Spectroscopic Imaging of NIR to Visible Upconversion from NaYF$_{4}$: Yb$^{3+}$, Er$^{3+}$ Nanoparticles on Au Nano-cavity Arrays*

We use spectroscopic imaging to assess the spatial variations in upconversion luminescence from NaYF$_{4}$:Er$^{3+}$,Yb$^{3+}$ nanoparticles embedded in PMMA on Au nano-cavity arrays. The nano-cavity arrays support a surface plasmon (SP) resonance at 980nm, coincident with the peak absorption of the Yb$^{3+}$ sensitizer. Spatially-resolved upconversion spectra show a 30X to 3X luminescence intensity enhancement on the nano-cavity array compared to the nearby smooth Au surface, corresponding to excitation intensities from 1 W/cm$^{2}$ to 300kW/cm$^{2}$. Our analysis shows the power dependent enhancement in upconversion luminescence can be almost entirely accounted for by a constant shift in the effective excitation intensity, which is maintained over five orders of magnitude variation in excitation intensity. The variations in upconversion luminescence enhancement with power are modeled by a 3-level-system near the saturation limit, and by simultaneous solution of a system of coupled nonlinear differential equations, both analyses agree well with the experiments. Analysis of the statistical distribution of emission intensities in the spectroscopic images on and off the nano-cavity arrays provides an estimate of the average enhancement factor independent of fluctuations in nano-particle density.