SPIP : A computer program implementing the Interaction Picture method for simulation of light-wave propagation in optical fibre

Balac, Stéphane; Fernandez, Arnaud

doi:10.1016/j.cpc.2015.10.012

Cited by 9 publications

(9 citation statements)

References 9 publications

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“…Other undesirable nonlinear effect like stimulated Raman scattering (SRS) may occur and disturb the Kerr comb generation too [41]. Contrary to SBS the SRS effect could be rapidly numerically computed by replacing propagation equation (5) with the GNLSE (4) [26,27].…”

Section: Resultsmentioning

confidence: 99%

“…Combined with an embedded Runge-Kutta (RK) scheme with order 4(3) to solve the nonlinear part of the GNLSE, it provides a robust and efficient step-size adaptive numerical method well suited for the purposes of the present study. Details on the RK4(3)-IP method, including a downloadable C++ software can be found in [26].…”

Section: B Intra-cavity Propagationmentioning

confidence: 99%

“…This is, however, at the expense of higher computation cost compared to the LL equation since the propagation step-size cannot be larger than the cavity length when using this model as the basis for simulations. A fourth order, Runge-Kutta method in the interaction picture (RK4IP) is used to solve the nonlinear Schrödinger equation over the length of the cavity and simulate intra-cavity field propagation [26].…”

Section: Introductionmentioning

confidence: 99%

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Numerical study on Kerr frequency comb generation in Si₃N₄ microresonators with frequency-dependent access coupler properties

et al. 2019

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Within the frame of vertically coupled silicon nitride (Si3N4) resonators characterized with 220 GHz free spectral range driven by a continuous wave laser at 1.55 µm for Kerr comb generation, the design of achromatic critically coupled resonators may bring severe issues because of the difficulty in designing dispersion-free access couplers with controlled coupling factor over a large spectral bandwidth. As a consequence of this, numerical simulations of Kerr frequency comb in these structures may drastically differ from reality if frequency-dependence of the access coupler's properties is not taken into account in the simulated model. In order to address this issue, we have developed a numerical model that takes into account the frequency dependence of the access coupler coefficients and remains valid even for the simulation of low Q factor resonators. Field propagation within the ring is described by the nonlinear Schrödinger equation. Novelty in the model resides in the computation of a complex-valued, frequency dependent coupling transfer function between resonant ring and underlying access waveguide that models frequency-dependent dispersion and losses in the access coupling region of the resonator. Based on simulation results, we discuss on the differences observed in Kerr comb generation in resonators with three different coupler designs initially intended to yield critical coupling over the largest achievable bandwidth.

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Section: Resultsmentioning

confidence: 99%

Section: B Intra-cavity Propagationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Numerical study on Kerr frequency comb generation in Si₃N₄ microresonators with frequency-dependent access coupler properties

et al. 2019

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“…[4]). The method from [7] has been implemented and applied to the simulation of light-wave propagation in optical fibers in [5]. A similar approach is adopted in [46], where comparisons are made also for the Burgers equation with shocks.…”

