Generalization of Berenger's absorbing boundary conditions for 3-D magnetic and dielectric anisotropic media

Villó-Pérez, Isidro; Garcia, S.G.; Martin, R.G.; Olmedo, B. García

doi:10.1002/(sici)1098-2760(19980605)18:2<126::aid-mop12>3.0.co;2-5

Cited by 6 publications

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“…Amongst the analytical boundary conditions, the scheme proposed by Mur [4] has been mainly utilised because of its accuracy in the simulation of the propagation of outgoing waves from the computational domain. Amongst the absorbing boundary conditions, the scheme proposed by Berenger [11] is the most employed [34][35][36][37][38]. The innovative idea proposed by Berenger is the introduction of a nonphysical absorbing layer to terminate the FDTD computational domain which absorbs all electromagnetic waves impinging on it.…”

Section: Perfectly Matched Layer (Pml) Boundary Conditionsmentioning

confidence: 99%

Complex‐Envelope Alternating‐Direction‐Implicit Finite‐Difference Time‐Domain Method

Obayya

2010

Computational Photonics

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In this chapter, emphasis will be put on the finite-difference time-domain technique, taking into account its advantages and its main drawbacks. In particular, a detailed description of how those drawbacks have been solved with the advent of the alternating-direction implicit FDTD (ADI-FDTD) technique and the complexenvelope ADI-FDTD (CE-ADI-FDTD) technique is given. Also, a comprehensive analysis of the perfectly matched layer (PML) boundary conditions will be also given, putting more emphasis on the new formulation of the uniaxial PML (UPML) boundary conditions for the CE-ADI-FDTD. At the end of the chapter, numerous examples will be given in order to assess the effectiveness of the new formulation of the UPML boundary conditions for the CE-ADI-FDTD in the context of photonic crystal devices. The great improvement in the absorption properties of the proposed boundary conditions will be shown to be positively reflected in the excellent enhancement of the stability properties of the numerical code. In this way, larger time-step sizes can be employed with negligible impact on the numerical accuracy of the numerical code and with consequent huge savings in computational resources. Computational PhotonicsSalah ObayyaThe finite-difference time domain (FDTD) method is one of the most popular computational techniques employed in the research environment for a wide variety of applications covering many different areas. The FDTD method was first proposed by Yee in 1966 [1] and it represented a simple and accurate yet efficient way to discretise Maxwell's equations. However, computer technology was not mature enough to fully exploit the potential of the method at the time. With the increase in computational power and its decreasing costs, the FDTD method started to become more and more attractive and its popularity has grown exponentially since. Taflove was one of the

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