Modeling optical coupling of plasmons and inhomogeneously broadened emitters

Optically coupling quantum emitters to nanoparticles provides the foundation for many plasmonic applications. Including quantum mechanical effects within the calculations can be crucial for designing new devices, but classical approximations are sometimes sufficient. Comprehending how the classical and quantum mechanical descriptions of quantum emitters alter their calculated optical response will lead to a better understanding of how to design devices. Here, we describe how the semiclassical Maxwell-Liouville method can be used to calculate the optical response from inhomogeneously broadened states. After describing the Maxwell-Liouville algorithm, we use the method to study the photon echoes from quantum dots and compare the results against analytical models. We then modify the quantum dot's state distribution to match a PbS 850 nm quantum dot's absorption spectra to see how the complete quasi-band structure affects their coupling to gold nanoislands. Finally, we compare the results with previously published work to demonstrate where the complete quantum dot description is necessary.