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

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