Imaginary-distance Beam Propagation Method Research Articles

Implicit Yee-mesh-based finite-difference full-vectorial beam-propagation method

A novel Yee-mesh-based finite-difference full-vectorial beam-propagation method is proposed with the aid of an implicit scheme. The efficient algorithm is developed by splitting the propagation axis into two steps. The eigenmode analysis of a rib waveguide is performed using the imaginary-distance procedure. The results show that the present method offers reduction in computational time and memory, while maintaining the same accuracy as the conventional explicit Yee-mesh-based imaginary-distance beam-propagation method. It is demonstrated by the analysis of a polarization converter that the present method can be used for not only the eigenmode analysis but also the propagating beam analysis.

Eigenmode analysis of a light-guiding metal line loaded on a dielectric substrate using the imaginary-distance beam-propagation method

Fundamental characteristics of a light-guiding metal line are revealed and discussed through the eigenmode analysis using the three-dimensional (3-D) imaginary-distance beam-propagation method (ID-BPM) based on the alternating-direction implicit scheme. For the present ID-BPM, the multiplication factor of the eigenmode is derived and the paper described how the present method works in the ID procedure. An efficient absorbing boundary condition is described, which is suitable for the eigenmode analysis using the ID-BPM. After confirming the effectiveness of the present method, the characteristics of the light-guiding line composed of a metal (Au) with a finite width and thickness on a substrate (SiO/sub 2/) are investigated. Numerical results for a metal thickness of 0.2 /spl mu/m show that the effective index and the propagation loss decrease as the metal width is reduced. It is shown that not only the higher order modes but also the first mode has a cutoff metal width. Near the cutoff width, the propagation loss of the first mode (/spl sime/10dB/mm at a wavelength of 1.55 /spl mu/m) is less than those of the higher order modes. Finally, in order to reduce the propagation loss, a dielectric core was added under the metal line.

Full vectorial finite element analysis of semiconductor lasers

The accurate full vectorial finite element based imaginary distance beam propagation method (IDVFEBPM) is applied to the modal analysis of semiconductor laser structures. The effects of the waveguide structure dimensions, the imaginary part of the refractive index of the active region and the carrier concentration on the fundamental mode effective index, gain and confinement factor are thoroughly examined and explained.

Single-Mode Behaviour Judgment of Optical Waveguides byImaginary-Distance Beam Propagation Method Under Perfectly Matched LayerBoundary Condition

Imaginary-distance beam propagation method under theperfectly matched layer boundary condition is applied to judgesingle-mode behaviour of optical waveguides, for the first time to ourknowledge. A new kind of silicon-on-insulator-based rib structures withhalf-circle cross-section is presented. The single-mode behaviour ofthis kind of waveguide with radius 2 μm is investigated by thismethod. It is single-mode when the slab height is not smaller than theradius.

New full-wave finite-element analysis of dielectric waveguides

The full-vectorial finite-element-based imaginary-distance beam-propagation method (IDVFEBPM) is applied to perform modal analysis of lossless and lossy microwave dielectric waveguides. The excellent agreement between the results obtained using the IDVFEBPM and those in the literature reveal its high numerical precision. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 44: 157–158, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20574

Single-mode condition for silicon rib waveguides with trapezoidal cross-section

Single-mode condition for silicon rib waveguides with trapezoidal cross-section was obtained using a numerical method based on imaginary-distance beam propagation method with non-uniform discretization. Both quasi-transverse-electric and quasi-transverse-magnetic modes were investigated. Simulated single-mode condition is given by a modified equation. Comparison with reported results shows that the Marcatili’s method is in a better agreement with our results.

Finite-difference imaginary-distance beam propagation method for modeling of the fundamental mode of photonic crystal fibers

The finite-difference imaginary-distance beam propagation method is successfully employed to investigate the effective index of the fundamental mode in the air-filled silica index-guiding photonic crystal fibers (PCFs). A PCF characterized by a hexagonal distribution of air holes with a central defect is taken as example. The convergence behavior of the modal index versus the air hole radius is investigated. It is demonstrated that the converging speed is proportional to the air hole radius. The modal birefringence in the HE state is numerically investigated and demonstrated to strongly depend on the precision of the numerical mesh.

