A Hybrid Approach for Solving Coupled Maxwell and Schrödinger Equations Arising in the Simulation of Nano-Devices

Computational Electromagnetics in Plasmonics

“…They are linear, and thus scalable. As long as quantum effects do not have to be taken into account, which is still the case for the plasmonic applications considered, since the structures are not that small [1], there is no fundamental problem. The underlying formulation of Maxwell's equations can remain unaffected.…”

Simulation of Plasmonics Nanodevices with Coupled Maxwell and Schrödinger Equations using the FDTD Method

“…O n t he other han d Maxwell equations ar e use d for electromagnetic effec ts. Therefore, these equa tions are coupled t o simulate t hose a pplications in w hich c ombined effects are needed [12][13]. In [12] a hybrid transmission line matrix ( TLM) [14] and FDTD [15], and in [13] a hybr id locally one dimensional (LO D)-FDTD [16] and F DTD methods are applied to coupled non-dispersive Maxwell and Schrödinger equations.…”

“…Therefore, these equa tions are coupled t o simulate t hose a pplications in w hich c ombined effects are needed [12][13]. In [12] a hybrid transmission line matrix ( TLM) [14] and FDTD [15], and in [13] a hybr id locally one dimensional (LO D)-FDTD [16] and F DTD methods are applied to coupled non-dispersive Maxwell and Schrödinger equations. In [12] the FDTD method is app lied to Schrödinger eq uation to simu late ca rbon n anotube whil e the TL M metho d is applied to t he conventional n ondispersive Ma xwell e quations to simula te the r est of the structure.…”

“…In [12] the FDTD method is app lied to Schrödinger eq uation to simu late ca rbon n anotube whil e the TL M metho d is applied to t he conventional n ondispersive Ma xwell e quations to simula te the r est of the structure. Whe reas in [13], the FDTD method is ap plied to Schrödinger equation to simulate a semiconductor nanowire and t he LOD-FDTD m ethod is a pplied to the c onventional non-dispersive Maxw ell e quations t o simulate rest of t he structure effi ciently. In brief, in [1 2-13] h ybrid ap proaches are a pplied t o na notube, nan owire and non d ispersive materials.…”

“…In brief, in [1 2-13] h ybrid ap proaches are a pplied t o na notube, nan owire and non d ispersive materials. In this paper, as compared to the [12][13], the LD dispersive model [17] i ncorporated Maxwell equa tions are coup led with S chrödinger equa tion t o sim ulate pl asmonic nanodevices. Schrödinger e quation i ncorporated Maxw ell equations are applied to sim ulate t he components i n w hich quantum effects are needed.…”