The purpose of dgffdtd is mainly to use fdtd from a system point of view, such that the accuracy and e. Open access fdtd models for complex materials andrew d. Applications of the nonlinear finite difference time. Since it is a timedomain method, fdtd solutions can cover a wide. The proposed algorithm is based on incorporating the crank nicolson cn scheme into the ce finite difference time domain fdtd implementations of the nearly perfectly matched layer npml formulations. The algorithm is based on the locally one dimensional fdtd formulations and it is suitable for bandlimited electromagnetic applications. In this paper, an improved complexenvelope alternatingdirectionimplicit finitedifference timedomain ceadifdtd method has been presented for the analysis of photonicbandgap cavities. The complex envelope representation of bandpasslimited signals is used to formulate a bandpasslimited vector wave equation and a new finitedifference timedomain fdtd scheme that solves the. Ceadi fdtd to construct the ce version of maxwells curl equations, we write,where representsacarrierfrequency. Jun 15, 2012 a complex envelope ce alternatingdirectionimplicit adi finitedifference timedomain fdtd approach to treat lightmatter interaction selfconsistently with electromagnetic field evolution for efficient simulations of active photonic devices is presented for the first time to our best knowledge.
Analysis of complex radiating structures by hybrid fdtd. Dual spatial grid is commonly used for coupled electric and magnetic fields. The extension is based on a twostep discretization of complex envelope fields that factors out, on one hand, into modified maxwells curl equations including complex stretching pml. A complexenvelope ce alternatingdirectionimplicit adi finitedifference timedomain fdtd approach to treat lightmatter interaction selfconsistently with electromagnetic field evolution for efficient simulations of active photonic devices is presented for the first time to our best knowledge.
Abstractwe examine two spurious numerical artifacts of the complex envelope ce alternatingdirectionimplicit finitedifference timedomain adifdtd method, viz. Envelope lod wave equation pml algorithm for dispersive band. New approach to far field analysis for radiation pattern. This method is stable for an arbitrarily large time step irrespective of space step, and accurate for a time step solely determined by sampling accuracy. A complexenvelope fdtd formulation using realvalued. The method is based on incorporating the crank nicolson scheme into the ce finite difference time domain algorithm. Complex envelope cranknicolson nearly pml algorithm for the. Comparison with analytic solution ilkka laakso aprasc10 toyama radial electric field at 200 mhz ecell overestimation analytical hcell plane wave. Cefdtd stands for complexenvelope finitedifference time domain. The onedimensional finitedi erence timedomain fdtd. Heh, m1d fdtd methods for mobile interactive teaching and learning of wave. Jul 19, 2007 unconditionally stable secondorder splitstep ss envelope perfectly matched layer pml formulations are presented for truncating finitedifference timedomain fdtd grids.
Notethat indicatesactualcomponentsand indicatesthece components. The complex frequency shifted cfs perfectly matched layer pml is proposed for the twodimensional auxiliary differential equation ade finitedifference timedomain fdtd method combined with associated hermite ah orthogonal functions. Use of the complexenvelope ce representation of bandpass limited sources and their resulting fields increases the allowable timestep in finitedifference timedomain fdtd simulations. The proposed fdtdcgf technique utilizes conventional yees fdtd grids and continuous cgfs for postprocessing and ecc computation, unlike the dgffdtd technique. Several examples are also given to demonstrate the fdtd in action. Unconditionally stable complex envelope ce perfectly matched layer pml formulations are presented for modelling bandlimited electromagetic applications. Understanding the finitedifference timedomain method. Being a direct time and space solution, it offers the user a unique insight into. Gpuaccelerated 3d timedomain simulation of rf fields. This paper presents complexenvelope locally one dimensional finitedifference timedomain ce lodfdtd method for ionospheric propagation. To avoid this constraint we have implemented an implicit, complexenvelope 3d adifdtd algorithm for. Unsplit field implicit pml algorithm for complex envelope. The complex envelop ce fdtd method and its numerical.
