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