Two to One: Entropic Considerations in Upconversion

Photon upconversion, a nonlinear optical process that converts low-energy photons into higher-energy photons, has garnered significant attention due to its wide range of potential applications in bioimaging, optogenetics, 3D printing and photoconversion. However, there is an oft-overlooked second-law requirement that free energy must be expended when decreasing photon number during the upconversion process. Interestingly, for practical applications under reasonable flux conditions, the second law of thermodynamics insists upon an ∼80 nm downshift in the emission wavelength, analogous to a Stokes shift. We also find that the maximum efficiency of the upconversion process must inherently be photon flux dependent, which is pleasingly consistent with reported upconversion experiments and so may be a fundamental and general property of an efficient upconversion system. Importantly, our results guide the design of molecular upconversion, as the demands of thermodynamics require that efficient systems intended to operate at a specific input flux must include a specific wavelength downshift, a hitherto overlooked design parameter.