Analysis of methods for the maxwellrandom lorentz model. Click sellmeier equation and input the corresponding values in the sellmeier equation table shown in figure 1 9. A drudetwocpfdtd method for drudecritical points model of. Modeling of dispersive materials using dispersion models. Pdf implementation of the fdtd method based on lorentzdrude.
For our discrete approximation to converge to the true solution, it must be consistent and stable. The dcp model has been proven capable of describing the dielectric dispersion of metals in the visir spectral region more accurately than the widely used drude. For the simulation of plasmonics devices, the lorentzdrude ld dispersive model is incorporated into maxwell equations, while the auxiliary difierential. Overcoming the multiwavelength fdtd challenge lumerical. In this work, we extend the newmarkfdtd method to modified lorentz medium, which can simply. An approach for the simulation of active plasmonics devices is presented in this paper. The update equations for lorentz media can be formulated in a similar fashion as for the above drude model. Dispersive models for nobel metals commonly employed in fdtd simulations are. Newmarkfdtd formulation for modified lorentz dispersive. The model, which is an application of kinetic theory, assumes that the microscopic behaviour of electrons in a solid may be treated classically and looks much like a pinball machine, with a sea of constantly jittering electrons bouncing. Fdtd formulation for the general dispersion model using the z. Explicit numerical integration in the fdtd framework we now demonstrate that integration of the nonlinear lorentz model in the fdtd framework can be made fully explicit. Material data is from paliks handbook of optical constants vol. A new model, referred to as the general model is proposed for modeling of dispersive materials in visible wavelength range using the fdtd method with high efficiency.
The finitedifference timedomain fdtd method has been popularly utilized to analyze the electromagnetic em wave propagation in dispersive media. An extended newmarkfdtd method for complex dispersive. Fdtd implementations of the dcp model have been thus far based on the recursive convolution rc 4 and the trapezoidal rc trc 6 techniques. Application of the finitedifference timedomain method to. The goal of this paper is to model a dng material with the fdtd method.
Modeling and simulation of active plasmonics with the fdtd. Lorentz model 7, 8 and drudecp model 4, 9, were also usually adopted. The curl equations of maxwells equations are presented as. This can be achieved with a lorentz model when the lorentz permittivity is negative. Memory efficient laguerrefdtd scheme for dispersive media. Optifdtd technical background and tutorials finite difference time domain photonics simulation software version 8. An extended newmarkfdtd method for complex dispersive media. Free electron laser simulation tool based on fdtdpic in the. Finitedifference timedomainbased optical microscopy. Based on polarizability in the form of a complex quadratic rational function, a novel finitedifference timedomain fdtd approach combined with the newmark algorithm is presented for dealing with a complex dispersive medium. Modeling of dispersive materials using dispersion models for. Many problems in nanophotonics require three dimensional full. For the simulation of plasmonics devices, the lorentz drude ld dispersive model is incorporated into maxwell equations, while the auxiliary.
The critical point model in a recent paper 15, a new analytical model was introduced for the description of the permittivity of gold over a wide wavelength range. The lorentz drude model incorporated maxwell equations are simulated by using the threedimensional finite difference time domain fdtd method and the method is parallelized on multiple graphics processing units gpus for plasmonics applications. Several finitedifference timedomain fdtd algorithms using the additional dif ferential equation. Double negative medium modeling using drude model in fdtd method. Behavior analysis of metamaterials with the fdtd method. And we modify the drudetwocp model into the form of standard lorentz. For the typical dispersive fdtd approaches, the recursive convolution rc method and z transform zt method. A symplectic fdtd algorithm for the simulations of lossy. The finitedifference timedomain fdtd method 1 successfully models a variety of electromagnetic phenomena in a variety of materials. The classical lorentz model of dielectric dispersion due. Consider a human muscle tissue modeled in the frequency range of 400 mhz3 ghz by qcrf as with the following parameters. Explicit formulation of second and third order optical. Double negative medium modeling using drude model in.
Kurt oughstun and natalie cartwright, on the lorentz lorenz formula and the lorentz model of dielectric dispersion, opt. Let m and, then the maximum time step satisfying the cfl stability limit of 1d fdtd in free space is ps and the. The z transforms of the electrical and magnetic susceptibilities for a lorentz material are given to eq. Pdf investigation of the stability of adefdtd methods for. Lorentz model for permeability drudemodel for metals generalizations other materials models lecture 2 2. The proposed gdm model is then used to simulate the spec. Kildishev,2 jieran fang, 2 joshua borneman, 2 mark d. Fdtd implementations of the dcp model have been thus far based on the recursive convolution rc. The optimized model parameters are used to calculate the complex relative permittivity of each material and compare it with experimental data. Aug 19, 2019 finitedifference time domain fdtd has been widely used to analyze electromagnetic wave interaction with dispersive media. In this section, we combine these two sets of formulations and propose the plrc method for drude lorentz model. Modeling dispersive materials with parameter distributions.
