Abstract
We provide a pedagogical introduction to the concept of the local density of optical states (LDOS), illustrating its application to both the classical and quantum theory of radiation. We show that the LDOS governs the efficiency of a macroscopic classical antenna, determining how the antenna’s emission depends on its environment. The LDOS is shown to similarly modify the spontaneous emission rate of a quantum emitter, such as an excited atom, molecule, ion, or quantum dot that is embedded in a nanostructured optical environment. The difference between the number density of optical states, the LDOS, and the partial LDOS is elaborated and examples are provided for each density of states to illustrate where these are required. We illustrate the universal effect of the LDOS on emission by comparing systems with emission wavelengths that differ by more than 5 orders of magnitude, and systems whose decay rates differ by more than 5 orders of magnitude. To conclude we discuss and resolve an apparent difference between the classical and quantum expressions for the spontaneous emission rate that often seems to be overlooked, and discuss the experimental determination of the LDOS.
Highlights
We provide a pedagogical introduction to the concept of the local density of optical states (LDOS), illustrating its application to both the classical and quantum theory of radiation
We return to consider what happens to an emitter above a mirror; this simple reflecting interface provides a convenient way to develop a better understanding about the effect of the local density of states on spontaneous emission, so powerful is it that we will use it as a leitmotif that runs throughout this article
0 p d 0 indicating that the rate of decay of a single emitter is determined by the partial local density of states (PLDOS), and is proportional to it, with a proportionality constant that depends on the physical constants ÿ and ò0 as well as the permittivity of the surrounding medium ò, the frequency of emission ω, and the emitter’s transition dipole moment
Summary
The local density of optical states (LDOS) measures the availability of electromagnetic (EM) modes at a given point in space. The straightforward part is that the exciton in a quantum dot is in essence a very small oscillating current, and the way it radiates is still governed by the availability of EM modes, just as for an antenna broadcasting radio waves. This is not to say that quantum mechanics is completely irrelevant. The subtlety is that a quantum emitter —such as an exciton in a quantum dot— experiences the local density of states in a second, non-classical way To appreciate this second contribution we can think of the allowed EM modes in some environment and ask whether quantum mechanics changes them in any way; the answer is both no and yes! Throughout the article we make use of an example system where the density of optical states is comprehended, the case of an emitter or antenna in front of a mirror; this system is our leitmotif
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