Finite-difference Vector Beam Propagation Method Research Articles

Explicit finite-difference vector beam propagation method based on the iterated Crank-Nicolson scheme

We introduce and develop a new explicit vector beam propagation method, based on the iterated Crank-Nicolson scheme, which is an established numerical method in the area of computational relativity. The proposed approach results in a fast and robust method, characterized by simplicity, efficiency, and versatility. It is free of limitations inherent in implicit beam propagation methods, which are associated with poor convergence or uneconomical use of memory in the solution of large sparse linear systems, and thus it can tackle problems of considerable size and complexity. The advantages offered by this approach are demonstrated by analyzing a multimode interference coupler and a twin-core photonic crystal fiber. A possible wide-angle generalization is also provided.

Improving triangular-lattice photonic-crystal-fiber couplers by introducing geometric nonuniformities

The coupling characteristics of newly proposed photonic-crystal-fiber couplers are rigorously analyzed using a 3-D finite-difference vector beam propagation method. The coupling length and efficiency of the couplers are investigated as a function of their geometrical parameters at different wavelengths. Size variability of the central hole is considered as a means of improving the coupling between the two cores. A determination of the guiding properties of the couplers, such as the propagation constants and the effective indices, is performed using a mode solver based on the plane-wave method. We show that it is possible to design very short photonic-crystal-fiber couplers with submillimeter coupling lengths. Nonuniformities are deliberately introduced in the coupler pattern to decrease the coupling length in comparison with the ideal structures. This study confirms that the designed coupler can act as an efficient ultrasmall-wavelength splitter or polarization-preserving directional coupler for wavelength division multiplexing systems.

Analysis of GaN-based single-mode rib waveguide with large cross section

A GaN-based optical single-mode rib waveguide with a large cross section is systematically designed and analyzed using the finite-difference vector beam propagation method (FD-VBPM). The method is a combination of numerical aperture and FD-VBPM, which is used to determine the single-mode conditions for a GaN/AlxGa1-xN optical rib waveguide. We analyze the optical propagation properties and loss characteristics of the designed waveguides. The analysis illustrates that optical power increases with an increase of the rib width or a decrease of the slab height. Therefore, our analysis results can be helpful in the process of designing a GaN-based rib waveguide for optical communications.

A three-wavelength Mach–Zehnder optical demultiplexer by one step ion-exchange in glass

A three-wavelength optical demultiplexer based on Mach–Zehnder interferometer parameters is presented. The combination of the effective index technique based Rung–Kutta method and a finite difference vector beam propagation method (FD-VBPM) provide for a computational design tool that yields useful results. The demultiplexer device is fabricated by a one-step K + ion-exchange in glass. The total device length obtained is 1.49 cm. The measured output light–power extinction ratios for the three wavelengths, 980, 1310 and 1550 nm are 19, 24 and 24 dB, respectively, and agree reasonably well with the FD-VBPM simulation.

Electromagnetic field in a slab of photonic crystal by BPM

The finite-difference vector beam propagation method is used to simulate propagation of Gaussian light beam in a finite slab of photonic crystal. A possibility to control light flow by the change of symmetry and polarisation of the incident light beam is demonstrated.

An explicit and stable finite difference 2-D vector beam propagation method

The DuFort-Frankel method is used to replace the Crank-Nicolson method in a two-dimensional finite-difference vector beam propagation method (VBPM). This new method is explicit, stable, and very efficient, and is particularly good for adaptation in a three dimensional finite-difference VBPM.

Efficient and accurate vector mode calculations by beam propagation method

An in-depth study of the beam propagation method for the vector mode calculation of optical waveguides is presented. It is established that the imaginary-distance propagation method may be generalized to vectorial modes for arbitrary structures by combining it with the finite-difference vector beam propagation method (FD-VBPM). A simple, unified theory and analysis are developed. An assessment of the accuracy and efficiency is carried out by comparing the simulated results with the analytical solutions for well-known structures.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Application of the finite-difference vector beam propagation method to directional coupler devices

The finite-difference vector beam propagation method (FD-VBPM) is applied to optical guided-wave devices based on two-dimensional directional couplers. The FD-VBPM is first validated for a parallel coupler made of two identical step-index slab waveguides by comparing with the exact analytical solutions. Subsequently, the polarization beamsplitters and wavelength filters based on directional couplers are simulated. The polarization properties of these devices are examined.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The finite-difference vector beam propagation method: analysis and assessment

The newly developed finite-difference vector beam propagation method (FD-VBPM) is analyzed and assessed for application to two-dimensional waveguide structures. The general formulations for the FD-VBPM are derived from the vector wave equations for the electric fields. The stability criteria, the numerical dissipation, and the dispersion of the finite-difference schemes are analyzed by applying the von Neumann method. Important issues regarding the implementation, such as the choice of reference refractive index, the application of numerical boundary conditions, and the use of numerical solution schemes, are discussed. The FD-VBPM is assessed by calculating the attenuation coefficients and the percentage errors of the propagation constants of the TE and TM modes of a step-index slab waveguide. Several salient features of the FD-VBPM are illustrated.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A finite-difference vector beam propagation method for three-dimensional waveguide structures

A finite-difference vector beam propagation method (FD-VBPM) for three-dimensional waveguide structures is developed. The polarization dependence and coupling of the optical guided-waves in the 3-D structures can be modeled and simulated.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>