This paper shows structural optimal design of optical waveguide components utilizing an efficient 3D frequency-domain and 2D time-domain beam propagation method (BPM) with an alternating direction implicit (ADI) scheme. Usual optimal design procedure is based on iteration of numerical simulation, and total computational cost of the optimal design mainly depends on the efficiency of numerical analysis method. Since the system matrices are tridiagonal in the ADI-based BPM, efficient analysis and optimal design are available. Shape and topology optimal design shown in this paper is based on optimization of density distribution and sensitivity analysis to the density parameters. Computational methods of the sensitivity are shown in the case of using the 3D semi-vectorial and 2D time-domain BPM based on ADI scheme. The validity of this design approach is shown by design of optical waveguide components: mode converters, and a polarization beam splitter.

In the beam-type microwave power transmission system, it is required to minimize the interference with communication and the influence on the human body. Retrodirective system that re-radiates a beam in the direction of arrival of a signal is well known as a beam control technique for accurate microwave power transmission. In this paper, we newly propose to apply the retrodirective system to both transmitting and receiving antennas. The leakage to the outside of the system is expected to minimize self-convergently while following the atmospheric fluctuation and the antenna movement by repeating the retrodirective between the transmitting and receiving antenna in this system. We considered this phenomenon theoretically using an infinite array antenna model. Finally, it has been shown by the equivalent circuit simulation that stable transmission can be realized by oscillating the system.

Recent progress in research on the finite element method (FEM) for optical waveguide design and analysis is reviewed, focusing on the author's works. After briefly reviewing fundamentals of FEM such as a theoretical framework, a conventional nodal element, a newly developed edge element to eliminate nonphysical, spurious solutions, and a perfectly matched layer to avoid undesirable reflections from computational window edges, various FEM techniques for a guided-mode analysis, a beam propagation analysis, and a waveguide discontinuity analysis are described. Some design examples are introduced, including current research activities on multi-core fibers.

For the construction of photonic crystal fiber (PCF) systems using their unique properties, a PCF coupler (PCFC) is one of the key components of the systems. The characteristics of the PCFC depend on the state of air holes in the tapered region of the PCFC because the state of air holes in the tapered region affects light propagation in the PCFC taper. In this paper, coupling characteristics of PCFCs were theoretically investigated. In PCFCs with air hole remaining tapers, we found that a smaller elongation ratio i.e. a stronger elongation is required to obtain optical coupling as an air hole pitch or a ratio of air hole diameter to pitch is larger. In PCFCs with air hole collapsed tapers, it was clarified that a dependence of extinction ratio on air hole collapsed elongation ratio is higher for smaller elongation ratio. It was also clarified that an air hole remaining PCFC has slow wavelength characteristics in extinction ratio compared to an air hole collapsed PCFC. Air hole remaining PCFCs and air hole collapsed PCFCs were fabricated using a CO2 laser irradiation technique. We could successfully control whether air holes in the PCFC taper were remaining or collapsed by adjusting the irradiated laser power in the elongation process of the PCFC fabrication. It was experimentally clarified that the air hole remaining PCFC has slow wavelength characteristics in extinction ratio compared to the air hole collapsed PCFC. The tendencies of the measured wavelength characteristics of PCFCs agree with those of numerical results.

Optical logic gates for OR, AND, NOT, and NOR operations in waveguides consisting of nonlinear material are numerically investigated by means of FD-BPM (Finite Difference Beam Propagation Method). The proposed devices are designed utilizing the self-routing characteristics of nonlinear X-crossing structures when they are operated with one input beam or two. The numerical simulations show that the proposed structures can favorably be applied to optical data processing and computing as fundamental logic gates.

A three-dimensional beam propagation method based on a finite element scheme is described for the analysis of second harmonic generation devices. For the wide-angle beam propagation analysis, the Pade approximation is applied to the differential operator along the propagation direction. In order to avoid spurious reflection from the computational windows edges, the transparent boundary condition is introduced. Numerical results are shown for quasi-phase matched second harmonic generation devices using periodically domain-inverted LiNbO3 and LiTaO3 waveguides. The influences of the shape of domain-inverted regions and the inversion width on the conversion efficiencies are investigated in detail.

In this paper, outlines of the derivation of two recently developed finite difference beam propagation methods based on the higher-order Pad approximations are given to simulate the optical field propagation of tilted and turning waveguides. In order to investigate the accuracy and limitation for a propagation angle of these approaches, numerical results are presented for two benchmark tests. The present algorithms will offer, to our knowledge, the new beam propagation methods in optics.

We propose novel all-optical functional devices using waveguide X-junctions with localized third order optical nonlinearity, where one branch is made from a Kerr-like nonlinear material and the rest are made from linear ones. All-optical switching operations can be obtained because of bistable like nonlinear dispersion characteristics in linear and nonlinear coupled guided-wave systems. The performances of the devices are analyzed by the Beam Propagation Method (BPM) modified for nonlinear waveguides combined with the nonlinear normal mode analysis. The methods to construct the waveguides with localized nonlinearity are also discussed by utilizing the technologies for the selective control of a band-gap energy of semiconductor Multi Quantum Well (MQW) structures and the performances of the designed devices are presented.

We propose novel all-optical functional devices using waveguide X-junctions with localized third order optical nonlinearity, where one branch is made from a Kerr-like nonlinear material and the rest are made from linear ones. All-optical switching operations can be obtained because of bistable like nonlinear dispersion characteristics in linear and nonlinear coupled guided-wave systems. The performances of the devices are analyzed by the Beam Propagation Method (BPM) modified for nonlinear waveguides combined with the nonlinear normal mode analysis. The methods to construct the waveguides with localized nonlinearity are also discussed by utilizing the technologies for the selective control of a band-gap energy of semiconductor Multi Quantum Well (MQW) structures and the performances of the designed devices are presented.

