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. The first model includes a drude term and five lorentzianpole pairs dl model whereas in the second one the lorentzian terms are replaced by two criticalpoint terms dcp model. Finitedifference timedomain method guides optical design of metallic nanostructures. The data files can be from references, user generated. The lorentzdrude model in 43 is in the frequency domain. Yee, born 1934 is a numerical analysis technique used for modeling computational electrodynamics finding approximate solutions to. Fdtd modeling of lorentzian dng metamaterials by auxiliary. Metamaterials and fdtd based numerical modeling studies. Then, we illustrate how this tool can facilitate the development of optical imaging techniques.
Modeling and simulation of active plasmonics with the fdtd. The model is based on treating electrons as damped harmonically bound particles subject to external electric fields. Drudelorentz model of semiconductor optical plasmons. However, multipole debye, drude and lorentz functions are often used to simulate the electric susceptibility of materials such as. Finitedifference timedomain simulation design softwareoptifdtd lorentzdrude model a lorentzdrude model for metallic integrated photonic circuits. Before performing fdtd simulation of any material, it needs to be.
Finite difference time domain fdtd simulation of a photonic crystal yjunction fdtd subgridding photon designs unique subgridding tool gives you the ability to create 2x, 4x or greater increased resolution in localised regions. The drudelorentz model is an improvement of drude model which takes into account the explicitly separated interband boundelectron effects expression to the initial model of drude. For the simulation of plasmonics devices, the lorentzdrude ld dispersive model is incorporated into maxwell equations, while the auxiliary differential equation ade technique is applied to the ld model. Dispersive material handling by drude, lorentz, drudelorentz and debye models. Nanophotonic fdtd simulation software lumerical fdtd. Modeling of dispersive materials using dispersion models for fdtd. Both models describe reasonably well, for all alloy compositions, the experimental data reported by penarodriguez et al. This lecture introduces the student to the lorentz model which describes the dielectric response of materials and drude model which describes metals. The first gyrotropy model is a drudelorentz model with an additional precession, which is intended to describe gyroelectric materials. Drude, lorentz, debyematerials and their stability conditions and accuracies are derived and discussed.
Thus the fdtd algorithm is derived based on the above equations. Nonlinear drude plasma model for ultrashort pulse simulation abstract. One of the distinct advantages of the fdtd method is that metals can be added to the material system via the lorentzdrude models. By adding this lorentzian term that is described by a semiquantum model, the validity range of. Pdf drudelorentz model of semiconductor optical plasmons. This transformation to time domain is accomplished by using the polarization philosophy within maxwells equation. Adefdtd scatteredfield formulation for dispersive materials. Optifdtd provides a builtin noble metal library along with other dispersive material models for the user.
Feb 03, 2014 this lecture introduces the student to the lorentz model which describes the dielectric response of materials and drude model which describes metals. For the simulation of plasmonics devices, the lorentzdrude ld dispersive model is incorporated into maxwell equations, while the auxiliary differential equation. One of the distinct advantages of the fdtd method is that metals can be added to the material system via the lorentz drude models. Lorentz drude model for metal and surface plasma introduction. Modelling the dielectric function of auag alloys sciencedirect. Nontrivial materials in emfdtd university college london. Finitedifference timedomainbased optical microscopy. Optifdtd also provides a sample for this lorentz drude model simulation. A flexible freesoftware package for electromagnetic. The drude lorentz model is an improvement of drude model which takes into account the explicitly separated interband boundelectron effects expression to the initial model of drude.
For the simulation of plasmonics devices, the lorentzdrude ld dispersive model is incorporated into maxwell equations, while the auxiliary. Maybe the point is only how to specify the susceptibility. Pdf implementation of the fdtd method based on lorentzdrude. Generalization of the fdtd algorithm for simulations of. Nanostructured metalsemiconductormetal photodetector for. Lorentz, debye and drude models, each representing a different way in which the material properties vary with frequency. Fdtd is a simulator within lumericals device multiphysics simulation suite, the worlds first multiphysics suite purposebuilt for photonics designers.
