Direct Observation of Non-Markovian Radiation Dynamics in 3D Bulk Photonic Crystals

Since the very first proposition of photonic crystals, their influence on the dynamics of spontaneous emission has been of great interest. The radiation dynamics is described by an integration kernel which—in a spectral representation—comprises two equally important contributions: the Lamb shift and the radiative contribution to the linewidth. The latter is connected to the density of states via Fermi’s golden rule. To our knowledge, we present the first spatially resolved measurement of the complete radiation dynamics in a photonic crystal and of its local density of states over a wide spectral range. To this end we study a single magnetic dipole situated in a photonic crystal with a band gap at microwave frequencies and find non-Markovian behavior in excellent agreement with ab initio calculations.

Figure 1

Ferromagnetic resonance of the YIG sample at position 1. (a) Experimental scan with respect to the external magnetic field at fixed microwave frequency $\omega /2\pi =14.9\mathrm{GHz}$. The solid (red) curve is a Lorentzian fit to the data points (blue crosses). (b),(c) Frequency scans at a constant magnetic field which corresponds to a bare emitter frequency of $\Omega /2\pi =14.9\mathrm{GHz}$. The resonance curves were reconstructed from linewidth and shift data obtained from experimental field scans at various values of $\omega$ (b) and from corresponding theoretical calculations (c).

Figure 2

Side-view (a) and top-view (b) photographs of the experimental photonic crystal (the scale bar corresponds to 10 mm). Experimental data were recorded for two different emitter positions: position 1 close to a dielectric rod, indicated by a red dot, and position “2” at a maximum distance from any dielectric rod, indicated by a blue dot. The dot size corresponds to the size of the YIG sphere; white rings were added for better contrast.

Figure 3

Linewidth and resonance shift obtained at the emitter position 1 [(a) and (c), respectively] and position 2 [(b) and (d)]. Experimental data points are depicted as blue crosses. The connecting blue solid lines were added to guide the eye. The results of corresponding ab initio numerics are shown as red solid lines. The computed photonic band gap is indicated by yellow-shaded areas. For comparison, the vacuum linewidth based on our experimentally determined coupling constant $\beta$ is indicated by a dashed line.