Semivectorial Beam Propagation Method Research Articles

Comments on "Investigation of 3D semivectorial finite-difference beam propagation method for bent waveguides"

The technique used to model curved waveguides described in the above paper is analyzed. Both the model and alternating direction implicit (ADI) method used to implement it are discussed.

Nonlinear finite-element semivectorial propagation method for three-dimensional optical waveguides

A nonlinear semivectorial beam propagation method based on the finite element method is presented. It applies to three-dimensional optical waveguides and accounts for polarization effects. To show the usefulness of this approach numerical results regarding both E/sup x/ (quasi-TE) and E/sup y/ (quasi-TM) waves are presented for directional couplers with nonlinear cores. The limits of scalar formulations are highlighted especially when working near and above the coupler threshold power.

An improved semivectorial beam propagation method using a finite-element scheme

A three-dimensional semivectorial finite-element beam propagation method, which treats only a linearly polarized transversal electric field and uses the Pade approximation, is described. The electric field should satisfy the conditions that either E/sub t/ or n/sup 2/E/sub t/ is continuous whether E/sub t/ is parallel to or perpendicular to the refractive-index discontinuous interface in an optical waveguide. The matrix-equation treated in this analysis is asymmetric, unlike the symmetric matrix-equation treated in the scalar analysis. Thus, this analysis needs twice the computer memory, but the number of calculation steps for the matrix elements is the same and the computing time is similar to that of the scalar analysis. This allows an accurate and efficient analysis of the polarization dependence of lightwave propagation in arbitrary step-index optical waveguides.

Investigation of 3D semivectorial finite-difference beam propagation method for bent waveguides

A three dimensions of semivectorial finite difference beam propagation method (FD-BPM) in cylindrical coordinates is investigated in order to analyze the optical wave propagation in the bent waveguides with the strong lateral confinement which will keep low radiation loss. The three dimensional (3D) semivectorial wave propagation equation is programmed in the quick and unconditionally stable procedure by using the alternating direction implicit method. This version of FD-BPM could well express the polarization characteristics of modal field near the dielectric interfaces and accurately simulate the wave propagation in bent waveguides even at a very small radius (<100 /spl mu/m). Moreover, it is pointed out that the numerical precision of the algorithm is intensively affected by the propagation loss of bent waveguides along with the propagation step length of beam propagation method.

Design of a spotsize-converter-integrated laser diode (SS-LD) with a lateral taper, thin-film core and ridge in the 1.3-μm-wavelength region based on the 3-D BPM

In order to develop spotsize-converter-integrated laser diodes (SS-LDs) with high efficiency and large-misalignment tolerances in the 13-/spl mu/m-wavelength region, spotsize converters (SSCs), which consist of lateral taper, thin-film core and ridge, are investigated employing the three-dimensional (3-D) semivectorial finite-difference beam propagation method (FD-BPM) with nonequidistant discretization. The sum of the spot-conversion loss and coupling loss between the laser diode (LD) eigenmode and the single-mode fiber (SMF) eigenmode are calculated for various structural parameters. Small loss of around 1.5 dB can be achieved by introducing a nonlinear taper. The fabrication tolerances for the SSCs are also clarified. The calculated results agree well with the results for actually fabricated SS-LD's. It is also shown that the radiation loss and coupling characteristics of the SS-LDs with a buried thin-film core structure can be improved using a nonlinear taper.

A novel couple-type power divider with large-angle low-loss characteristics

A novel large-angle low-loss direction-coupler type power divider with designed ratio between output waveguides is proposed. The radiation loss is greatly reduced by using a micro-prism at the bend corner to compensate the phase mismatch due to bending. A normalized transmitted power of the power divider with a bend angle of 10/spl deg/ simulated by the semivectorial beam propagation method is about 93%, which is much larger than those were reported for single-mode waveguides. Application of more micro-prisms is also shown. The calculated loss of a symmetric large-angle 3-dB directional coupler with eight micro-prisms is less than 0.953 dB.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The semivectorial beam propagation method

Details of an efficient semivectorial beam propagation method are presented. The propagation is determined by solving the finite-difference equation in alternating directions. Unlike the traditional split-operator beam propagation method, in the semivectorial method the index term is not separated from the spatial differentiations. Since boundary conditions at dielectric interfaces can be satisfied by two orthogonal polarizations individually, the method is semivectorial. The performance can be enhanced by using a nonuniform grid. By modifying the routine, it can also be applied to periodic structures. Numerical results for rib waveguides are presented. >

Semivectorial beam-propagation method for analyzing polarized modes of rib waveguides

The authors report a semivectorial beam-propagation method which can determine the form birefringence in rib or channel waveguides. In this approach, a finite-difference equation is solved by using the alternating-implicit method to simulate the propagation of the optical beam. Since boundary conditions are incorporated into the finite-difference equation, polarized modes can be simulated. Numerical results on three well-known rib waveguides are presented with comparisons to published data. >

Study of form birefringence in waveguide devices using the semivectorial beam propagation method

Waveguide devices based on nonbirefringent substrates may still have form birefringence if index discontinuities exist. It is demonstrated that the semivectorial beam propagation method can be used to study the polarization dependence in waveguide devices. It is shown that the calculated coupling lengths of planar directional couplers match within 3.5% of analytical solutions. Results on polarization dependencies of coupling lengths and bending losses of rib waveguide devices are presented. Results of rib waveguide directional couplers indicate that the form birefringence can be significant. Losses of S-shaped bends are weakly polarization dependent in the low-loss regime.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>