Advances in finite-difference time-domain calculation methods

Cole, James B.; Okada, Naoki; Banerjee, Saswatee

doi:10.1007/978-3-642-15531-4_4

Cited by 5 publications

(4 citation statements)

References 24 publications

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“…Although ϕ is a solution of the wave equation it is not a solution of its FD model. This error can be reduced by using higher order FDs, but the resultant FDTD algorithm is unstable [2,3]. Regarding u as free parameter we find that 0…”

Section: Nonstandard Finite Difference Modelsmentioning

confidence: 95%

Numerical simulation and philosophy: Devils in the details and discrete Green's function solution of a nonstandard finite difference model

Cole

2015

2015 2nd International Conference on Opto-Electronics and Applied Optics (IEM OPTRONIX)

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We first discuss the philosophy of modeling and numerical simulation. Many researchers believe that the more accurate the model -i.e. the better it fits the data -the better. But this is not necessarily true. Besides accuracy, a good model must have the same essential mathematical characteristics as the phenomenon which it is supposed to describe. When this is not the case, a model can be very accurate but numerically unstable. Next we introduce high precision finite difference models of the wave equation and Maxwell's equations based on what are called nonstandard (NS) finite differences (FD). Finally we introduce a new methodology to solve electromagnetic scattering and propagation problems based on solving NS-FD models with discrete Green's functions.

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Section: Nonstandard Finite Difference Modelsmentioning

confidence: 95%

Numerical simulation and philosophy: Devils in the details and discrete Green's function solution of a nonstandard finite difference model

Cole

2015

2015 2nd International Conference on Opto-Electronics and Applied Optics (IEM OPTRONIX)

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“…The additional layers use low‐loss semiconducting media. Depending on the nature of the material, FDTD update equations change …”

Section: Finite‐difference Time‐domain Algorithmmentioning

confidence: 99%

“…Depending on the nature of the material, FDTD update equations change. 18 In all cases, the metallic region is simulated using a monochromatic implementation of RC-FDTD. 14 The substrate and the incident medium are simulated using ordinary FDTD suitable for lossless dielectric media.…”

Section: 'Ab Initio' Designmentioning

confidence: 99%

Designing multilayered wire‐grid polarizers using a monochromatic recursive convolution finite‐difference time‐domain algorithm

Banerjee

2014

J Soc Info Display

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Multilayered wire‐grid polarizers (WGP) find application as low‐reflection polarizers in projection‐type liquid crystal display devices. A multilayered WGP is formed by adding thin layers on top of the metal ridges of an ordinary WGP. The ordinary WGP consists of a periodic array of parallel metal ridges, where the period of the array and the width of any individual metal ridge are typically less than the wavelength of the incident light. Such WGPs are often used as efficient polarizers. However, in certain applications, it is important to reduce the reflection from the WGP while preserving the polarization efficiency. One of the ways to achieve this goal is to add thin layers on top of the metal ridges of the ordinary WGP. The reduction in reflection from the multilayered WGP depends on the number and material of these additional layers. In this paper, we describe a design method for multilayered WGPs based on an effective medium theory, thin‐film computation method and a monochromatic recursive convolution finite‐difference time‐domain algorithm. The goal of design process is to identify suitable materials and thicknesses for the additional thin layers needed to lower the reflection appreciably. The design method is explained with the help of bilayered WGPs.

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“…[17][18][19] Optical resonances in microdisks 20 and pillars 21 have also been widely investigated and reviewed, partly due to the ability to control the spontaneous emission rate for atoms or quantum dots placed in the cavity. [22][23][24][25][26] The cylindrical WGMs have also been reviewed, 27,28 although mostly without a sensor 29 focus. The intent of this work is to overview the work so far on capillary WGM-type sensor structures, and to outline the basic physics and experimental issues that would be helpful for researchers wishing to enter the field.…”

Section: Introductionmentioning

confidence: 99%

Capillary-Type Microfluidic Sensors Based on Optical Whispering Gallery Mode Resonances

Meldrum¹,

Marsiglio²

2014

Rev Nanosci Nanotech

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Microfluidic capillary-type sensors could potentially find applications in a range of medical and environmental diagnostic technologies. Refractive-index sensors-as well as biosensors-based on the whispering gallery mode resonances of a thin-walled capillary offer several modes of operation and the capacity to detect a wide range of analytes through standard silica surface functionalization methods. This article reviews the basic optical physics associated with the resonances and how they respond to changes in the local refractive index. The sensitivity and detection limits of these devices are explored, and at least one old assumption concerning the inverse relationship between the quality factor of the resonance and the detection limit is shown to be valid only under a restricted set of circumstances. Problems and pitfalls associated with whispering-gallery-mode capillary sensors are examined, as well as the experimental methods needed for analysis. Finally, relevant capillary sensor examples from the literature are summarized.

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Advances in finite-difference time-domain calculation methods

Cited by 5 publications

References 24 publications

Numerical simulation and philosophy: Devils in the details and discrete Green's function solution of a nonstandard finite difference model

Numerical simulation and philosophy: Devils in the details and discrete Green's function solution of a nonstandard finite difference model

Designing multilayered wire‐grid polarizers using a monochromatic recursive convolution finite‐difference time‐domain algorithm

Capillary-Type Microfluidic Sensors Based on Optical Whispering Gallery Mode Resonances

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