Section: Lawson Methodsmentioning

confidence: 99%

Convergence of exponential Lawson-multistep methods for the MCTDHF equations

Koch

2019

ESAIM: M2AN

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We consider exponential Lawson multistep methods for the time integration of the equations of motion associated with the multi-configuration time-dependent Hartree-Fock (MCTDHF) approximation for high-dimensional quantum dynamics. These provide high-order approximations at a minimum of evaluations of the computationally expensive nonlocal potential terms, and have been found to enable stable long-time integration. In this work, we prove convergence of the numerical approximation on finite time intervals under minimal regularity assumptions on the exact solution. A numerical illustration shows adaptive time propagation based on our methods.Mathematics Subject Classification. 65L05, 65L06, 65M12, 65M15, 65M20, 81-08. on the Hilbert space L 2 . Here, A : D ⊆ L 2 → L 2 is a self-adjoint differential operator and B a generally unbounded nonlinear operator. We will denote the flow of −iĤ by E −iĤ , that is, ψ(t) = E −iĤ (t, ψ 0 ) is the solution of ∂ t ψ = −iĤ(ψ), ψ(0) = ψ 0 , and similarly for E A and E B .Equations of this type commonly arise from model reductions of high-dimensional quantum dynamical systems serving to make many-particle quantum simulations computationally tractable. Examples of such model reductions are the Gross-Pitaevskii equation (GPE) for Bose-Einstein condensates (BEC) [41], which constitutes a meanfield theory for ultracold dilute bosonic gases, the multiconfigurational time-dependent Hartree for bosons (MCTDHB) method for ultracold bosonic atoms [1], the multiconfigurational time-dependent Hartree-Fock (MCTDHF) method [27,32,48] and its most current extension, the time-dependent complete-active-space self-consistent-field (TD-CASSCF) method for electron dynamics in atoms and small molecules [44], and timedependent density functional theory (TDDFT) for extended systems such as large molecules, nanostructures

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“…For particular problems, however, less conditions are often required for obtaining a certain order of convergence. 1 It was already observed in [10] that periodic boundary conditions do not lead to any order reduction in exponential integrators of collocation type in contrast to homogeneous Dirichlet boundary conditions, which restrict the order of convergence considerably (close to the stage order, depending on the precise situation). Full-order convergence for periodic boundary conditions was also noticed for exponential time-differencing methods in [13].…”

Section: Introductionmentioning

confidence: 99%

On the convergence of Lawson methods for semilinear stiff problems

2020

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Since their introduction in 1967, Lawson methods have achieved constant interest in the time discretization of evolution equations. The methods were originally devised for the numerical solution of stiff differential equations. Meanwhile, they constitute a well-established class of exponential integrators, which has turned out to be competitive for solving space discretizations of certain types of partial differential equations. The popularity of Lawson methods is in some contrast to the fact that they may have a bad convergence behaviour, since they do not satisfy any of the stiff order conditions. The aim of this paper is to explain this discrepancy. It is shown that non-stiff order conditions together with appropriate regularity assumptions imply high-order convergence of Lawson methods. Note, however, that the term regularity here includes the behaviour of the solution at the boundary. For instance, Lawson methods will behave well in the case of periodic boundary conditions, but they will show a dramatic order reduction for, e.g., Dirichlet boundary conditions. The precise regularity assumptions required for high-order convergence are worked out in this paper and related to the corresponding assumptions for splitting schemes. In contrast to previous work, the analysis is based on expansions of the exact and the numerical solution along the flow of the homogeneous problem. Numerical examples for the Schrödinger equation are included.

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SPIP : A computer program implementing the Interaction Picture method for simulation of light-wave propagation in optical fibre

Cited by 9 publications

References 9 publications

Numerical study on Kerr frequency comb generation in Si₃N₄ microresonators with frequency-dependent access coupler properties

Numerical study on Kerr frequency comb generation in Si₃N₄ microresonators with frequency-dependent access coupler properties

Convergence of exponential Lawson-multistep methods for the MCTDHF equations

On the convergence of Lawson methods for semilinear stiff problems

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SPIP : A computer program implementing the Interaction Picture method for simulation of light-wave propagation in optical fibre

Cited by 9 publications

References 9 publications

Numerical study on Kerr frequency comb generation in Si3N4 microresonators with frequency-dependent access coupler properties

Numerical study on Kerr frequency comb generation in Si3N4 microresonators with frequency-dependent access coupler properties

Convergence of exponential Lawson-multistep methods for the MCTDHF equations

On the convergence of Lawson methods for semilinear stiff problems

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Numerical study on Kerr frequency comb generation in Si₃N₄ microresonators with frequency-dependent access coupler properties

Numerical study on Kerr frequency comb generation in Si₃N₄ microresonators with frequency-dependent access coupler properties