[신간안내] Computational Electrodynamics (the finite difference time - domain method)

We investigate the properties of the modes that are supported by 3-D subwavelength plasmonic slot waveguides. We first show that the fundamental mode that is supported by a symmetric plasmonic slot waveguide, which is composed of a subwavelength slot in a thin metallic film embedded in an infinite homogeneous dielectric, is always a bound mode for any combination of operating wavelength and waveguide parameters. Its modal fields are highly confined over a wavelength range extending from zero frequency to the ultraviolet. We then show that for an asymmetric plasmonic slot waveguide, in which the surrounding dielectric media above and below the metal film are different, there may exist a cutoff slot width and/or a cutoff metal film thickness above which the mode becomes leaky, and there always exists a cutoff wavelength above which the mode becomes leaky. We investigate in detail the effect of variations of the parameters of the symmetric and asymmetric plasmonic slot waveguides. We also consider related alternative 3-D plasmonic waveguide geometries, such as a plasmonic slot waveguide, in which the two metal film regions that form the slot have a finite width, and a plasmonic strip waveguide, which is formed between a metallic strip and a metallic substrate. We show that for a specific modal size, the fundamental mode of the standard plasmonic slot waveguide has a larger propagation length compared with the corresponding modes of these plasmonic waveguides.

/pdf/modes-of-subwavelength-plasmonic-slot-waveguides-rz9ijrq9iy.pdf

Modes of Subwavelength Plasmonic Slot Waveguides

We demonstrate the existence of a bound optical mode supported by a slot in a thin metallic film deposited on a substrate, with slot dimensions much smaller than the wavelength. The modal size is almost completely dominated by the near field of the slot. Consequently, the size is very small compared with the wavelength, even when the dispersion relation of the mode approaches the light line of the surrounding media. In addition, the group velocity of this mode is close to the speed of light in the substrate, and its propagation length is tens of micrometers at the optical communication wavelength.

/pdf/guided-subwavelength-plasmonic-mode-supported-by-a-slot-in-a-1d7z8gcubt.pdf

Guided subwavelength plasmonic mode supported by a slot in a thin metal film

Extensions of finite-difference time-domain (FDTD) and finite-element time-domain (FETD) algorithms are reviewed for solving transient Maxwell equations in complex media. Also provided are a few representative examples to illustrate the modeling capabilities of FDTD and FETD for complex media. The term complex media refers here to media with dispersive, (bi)anisotropic, inhomogeneous, and/or nonlinear properties present in the constitutive tensors.

/pdf/time-domain-finite-difference-and-finite-element-methods-for-1j9aewvbsu.pdf

Time-Domain Finite-Difference and Finite-Element Methods for Maxwell Equations in Complex Media

The finite-difference time-domain (FDTD) method is arguably the most popular numerical method for the solution of problems in electromagnetics. Although the FDTD method has existed for nearly 30 years, its popularity continues to grow as computing costs continue to decline. Furthermore, extensions and enhancements to the method are continually being published, which further broaden its appeal. Because of the tremendous amount of FDTD-related research activity, tracking the FDTD literature can be a daunting task. We present a selective survey of FDTD publications. This survey presents some of the significant works that made the FDTD method so popular, and tracks its development up to the present-day state-of-the-art in several areas. An "on-line" BibT/sub E/X database, which contains bibliographic information about many FDTD publications, is also presented. >

A selective survey of the finite-difference time-domain literature

This paper addresses the problem of stability analysis of finite-difference time-domain (FDTD) approximations for Maxwell's equations. The combination of the von Neumann method with the Routh-Hurwitz criterion is proposed as an algebraic procedure for obtaining analytical closed-form stability expressions. This technique is applied to the problem of determining the stability conditions of an extension of the FDTD method to incorporate dispersive media previously reported in the literature. Both Debye and Lorentz dispersive media are considered. It is shown that, for the former case, the stability limit of the conventional FDTD method is preserved. However, for the latter case, a more restrictive stability limit is obtained. To overcome this drawback, a new scheme is presented, which allows the stability limit of the conventional FDTD method to be maintained.

/pdf/analyzing-the-stability-of-the-fdtd-technique-by-combining-1wzo4zutwh.pdf

Analyzing the stability of the FDTD technique by combining the von Neumann method with the Routh-Hurwitz criterion

This paper introduces a technique for finite-difference time-domain modeling of wave propagation in general Mth-order dispersive media. Ohm's law in the Laplace domain with an Mth-order rational model for the complex conductivity is considered as a constitutive relation. In order to discretize this model, the complex conductivity is mapped onto the Z-transform domain by means of the Mobius transformation. This leads finally to a set of difference equations that is consistent with Yee's scheme. The resulting formulation is explicit, it has a second-order accuracy, and the need for additional storage variables is minimal. The numerical stability problem is discussed and the numerical dispersion equation for Mth-order media is given.

https://personales.unican.es/peredaj/pdf/Pereda_MTT_Jul_2002.pdf

FDTD modeling of wave propagation in dispersive media by using the Mobius transformation technique

The finite-difference time-domain (FDTD) method is extended to include magnetized ferrites. The treatment of the ferrite material is based on the equation of motion of the magnetization vector. Magnetic losses are also included in the equation of motion by means of Gilbert's approximation of the phenomenological Landau-Lifschitz damping term. The discretization scheme is based on central finite-differences and linear interpolation. This scheme allows the fully explicit nature of the FDTD method to be maintained. This extension of the FDTD method to magnetized ferrites is applied to the full-wave analysis of ferrite-loaded waveguides. The dispersion curves are calculated by using a recently proposed 2D-FDTD formulation for dispersion analysis which has been adapted to the present problem. The results for both the phase and attenuation constants of various transversely and longitudinally magnetized ferrite-loaded waveguides are compared with the exact values and with those obtained by means of Schelkunoff's method. >

FDTD analysis of magnetized ferrites: application to the calculation of dispersion characteristics of ferrite-loaded waveguides

The finite-difference-time-domain (FDTD) method is extended to include magnetized ferrites. The treatment of the ferrite material is based on the equation of motion, using Gilbert's approximation of the damping term. The validity of the formulation is verified by applying it to the calculation of propagation constants in waveguides containing ferrites with transverse magnetization. The results for a rectangular waveguide filled with ferrites and those for a rectangular waveguide loaded with a centered ferrite slab are compared with the exact results, showing good agreement. >

A treatment of magnetized ferrites using the FDTD method

Two different extensions of the finite-difference time-domain (FDTD) method for the treatment of lossy dielectrics are considered: the time-average (TA) and the time-forward (TF) difference schemes. An analytical study of the stability properties and numerical dispersion of these schemes is presented. The stability analysis is based on the Von Neumann (Fourier series) method, while the numerical dispersion properties are established in terms of the numerical permittivity of discrete lossy dielectrics. The analytical stability limits are compared with those obtained numerically in previous works. The accuracy of the two schemes is compared by computing the reflection coefficient of a lossy dielectric slab.

https://personales.unican.es/peredaj/pdf/Pereda_MGWL_Jul_1998.pdf

Numerical dispersion and stability analysis of the FDTD technique in lossy dielectrics

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