Absorbing boundary condition (ABC) and perfectly matched layer (PML) in numerical beam propagation: a comparison

Kumar, Rahul; Sharma, Anurag

doi:10.1007/s11082-019-1770-7

Cited by 11 publications

(9 citation statements)

References 30 publications

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“…Both these affect the wave propagating through structure such that the field in the layer is attenuated avoiding significant reflections. In an earlier work, we had shown that the PML and the gradual ABC compare well in their performance and in some cases PML is better than the ABC while in some other cases the ABC is better than the PML (Kumar and Sharma 2019).…”

Section: Introductionmentioning

confidence: 83%

“…In order to suppress these unwanted reflections from the numerical boundaries, various boundary conditions have been devised: absorption boundary condition (ABC) (Mur 1981;Yevick and Jun 1994;Vasallo and Collino 1996;Koshiba and Tsuji 2001;Kumar and Sharma 2019), transparent boundary condition (TBC) (Hadley 1991(Hadley ,1992a and the perfectly matched layer boundary condition(PML) (Berenger 1994;Chew and Weedon 1994). Each one has some advantages and some limitations which have been discussed elsewhere (Jimenez and Perez-Murano 2001;Kumar and Sharma 2019). These boundary conditions are in the form of a layer next to the numerical boundary, in which the wave is attenuated in a suitable manner.…”

Section: Introductionmentioning

confidence: 99%

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A new method to suppress reflections from numerical boundaries in wave propagation

Choudhary,

Sharma

2024

J Opt

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To suppress numerical reflections, various boundary conditions, such as the transparent boundary condition (TBC), the absorbing boundary condition (ABC), and the perfectly matched layer (PML), are used in wave propagation methods. We propose a new boundary condition that works directly on the field. We show through examples that the field-domain boundary condition (FDBC) performs as well as the ABC and the PML. It is much easier to implement as it requires only multiplication of the field in the absorbing layer by a factor. Another advantage with the FDBC is that its performance does not depend critically on the choice of numerical parameters such as the absorption profile and the strength of absorption.

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Section: Introductionmentioning

confidence: 83%

Section: Introductionmentioning

confidence: 99%

A new method to suppress reflections from numerical boundaries in wave propagation

Choudhary,

Sharma

2024

J Opt

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“…The step size for numerical propagation was taken as 0.04µm, since the propagation is unaffected by further reduction in the step size. A gradually absorbing boundary condition (gABC) was implemented, which has been shown to be comparable to PML [39]. The gABC strength for a width of 40% was taken to be 0.89 with a sin 2 profile [39].…”

Section: Three Core Photonic Lanternmentioning

confidence: 99%

“…A gradually absorbing boundary condition (gABC) was implemented, which has been shown to be comparable to PML [39]. The gABC strength for a width of 40% was taken to be 0.89 with a sin 2 profile [39]. The gABC parameters are optimized and its effect on the propagation can be considered to be similar for both the cases.…”

Section: Three Core Photonic Lanternmentioning

confidence: 99%

Engineering Adiabaticity for Efficient Design of Photonic Lanterns

Sunder

Sharma

2021

IEEE Photonics J.

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We present a comprehensive systematic framework for optimizing adiabaticity in photonic lanterns. The framework considers the effects of both the cross-sectional and longitudinal device parameters on adiabaticity. Photonic lanterns are adiabatic photonic devices and are therefore known to have large device lengths. A Shortcuts-to-adiabaticity (STA) protocol is employed to optimize the adiabatic taper profile in all-fibre photonic lanterns. The method tailors adiabatic propagation of light in the system by appropriately correcting the local slope of the taper profile. A quantifiable measure of adiabaticity is established, based on the adiabaticity criterion. This measure relates inversely to the device length and is a useful parameter in taper optimization. We apply the protocol to reported photonic lantern devices to obtain optimal adiabatic taper profiles having shorter device lengths. The optimized taper profile refers to that taper profile which corresponds to the minimum local intermodal coupling at every point along the quasi-adiabatic transition for a given device length. While optimizing the adiabatic transition by minimizing intermodal coupling is the basic aim of this work, length optimization is an extremely useful by-product. This procedure can be used to either reduce the device length or to reduce the mode-coupling losses or both. This study analyses reported three and six-core mode selective photonic lanterns as examples. We also discuss ways to make the optimum profiles practically realizable.

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“…Further, researchers have constructed, studied, and compared the applicability and effectiveness of ABCs for problems arising in areas such as acoustics, geophysics, fluid dynamics, materials science, meteorology, antennas, seepage, and heat transfer problems. [9–34] Often, the necessity of using ABCs occurs in nonlinear optics and laser physics, and these fields of modern physics are extensively studied because of their widespread laser application [35–39]. In this regard, the development of ABCs for linear and nonlinear Schrödinger equations is a meaningful task that has attracted the attention of numerous scientists [40–61].…”

Section: Introductionmentioning

confidence: 99%

Cross‐impact of beam local wavenumbers on the efficiency of self‐adaptive artificial boundary conditions for two‐dimensional nonlinear Schrödinger equation

Trofimov

Loginova

Egorenkov

et al. 2023

Math Methods in App Sciences

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In this paper, we propose self‐adaptive artificial boundary conditions (ABCs) for the two‐dimensional (2D) time‐dependent nonlinear Schrödinger equation and studied their efficiency. This equation describes the laser pulse interaction with a semiconductor layer under laser‐induced plasma generation. Because of its nonlinearity, the interaction process is very sensitive to the appearance of the optical beam spurious reflection; therefore, highly transparent ABCs are urgently required to avoid disturbing the interaction process by an unphysical reflected wave. This can be achieved by using time‐ and spatial‐dependent local wavenumbers computed near the artificial boundaries. We claim that it is necessary to account for both wavenumbers in each of the adaptive ABCs stated on both spatial coordinates. Based on computer simulation, we demonstrate an increase in the efficiency of the adaptive ABC stated on the coordinate along which the optical pulse propagates by involving both local wavenumbers. The accuracy of the developed approach is verified using a well‐known analytical solution of the linear Schrödinger equation as well as the reference problem solution, obtained by solving the problem with zero‐value boundary conditions on the extended spatial domain. For computer modeling, the finite‐difference scheme, possessing asymptotic stability, is applied together with a two‐stage iterative process for its realization. The algorithm and peculiarities of the local wavenumber computation are discussed in detail. The applicability of the developed approach is also demonstrated via the solution of both linear and nonlinear problems. The proposed method has widespread application for solving various laser physics problems governed by the Schrödinger equation.

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Absorbing boundary condition (ABC) and perfectly matched layer (PML) in numerical beam propagation: a comparison

Cited by 11 publications

References 30 publications

A new method to suppress reflections from numerical boundaries in wave propagation

A new method to suppress reflections from numerical boundaries in wave propagation

Engineering Adiabaticity for Efficient Design of Photonic Lanterns

Cross‐impact of beam local wavenumbers on the efficiency of self‐adaptive artificial boundary conditions for two‐dimensional nonlinear Schrödinger equation

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