Comparison Between Maxwell–Schrödinger and Maxwell–Newton Hybrid Simulations for Multi-Well Electrostatic Potential

Abstract

A novel hybrid approach to the dynamics of electron interacting with time-dependent electromagnetic fields, namely, the Maxwell-Schrödinger approach, has been employed to study a system of electron confined in single-and multi-well electrostatic potentials subjected to pulsed laser fields. A comparison of the results of simulation to those obtained by the conventional Maxwell-Newton approach has been made by calculating the time response of the current density and the time-evolution of the electric field at an observation point. The results obtained by these two distinct approaches agree very well for the singlewell potential while disagree qualitatively for the multi-well potential. This clearly demonstrates limitation of applicability of the conventional Maxwell-Newton scheme to study electron dynamics in electromagnetic fields. IndexTerms-FDTD method, Maxwell-Schrödinger equations, multi-physics simulation, tunneling effect.

HYBRID SIMULATION OF MAXWELL-SCHRODINGER EQUATIONS FOR MULTI-PHYSICS PROBLEMS CHARACTERIZED BY ANHARMONIC ELECTROSTATIC POTENTIAL (Invited Paper)

“…Very recently, we have examined a reliability of the conventional Maxwell-Newton hybrid scheme for an electron confined in one-dimensional potential wells. A comparison of computational results with those obtained by the corresponding Maxwell-Schrödinger scheme [6] has revealed that both results agree very well for a harmonic single-well potential while disagree qualitatively for a triple-well potential where a harmonic potential is artificially supplemented by two small humps allowing bifurcation of the electron wave packet. Although this study clearly demonstrates necessity of use of the Maxwell-Schrödinger scheme over the conventional Maxwell-Newton one particularly when quantum-mechanical tunnelling takes place, an effect of anharmoicity in a singlewell confining potential on computational results has not been fully explored.…”

“…where J represents the polarization current density which is defined by the time derivative of the polarization vector P. Since the electromagnetic fields have only E y and H z components in the present study, they can be updated by the following recursion relations based on the Maxwell FDTD method [5,6,10]:…”

“…In the last decade this cooperative lightmatter interaction has been actively studied with growing interests particularly in designing innovative photonic devices such as plasmonic antennas, quantum dot laser, and so on [1][2][3]. Currently, the multi-physics phenomena in such devices have been studied by two distinct hybrid schemes, namely, based on the Maxwell-Schrödinger and Maxwell-Newton theories [4][5][6][7][8][9]. The Maxwell-Schrödinger hybrid scheme [4][5][6][7][8] is computationally demanding but physically precise, where the laser field is governed by Maxwell's equations and the electrons by Schrödinger's equation.…”

“…Currently, the multi-physics phenomena in such devices have been studied by two distinct hybrid schemes, namely, based on the Maxwell-Schrödinger and Maxwell-Newton theories [4][5][6][7][8][9]. The Maxwell-Schrödinger hybrid scheme [4][5][6][7][8] is computationally demanding but physically precise, where the laser field is governed by Maxwell's equations and the electrons by Schrödinger's equation. This scheme has been successfully used recently in pioneering numerical simulations such as for a carbon nanotube transistor [4], H + 2 gas interacting with ultrashort laser pulses [7,8], and so on.…”

“…This scheme has been successfully used recently in pioneering numerical simulations such as for a carbon nanotube transistor [4], H + 2 gas interacting with ultrashort laser pulses [7,8], and so on. The other approach, namely, the well-known Maxwell-Newton hybrid scheme [9], where the laser field and electrons are described by solving Maxwell's equations and Newton's equation of motion, respectively, requires much less computational resources, and thus has been very often employed to perform multi-physics simulations [1][2][3][4][5][6][7][8][9] without, however, paying much attention to its physical reliability. Very recently, we have examined a reliability of the conventional Maxwell-Newton hybrid scheme for an electron confined in one-dimensional potential wells.…”