Variational integrators for maxwells equations with sources a. Finitedifference timedomain simulation of the maxwellschrodinger system. Blochs theorem tells us that for periodic structure, field components have the following properties. In addition to solving the fullvector maxwells equations, fdtd simulations may accommodate not only complex geometries. The results obtained from the fdtd method would be approximate even if we. The main reasons for choosing the fdtd computational method in our simulations of ultrashort optical pulse propagation are. For example, below is the code for the first example shown above. Variational integrators for maxwells equations with sources. May 23, 2017 the finite difference time domain fdtd method is a powerfull numerical technique to solve the maxwell equations.
The fdtd method makes approximations that force the solutions to be approximate, i. It has been successfully applied to an extremely wide variety of problems, such as scattering from metal objects and. Classical model of quantum noise with the fdtd method. Raumzeitliche, nichtlineare laserdynamik in mikrokavitaten. The electric field propagation and the carrier dynamics of qds embedded into a 2d wetting layer wl are calculated using qdwl maxwell bloch equations. The incorporation of microscopic material models into the fdtd approach for. Maxwellbloch equations with number stochastic noise terms. The program is designed for quick and efficient programming of fdtd simulations and for extending the available fdtd algorithms with new techniques and features.
We investigate the process of light matter interaction in a spherical mie nanolaser. A second goal is to prove linear stability and convergence for the modified nsfdtd method. Nanophotonic fdtd simulation software lumerical fdtd. Photonic crystal fiber analysis using cylindrical fdtd with. The results obtained from the fdtd method would be approximate even if we used computers that offered in. Fdtd method, but the atomic response was described by a steadystate susceptibility and. Bloch oscillations in plasmonic waveguide arrays nature. Variables and parameters of the light, gain material, cavity, and fdtd. Finite difference time domain fdtd methods for solution of. Chapter maxwells equations and electromagnetic waves. Finite difference time domain fdtd methods for solution of maxwell s equations case study in simulation sciences dr. A high resolution nonstandard fdtd method for the tm mode of.
Phenomenological pure dephasing and incoherent pumping is added to the optical bloch. Development of a 2d fullwave je fdtd maxwell xmode code for re. In this research, we present the first multigpu fdtd implementation of maxwells equations in dispersive media that uses the openmp api to synchronize the operation of gpus and their corresponding cpus. The wave front propagates with speed of light and meets in the middle of space on a. The maxwellbloch equations, also called the optical bloch equations describe the dynamics of a twostate quantum system interacting with the electromagnetic mode of an optical resonator. The finitedifference timedomain fdtd solution of the fullwave vectorial maxwellbloch equations has been previously used for the investigation of nonlinear gain spatiotemporal dynamics of. Resonance an oscillating mode trapped for a long timein some volume of light, sound, frequency. Jun 25, 2008 rareearthdoped crystals contain inhomogeneously broadened twolevel atoms. Introduction fdtd finite difference time domain fdtd is a stateoftheart method for solving maxwells equations for complex geometries few inherent approximations general technique that can deal with many types of problems arbitrary complex geometries one simulation gives broadband results. Initial excitation unlike conventional fdtd simulations where time domain excitation is continuous wave and lasts on only some time steps, more info. Equation 60 is the boundary condition used in the optifdtd band solver. Using a finitedifference timedomain fdtd technique, maxwell bloch equations representing a system of thousands of statistically independent and randomly positioned twolevel emitters are solved numerically. Hofmann and hess obtained the quantum maxwellbloch equations including.
Finally, we investigate the high resolution of the proposed method by solving benchmark tests. Nusod 2017 performance evaluation of numerical methods. Osa mode competitions and dynamical frequency pulling in. Chapter 2 maxwellbloch equations mit opencourseware. Here you can find parallel fdtd codes developed by zsolt szabo. Fdtd is the goldstandard for modeling nanophotonic devices, processes, and materials. Numerical methods for the bidimensional maxwellbloch. Pdf rareearthdoped crystals can be modelled as inhomogeneously broadened. They are analogous to but not at all equivalent to the bloch equations which describe the motion of the nuclear magnetic moment in an electromagnetic field. Selfconsistent maxwellbloch model of quantumdot photonic. The last scheme presented is a fdtd scheme, which should address the main draw. Ziolkowski, fellow, ieee abstractin this paper, we use the. George street, toronto, ontario m5s 1a7, canada, and. Understanding the finitedifference timedomain method.
