  High-quality micro-lasers are key ingredients in non-linear optics,
communication, sensing and low-threshold solar-pumped lasers. However, such
micro-lasers exhibit negligible absorption of free-space broadband pump light.
Recently, this limitation was lifted by cascade energy transfer, in which the
absorption and quality factor are modulated with wavelength, enabling
non-resonant pumping of high-quality micro-lasers and solar-pumped laser to
operate at record low solar concentration. Here, we present a generic
theoretical framework for modeling the absorption, emission and energy transfer
of incoherent radiation between cascade sensitizer and laser gain media. Our
model is based on linear equations of the modified net radiation method and is
therefore robust, fast converging and has low complexity. We apply this
formalism to compute the optimal parameters of low-threshold solar-pumped
lasers. It is revealed that the interplay between the absorption and
self-absorption of such lasers defines the optimal pump absorption below the
maximal value, which is in contrast to conventional lasers for which full pump
absorption is desired. Numerical results are compared to experimental data on a
sensitized Nd:YAG cavity, and quantitative agreement with theoretical models is
found. Our work modularizes the gain and sensitizing components and paves the
way for the optimal design of broadband-pumped high-quality micro-lasers and
efficient solar-pumped lasers.
