predicted dc bias voltage range.

Effects of the sample insertion holes of the TM010 mode cylindrical cavity are analyzed on the basis of rigorous analysis by the Ritz-Galerkin method. The measurement accuracy of complex permittivity is examined by comparing the values by the perturbation method with ones by the rigorous analysis. Charts of relative errors Δ ε/εp and Δ tan δ/tan δp are presented, which are useful to measure the complex permittivity accurately by the perturbation method. The present analysis extends the validity of the conventional perturbation method.

In this letter, we propose a frequency domain active noise control system using the time difference simultaneous perturbation method. This method is an algorithm based on the simultaneous perturbation method which updates the coefficients of the noise control filter only by use of the error signal. The time difference simultaneous perturbation method updates the filter coefficients by using one kind of error signal, while the simultaneous perturbation method updates the filter coefficients by using two kinds of error signal. In the ANC systems, the time difference simultaneous perturbation method is superior because ANC systems cannot obtain two error signals at the same time. When this method is applied to ANC systems, the convergence speed can be increased to a maximum of twice that of the conventional method.

To measure temperature dependent complex permittivity of dielectric materials, a rectangular cavity resonator with a heating system has been developed. In the experiment, microwave power with the frequency of 2.45 GHz is applied to heat the dielectric material. In order to reduce the error of the complex permittivity of dielectric material obtained from the perturbation method, an electromagnetic (EM) field simulator is applied which uses the Transmission Line Modeling (TLM) method. The uniformity of the temperature is also discussed by the use of heat transfer equation which applies the results of TLM simulation. It is found from the results that the accurate temperature dependence of complex permittivity of the material can be obtained by the method presented here.

In this paper, we propose a frequency domain active noise control (ANC) system without a secondary path model. The proposed system is based on the frequency domain simultaneous perturbation (FDSP) method we have proposed. In this system, the coefficients of the adaptive filter are updated only by error signals. The conventional ANC system using the filtered-x algorithm becomes unstable due to the error between the secondary path, from secondary source to error sensor, and its model. In contrast, the proposed ANC system has the advantage not to use the model. In this paper, we show the principle of the proposed ANC system, and examine its efficiency through computer simulations.

Nonlinear behavior of electromagnetic surface waves propagating along a tangentially magnetized ferrite slab is investigated. The nonlinear Schrodinger equation (NLSE) which describes the temporal evolution of the electromagnetic wave pulses has been derived directly from the Maxwell equations and the equation of precessional motion for the magnetization in the ferrite slab with the aid of the reductive perturbation method without magnetostatic approximation. Based on the formula derived, we have numerically evaluated the frequency-dependence of the nonlinear coefficient in the NLSE for both a magnetostatic surface wave mode and a dynamic mode. As a result, we have confirmed the possibility of the propagation of solitons in the waveguide.