A python package for solving maxwells equations using. Source implementation and the effects of various boundaries such as. Using a finite difference timedomain fdtd technique, maxwellbloch equations representing a. In this research, we present the first multigpu fdtd implementation of maxwell s equations in dispersive media that uses the openmp api to synchronize the operation of gpus and their corresponding cpus. The finite difference time domain fdtd method is a powerfull numerical technique to solve the maxwell equations. Finitedifference timedomain simulation of the maxwellschr. Fdtd method by directly discretizing the time and the space 2628. Their approach combines the finite difference time domain fdtd method for maxwells equations with the cranknicholson scheme for the optical bloch equations. The finitedifference timedomain fdtd method 1 has been extensively used in solving maxwell s equations for dynamic electromagnetic em fields. Modified splitting fdtd methods for twodimensional. The views and opinions expressed herein do not necessarily reflect. Finite difference time domain fdtd methods for solution of maxwells equations case study in simulation sciences dr.
The finitedifference timedomain fdtd method for maxwells equations, which was first proposed by yee see, also called yees scheme in 1966, is a very efficient numerical algorithm in computational electromagnetism see and has been applied in a broad range of practical problems by combining absorbing boundary conditions see 37. We derive a rigorous theory based on a three dimensional vector set of maxwellbloch equations and solve the resulting equations through a parallel finitedifference timedomain maxwellbloch fdtdmb code. Shukor5 1center for telecommunication research and innovation cetri, faculty of electronic and computer engineering. Fdtd geometry staircasing significant deformations of the original geometry inflexible meshing capabilities standard fdtd edge is a single material fdtd grid cell is entirely inside or outside material pec boundary on2 accuracy does not include meshing inaccuracies uspas june 2010. Optical propagation and nonlinear interaction in the crystals can be described by the maxwellbloch equations. Our goal is to develop a high resolution nonstandard fdtd method for the transverse magnetic tm mode of 2d maxwells equations.
Comparison with analytic solution ilkka laakso aprasc10 toyama radial electric field at 200 mhz ecell overestimation analytical hcell plane wave. Numerical studies of lasing and electromagnetic fluctuations in. The absorbing boundary of a onedimensional 1d fdtd. The equations are evaluated using the finitedifference timedomain fdtd method. Multilevel maxwellbloch simulations in inhomogeneously.
Beam propagation in the crystals can be described by the maxwellbloch equations. Finite difference time domain fdtd methods for solution. Finitedifference timedomain formulation of stochastic. Finitedifference timedomain simulation of the maxwell. Photonic crystal fiber analysis using cylindrical fdtd with bloch boundary conditions adam mock and paul trader school of engineering and technology central michigan university piers 2010 in cambridge, ma usa session. Our goal is to develop a fdtdbased numerical method to simulate fluctuations. The electric field propagation and the carrier dynamics of qds embedded into a 2d wetting layer wl are calculated using qdwl maxwellbloch equations.
Video shows a 2d simulation of a 5ghz antenna in vacuum. We derive a rigorous theory based on a three dimensional vector set of maxwell bloch equations and solve the resulting equations through a parallel finitedifference timedomain maxwell bloch fdtd mb code. Coupled maxwellpseudospin equations for investigation of. It is described for the first time in a semiclassical, self consistent three dimensional formalism by the discretised optical bloch equations as separate difference equations. Shukor5 1center for telecommunication research and innovation cetri. A fdtd simulation of microcavity lasers including quantum. They are analogous to but not at all equivalent to the bloch equations which describe the motion of the nuclear magnetic moment in. This finelytuned implementation of the fdtd method delivers reliable, powerful, and scalable solver performance over a broad spectrum of applications. Photonic crystal fiber analysis using cylindrical fdtd. We show a consistent numerical approach that solves maxwells equations by using the fftfinite difference beam propagation method and the bloch equations by using the finite difference method. But, why go through the hassle of publishing through a publisher when you can give away something for free. This method is based on the maxwellbloch equations for twolevel atoms with real noise terms.
We compare here different ways of coupling maxwell and bloch equations in time. Rareearthdoped crystals contain inhomogeneously broadened twolevel atoms. The pioneering work was done by ziolkowski, arnold and gogny 3. Fdtd simulation of the nonlinear gain dynamics in active optical waveguides and semiconductor microcavities gabriela m. The third chapter is where the fdtd material really starts and i believe and hope you agree that things are pretty decent beginning from there. However, the direct discretization of the maxwellbloch. Marsden1 1california institute of technology, usa 2michigan state university, usa abstract in recent years, two important techniques for geometric numerical discretization have been developed. The incorporation of auxiliary differential equations, such as the rate equations for atomic populations 2 and the bloch equations for.
