Direct Measurement of the Local Density of Optical States in the Time Domain

One of the most fundamentaland relevant properties of a photonicsystem is the local density of optical states (LDOS) as it definesthe rate at which an excited emitter dissipates energy by couplingto its surrounding. However, the direct determination of the LDOSis challenging as it requires measurements of the complex electricfield of a point dipole at its own position. We introduce here a near-fieldsetup which can measure the terahertz electric field amplitude atthe position of a point source in the time domain. From the measuredamplitude, the frequency-dependent imaginary component of the electricfield can be determined and the LDOS can be retrieved. As a proofof concept, this setup has been used to measure the partial LDOS (theLDOS for a defined dipole orientation) as a function of the distanceto planar interfaces made of gold, InSb, and quartz. Furthermore,the spatially dependent partial LDOS of a resonant gold rod has beenmeasured as well. These results have been compared with analyticalresults and simulations. The excellent agreement between measurementsand theory demonstrates the applicability of this setup for the quantitativedetermination of the LDOS in complex photonic systems.