The lorentzian model extracting the lorentzian model parameters from measurements is based on solving a system of nonlinear equations. A drudetwocpfdtd method for drudecritical points model. Implementation of the critical points model in the. Metamaterials and fdtd based numerical modeling studies. Model dispersive media in finitedifference timedomain method. Lee implemented fdtd method on lorentz drude dispersive model 23. Select lorenz dispersive, and define the following parameters name. A brief introduction to the fdtd method for modeling metamaterials. For this reason, we propose to integrate the dielectric function of the lorentz drude model with the finite difference timedomain fdtd method, which will permit to study the surface and internal effects within the metal nanostructure system added to the dielectric system, and the interaction of electromagnetic fields with atoms, ions or. In particular, our original formulation is compared to the classical recursiveconvolution technique for the lorentz oscillator using a complex recursive accumulator. Only lorentz and the drude models can produce negative permittivities or permeabilities when the coupling coefficient is positive.
Using sf fdtd, especially in the case of dispersive media, faces. However, the introduction of these new dispersion models and their hybrid models undoubtedly challenges the versatility of the existing fdtd methods. The stability of the extended newmark fdtd method is also investigated by the root locus of the stability polynomial in zplane as. For the simulation of plasmonics devices, the lorentzdrude ld dispersive model is incorporated into maxwell equations, while the auxiliary. Drachev 2 1institute for computational technologies, russian academy of sciences, novosibirsk, russia 2birck nanotechnology center, school of ece, purdue university, west. This transformation to time domain is accomplished by. Effects of the nanostructure on dielectric and magnetic properties of the material are taken into account by introducing the drude lorentz model.
Mar 01, 2014 the finitedifference timedomain fdtd method, as an efficient numerical analysis technique used for modeling computational electrodynamics, has been shown to be one of the most widely used methods in electromagnetic simulations. We will then give an example of the usefulness of this model by comparison with the drude lorentz model for the speci. The lorentz drude model in 43 is in the frequency domain. Lorentz model fit to silicon across the visible, and a drude model fit to gold in the near infrared. The frequencydependent lorentz model of order n can be written as. Pdf investigation of the stability of adefdtd methods. Numerical simulations of surface plasmons superresolution. In conclusion, we have rigorously investigated the stability of two ade fdtd implementations for media with modified lorentz dispersion, a generalized model that encompasses the most commonly used models for the description of dielectrics 2, semiconductors 8, metals 5, 7 or complex structures, such as metamaterials 3. Thisimplementation ofdrude lorentz modelhasconsiderably reduced number of variables compared to the previously reported works 9,10. Finite difference time domain photonics simulation software version 8. The drude model of electrical conduction was proposed in 1900 by paul drude to explain the transport properties of electrons in materials especially metals. Fdtd formulation of lorentz model the lorentz material equations for a dispersive material eq. Optical dispersion is typically modelled with the following ordinary differential equation 14, 15, 16 d 2 p d.
Modeling dispersive materials with parameter distributions in. The use of a lorentz boosted coordinate system causes the very di erent length scales to transform into val. Nanoplasmonics fdtd simulations using a generalized. A nonlinear optimization algorithm based on the nelder mead method is used to characterize the frequency dependent permittivity of 15 materials based on lorentz, modified lorentz, drude and lorentz drude models.
For the simulation of plasmonics devices, the lorentz drude ld dispersive model is incorporated into maxwell equations, while the auxiliary difierential. It is of great necessity to incorporate a dispersion model into fdtd formulation for electromagnetic wave analysis of dispersive media. Click sellmeier equation and input the corresponding values in the sellmeier equation table shown in figure 1. Lorentz models are used to represent the frequency dependence of the. Pdf implementation of the fdtd method based on lorentz. Various dispersion models were introduced to consider the frequencydependent permittivity, including debye, drude, lorentz, quadratic complex rational function, complexconjugate poleresidue, and critical point models. We consider the optical constant data of ag over a very broad frequency range 0. While other authors also consider magnetized plasmas 24, the model. In this work, we extend the newmark fdtd method to modified lorentz medium, which can simply.
