Slanted-Wall Beam Propagation

Hadley, G. Ronald

doi:10.1109/jlt.2007.901522

Cited by 8 publications

(5 citation statements)

References 13 publications

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“…In ( 5) j = √ −1 and E t = E t e −j β z = E t e −j kn 0 z , where β = kn 0 is the propagation constant and n 0 denotes a reference (modal) index. The further assumption used in (5) is that the field envelope variation with z is sufficiently small and the field propagation is dependent only on the first derivative of z. Equation ( 5) is known as the paraxial full-vectorial approximation of (2) and has initiated the development of the very efficient and well-established numerical simulation techniques in photonics and optoelectronics, recognized today as "the beam propagation methods -(BPM)", [3].…”

Section: Outline Of the Methods 21 Basic Theoretical Conceptmentioning

confidence: 99%

“…Equation ( 5) is known as the paraxial full-vectorial approximation of (2) and has initiated the development of the very efficient and well-established numerical simulation techniques in photonics and optoelectronics, recognized today as "the beam propagation methods -(BPM)", [3]. In the single most oftenused BPM, by using finite difference discretization techniques, we arrive to FD-BPM, [1,[3][4][5][6][7][8]. In FD-BPM the transverse (e.g.…”

Section: Outline Of the Methods 21 Basic Theoretical Conceptmentioning

confidence: 99%

“…In the finite difference approaches of (4) (the standard FDM) and (3), (5) (frequency domain FD-BPM), the main research interests are: developing of socalled improved FD schemes with more accurate treatment of the dielectric interfaces, [9][10][11][12], and extending the range of FD-BPM applicability to the waveguide structures changing in the direction of propagation, [5,6,13,14].…”

Section: Outline Of the Methods 21 Basic Theoretical Conceptmentioning

confidence: 99%

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New finite-difference formulas for dielectric interfaces

Djurdjevic

2010

FACTA U EE

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The finite difference method is often-used numerical simulation method in electromagnetics. In this paper a new methodology is presented that allows the derivation of finite difference formulas near dielectric interfaces with high accuracy. Derived finite difference formulas have been used in the electric field computations in electrostatics (the two-dimensional Laplace's equation is employed) and in full-vectorial waveguide simulations in photonics (the three-dimensional Helmholtz's equation and the beam propagation simulation technique in frequency domain are employed). The finite difference formulas derivation is made under a power series expansion of the transverse field components in the case for uniform rectangular discretization mesh. The resulting finite difference formulas provide highly accurate solutions, both for electrostatic and waveguide propagation problems even on coarse grids and thus enable a very cost-effective and rapid numerical field simulations. Reported methodology and derived formulas have not been used in finite difference method formulations in literature. Some results for the electric field computation and dielectric waveguide eigenmode and propagation analysis are presented. .

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Section: Outline Of the Methods 21 Basic Theoretical Conceptmentioning

confidence: 99%

Section: Outline Of the Methods 21 Basic Theoretical Conceptmentioning

confidence: 99%

Section: Outline Of the Methods 21 Basic Theoretical Conceptmentioning

confidence: 99%

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New finite-difference formulas for dielectric interfaces

Djurdjevic

2010

FACTA U EE

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“…The sampling grid of the SR mesh is aligned with the component material boundary thus eliminating staircase error and allowing relaxation in mesh size. Various SR-BPM schemes have been introduced [5][6][7][8][9][10][11] and different schemes can be combined together to map out the optical component. Furthermore, the SR coordinate system ensures high accuracy for the simple paraxial BPM formulation even without the use of wide-angled schemes [10].…”

Section: Introductionmentioning

confidence: 99%

Oblique Du-Fort Frankel Beam Propagation Method

Chan

Sewell

Vuković

et al. 2011

Advances in OptoElectronics

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“…Nevertheless, they still suffer from the staircase approximation problem when applying the finite difference beam propagation method (BPM) for the analysis of beam propagation in high-index-contrast structures. Recently, a solution for this problem was suggested in [9]. The proposed algorithm results in the so-called slanted-wall beam propagation, which is well suited for studying wide-angle (WA) propagation through a general class of optical WG structures defined by dielectric interfaces that may be slanted with respect to the propagation direction.…”

Section: Introductionmentioning

confidence: 99%

Fast three-dimensional generalized rectangular wide-angle beam propagation method using complex Jacobi iteration

Bienstman

2009

J. Opt. Soc. Am. B

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A fast and efficient three-dimensional generalized rectangular wide-angle beam propagation method (GR-WA-BPM) based on a recently proposed modified Padé (1,1) approximant is presented. In our method, at each propagation step, the beam propagation equation is recast in terms of a Helmholtz equation with a source term, which is solved quickly and accurately by a recently introduced complex Jacobi iterative (CJI) method. The efficiency of the GR-WA-BPM for the analysis of tilted optical waveguides is demonstrated in comparison with the standard wide-angle beam propagation method based on Hadley's scheme. In addition, since the utility of the CJI method depends mostly on its execution speed in comparison with the traditional direct matrix inversion, several performance comparisons are also presented.

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Slanted-Wall Beam Propagation

Cited by 8 publications

References 13 publications

New finite-difference formulas for dielectric interfaces

New finite-difference formulas for dielectric interfaces

Oblique Du-Fort Frankel Beam Propagation Method

Fast three-dimensional generalized rectangular wide-angle beam propagation method using complex Jacobi iteration

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