Numerical analysis of a dielectric rod antenna- demonstration of the discontinuity-radiation concept

A technique combining the finite-difference time-domain method and the imaginary-distance beam-propagation method is used to demonstrate the discontinuity-radiation concept for a dielectric rod antenna. The field near the rod is decomposed into a guided and an unguided wave. Using the two waves, the feed and terminal patterns are evaluated. It is numerically revealed that superposing the two patterns forms the radiation field of the antenna. The decomposition technique enables us to efficiently evaluate the directivity of a long rod antenna.

A modified imaginary distance BPM for directly computing arbitrary vector modes of 3-D optical waveguides

A method for the direct calculation of arbitrary vector modes of three-dimensional optical waveguides is presented. The proposed mode-solving scheme, based on a modified imaginary distance beam propagation method, provides an easy to implement explicit algorithm. A finite-difference discretization is used in the transverse plane and a Chebyshev approximation in the propagation direction. Approximate values of the propagation constants of the modes to be calculated are required and it is demonstrated that this data can be obtained in an efficient way by using the least squares Prony method.

Beam propagation method based on finite element scheme and its application to optical waveguide analysis

AbstractIn regard to the beam propagation method (BPM), one of the indispensable analysis tools for the design of optical waveguide devices and optical circuits, this paper treats the FE‐BPM based on the finite element method, which allows an efficient analysis using adaptive meshes and provides basic concepts. The paper also refers to the time‐domain BPM, which can automatically take care of the reflected wave, and to the imaginary‐distance BPM, which can easily carry out eigenmode analysis including leaky modes. In addition to examples of generated adaptive meshes, analysis examples of photonic crystal circuits and three‐dimensional ARROW waveguides are presented so that the effectiveness and usefulness of the FE‐BPM are demonstrated. © 2002 Wiley Periodicals, Inc. Electron Comm Jpn Pt 2, 85(10): 29–39, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjb.1112

Full-vectorial imaginary-distance beam propagation method based on a finite element scheme: application to photonic crystal fibers

A full-vectorial imaginary-distance beam propagation method based on a finite element scheme is newly formulated and is effectively applied to investigating the problem of leakage due to a finite number of arrays of air holes in photonic-crystal holey fibers (HFs). In order to treat arbitrarily shaped air holes and to avoid spurious solutions, a curvilinear edge/nodal hybrid element is introduced. Furthermore, in order to evaluate propagation characteristics of not only bound modes but leaky modes in HFs, an anisotropic perfectly matched layer is also employed as a boundary condition at computational window edges. It is confirmed from numerical results that the propagation loss increases rapidly with increasing wavelength, especially for HFs with one ring of smaller air holes, and that the propagation loss is drastically reduced by adding one more ring of air holes to the cladding region.

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.

Direct computation of higher-order propagation modes using the imaginary-distance beam propagation method

In this paper we present an extension to the standard method of eigenmode-extraction using the imaginary-distance beam propagation method. We show that it is possible to directly extract higher-order propagation modes of arbitrary shaped waveguide structures by propagating the field along the imaginary axis when the parameters are chosen in an appropriate manner. This method requires an assumption of the propagation constant of the eigenmode. In many cases this value can be determined using fast approximate techniques like the effective index method. Additionally, the approximate mode shape may be introduced as a starting condition and can further accelerate the extraction of the eigenmode. The overall number of propagation steps needed to extract multiple eigenmodes is then significantly smaller than in the case when extracting the modes sequentially with the former method.

Modified finite-difference formula for semivectorial H-field solutions of optical waveguides

The propagation constants of rib waveguides are analyzed by the imaginary distance beam-propagation method based on a newly derived finite-difference formula for semivectorial H-fields. The formula ensures a truncation error of O(/spl Delta/x)/sup 2/, provided that the discontinuity lies midway between two mesh points. Comparison with previously published results for a rib waveguide as a classical benchmark shows the effectiveness of the present method.