The values for the respective plasma frequencies are summarized in table 1 therein. Lesson 10 lorentz drude model for metal and surface plasma. The device suite enables designers to accurately model components where the complex interaction of optical, electronic, and thermal phenomena is critical to performance. Analytical plot of dielectric function of lorentz medium. The following matlab project contains the source code and matlab examples used for drude lorentz and debye lorentz models for the dielectric constant of metals and water. Finitedifference timedomain or yees method named after the chinese american applied mathematician kane s. Jun 06, 2005 material modeling is one area that has received a lot of attention, and the ability to include dispersive media has been added to the software. Specifically, the auxiliary differential equation method is applied to drude and lorentz media for a scattered field fdtd model. Lorentz drude model in time domain the lorentz drude model shown in 10 is in the frequency domain form. Lossy and lossless lorentzdrude types of dng metamaterials are characterized theoretically, used in several experiments, and fabricated for new devices in these studies. Study on dielectric function models for surface plasmon. All of the features that one would expect from a sophisticated code are implemented. Lorentzdrude fitting of user data further improving the user experience, optifdtd 14. However, the fdtd is a time domain method and therefore it would be suitable for broadband simulations.
How to model drude materials using fdtd physics forums. Added some small changes to improve the overall performance. This algorithm forms the basic concept of the formulation of an advanced. The image to the right shows the permittivities of silver and gold fit to such a model 4, demonstrating the accuracy that can be achieved. Lorentzdrude model for metal and surface plasma introduction. The lorentzdrude model in time domain can be expressed as follows finite difference time domain photonics simulation software. The current contribution from the ions is to be neglected due to the very fast time scale, and the.
Angora is a free, opensource software package that computes numerical solutions to electromagnetic radiation and scattering problems. Only lorentz and the drude models can produce negative permittivities or permeabilities when the coupling coefficient is positive. Added a new material pure water whose dielectric constant is computed via the debyelorentz model. Numerical simulation of metallic nanostructures interacting with electromagnetic fields using the lorentzdrude model and fdtd method. First, it would have been nice to write out what fdtd stands for finite difference time domain instead of leaving it to us to find out. Given the resonant frequency, damping term and frequency axis, this code calculates complex dielectric function of a lorentz medium using its analytical formula given in many elementary electrodynamics texts. Metallic nanostructures for polarizationindependent multi. The fdtd algorithm can be derived based on the above equation. Yee, born 1934 is a numerical analysis technique used for modeling computational electrodynamics finding approximate solutions to the associated system of differential equations. However, the fdtd is a time domain method and therefore it. In particular, we focus on aspects of implementing a fullfeatured fdtd package that go beyond standard textbook descriptions of the algorithm, or ways in which meep differs from typical fdtd implementations. This letter presents a scatteredfield formulation for modeling dispersive media using the finitedifference timedomain fdtd method.
Included a screenshot to show the comparison between the drude, lorentzdrude and exact experimental values of the permittivity of. Pdf numerical simulation of metallic nanostructures interacting. The drude model of electrical conduction was proposed in 1900 by paul drude to explain the transport properties of electrons in materials especially metals. Drudelorentz and debyelorentz models for the dielectric. Numerical simulation of metallic nanostructures interacting with. Basic assumptions of drude model a gas of conduction electrons of mass m, which move against a background of heavy immobile ions electron density a z n m 0. Jan 31, 2012 added a new material pure water whose dielectric constant is computed via the debye lorentz model. Fdtd is ideal for modelling complex optical structures including ring resonators, optical gratings, photonic crystals and nanophotonics. In the drude model is that the complex value of the susceptibility arises once you specify a positive value for the damping g. Ziolkowski also investigated the wave propagation in drude type 20 and lorentz type 21 lhms media in 2001. Included a screenshot to show the comparison between the drude, lorentz drude and exact experimental values of the permittivity of. Optifdtd is the first software to employ the lorentzdrude model into the fdtd algorithm.
