Applications of the wave packet method to resonant transmission and reflection gratings

Borisov, Andrei G.; Shabanov, Sergei V.

doi:10.1016/j.jcp.2004.03.013

Cited by 10 publications

(16 citation statements)

References 30 publications

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“…The squared norm of the wave function, kwk 2 ¼ R dr w y w, is proportional to the total electromagnetic energy of the wave packet [12,30]. When attenuation is not present, g = 0, the Hamiltonian is Hermitian, H y ¼ H, and the norm (or energy) is conserved.…”

Section: Ionic Crystal Materialsmentioning

confidence: 99%

“…If V 11 is the element in the upper left corner of the attenuation potential V, then it has to be changed to V 11 À 4pr to include the absorbing layer. The function r P 0 is constructed according to the frequency band of the initial pulse (for details see [12,30] and references therein).…”

Section: Absorbing Boundary Conditionsmentioning

confidence: 99%

“…The amplitude of the fields at the initial time t = 0 is given by The scheme is conditionally stable, and the time step must be chosen accordingly, DtkHk 6 1 for H y ¼ H (for the non-Hermitian case see the discussion in [30]). The simulated electric field is recorded by a detector placed at z = z det = 18D.…”

Section: Free Space Propagation Phase and Amplitude Errorsmentioning

confidence: 99%

“…The zero diffraction mode is studied here for wavelengths k P D g so that reflected and transmitted beams propagate along the z-axis. Similar to our previous work [30], we use a change of variables in both x (x = f 1 (n)) and z (z = f 2 (f)) coordinates to enhance the sampling efficiency in the vicinity of medium interfaces so that the boundary conditions are accurately reproduced by the Fourier-grid pseudospectral method. A typical size of the mesh corresponds to À15D g 6 z 6 15D g , and À0.5D g 6 x 6 0.5D g with, respectively, 512 and 128 mesh points.…”

Section: Applications To Nanostructured Periodic Materialsmentioning

confidence: 99%

“…Similar results have been obtained for dielectric grating structures with rectangular geometry. The resonant pattern is associated with the so-called Wood anomalies [19], and can be explained by the existence of trapped modes or guided wave resonances [20,30]. The widths of the resonances in the reflection (transmission) coefficient are determined by the lifetime of a corresponding quasi-stationary trapped mode which is a standing wave along the x-axis and is excited by the incoming wave.…”

Section: Array Of Dielectric Cylindersmentioning

confidence: 99%

See 4 more Smart Citations

Lanczos pseudospectral method for initial-value problems in electrodynamics and its applications to ionic crystal gratings

Borisov

Shabanov

2005

Journal of Computational Physics

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Section: Ionic Crystal Materialsmentioning

confidence: 99%

Section: Absorbing Boundary Conditionsmentioning

confidence: 99%

Section: Free Space Propagation Phase and Amplitude Errorsmentioning

confidence: 99%

Section: Applications To Nanostructured Periodic Materialsmentioning

confidence: 99%

Section: Array Of Dielectric Cylindersmentioning

confidence: 99%

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Lanczos pseudospectral method for initial-value problems in electrodynamics and its applications to ionic crystal gratings

Borisov

Shabanov

2005

Journal of Computational Physics

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Wave packet propagation by the Faber polynomial approximation in electrodynamics of passive media

Borisov¹,

Shabanov²

2006

Journal of Computational Physics

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Maxwell's equations for propagation of electromagnetic waves in dispersive and absorptive (passive) media are represented in the form of the Schrödinger equation i∂Ψ/∂t = HΨ, where H is a linear differential operator (Hamiltonian) acting on a multi-dimensional vector Ψ composed of the electromagnetic fields and auxiliary matter fields describing the medium response. In this representation, the initial value problem is solved by applying the fundamental solution exp(−itH) to the initial field configuration. The Faber polynomial approximation of the fundamental solution is used to develop a numerical algorithm for propagation of broad band wave packets in passive media. The action of the Hamiltonian on the wave function Ψ is approximated by the Fourier grid pseudospectral method. The algorithm is global in time, meaning that the entire propagation can be carried out in just a few time steps. A typical time step is much larger than that in finite differencing schemes, ∆t F ≫ H −1 . The accuracy and stability of the algorithm is analyzed. The Faber propagation method is compared with the Lanczos-Arnoldi propagation method with an example of scattering of broad band laser pulses on a periodic grating made of a dielectric whose dispersive properties are described by the Rocard-Powels-Debye model. The Faber algorithm is shown to be more efficient. The Courant limit for time stepping, ∆t C ∼ H −1 , is exceeded at least in 3000 times in the Faber propagation scheme.

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Quantum and electromagnetic propagation with the conjugate symmetric Lanczos method

Acevedo

Lombardini²,

Turner³

et al. 2008

The Journal of Chemical Physics

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The conjugate symmetric Lanczos (CSL) method is introduced for the solution of the time-dependent Schrodinger equation. This remarkably simple and efficient time-domain algorithm is a low-order polynomial expansion of the quantum propagator for time-independent Hamiltonians and derives from the time-reversal symmetry of the Schrodinger equation. The CSL algorithm gives forward solutions by simply complex conjugating backward polynomial expansion coefficients. Interestingly, the expansion coefficients are the same for each uniform time step, a fact that is only spoiled by basis incompleteness and finite precision. This is true for the Krylov basis and, with further investigation, is also found to be true for the Lanczos basis, important for efficient orthogonal projection-based algorithms. The CSL method errors roughly track those of the short iterative Lanczos method while requiring fewer matrix-vector products than the Chebyshev method. With the CSL method, only a few vectors need to be stored at a time, there is no need to estimate the Hamiltonian spectral range, and only matrix-vector and vector-vector products are required. Applications using localized wavelet bases are made to harmonic oscillator and anharmonic Morse oscillator systems as well as electrodynamic pulse propagation using the Hamiltonian form of Maxwell's equations. For gold with a Drude dielectric function, the latter is non-Hermitian, requiring consideration of corrections to the CSL algorithm.

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Applications of the wave packet method to resonant transmission and reflection gratings

Cited by 10 publications

References 30 publications

Lanczos pseudospectral method for initial-value problems in electrodynamics and its applications to ionic crystal gratings

Lanczos pseudospectral method for initial-value problems in electrodynamics and its applications to ionic crystal gratings

Wave packet propagation by the Faber polynomial approximation in electrodynamics of passive media

Quantum and electromagnetic propagation with the conjugate symmetric Lanczos method

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