Local optical density of states in SiO₂ spherical microcavities: Theory and experiment

The local optical density of states (LDOS) in 340-nm-diam SiO₂ spherical microcavities was calculated and probed experimentally by measuring the luminescence decay rate at 1.54 μm of erbium ions implanted in the colloids. To separate the effect of nonradiative processes, first the radiative decay rate of Er³⁺ in bulk SiO₂ was determined. This was done by varying the LDOS in an Er-doped planar SiO₂ film by bringing the film into contact with liquids of different refractive index in the range n=1.33–1.57. By comparing the calculated LDOS with the observed changes in decay rate with index, the radiative rate was found to be 54±10s^-1 (τ=18±3ms) in bulk SiO₂. This value was then used to analyze the difference in decay rate in colloids surrounded by air or immersed in an index-matching liquid. Within the experimental error, agreement was found between the calculated and experimentally probed LDOS in the colloids. Finally, a full determination of the LDOS vs size in SiO₂ microcavities is presented (2πR/λ=0.1–6.9), which shows the appearance of a number of maxima, corresponding to the position of the electric-type resonances inside the microcavity.