It is based on the finitedifference timedomain fdtd method, which is one of the most popular approaches for solving maxwells equations of electrodynamics. A particularly powerful model for fitting experimental optical data, for example, is a drude model in combination with two lorentz oscillator poles. The lorentzdrude model in time domain can be expressed. Nowadays, the fdtd method is very much efficient, accurate and widely used for electromagnetism computations such as, fields and resonant modes. However, fdtd is a time domain method and therefore would be suitable for broadband simulations. Here, we first introduce the fdtd modeling of drude and lorentz dispersions in angora and validate the module. Sep 12, 20 ahmed i, khoo e, kurniawan o, li e 2011 modeling and simulation of active plasmonics with the fdtd method by using solid state and lorentzdrude dispersive model. This code computes the complex dielectric constant i. Finitedifference timedomain method guides optical design of. Lorentzdrude model in time domain the lorentzdrude model shown in 10 is in the frequency domain form.
Lorentz, debye and drude models, each representing a different way in. The lorentzdrude model incorporated maxwell equations are simulated by using the threedimensional finite difference time domain fdtd method and the method is parallelized on multiple graphics. Given the resonant frequency, damping term and frequency axis, this code calculates complex dielectric function of a lorentz medium using its analytical formula. Feb 11, 2014 first, it would have been nice to write out what fdtd stands for finite difference time domain instead of leaving it to us to find out. Lesson 11 analyzing 1d photonic crystals bragg gratings. The polarization equation is optionally, the polarization may be of drude form, in which case the term on the left is omitted. 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. Using modified lorentz term allows to obtain more accurate fittings. Design software offering both fdtd and mom analysis. The first gyrotropy model is a drude lorentz model with an additional precession, which is intended to describe gyroelectric materials. Ahmed i, khoo e, kurniawan o, li e 2011 modeling and simulation of active plasmonics with the fdtd method by using solid state and lorentzdrude dispersive model.
Native 2d material model, ideal for graphene modelling. Minimum wavelength nm a minimum wavelength is required. Shg and volume chi3 thg nonlinearity nonlinearity, with dispersion. Implementation of the lorentzdrude model incorporated fdtd. Our numerical experiments based on typical domain sizes as well as plasmonics environment demonstrate that our implementation of the fdtd method on gpu o. May 21, 2014 finitedifference timedomain simulation design softwareoptifdtd lorentzdrude model a lorentzdrude model for metallic integrated photonic circuits. We present a threedimensional finite difference time domain fdtd method on graphics processing unit gpu for plasmonics applications. Drude lorentz and debye lorentz models for the dielectric. For the simulation of plasmonics devices, the lorentz drude ld dispersive model is incorporated into maxwell equations, while the auxiliary differential equation ade technique is applied to the ld model.
Material modeling is one area that has received a lot of attention, and the ability to include dispersive media has been added to the software. This paper describes meep, a popular free implementation of the finitedifference timedomain fdtd method for simulating electromagnetism. The omnisim and crystalwave frameworks includes a highly efficient fdtd finite difference time domain engine to simulate the propagation of light through your designs. For example, two modified lorentz terms are sufficient to fit silicon dielectric function over the wavelength range from 300 to nm, whereas even a large number of debye, drude or lorentz terms is inadequate there 1. Modeling and simulation of active plasmonics with the fdtd method by using solid state and lorentzdrude dispersive model. Lorentz drude fitting of user data further improving the user experience, optifdtd 14. Fdtd figure 2 lorentzdrude dispersive material dialog box.
The present technique can also be applied in a straightforward manner to debye media. By adding this lorentzian term that is described by a semiquantum model, the validity range of drude model can be extended 26. This advanced materials model will allow users to perform more accurate, truly fullwave simulations for metallic structures another industry first captured by optifdtd. Optifdtd technical background and tutorials finite difference time domain photonics simulation software version 8. Efficient wideband numerical simulations for nanostructures.