We present a multijunction detailed balance model that includes the effects of luminescent coupling, light trapping and nonradiative recombination, suitable for treatment of multijunction solar cells and photonic power converters -- photovoltaic devices designed to convert narrow-band light. The model includes both specular and Lambertian reflections using a ray-optic formalism and treats nonradiative processes using an internal radiative efficiency. Using this model, we calculate and optimize the efficiency of multijunction photonic power converters for a range of material qualities and light-trapping schemes. Multijunction devices allow increased voltage with lower current, decreasing series resistance losses. We show that efficiency increases significantly with increased number of junctions, even without series resistance, when the device has an absorbing substrate. Such an increase does not occur when the device has a back reflector. We explain this effect using a simplified model, which illustrates the origin of the decreased radiative losses in multijunction devices on substrates.
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