Coupled analysis of Maxwell–Schrödinger equations by using the length gauge: harmonic model of a nanoplate subjected to a 2D electromagnetic field

Abstract

A novel algorithm is proposed for solving coupled Maxwell and Schrödinger equations relying on the use of a length gauge form of the coupling between an electromagnetic field and electrons. Numerical simulations using codes implemented with the proposed and conventional algorithms have been performed for a harmonic model of a nanoplate subjected to a pulsed laser field whose central frequency is close to the plasmon frequency. We verify that the proposed algorithm can reduce computational time almost by half as compared with the conventional method. Figure 4. Relative error « of the time-dependent probability density measured at y = 0, | c (y = 0, t)| 2 for an electron confined by a 1D harmonic oscillator potential. in 2002. His research interest is concerned with computational electromagnetics. 544 S. OHNUKI ET AL.

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

“…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]:…”

“…The following recursion relations based on the Schrödinger FDTD method [4][5][6][7][8]12] can be obtained by separating the real and imaginary parts of the Schrödinger equation:…”

“…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.…”