Since it is a timedomain method, fdtd solutions can cover a wide frequency range with a single simulation run. Comprehensive study on numerical aspects of modified lorentz. Pdf finitedifference timedomain methods and material models. For the lorentz case, the following relation is used for the polarization current. Also, we extend the fdtd method to include interband transitions of electron at optical frequencies by introducing the drude lorentz dispersion function.
Ieee transactions on antennas and propagation, e73, 2628. Nanoplasmonics fdtd simulations using a generalized dispersive material model ludmila j. First, we consider the aforementioned modied lorentz parameters that satisfy the numerical stability conditions of and for all possible values of. Numerical modeling of lefthanded material lhm using dispersive fdtd. In this case, the permittivity can be calculated with the following formula. The finitedifference timedomain fdtd method has been widely used to solve transient electromagnetic problems for decades. In this paper, finite difference time domain fdtd is utilized to simulate metamaterials of double negative dng origin that refers to those materials having simultaneous negative permittivity and permeability. However, fdtd is a time domain method and therefore would be suitable for broadband simulations. In order to overcome this problem, we exploit the lorentz coordinate system transformation into the bunch rest frame and implement a finite di erence time domain fdtd method combined with particle in cell pic simulation in this frame. In this formulation, we use only single pole for lorentz model and is enough for the required accuracy. Express 11, 15411546 2003 sampled data 3d the sampled data model is used to import experimental refractive index or permittivity data. This letter addresses the stability problem of two auxiliary differential equation ade finitedifference timedomain fdtd methods for the case of modified lorentz media, using the combination.
The principle consists in replacing the electric field vector e byd. In this paper, the timestepping equation of the polarization vector is derived by applying simultaneously the newmark algorithm to the two sides of a secondorder time. In this paper the extended formulation for implementing lorentz model in sf fdtd is reported. The compute unified device architecture cuda is used for gpu parallelization. To overcome the intrinsic stability issue due to the. Fdtd analysis on optical con nement structure with. By establishing the corresponding relationship between drudetwocp model and drude lorentz model, the conversion coefficients between the two models are calculated.
Click transform to lorentz model, then click lorentz model radio button the lorentz model resonant frequency, damping. Effects of the nanostructure on dielectric and magnetic properties of the material are taken into account by introducing the drudelorentz model. The purpose being to be able to obtain negative values of the permittivity as well as of the permeability from the drude model. Optical material models in dgtd and feem lumerical support. Behavior analysis of metamaterials with the fdtd method and. To show the stability of the lorentz fdtd model in two dimensions, we borrow notation from that will ease the proof. A parameter estimation method is introduced for the general model to fit material permittivity functions fast and accurately. Introduction finitedifference timedomain fdtd simulations play a prominent role in numerical electromagnetic calculations1. Implementation of the critical points model in the recursive. In this formulation, we use only single pole for lorentz model. The problem regarding space formulation is achieved by means of auxiliary differential equation method ade, which is easy, reliable and also causal process in nature thus making it. Value of the parameters used in the drude and the dl model. Recently, it was reported that the modified lorentz model can cover debye, drude, lorentz, critical point, and quadratic complex. In this paper we use finitedifferencetimedomain fdtd computer simulations to.
Nijm, optical constants in the infrared for aqueous solutions of nacl, j. The finitedifference timedomain fdtd method has been used extensively. Numerical simulation of metallic nanostructures interacting. Dispersion models and electromagnetic fdtd analyses of. The frequencydomain susceptibility function for a dielectric in 1 or magnetic in 3 is complex. Lorentz formula depends on the material but usually the fit is performed over the region. This combination simplifies the implementation of lorentz and drude models in fdtd. Fdtd formulation for the general dispersion model using. We investigate the effects of energy loss in the medium on the confinement efficiency. Oct 10, 2020 based on drudecritical points drudetwocp model for a dispersive media, a finitedifference timedomain fdtd method for metal nanofilms is proposed. To create a material with gain, we need a material with a negative imaginary index. Comprehensive study on numerical aspects of modified. Free electron laser simulation tool based on fdtdpic in.
One phenomenon of interest is the propagation of electromagnetic waves in a magnetized plasma, which behaves as a gyrotropic medium. Fdtd modeling of lorentzian dng metamaterials by auxiliary. Lefthanded metamaterials lhms and their applications. Click transform to lorentz model, then click lorentz model radio button. We need to transform 43 to time domain so that fdtd can handle the fullwaveanalysis for the lorentz drude material. To do this, the drude model will be used for modeling the electrical and magnetic susceptibilities of a dispersive medium.
41 1024 75 479 1522 310 806 1182 1188 587 1000 2 735 209 984 765 121 1287 1014 1033 344 1274 1266 1468 332 1600 122 215 51 357 824 1540