We examine crossing waveguides with three channels consisting of nonlinear material by means of FD-BPM (Finite Difference Beam Propagation Method). Specifically, we investigate how the insertion of a multimode waveguide into the crossing section of both 13 and 23 structures influences the switching characteristics of output power. We then confirm that these structures can be favorably applied to a wide variety of all-optical devices for integrated optics such as intensity-dependent optical switches, optical power distributors and so on.

A simple and efficient adaptive mesh generation for the approximate scalar analysis of optical waveguides is proposed. Two types of local weight estimates which can take into account both a field amplitude and its variation on a problem domain are introduced. One is a difference between linear and quadratic element solutions and the other is a residual for the partial differential equation to be solved. To show the validity and usefulness of the present scheme, the guided-mode analysis of a rib waveguide and the beam propagation analysis of a tilted slab waveguide and a Y-branching rib waveguide are performed.

Investigated is a guided-wave device for dividing optical power into three equal parts. The device fundamentally consists of a three-waveguide tapered-velocity coupler which is designed to operate under the adiabatic condition. Field distributions of the local normal modes along the coupler explain basic principles of the device. Its performance is confirmed through numerical simulations by means of finite difference beam propagation method.

Thermally-diffused expanded core (TEC) techniques brought the fibers with the mode fields expanded by thermal diffusion of core dopants. The techniques are effective to the reduction of splice or connection losses between the different kind of fibers, and are applied to the integrations of thin film optical devices in fiber networks, the fabrications of chirped fiber gratings, and so on. In the practical use of TEC techniques, the fibers are heated high temperature of about 1650 because of a short peried of time in processing by microburners. The mode field diameter expansion (MFDE) ratio, which is defined as the ratio of the mode field diameter in the fiber section having the core expanded and that unexpanded, is desired to be more than 2.0 from the viewpoint of loss reduction in industrial uses of the TEC techniques. When the TEC techniques are applied to polarization-maintaining optical fibers (PM fibers), such as PANDA fibers, both core dopants and stress applying part (SAP) dopants diffuse simultaneously. So the MFDE ratio is less than two without mode field deformation in conventional PANDA fibers which are practically used as PM fibers. In this paper a PANDA fiber design suitable for the TEC techniques is newly proposed. The fiber has 1.28 µm cutoff wavelength and the mode field diameter is about 11 µm before core expansion at 1.3µm wavelength.

A 3-dimensional beam propagation method is described for the analysis of nonlinear optical fibers, where the finite element and finite difference methods are, respectively, utilized for discretizing the fiber cross section and the propagation direction. For efficient evaluation of wide-angle beam propagation, Pade approximation is applied to the differential operator along the propagation direction. In order to improve accuracy of solutions, isoparametric elements and numerical integration formulae derived by Hammer et al. are introduced. The propagation characteristics of nonlinear optical fibers with linear core and nonlinear cladding are analyzed, and unique features of nonlinear guided-wave propagation, such as spatial soliton emission, are investigated.

The design, fabrication, and testing of a highly multimode polymeric 88 star coupler is described. The design process allowed a comparison to be made of ray tracing and beam propagation methods for the design of such highly multimode waveguide devices. The results obtained with either of these two different methods agree well with actual measurements on a fabricated 88 multimode-input star coupler with a refractive index difference of Δn=0.0274 and a device length of L=4.25 cm. The reduction in the rms power fluctuation in the output guides with the choice of a higher refractive index difference is demonstrated.

A new type of guided-wave polarization splitter is proposed for the operation at optical frequencies. The basic structure of the device is a bifurcating waveguide fabricated in a uniaxial crystalline material such as LiNbO3. The splitting behavior of optical waves into two waves with mutually perpendicular directions of polarization by an optically anisotropic material is utilized in the branching section of the present polarization splitter. Once of the conspicuous features of the device is free of any electrical control via the electro-optic effects. Some numerical results obtained with the finite difference beam propagation method indicate that extinction ratios better than 20dB are possible of realization for both TE and TM modes.

A two-waveguide tapered velocity coupler is presented for a variable divider of optical beams. The coupler consists of one tapered slab waveguide in dimension and the other slab waveguide with a constant film thickness. It is assumed that the device is fabricated on a LiNbO3 substrate, with a push/pull external electric field parallel with the optic axis applied only in the film regions of the coupler. Various numerical simulations through the finite difference beam propagation analysis show that a wide range of dividing ratios from - 15 dB to 15 dB or more can be achieved with considerably small values of driving-voltage electrode-length product and that the dividing characteristics are stable over a wide range of frequencies.

A beam adaptive frame for finite-element beam-propagation analysis is proposed. The width of the frame can be adapted itself to either the guiding structure or the propagating beam in optical circuits, so the size of the computational window can be reduced.

We propose a beam tracing frame which shifts together with either the guiding structure or the beam propagation in optical circuits. This frame is adaptive to the beam propagation analysis based on the finite-element method and can reduce the computational window size.

The power transfer characteristics of a symmetric nonlinear directional coupler (NLDC) are analyzed rigorously using the beam propagation method based on the finite difference scheme. The NLDC consists of two linear waveguides separated by a Kerr-like nonlinear gap layer. The change of nonlinear refractive index along the coupler is precisely evaluated by making use of the second-order iteration procedure with respect to a small propagation length. For the incidence of TE0 mode of the isolated linear waveguide, the highly accurate numerical results are obtained for the behavior of power transfer, and the coupling length and critical power for optical switching. The dependencies of the coupling length and critical power on the width of the gap layer and the input power levels are discussed, compared with those predicted by the coupled-mode approximations.