One can display an image by scanning a laser light on a fluorescent waveguide. Solar cells attached to its edge surfaceharvest the photoluminescent photons. Its optical efficiency is defined as the ratio of the number of thephotoluminescent photons collected by the solar cells over the number of incident photons. There are models reportedon this topic for a luminescent solar concentrator and most of them are based on either numerical integration or MonteCarlo simulation. In our model, an isotropic emitter is placed at a single spot in a square waveguide. First, we ignoreoptical losses during propagation for simplicity and calculate the efficiency as the product of three factors: the trappingprobability in the waveguide, the ratio of the angle subtended by one edge from the single spot over 2π , and theprobability of exiting from the edge. The other three edges are assumed to be absorbing. This simple calculation givesthe efficiency as a function of the coordinates of the excitation spot. Next, we introduce an attenuation coefficient toaccount for optical losses. Adding contribution from each wavelength of a photoluminescent spectrum would give theoverall efficiency. In experiment, we can measure this efficiency by coupling a photodiode array to one edge of afluorescent waveguide and exciting a single spot by a laser beam. Our preliminary result indicates that the model roughlyreproduces the value of the efficiency and its dependency on the position of the excitation spot.
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