Complex Padé approximant operators for wide-angle beam propagation

Le, Khai Q.

doi:10.1016/j.optcom.2008.12.014

Cited by 17 publications

(10 citation statements)

References 11 publications

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“…(11), ( ) ( ) not give correct damping to evanescent modes. This drawback is circumvented by application of the modified Padé approximation [28]. Application of the finite-differences (FD) scheme for the discretization of the transverse derivatives converts the operators p A and p B from Eq.…”

Section: Optical Modelmentioning

confidence: 99%

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Simulation of spectral stabilization of high-power broad-area edge emitting semiconductor lasers

Holly¹,

Hengesbach²,

Traub³

et al. 2013

Opt. Express

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The simulation of spectral stabilization of broad-area edge-emitting semiconductor diode lasers is presented in this paper. In the reported model light-, temperature- and charge carrier-distributions are solved iteratively in frequency domain for transverse slices along the semiconductor heterostructure using wide-angle finite-difference beam propagation. Depending on the operating current the laser characteristics are evaluated numerically, including near- and far-field patterns of the astigmatic laser beam, optical output power and the emission spectra, with central wavelength and spectral width. The focus of the model lies on the prediction of influences on the spectrum and power characteristics by frequency selective feedback from external optical resonators. Results for the free running and the spectrally stabilized diode are presented.

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Section: Optical Modelmentioning

confidence: 99%

“…There are several applications presented in literature [24][25][26][27] and [28] where the FD-BPM is successfully applied to compute light field propagations. The right hand side of Eq.…”

Section: Optical Modelmentioning

confidence: 99%

Simulation of spectral stabilization of high-power broad-area edge emitting semiconductor lasers

Holly¹,

Hengesbach²,

Traub³

et al. 2013

Opt. Express

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“…Using standard techniques, evanescent modes are interpreted as propagating modes and will not be damped exponentially in propagation direction [7]. The introduction of complex Padé approximations might provide a solution for the problem described [11], [12]. Eigenvector expansion methods are inherently accurate, because evanescent fields, radiation field and guided waves can be described.…”

Section: Introductionmentioning

confidence: 99%

Fourier Expansion of the Beam Propagation Operator in the Eigenvalue Domain

Balkenohl

Schulz

2014

J. Lightwave Technol.

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Propagation methods in the frequency domain are powerful tools for the analysis of electromagnetic field propagation within photonic waveguide devices. They can be classified as wide angle beam propagation or eigenvector expansion methods. In comparison to the wide angle beam propagation methods, eigenvector expansion methods inherently include an accurate computation of radiation waves, guided modes, and evanescent waves. Common numerical methods rely on the solution of eigenvalue problems or the solution of matrix equations of high order. Consequently, the computation time needed can be tedious. A method is proposed, which exploits the inherent advantage of eigenvector expansion methods, but reduces the computation time considerably as the resulting propagation algorithm is based on simple matrix vector multiplications, allowing a large number of discretization points. The method takes advantage of the compact eigenvalue spectrum of the system matrix. The operator can be periodically expanded so that a Fourier decomposition can be applied. The expansion is carried out under consideration of the physical interpretation of eigenvalues for radiation waves, guided modes, and evanescent waves.Index Terms-Beam propagation methods, frequency domain methods, photonic waveguide devices.

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“…In these approaches the field is assumed to be separated into two parts including the complex field amplitude and a propagation factor. There exist real Padé approximant operators (Hadley 1992) and complex Padé approximant operators (Le 2009). In addition, treatments of WA-BPM without having to make the SVEAs have also been reported, including the series expansion technique of the propagator (Lee and Voges 1994), the split-step of beam propagation equation (Sharma and Agrawal 2004), and the recently proposed rational KP approximant operators (Le and Bienstman 2009).…”

Section: Introductionmentioning

confidence: 99%

“…These modes can cause serious instability problems when implementing WA-BPMs based on real propagators. To circumvent this problem, we recently proposed modified Padé approximant operators, which give evanescent waves the desired damping and allow more accurate approximation to the Helmholtz equation than the conventional operators (Le 2009). …”

Section: Introductionmentioning

confidence: 99%

A stable complex Jacobi iterative solution of 3D semivectorial wide-angle beam propagation using the iterated Crank–Nicholson method

Bienstman

2009

Opt Quant Electron

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An extension of the recently proposed three-dimensional (3D) wide-angle (WA) beam propagation method (BPM) using complex Jacobi iteration (CJI) taken into account polarization effects is presented. The resulting iterative BPM is faster than BPMs based on the traditional direct matrix inversion for waveguides with unchanging refractive index profiles during propagation direction. However, for varying refractive index waveguides the iterative method suffered from the fact that the iteration count between two successive crosssections increases dramatically during the propagation direction. To overcome this problem, we propose the utility of the iterated Crank-Nicholson method. At each propagation step, the propagation equation is divided in multiple stages by the iterated Crank-Nicholson method and then each stage is recast in terms of a Helmholtz equation with source term, which is solved effectively by the complex Jacobi iterative method. The resulting approach is stable and well-suited for large structures with long propagation paths.

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Complex Padé approximant operators for wide-angle beam propagation

Cited by 17 publications

References 11 publications

Simulation of spectral stabilization of high-power broad-area edge emitting semiconductor lasers

Simulation of spectral stabilization of high-power broad-area edge emitting semiconductor lasers

Fourier Expansion of the Beam Propagation Operator in the Eigenvalue Domain

A stable complex Jacobi iterative solution of 3D semivectorial wide-angle beam propagation using the iterated Crank–Nicholson method

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