Simple treatment of multi-term dispersion in FDTD

Okoniewski, M.; Mrozowski, Michał; Stuchly, M.A.

doi:10.1109/75.569723

Cited by 179 publications

(103 citation statements)

References 3 publications

Supporting

Mentioning

101

Contrasting

Unclassified

Order By: Relevance

“…In fact, the symmetry of (3) allows the simulation of a dynamically changing c by changing the coefficients A l and B l accordingly in (4) and (5). In light of this, we conducted numerical experiments similar to the slow light experiments reported in 1999 by Hau et al [2] in which the control field Rabi frequency was decreased while the pulse was contained in the EIT medium, offering a even more dramatic slow down.…”

Section: Slow Light Calculationsmentioning

confidence: 99%

“…Two such finite-difference time-domain (FDTD) techniques which have risen to prominence in recent years are the piecewise linear recursive convolution (PLRC) method and the auxiliary differential equation (ADE) method [3,4]. Both methods have identical accuracy and memory requirements in the case of Lorentz media [5]. However, the latter makes no assumptions about the linearity of the media in the calculations.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Modelling electromagnetically induced transparency media using the finite-difference time-domain method

Neff¹,

Andersson

Qiu

2007

New J. Phys.

View full text Add to dashboard Cite

Simultaneous electromagnetically induced transparency for two circularly polarized lasers coupled to the same linearly polarized laser in a four-level atomic system in the W scheme Cristian Bahrim and Chris Nelson Abstract.Time-domain electromagnetic modelling of complex structures which include both non-dispersive media and media exhibiting electromagnetically induced transparency (EIT) require a general, robust calculation method such as finite-difference time-domain (FDTD). We propose a complex-valued, exact two-pole representation of the permittivity of a three-level system which is suitable for integration into the FDTD algorithm via the auxiliary differential equation method. Our calculation model confirmed reported results which were calculated with an approximate representation of the EIT permittivity. Additionally, propagation calculations which mimic slow light experiments were performed. A major advantage of our representation is the ease with which changes in the control field Rabi frequency can be implemented by using a timedependent permittivity.

show abstract

Section: Slow Light Calculationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Modelling electromagnetically induced transparency media using the finite-difference time-domain method

Neff¹,

Andersson

Qiu

2007

New J. Phys.

View full text Add to dashboard Cite

show abstract

“…The approach followed in [1] leads to a fast and memory efficient formulation for Drude, however the second-order nature of the material is partially lost in the derivation, leading to an implementation that has relatively high computational error. In this Letter, we reformulate the Drude ADE method in a manner similar to that introduced by [5]. The new method shows excellent accuracy; however, while it retains the computational speed of the original formulation, it does require one additional memory location per electric field component.…”

Section: Introductionmentioning

confidence: 99%

Drude dispersion in ADE FDTD revisited

Okoniewski

Okoniewska

2006

Electron. Lett.

View full text Add to dashboard Cite

Studies of double negative materials and of metals at optical frequencies have lead to renewed interest in modelling of materials characterised by Drude or multi-pole Lorentz-Drude frequency dispersion. The auxiliary differential equation method of treatment of Drude dispersion in the finite difference time domain method is revisited, and a substantially more accurate formulation is derived. Introduction:The finite difference time domain technique (FDTD) [1] has been successfully applied by many authors to analyse problems with heterogeneous, complex materials. In the context of this Letter, of particular interest is the ability of FDTD to model materials characterised by frequency dispersive behaviour approximated by Drude or multi-pole Lorentz-Drude models. Luebbers et al.[2] introduced convolution based extensions of FDTD to simulate a variety of dispersive materials. Sullivan [3] and Rappaport [4] incorporated z transform based techniques to extend FDTD to general dispersive media. However, the auxiliary differential equation (ADE) methods lead, in general, to the most efficient numerical implementations, both in terms of memory and operational count. An excellent review of ADE extensions of FDTD is included in [1], where ADE is also used to model Drude media. The approach followed in [1] leads to a fast and memory efficient formulation for Drude, however the second-order nature of the material is partially lost in the derivation, leading to an implementation that has relatively high computational error. In this Letter, we reformulate the Drude ADE method in a manner similar to that introduced by [5]. The new method shows excellent accuracy; however, while it retains the computational speed of the original formulation, it does require one additional memory location per electric field component.

show abstract

“…Vial [13] implemented the DCP model by using RC method while Sullivan [14], Weedon and Rappaport [15] used the Z-transform technique to implement dispersive media into the FDTD algorithm. An auxiliary differential equation (ADE) technique to implement the Lorentz dispersive model was proposed [16] and it was shown by Okoniewski et al [17] that the usage of the ADE scheme resulted in reduced computational burden compared to that of PLRC technique.…”

Section: Introductionmentioning

confidence: 99%

PLRC and Ade Implementations of Drude-Critical Point Dispersive Model for the FDTD Method

Chun¹,

Kim²,

Kim³

et al. 2013

PIER

View full text Add to dashboard Cite

Abstract-We describe the implementations of Drude-critical point model for describing dispersive media into finite difference time domain algorithm using piecewise-linear recursive-convolution and auxiliary differential equation methods. The advantages, accuracy and stability of both implementations are analyzed in detail. Both implementations were applied in studying the transmittance and reflectance of thin metal films, and excellent agreement is observed between analytical and numerical results.

show abstract

Simple treatment of multi-term dispersion in FDTD

Cited by 179 publications

References 3 publications

Modelling electromagnetically induced transparency media using the finite-difference time-domain method

Modelling electromagnetically induced transparency media using the finite-difference time-domain method

Drude dispersion in ADE FDTD revisited

PLRC and Ade Implementations of Drude-Critical Point Dispersive Model for the FDTD Method

Contact Info

Product

Resources

About