<p>An edge collection function is proposed for characterizing the optical efficiency of an energy-harvesting system that utilizes photoluminescence (PL) in a waveguide. We assume that a single spot in a waveguide is excited and that PL is isotropic. For the photons to be collected by one edge of the waveguide, they must be emitted toward the edge, trapped in the waveguide and they must survive self-absorption on the way. The optical efficiency is formulated as the product of these probabilities. When this function is calculated for every spot on the waveguide and for each wavelength of the PL spectrum, the efficiency of the system is given by superposition. Its validity is checked by a Monte Carlo simulation for the case of no self-absorption loss. In experiment, we fabricate a 5-cm<sup>2</sup> waveguide with a thin layer of Lumogen F Red 305 and measure its efficiency by placing a photodiode array in the vicinity of its edge with a small air gap. The formula roughly reproduces the efficiency and its dependency on the position of the excitation spot. This analytical approach allows one to estimate the optical efficiency for an arbitrary incident light distribution with small computational complexity.</p>
One can display an image by scanning a laser light on a fluorescent waveguide. Solar cells attached to its edge surface harvest the photoluminescent photons. Its optical efficiency is defined as the ratio of the number of the photoluminescent photons collected by the solar cells over the number of incident photons. There are models reported on this topic for a luminescent solar concentrator and most of them are based on either numerical integration or Monte Carlo simulation. In our model, an isotropic emitter is placed at a single spot in a square waveguide. First, we ignore optical losses during propagation for simplicity and calculate the efficiency as the product of three factors: the trapping probability in the waveguide, the ratio of the angle subtended by one edge from the single spot over 2π, and the probability of exiting from the edge. The other three edges are assumed to be absorbing. This simple calculation gives the efficiency as a function of the coordinates of the excitation spot. Next, we introduce an attenuation coefficient to account for optical losses. Adding contribution from each wavelength of a photoluminescent spectrum would give the overall efficiency. In experiment, we can measure this efficiency by coupling a photodiode array to one edge of a fluorescent waveguide and exciting a single spot by a laser beam. Our preliminary result indicates that the model roughly reproduces the value of the efficiency and its dependency on the position of the excitation spot.