The formulations are based on incorporating the alternating direction implicit adi scheme into the ce fdtd implementations of the scalar waveequation derived in the pml region at. Pdf on numerical artifacts of the complex envelope adi. A complexenvelope fdtd cefdtd scheme 18 is a general fdtd formulation that can be important tool to combat the numerical dispersion problem, which is especially a concerning issue in multiple grid algorithms. Numerical examples carried out in twodimensional domains are included to show the validity of the proposed. Applications of the nonlinear finite difference time domain. Cefdtd is defined as complexenvelope finitedifference time domain very rarely. The complex envelope representation transforms bandpass limited fields and sources to complexvalued lowpass limited form and maxwells equations from realvalued partial differential. According to the property of constitutive parameters of cfspml cpml absorbing boundary conditions abcs, the. The complex envelope ce adifdtd method request pdf. Gpuaccelerated 3d timedomain simulation of rf fields and. In the proposed algorithm, the perfectlymatchedlayer pml is straightforwardly incorporated in maxwells curl equations. The nlfdtd approach and its application to the modeling of the interaction of an ultrashort, optical pulsed gaussian beam with a kerr nonlinear material will be described. The main focus is put on the stability and the numerical dispersion issues of the complex envelope explicit and implicit methods.
The complex envelope ce alternatingdirectionimplicit finitedifference timedomain adi fdtd algorithm augmented by perfectly matched layers pml is extended for lossy anisotropic dielectric media. Complex envelope cranknicolson nearly pml algorithm for. Unconditionally stable envelope scalar wave equation perfectly matched layer algorithm is presented for truncating dispersive finite difference time domain fdtd grids. According to the property of constitutive parameters of cfspml cpml absorbing boundary conditions abcs, the auxiliary differential variables are. The complex envelope representation transforms bandpass limited fields and sources to complex valued lowpass limited form and maxwells equations from realvalued partial differential equations pdes to. Heh, multiple 1d fundamental adifdtd method for coupled transmission lines on mobile devices, ieee journal on multiscale and multiphysics computational techniques, vol. Bandpass st ht bandpass yt if hf is a bandpassfilter centered around fc, we can also define its complex envelope. Unconditionally stable secondorder splitstep ss envelope perfectly matched layer pml formulations are presented for truncating finitedifference timedomain fdtd grids. However, as main drawback, fdtd requires high computational resources due to courant criterion which limits the time step size in order to preserve the numerical stability of the scheme. Notethat indicatesactualcomponentsand indicatesthece. Analysis of complex radiating structures by hybrid fdtdmompo method a. It is based on the finitedifference timedomain fdtd method, which is one of the most popular approaches for solving maxwells equations of electrodynamics. The formulations are based on incorporating the alternating direction implicit adi scheme into the ce fdtd implementations of the scalar.
Ce fdtd stands for complex envelope finitedifference time domain. Curriculum vitae fernando lisboa teixeira professor. Fdtd is widely used by engineers, especially those designing antennas, doing computational electrodynamics, studying plasmonics, etc. The cfspml for 2d auxiliary differential equation fdtd. Yee, born 1934 is a numerical analysis technique used for modeling computational electrodynamics finding approximate solutions to the associated system of differential equations. A 3d grid can be viewed as stacked layers of tez and tmz grids which are offset a half spatial step in the z direction. The fdtd method requires the discretization of time and space. A complexenvelope fdtd formulation using realvalued field. An improved 3d complexenvelope fourstage adifdtd using. Dispersive fdtd in this section, we discuss the implementation of the dispersion of permittivity for timedomain methods. Cefdtd complexenvelope finitedifference time domain. For structures that are small comparedtotherfwavelength,orthatrequire. The proposed method is based on the secondorder ss fdtd algorithm. Moloney,3 and nasser peyghambarian2 1photonics center, college of physics, nankai university, tianjin 300071, china.