Eigenmode analysis of optical waveguides by an improved finite-difference imaginary-distance beam propagation method

The imaginary-distance method is applied to an improved finite-difference beam propagation method (IFD-BPM) based on the generalized Douglas method in order to carry out eigenvalue analysis of an optical waveguide. First, we formulate the IFD-BPM to include the polarization dependence. The imaginary-distance method is explained, in which only the eigenmode is generated from an arbitrary incident field including the eigenmode. Next, in order to verify the effectiveness of the method, eigenmode analysis is carried out for a step index type slab waveguide. We found that by using the IFD-BPM, a much more accurate eigenmode analysis than obtained by the conventional method is possible. Further, in regard to the method for choosing the reference index of refraction, important in the evaluation of the effective index of refraction, a simple method was conceived in which the reference index is successively updated. To provide an application example, the present method and the effective index method were combined for the eigenmode analysis of a three-dimensional multiple quantum well waveguide. The agreement with the results obtained by other methods was excellent. Finally, by using the alternate directional implicit solution method based on the GD method, a graded index fiber is analyzed. From the evaluation of the effective index of refraction, the effectiveness of the method in direct three-dimensional analysis is demonstrated. © 1998 Scripta Technica, Electron Comm Jpn Pt 2, 81(4): 1–9, 1998

Rib waveguide analysis by the imaginary-distance vectorial beam-propagation method based on Yee's mesh

The effective index and the mode profile of rib waveguides are calculated using the vectorial beam-propagation method using the imaginary-distance procedure. Yee's mesh originally developed in the finite-difference time-domain method is employed to discretize a waveguide geometry. The refractive index at the interface between two different media is determined by Ampere's circuital law. The field discontinuities at the interface and singularities at the corners of the waveguide are clearly displayed.

Modified finite-difference formula for the analysis of semivectorial modes in step-index optical waveguides

The modified finite-difference formula is presented for the second derivative of a semivectorial field in a step-index optical waveguide. The present formula achieves a truncation error of O(/spl Delta/x/sup 2/) provided the discontinuity coincides with a mesh point or lies midway between two mesh points. Furthermore, the formula allows a general position of the interface, when used with the beam-propagation method (BPM). To demonstrate the effectiveness of the formula, asymmetric step-index waveguides are analyzed using the imaginary-distance BPM.

Evaluation of Coupling Coefficients for Laterally-Coupled Distributed Feedback Lasers

Dependence of coupling coefficient, κ, on laterally-coupled distributed feedback (LC-DFB) laser structure is investigated. In LC-DFB lasers, gratings are fabricated on and around the ridge after ridge-waveguide formation and, thus, neither epitaxial regrowth nor growth on corrugated substrates is required. For κ calculation, coupled-mode theory is used with the two-dimensional field intensity calculated using the imaginary-distance beam propagation method. Comparisons are made for LC-DFB lasers with different layer, ridge and grating structures and parameters that affect κ are identified. In addition, it is shown that LC-DFB structure is less sensitive to processing variations and, thus, more manufacturable than a conventional buried heterostructure DFB structure.

Optical bent rib waveguide with reduced transition losses

Large losses occur at the transition between straight and curved rib waveguide segments. A bent optical rib waveguide is analyzed by the 3D imaginary-distance beam propagation method (BPM). The BPM is implemented with 3D finite differences. The transition losses are reduced with several techniques: (1) the offset between bent and straight guides, (2) trench location and sizes, (3) optimized slope of rib sidewall.

Computation of higher-order waveguide modes by imaginary-distance beam propagation method

Yevick and Hermansson presented an efficient numerical method for calculating fundamental modes of optical waveguides. We extend their technique to higher-order eigenmodes. Using a finite-difference beam propagation method, we obtain propagation constants and field profiles for the three lowest-order TE modes in an asymmetric rib waveguide.