Tokuo Miyamoto

Numerical analysis of a thin-film waveguide by mode-matching method

A new numerical analysis is proposed to investigate accurately the propagation characteristics of a dielectric thin-film waveguide, and its algorithm is presented. In this method, the Rayleigh principle previously used in conventional mode-matching techniques is extended to the Fourier transform of the wave field in the boundary-value problem for an unbounded object. Successful numerical results for dispersion relations and field distributions in a rib waveguide are obtained in detail, accompanied by their error estimations. The propagation characteristics, including field distributions in an optical rib waveguide, are investigated precisely for several geometries, and it is confirmed that the mode-matching method is accurate and effective for numerical analysis, not only with bounded objects, but also with unbounded objects such as thin-film waveguides in integrated optics.

Full-wave analysis of optical waveguides using periodic boundary conditions

A numerical approach for three-dimensional optical waveguides using periodic boundary conditions in both transverse directions is presented. Expanding the electric and magnetic fields in a double Fourier series of complex trigonometric functions, Maxwells equations are reduced to the eigenvalue problem of a linear system for the Fourier coefficients. The solutions yield the vectorial eigenmode fields for guided and radiation modes, both propagating in forward and backward directions. The method is used to analyze the junction of a fiber to an embedded waveguides and the power transfer between two parallel embedded waveguides.

Measurement of the Beam Parameters of a Laser Beam and Its Diffraction Field, Using a Hologram

A simple method for measuring the beam parameters of a laser beam, using a hologram, is proposed, and the accuracy is examined. By measuring the beam width and radius of curvature of the wavefront of a He-Ne gas laser, including several higher order modes, the behavior of a laser beam is investigated experimentally. As another application of this method, the phase distribution of the diffracted field from an aperture and a slit illuminated by a laser beam is measured, and the effects of a beam upon the diffracted field are studied experimentally.

Numerical analysis of a rib optical waveguide with trapezoidal cross section

Abstract Dispersion relations and field distributions in rib optical waveguides with several sizes of trapezoidal cross sections are investigated by using a new highly accurate numerical method, which is based on the Rayleigh principle and on the least-squares method.

Numerical Analysis on Isotropic Elastic Waveguides by Mode-Matching Method - I. Analytical Foundations and General Algorithms

A new method for computer-aided calculation, the mode- motching merhod, based on the Rayleigh expansion theorem, is pro- posed in order to analyze the boundary condition problem of elastic fields, and its analytical foundations and general algorithms are dis- cussed. The alastic fields are represented by scalar potential functions which are solutions of Helmholtz equations and expanded by the well- known separated solutions. Introducing the formal Green functions, the integral representations of the potentials are derived. The Rayleigh expansion theorem assures the existence of the infinite sequence of the truncated modal expansions which uniformly converges to the true field in arbitrarily shaped cross section. Through this theorem and the integral representations, the procedure of the mode-matching method is described simply so that the truncated modal expansions are made to fit for the boundary conditions in the least squares sense. Conse- quently this new method may ensure more precise analyses not only on the dispersion characteristics, but also on the field distributions of the particle velocity or the stress by small amount of computational efforts, than the other numerical methods reported so far. The general algo- rithm for the mode-matching method is described in the cases of forced and free vibrations of the homogeneous isotropic elastic waveguide with arbitrarily shaped cross section.

Analysis of an embedded dielectric waveguide with parabolic index distribution in the two-dimensional cross section

A Fourier series expansion method is applied to an accurate analysis of an embedded dielectric waveguide with parabolic index profile in a rectangular cross section. The case where the same waveguide has one discontinuity is also analyzed.

Propagation characteristics of a multilayered thin-film optical waveguide with a buffer layer

A mode-matching method is applied for precise numerical analysis of the propagation characteristics of a four-layer thin-film optical waveguide with a plano-convex layer, whose accurate description has been difficult so far. In the computation, the effects of the buffer layer on the dispersion relation and the field distribution for a few lower-order modes are investigated.

Method of determining capture cross section including a slow capture of carriers in the depletion edge region

The capture process of carriers in the pulse‐filling measurements is analyzed by including the slow capture on the edge of a depletion layer. An analytical expression is derived to determine the capture cross section of majority carriers from the initial slope of the semilogarithmic plot of capacitance versus capture time in the case of low trap concentration. A method is proposed to determine the fast capture rate in the bulk region from a slow capture process in the edge region when the trap concentration is not negligible compared with the concentration of the shallow dopant. The edge effect is intentionally enhanced to observe the capacitance variation with the capture time. Pulse‐filling measurements on Au‐doped Si p+n and undoped liquid‐encapsulated Czochralski n‐GaAs Schottky diodes are made to verify the method.

Output Beam from a Confocal Resonator with a Pinhole for Mode Selection

An approximate expression for the output beam from a confocal resonator, into which a pinhole for mode selection is inserted at an arbitrary position near the mirror at one end, is studied experimentally. The output beam consists of the fundamental component, in which the diffraction from the pinhole edge is not considered, and a field of the higher order component including the diffraction. In the region of the pinhole aperture larger than the beam width of the confocal resonator before the insertion of the pinhole, the diffraction component can be neglected. The output beam then may be approximated by the beam of the fundamental component, which is expressed simply by the field of the confocal resonator with unequal-sized mirrors of Boyd and Kogelnik. These results are confirmed by both experimental and theoretical examinations.

Determination of free‐carrier‐enhanced emission rate of carriers in depletion‐edge region by constant capacitance technique

The rate of majority‐carrier emission at the trap level located in the edge of the depletion layer is enhanced by the influence of a free‐carrier tail. This causes a nonexponential change in transient capacitance with time after the application of a filling pulse. The emission rates of the midgap level in GaAs and the Au acceptor level in Si are measured by the constant capacitance technique which eliminates the additional nonexponential factor due to the high trap concentration. The apparent emission rate determined from the initial slope of transient voltage increases with decreasing the difference of the depletion widths in the emission and capture processes. The enhanced emission rate due to the free‐carrier tail is observed even on the sample of the low carrier concentration. Fitting the calculated emission rate to the experimental results enables the estimation of the capture cross section of majority carriers in the trap level as well as the emission rate.