In order to overcome this problem, a complex envelope fdtd ce fdtd scheme has been proposed 5. In this paper, an improved complex envelope alternatingdirectionimplicit finitedifference timedomain ceadi fdtd method has been presented for the analysis of photonicbandgap cavities. How is complexenvelope finitedifference time domain abbreviated. An introduction as we know that fdtd is a timedomain solver the question is how do we solve those 6 equations above. A complex envelope fdtd ce fdtd scheme 18 is a general fdtd formulation that can be important tool to combat the numerical dispersion problem, which is especially a concerning issue in multiple grid algorithms. An explicit and unconditionally stable fdtd method for the. The physics of the fdtd algorithm the finitedifference timedomain fdtd method1,2 is a stateoftheart method for solving maxwells equations in complex geometries. The complexenvelope representation of bandpasslimited signals is used to formulate a bandpasslimited vector wave equation and a new finitedifference timedomain fdtd scheme that solves the. In section 3, we show the results of 2d and 3d simulations performed with the proposed dispersive fdtd. Source implementation and the effects of various boundaries such as. On numerical artifacts of the complex envelope adifdtd method. Kildishev,2 jieran fang, 2 joshua borneman, 2 mark d. A numerical example carried out in twodimensional linear lorentz dispersive.
A numerical dispersion is reduced using more general complexenvelope finite difference time domain cefdtd formulation and high order accuracy fdtd. The complexenvelope ce fdtd algorithm was proposed by pursel and goggans. Pdf efficient complex envelope adifdtd method for the. Three corresponding reference methods are developed. The formulations are free from the courant friedrich levy stability limit of the explicit fdtd algorithm. In addition the book presents the stateoftheart in computational photonics techniques, covering methods such as fullvectorial finiteelement beam propagation, bidirectional beam propagation, complexenvelope alternative direction implicit finite difference time domain, multiresolution time domain, and finite volume time domain. Complex envelope pmladifdtd method for lossy anisotropic. Publications international journals and book chapters e. Use of the complex envelope ce representation of bandpass limited sources and their resulting fields increases the allowable timestep in finitedifference timedomain fdtd simulations. Greenwood air force research laboratory, directed energy directorate, kirtland afb, nm 871175776 usa abstract. Complex envelope locally onedimensional lod perfectly matched layer pml formulations are presented for truncating dispersive finitedifference timedomain fdtd simulations. Jul 27, 2006 unconditionally stable complex envelope ce perfectly matched layer pml absorbing boundary conditions abcs are presented for truncating the scalar waveequation finite difference time domain we fdtd grids.
Being a direct time and space solution, it offers the user a unique insight into all types of problems in electromagnetics and photonics. Greenwood air force research laboratory, directed energy directorate, kirtland afb, nm 871175776 usa. Complexenvelope lodfdtd method for ionospheric propagation. At this point, it should be noted that the prescribed fdtdcgf technique is fundamentally di. How is complex envelope finitedifference time domain abbreviated. Nanoplasmonics fdtd simulations using a generalized. Fdtd is its simplicity of implementation and its ability to visualize the solutions as they act out in both space and time. Numerical assessment of finite difference time domain and.
The improvement relies on a different approach of the perfectly matchedlayer absorbingboundary condition in order to avoid the formation of instability, as reported in the literature. We develop an unconditionally stable complexenvelop alternatingdirectionimplicit finitedifference timedomain method ceadifdtd suitable for the transient analysis of anisotropic dielectrics and ferromagnetic materials. The proposed method is based on the secondorder ssfdtd algorithm. A numerical example carried out in onedimensional domain is included to show the. H components surrounded by four circulating e fields and vice versa. In order to overcome this problem, a complexenvelope fdtd cefdtd scheme has been proposed 5. The nl fdtd approach and its application to the modeling of the interaction of an ultrashort, optical pulsed gaussian beam with a kerr nonlinear material will be described. Angora is a free, opensource software package that computes numerical solutions to electromagnetic radiation and scattering problems. Analysis of complex radiating structures by hybrid fdtdmom. The ce explicit fdtd method is used to solve the problem with a point source and perfect electric. Application of crosscorrelation greens function along. Although there is possibility of using cgfs along with dgffdtd, that aspect is not explored in this paper.
