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Analytical equations quantifying self-absorption losses in circular luminescent solar concentrators (LSCs) are presented that can easily be solved numerically by commercial math software packages. With the quantum efficiency, the absorption and emission spectra of a luminescent material, the LSC dimensions, and the refractive index as the only input parameters, the model gives an accurate account of the decrease of LSC efficiency due to self-absorption as a function of LSC radius, thickness, and luminescence quantum efficiency. Results give insight into how many times light is reabsorbed and reemitted, the red shift of the emission spectrum, and on how multiple reabsorptions and reemissions are distributed over the LSC. As an example case the equations were solved for a circular LSC containing a Lumogen F Red 305 dye with 80% luminescence quantum efficiency, and it follows that for an LSC with a 50 cm radius the self-absorption reduces the number of photons reaching the LSC edge by a factor of four compared to the case when there would be no self-absorption. The equations can just as well be solved for any material for which the optical properties are known like type I and type II quantum dots.
© 2014 Optical Society of America
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