Self-interaction-free approaches for self-consistent solution of the Maxwell-Liouville equations

Abstract

We propose two complementary approaches for solution of the coupled Maxwell-Liouville equations within the finite-difference time domain (FDTD) framework. The two methods are specifically designed to eliminate self-interaction, which often appears spuriously in simulation of the coupled Maxwell-Liouville equations, and hence can be used for modeling of single as well as ensembles of quantum emitters (such as molecules or quantum dots) in an arbitrary dielectric environment. One approach borrows from the familiar total field-scattered field technique that has been applied in the past in a different context. The second recognizes an opportunity to average over the electric field at a set of specifically chosen points around the quantum emitter. The methods introduced are applied to two problems of growing current interest that also present useful test cases. One is the modeling of spontaneous emission, where comparison with an analytical solution illustrates the accuracy and efficiency of the methodology. The second is quantum-emitter-induced transparency in a resonator formed by two gold ellipsoids, where Fano interferences suggest interesting potential applications.

Optoelectronic Device Simulations Based on Macroscopic Maxwell–Bloch Equations

“…Several research groups use the fourth-order Runge-Kutta (RK) method to solve the Bloch equations. [55,60,239,264] As illustrated in Figure 17b, the method is strongly coupled since electric field and density matrix are discretized at the same time steps. The exact procedure is not always described in related work, but can be outlined as follows.…”

“…The Electromagnetic Template Li-brary (EMTL) is a free C++ library with Message Passing Interface (MPI) support, [238] which has, for example, been used to model quantum emitters with the full-wave MB equations in two dimensions. [239] Another solver library for the full-wave MB equations is the open-source MEEP project, [240] using a similar representation of the Bloch equations as given in Equation (72). The mbsolve project [241] solves the full-wave MB equations using different parallel acceleration techniques and features an open-source codebase.…”

“…In principle, the current/polarization contribution of an individual quantum system at a given position can be directly represented in Maxwell's equations by a point source, [239] without using ensemble averaging as in Section 4.1. However, the complexity of such an approach increases significantly with the number of quantum systems to be included.…”

Comparison of Different Classical, Semiclassical, and Quantum Treatments of Light–Matter Interactions: Understanding Energy Conservation

“…If we take the Fourier transform of the definition of χ(ω) in Eqs. (30)(31), we find that the equation of motion for the optical polarization reads…”

Some exact properties of the nonequilibrium response function for transient photoabsorption

“…In this case the quantum evolution of the system should be coupled to the Maxwell equations to determine the total field selfconsistently. 23,35,40,70,75,[90][91][92][93][94][95][96][97] For a typical sub-as pulse e(t) centered around a resonant frequency ω 0 the total electric field E(t) is dominated by oscillations of frequency ω 0 decaying over the same time-scale of the induced dipole moment (in atomic gases this time-scale can be as long as hundreds of fs). Let us explore the outcome of a TR-PA experiment for a total field of the form, e.g., E(t) = E 0 θ(t) sin(ω 0 t), ω 0 > 0.…”