Complex materials are of increasing interest in finitedifference time. Chapter 5 scaling fdtd simulations to any frequency. Nanoplasmonics fdtd simulations using a generalized dispersive material model ludmila j. Jung et al on numerical artifacts of the complex envelope adi fdtd method 493 combining 14 and 15, we have the dispersion relation of adi fdtd 10 16 b. Abstractrealvalued partial differential equations pdes are obtained by substituting the rectangular form of the complex envelope. Wojcik silesian university of technology, gliwice, poland abstract in this paper, the fdtdmompo hybrid technique is presented. Jung et al on numerical artifacts of the complex envelope adifdtd method 493 combining 14 and 15, we have the dispersion relation of adifdtd 10 16 b. Higher order ho 3d fdtd methodology to be a powerful numerical method for such complex and multiple materials structures simulation. Complex envelope representation of bandpass systems application of complex envelope. Jun 27, 2007 unconditionally stable complex envelope ce absorbing boundary conditions abcs are presented for truncating left handed material lhm domains. Implementation and adjustment of cpml for cefdtd algorithm. Ceadifdtd to construct the ce version of maxwells curl equations, we write,where representsacarrierfrequency.
Nov 09, 2006 unconditionally stable complex envelope ce perfectly matched layer pml formulations are presented for modelling bandlimited electromagetic applications. We examine two spurious numerical artifacts of the complex envelope ce alternatingdirectionimplicit finitedifference timedomain adi fdtd method, viz. Drachev 2 1institute for computational technologies, russian academy of sciences, novosibirsk, russia 2birck nanotechnology center, school of. The complex envelope can be used to represent the bandpass bp system by a lowpass system, which is easier to simulate by software. Finitedifference timedomain or yees method named after the chinese american applied mathematician kane s. Complexenvelope alternatingdirectionimplicit fdtd method. Ce fdtd is defined as complex envelope finitedifference time domain very rarely. Like most of differentialequation solving methods, fdtd discretizes the spacetime, and different dis. The method combines the ability of the fdtd method to deal with arbitrary material properties, and the.
The finitedifference timedomain method fdtd the finitedifference timedomain method fdtd is todays one of the most popular technique for the solution of electromagnetic problems. Using this method, the signal can be sampled in accordance with the bandwidth of the signal rather than its maximum frequency, which yields the time step significantly increased in comparison with the conventional fdtd. Unconditionally stable complex envelope ce perfectly matched layer pml absorbing boundary conditions abcs are presented for truncating the scalar waveequation finite difference time domain wefdtd grids. Efficient complex envelope adi fdtd method for the analysis of anisotropic photonic crystals article pdf available in ieee photonics technology letters 2312. It has been successfully applied to an extremely wide variety of problems, such as scattering from metal objects and. To avoid this constraint we have implemented an implicit, complexenvelope 3d adifdtd. Envelope lod wave equation pml algorithm for dispersive. Application of crosscorrelation greens function along with. In addition the book presents the stateoftheart in computational photonics techniques, covering methods such as fullvectorial finiteelement beam propagation, bidirectional beam propagation, complex envelope alternative direction implicit finite difference time domain, multiresolution time domain, and finite volume time domain. Efficient complex envelope adifdtd method for the analysis of anisotropic photonic crystals article pdf available in ieee photonics technology letters 2312.
Unconditionally stable complex envelope wave equation pml. Secondorder splitstep envelope pml algorithm for 2d fdtd. On numerical artifacts of the complex envelope adifdtd. On some aspects of the complexenvelope finitedifferences.
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