Chew, fellow, ieee abstracta thorough study on the. This paper describes gmes, a free python package for solving maxwells equations using the finitedifference timedomain fdtd method. Okay, i can think of several reasons, but im going to ignore them. An introduction then, the above 6 equations from 2 maxwells curl equations reduce to 2 equations for 1d fdtd ex 1 hy t z. Pdf simulations of 2d maxwellbloch equations researchgate. Yee, born 1934 is a numerical analysis technique used for modeling computational electrodynamics finding approximate solutions to the associated system of differential equations. The maxwell material equations introduce the polarisation into the fdtd algorithm. Schneider is licensed under a creative commons attributionsharealike 4. In section ii, we describe the model developed to include noise in the maxwellbloch equations. Dual spatial grid is commonly used for coupled electric and magnetic fields. Classical model of quantum noise with the fdtd method ursi. Selfconsistent maxwell bloch modelling of the threshold. Slow scale maxwellbloch equations for active photonic crystals gandhi alagappan department of electronics and photonics, institute of high perfor. The finitedifference timedomain fdtd method 1 has been extensively used in solving maxwells equations for dynamic electromagnetic em fields.
Beam propagation in the crystals can be described by the maxwell bloch equations. Fdtd method, but the atomic response was described by. We use a lowdispersion pseudospectral scheme with fourth order time stepping for maxwells equations, and a weakly coupled operator splitting method for the bloch equations where inhomogeneous broadening and relaxations are also taken into account. The fdtd implementation of this model is presented in section iii. The codes can be run under unix and windows operating systems. Fdtd simulation of the maxwellschrodinger system in the semiclassical regime is. A new energyconserved sfdtd scheme for maxwells equations in metamaterials wanshan li, dong liang, and yanping lin abstract. Development of a 2d fullwave jefdtd maxwell xmode code. Bloch oscillationsoscillatory motions of wave packets in periodic potentials acting under constant forceshave been observed in semiconductor superlattices and. Our results predicts a rich physical scenario, ranging from nontrivial vectorial energy matter. Chapter 3 basic fdtd techniques for solving maxwells equations. The incorporation of auxiliary differential equations, such as the rate equations for atomic populations 2 and the maxwell bloch equations for the densityofstates of atoms 3, has. Pdf fdtd simulation of the nonlinear gain dynamics in. A compact numerical method for simulating ultrafast pulse interaction with inhomogeneously broadened multilevel media is reported.
Finitedifference timedomain or yees method named after the chinese american applied mathematician kane s. Pdf fdtd for hydrodynamic electron fluid maxwell equations. Finitedifference timedomain formulation of stochastic noise. The finitedifference timedomain fdtd solution of the fullwave vectorial maxwell bloch equations has been previously used for the investigation of nonlinear gain spatiotemporal dynamics of. The incorporation of auxiliary differential equations, such as the rate equations for atomic populations 2 and the maxwellbloch equations for the densityofstates of atoms 3, has.
Modified splitting fdtd methods for twodimensional maxwells. Selfconsistent maxwellbloch theory of quantumdotpopulation switching in photonic crystals hiroyuki takeda department of physics, university of toronto, 60 st. A high resolution nonstandard fdtd method for the tm mode. Feb 15, 2011 video shows a 2d simulation of a 5ghz antenna in vacuum. Since it is a timedomain method, fdtd solutions can cover a wide frequency range with a. In this paper, we develop a new energyconserved sfdtd scheme for the maxwells equations in metamaterials. Using a finitedifference timedomain fdtd technique, maxwellbloch equations representing a. Finite differencestime domain fdtd scheme with different temporal scales for the. The derivation of the maxwellbloch equations can be found in quantum.
We present a powerful computational approach to simulate the threshold behavior of photoniccrystal quantumdot qd lasers. The design of gmes follows the objectoriented programming oop approach and adopts a unique design strategy where the voxels in the computational domain are grouped and then updated according to its material type. Fdtd multigpu implementation of maxwells equations in. I once considered publishing a book on the finitedifference timedomain fdtd method based on notes i wrote for a course i taught.
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