C.L. Xu

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. >

Simulation of three-dimensional optical waveguides by a full-vector beam propagation method

Simulations of optical guided waves in three-dimensional waveguide structures by a full vector beam propagation method are described. Two sets of coupled equations governing the propagation of the transverse electric and magnetic fields are derived systematically. Polarization dependence and coupling due to the vectorial nature of the electromagnetic fields are considered in the formulations. The governing equations are solved subsequently by finite-difference schemes. The vector BPM is first assessed for a step-index circular fiber by comparing the numerical results with the exact analytical solutions. The guided modes of a rib waveguide are then investigated in detail. Comparisons among the scalar, semi-vector and full-vector simulations of the rib waveguide are made. Finally polarization rotation of a periodically loaded rib waveguide operated fully based on the vector nature of the electromagnetic waves is modeled and simulated. >

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. >

A full-vectorial beam propagation method for anisotropic waveguides

An extension of the full-vectorial beam propagation method to anisotropic media is presented. Optical waveguides made of anisotropic materials can be modeled and simulated. The polarization dependence and coupling due to both the material and the geometric effects are considered. >

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>>

A wide-angle vector beam propagation method

A wide-angle vector beam propagation method is developed and presented. Considerable improvement in accuracy over the paraxial vector propagating algorithms is achieved with virtually no additional computation.<<ETX>>

A vector beam propagation method for guided-wave optics

A vector beam propagation method (BPM) for the modeling and simulation of electromagnetic wave propagation in optical guided-wave devices is proposed. The vector BPM is based on a finite-difference scheme which takes into account the boundary conditions of the transverse electric fields over the waveguide cross section. By incorporating the vector boundary conditions in the finite-difference scheme, the polarization property of the propagation electromagnetic waves is included in the analysis. The method is applied to a directional coupler made of parallel slabs, and is shown to be in excellent agreement with the exact solutions. >

A vector beam propagation method based on H fields

A vector beam propagation (VBM) method based on transverse magnetic fields (H-formulation) is developed and presented. By considering the vector property of the transverse differential operators, the polarizations of the propagating electromagnetic waves are modeled and simulated by the finite-difference solutions. A comparison with the vector beam propagation method based on the E fields is made and the results are found to be in excellent agreement. It is shown that the FD-VBPM based on the H formulation is equivalent to that based on the E formulation.<<ETX>>

An unconditionally stable vectorial beam propagation method for 3-D structures

An unconditionally stable vectorial beam propagation method for three-dimensional structures is developed and presented. The stability criteria is theoretically proved, and verified numerically. Since this new algorithm conserves power it can be used to calculate the loss of optical guided-wave structures accurately.<<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. >