A generalized finite-difference time-domain scheme for solving nonlinear Schrödinger equations

Moxley, Frederick Ira; Chuss, David T.; Dai, Weizhong

doi:10.1016/j.cpc.2013.03.006

Cited by 28 publications

(27 citation statements)

References 31 publications

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“…Finally, the derivatives in space are approximated using higher-order finite difference methods. The G-FDTD has been successfully applied for solving both linear and nonlinear Schrödinger equations [51,52].…”

Section: B Exciton-polariton Bec Dynamicsmentioning

confidence: 99%

Sagnac interferometry with coherent vortex superposition states in exciton-polariton condensates

et al. 2016

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We investigate prospects of using counter-rotating vortex superposition states in non-equilibrium exciton-polariton Bose-Einstein condensates for the purposes of Sagnac interferometry. We first investigate the stability of vortex-antivortex superposition states, and show that they survive at steady-state in a variety of configurations. Counter-rotating vortex superpositions are of potential interest to gyroscope and seismometer applications for detecting rotations. Methods of improving the sensitivity are investigated by targeting high momentum states via metastable condensation, and the application of periodic lattices. The sensitivity of the polariton gyroscope is compared to its optical and atomic counterparts. Due to the large interferometer areas in optical systems and small de Broglie wavelengths for atomic BECs, the sensitivity per detected photon is found to be considerably less for the polariton gyroscope than with competing methods. However, polariton gyroscopes have an advantage over atomic BECs in a high signal-to-noise ratio, and have other practical advantages such as room-temperature operation and robust design. We estimate that the final sensitivities including signal-to-noise aspects are competitive with existing methods.

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Section: B Exciton-polariton Bec Dynamicsmentioning

confidence: 99%

Sagnac interferometry with coherent vortex superposition states in exciton-polariton condensates

et al. 2016

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“…When the potential is time-dependent, the time step will be limited by the speed of potential variation [39], thus, greatly reducing the efficiency of this technique. In addition, there are also many other approaches based on the above FDTD methods for further modifications [17][18][19][20]. are the source of EM fields.…”

Section: One-step Chebyshev Methodsmentioning

confidence: 99%

“…With FDTD-Q method, the time behavior of the wave function for the quantum well wire (QWW) was obtained, and the analysis of stability and convergence of this method was also carried out [16]. Besides, there are also many modified methods proposed with better performance [17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Computational Investigation of Nanoscale Semiconductor Devices and Optoelectronic Devices From the Electromagnetics and Quantum Perspectives by the Finite Difference Time Domain Method (Invited Review)

Duan¹,

Fang²,

Wang³

et al. 2021

PIER

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In the simulation of high frequency nanoscale semiconductor devices in which electromagnetic (EM) fields and carrier transport are coupled, and optoelectronic devices in which strong interactions between EM fields and charged particles exist, both the Maxwell's equations and the time-dependent Schrödinger equation (TDSE) need to be solved to capture the interactions between EM and quantum mechanics (QM). One of the numerical simulation methods for solving these equations is the finite difference time domain (FDTD) method. In this review paper, the development of FDTD method applied in EM and QM simulation is discussed. Several widely used FDTD techniques, i.e., explicit, implicit, explicit staggered-time, and Chebyshev methods, for solving the TDSE are introduced and compared. The hybrid approaches based on FDTD method, which are used to solve the Poisson-TDSE and Maxwell-TDSE coupled equations for EM-QM simulation, are also discussed. Furthermore, the applications of these simulation methods for nanoscale semiconductor devices and optoelectronic devices are introduced. Finally, a conclusion is given.

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“…The stability of a time-stepping scheme is of utmost importance. For uniform grids, a condition on the time step is generally derived by a Von Neumann analysis, where the grid is implicitly assumed infinite and the potential constant [7,8,13,20,21]. This approach was further verified for the Schrödinger equation in [6], where a more rigorous criterion was determined by explicitly allowing the potential to vary.…”

Section: Stabilitymentioning

confidence: 99%

Nonuniform and Higher-order FDTD Methods for the Schrödinger Equation

Decleer

Londersele

Rogier

et al. 2021

Journal of Computational and Applied Mathematics

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A generalized finite-difference time-domain scheme for solving nonlinear Schrödinger equations

Cited by 28 publications

References 31 publications

Sagnac interferometry with coherent vortex superposition states in exciton-polariton condensates

Sagnac interferometry with coherent vortex superposition states in exciton-polariton condensates

Computational Investigation of Nanoscale Semiconductor Devices and Optoelectronic Devices From the Electromagnetics and Quantum Perspectives by the Finite Difference Time Domain Method (Invited Review)

Nonuniform and Higher-order FDTD Methods for the Schrödinger Equation

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