We present a novel method to extract the various contributions to the photonic local density of states from near-field fluorescence maps. The approach is based on the simultaneous mapping of the fluorescence intensity and decay rate, and on the rigor
ous application of the reciprocity theorem. It allows us to separate the contributions of the radiative and the apparent non-radiative local density of states to the change in the decay rate. The apparent non-radiative contribution accounts for losses due to radiation out of the detection solid angle and to absorption in the environment. Data analysis relies on a new analytical calculation, and does not require the use of numerical simulations. One of the most relevant applications of the method is the characterization of nanostructures aimed at maximizing the number of photons emitted in the detection solid angle, which is a crucial issue in modern nanophotonics.
Estimation of autocorrelations and spectral densities is of fundamental importance in many fields of science, from identifying pulsar signals in astronomy to measuring heart beats in medicine. In circumstances where one is interested in specific auto
correlation functions that do not fit into any simple families of models, such as auto-regressive moving average (ARMA), estimating model parameters is generally approached in one of two ways: by fitting the model autocorrelation function to a non-parameteric autocorrelation estimate via regression analysis or by fitting the model autocorrelation function directly to the data via maximum likelihood. Prior literature suggests that variogram regression yields parameter estimates of comparable quality to maximum likelihood. In this letter we demonstrate that, as sample size is increases, the accuracy of the maximum-likelihood estimates (MLE) ultimately improves by orders of magnitude beyond that of variogram regression. For relatively continuous and Gaussian processes, this improvement can occur for sample sizes of less than 100. Moreover, even where the accuracy of these methods is comparable, the MLE remains almost universally better and, more critically, variogram regression does not provide reliable confidence intervals. Inaccurate regression parameter estimates are typically accompanied by underestimated standard errors, whereas likelihood provides reliable confidence intervals.
