A full vectorial generalized discontinuous Galerkin beam propagation method (GDG–BPM) for nonsmooth electromagnetic fields in waveguides

Fan, Kai; Cai, Wei; Ji, Xia

doi:10.1016/j.jcp.2008.03.044

Cited by 7 publications

(6 citation statements)

References 15 publications

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“…Similarly to the general procedure in isotropic media [9], we want to eliminate E z from Eqs. (1) and (2) to obtain a simple propagation equation involving only the transverse field E β . Before doing this, let us split the birefringent media in a series of slabs normal to the z-direction and assume that the permittivity tensor is z-independent in each slab -thereby greatly simplifying the derivation of the propagation equation in each slab.…”

Section: General Propagation Equations and Approximationsmentioning

confidence: 99%

“…On the other hand, BPM allows accurate simulation of light propagation on much coarser meshes provided that light don't deviate too much from a given reference direction of propagation. BPM is very well established in isotropic media, with a number of sub-class of methods based on Finite-Difference [1], Finite-Element [2] or Fast-Fourier-Transform [3]. Among these methods, paraxial BPM makes use of the Slowly-Varying-Amplitude-Approximation to yield methods which are very efficient but limited in terms of accuracy, while wide-angle BPM is a class of methods which are more accurate (but a bit more expansive) [4].…”

Section: Introductionmentioning

confidence: 99%

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Physics-based multistep beam propagation in inhomogeneous birefringent media

Poy¹,

Žumer²

2020

Opt. Express

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We present a unified theoretical framework for paraxial and wide-angle beam propagation methods in inhomogeneous birefringent media based on a minimal set of physical assumptions. The advantage of our schemes is that they are based on differential operators with a clear physical interpretation and easy numerical implementation based on sparse matrices. We demonstrate the validity of our schemes on three simple two-dimensional birefringent systems and introduce an example of application on complex three-dimensional systems by showing that topological solitons in frustrated cholesteric liquid-crystals can be used as light waveguides.

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Section: General Propagation Equations and Approximationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Physics-based multistep beam propagation in inhomogeneous birefringent media

Poy¹,

Žumer²

2020

Opt. Express

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“…BPM is widely used in isotropic systems and very popular in waveguiding. Implementations based on fast Fourier transform [7], finite difference [8,9], or finite elements [10,11] exist. However, in birefringent material, the anisotropic nature of the permittivity tensor complicates the implementation of the BPM method.…”

Section: Introductionmentioning

confidence: 99%

Polarization microscope simulations using an efficient transfer matrix-based beam propagation method

Petelin¹,

Nys²,

Neyts³

2023

Preprint

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A technique for white light polarizing microscope simulations is presented. It uses wide-angle diffraction and accurately simulates the transfer properties of the imaging system, including the objective's finite numerical aperture, coherence properties of the illuminant, and camera spectral response. The technique is based on the transfer matrix formalism, which we generalize for 3D and build a split-step fast Fourier transform beam propagation method (FFT-BPM) to study birefringent optical elements, such as liquid crystals. The implementation of the algorithm is numerically efficient, allowing tunable diffraction calculation accuracy and fast calculation speed. To demonstrate the technique, we calculate the diffraction efficiency of a 1D circular polarization grating, compute micrographs of 2D diffraction gratings, and compare the results with experiments and computations using finite difference time domain (FDTD).

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“…First, our propagation model makes minimal assumptions on the electromagnetic fields in question, unlike the scalar beam propagation method (BPM, see [53,58,48,64,4] and references therein), which assumes a polarization maintaining propagation of the electromagnetic fields in an optical fiber, whereas our treatment is truly vectorial. Though both semi-vectorial and full vectorial BPM approaches have already been implemented (see [36,37,56,57,26] and references therein), we are introducing a fiber model that is a full boundary value problem rather than an initial value problem. In addition, we employ 3D isoparametric curvilinear elements to model the curved fiber (core and inner cladding) geometry, which can also later be used for studying microstructure fibers or hollow-core gas-filled fiber lasers.…”

Section: Introductionmentioning

confidence: 99%

A 3D DPG Maxwell approach to nonlinear Raman gain in fiber laser amplifiers

Nagaraj

Grosek

Petrides

et al. 2019

Journal of Computational Physics: X

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We propose a three dimensional Discontinuous Petrov-Galerkin Maxwell approach for modeling Raman gain in fiber laser amplifiers. In contrast with popular beam propagation models, we are interested in a truly full vectorial approach. We apply the ultraweak DPG formulation, which is known to carry desirable properties for high-frequency wave propagation problems, to the coupled Maxwell signal/pump system and use a nonlinear iterative scheme to account for the Raman gain. This paper also introduces a novel and practical full-vectorial formulation of the electric polarization term for Raman gain that emphasizes the fact that the computer modeler is only given a measured bulk Raman gain coefficient. Our results provide promising qualitative corroboration of the model and methodology used.

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A full vectorial generalized discontinuous Galerkin beam propagation method (GDG–BPM) for nonsmooth electromagnetic fields in waveguides

Cited by 7 publications

References 15 publications

Physics-based multistep beam propagation in inhomogeneous birefringent media

Physics-based multistep beam propagation in inhomogeneous birefringent media

Polarization microscope simulations using an efficient transfer matrix-based beam propagation method

A 3D DPG Maxwell approach to nonlinear Raman gain in fiber laser amplifiers

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