Yasuhide Tsuji

Time-domain beam propagation method and its application to photonic crystal circuits

A time-domain beam propagation method (BPM) based on the finite-element scheme is described for the analysis of reflections of both transverse electric and transverse magnetic polarized pulses in waveguiding structures containing arbitrarily shaped discontinuities. In order to avoid nonphysical reflections from the computational window edges, the perfectly matched layer boundary condition is introduced. The present algorithm using the Pade approximation is, to our knowledge, the first time-domain beam propagation method which can treat wide-band optical pulses. After validating this method for an optical grating with modulated refractive indexes, various photonic crystal circuit components are simulated.

Curvilinear hybrid edge/nodal elements with triangular shape for guided-wave problems

A unified approach using curvilinear hybrid edge/nodal elements with triangular shape is, for the first time, described for the study of guided-wave problems. Not only the lowest order (fundamental) but the higher order elements are systematically constructed. The advantage of curvilinear elements lies in the fact that they can model curved boundaries with more accuracy and lesser number of degrees of freedom than rectilinear elements. The vector basis functions derived here are also applicable to rectilinear cases. To show the validity and usefulness of the present approach, computed results are illustrated for rib waveguides with straight boundaries and circular waveguides with large refractive-index differences.

High-performance absorbing boundary conditions for photonic crystal waveguide simulations

A high-performance absorbing boundary condition is newly developed for the reduction of spurious reflections in photonic crystal (PC) waveguide simulations. The PC waveguide is terminated with a perfectly matched layer (PML) in which the original PC structure remains as is. This PC-based PML works well, compared to a conventional PML, which acts as a homogeneous absorbing medium, simulating a semi-infinite free space and to a distributed-Bragg-reflector waveguide, which was recently developed to reduce reflections from PC waveguide ends, improving a wavenumber matching condition for PC waveguide modes.

Finite element method using port truncation by perfectly matched layer boundary conditions for optical waveguide discontinuity problems

A powerful algorithm based on a finite element method (FEM) is newly formulated for the analysis of waveguide discontinuities. In an earlier approach, FEM was applied to the finite region with discontinuities, and a mode expansion technique was applied to the uniform waveguides that are connected to the input and output ports of finite region. Although, in the present approach, the uniform waveguides are replaced by perfectly matched layer (PML) boundary conditions, it is possible to treat periodically varying waveguide structures such as photonic crystal (PC) waveguides. A combined method of beam propagation method (BPM) and FEM is also shown in such a form that a mode expansion technique is not required. To show the validity and usefulness of the present approach, numerical examples for optical gratings, circuit components based on PC waveguides and optical directional couplers are presented.

Hole-assisted lightguide fiber for large anomalous dispersion and low optical loss

Hole-assisted lightguide fiber (HALF) is a microstructured fiber comprising a material index profile for waveguiding and air holes for modifying optical properties. Anomalous dispersion larger than those of the conventional fibers can be realized without severe degradation in optical loss, because of low power fraction in the holes and structural simplicity. We investigate into the causes of the loss of the fabricated HALFs, and show that a GeO2-doped core, in addition to the low power fraction, is desirable for low loss. The fabricated HALF exhibits a loss as low as 0.41 dB/km and a large anomalous dispersion of +35 ps/nm/km at 1550 nm.

Guided-mode and leaky-mode analysis by imaginary distance beam propagation method based on finite element scheme

As a simple analysis method to solve eigenmodes of optical waveguides, we present an imaginary distance beam propagation method (BPM) based on finite element scheme. The matrices used in the beam propagation analysis are essentially complex, so lossy optical waveguides can be easily treated. Moreover, employing the transparent boundary condition or perfectly matched layer boundary condition, the validity of a which has been already confirmed in the real distance BPM, we can easily treat not only guided modes but leaky ones. To show the validity and usefulness of this approach, eigenmodes of twoand three-dimensional leaky waveguides, and optical fibers are calculated.

Finite-element modeling of broad-band traveling-wave optical modulators

A full-wave finite-element method with hybrid edge/nodal elements is, for the first time, applied to investigating the frequency dispersion of microwave propagation characteristics of broad-band traveling-wave (TW) optical modulators using planar electrode configurations. In order to produce a two-step analysis of electrooptic modulation of optical waveguides, the microwave electrode solver is linked to the optical waveguide solver. Numerical results are shown for an ultrabroad-band TW LiNbO/sub 3/ Mach-Zehnder optical modulator with a ridge structure, and the necessity of using the full-wave solver is verified by comparing the calculated 3-dB bandwidth and half-wavelength voltage with the experimental data.

Finite element beam propagation method for three-dimensional optical waveguide structures

A beam propagation method (BPM) based on the finite element method (FEM) is described for longitudinally varying three-dimensional (3-D) optical waveguides. In order to avoid nonphysical reflections from the computational window edges, the transparent boundary condition is introduced. The present algorithm using the Pade approximation is, to our knowledge, the first wide-angle finite element beam propagation method for 3-D waveguide structures. To show the validity and usefulness of this approach, numerical results are shown for Gaussian-beam excitation of a straight rib waveguide and guided-mode propagation in a Y-branching rib waveguide.

A wide-angle finite-element beam propagation method

A wide-angle finite-element beam propagation method based on the Pade approximation is developed. Considerable improvement in accuracy over the paraxial approximation is achieved with virtually no additional computation. In the present algorithm, the quadratic element, transparent boundary condition, adaptive reference index, and adaptive grid are effectively utilized.

Single-mode single-polarization holey fiber using anisotropic fundamental space-filling mode.

We present the single-mode single-polarization regime of a circular-hole holey fiber consisting of a core with large elliptical holes. The elliptical holes in the core, which produce large anisotropies, split the fundamental mode into two orthogonally polarized fundamental modes, often referred to as slow and fast modes. This fiber can guide only one polarization state of the fundamental mode when a fundamental space-filling mode index of the cladding region is designed to lie between these indices of the slow and fast modes of the core region. We demonstrate one design example of this fiber and show that the single-polarization regime can be achieved over a wide wavelength range.