Abstract
Broadband light sources are a wide class of pumping schemes for lasers including LEDs, sunlight and flash lamps. Recently, efficient coupling of broadband light to high-quality micro-cavities has been demonstrated for on-chip applications and low-threshold solar-pumped lasers via cascade energy transfer. However, the conversion of incoherent to coherent light comes with an inherent price of reduced efficiency, which has yet to be assessed. In this paper, we derive the detailed balance limit of efficiency of broadband-pumped lasers and discuss how it is affected by the need to maintain a threshold population inversion and thermodynamically dictated minimal Stokes’ shift. We show that lasers’ slope efficiency is analogous to the nominal efficiency of solar cells, limited by thermalisation losses and additional unavoidable Stokes’ shift. The lasers’ power efficiency is analogous to the detailed balance limit of efficiency of solar cells, affected by the cavity mirrors and impedance matching factor, respectively. As an example we analyze the specific case of solar-pumped sensitized Nd3+:YAG-like lasers and define the conditions to reach their thermodynamic limit of efficiency. Our work establishes an upper theoretical limit for the efficiency of broadband-pumped lasers. Our general, yet flexible model also provides a way to incorporate other optical and thermodynamic losses and, hence, to estimate the efficiency of non-ideal broadband-pumped lasers.
Highlights
Broadband free-space pumping is a conventional excitation scheme of optical resonators[1], which recently gained momentum owing to the demonstration of effective broadband excitation of high-finesse on-chip micro-cavities[2] and low-threshold solar-pumped lasers[3, 4] (SPLs) via cascade energy transfer[5]
We describe how the thermodynamic limit on broadband- pumped lasers (BPL) slope efficiency is influenced by the absorption properties of the gain medium, pumping intensity, temperature and the thermodynamically unavoidable Stokes’ shift
At non-zero temperature the lasers’ gain medium emission wavelength must be displaced from the absorption band edge by a Stokes’ shift that is larger than the thermodynamic minimum[20], which is on a scale of hundreds of nanometers at room-temperature
Summary
State-of-the-art SPLs operate far below the thermodynamic limit presented in the manuscript[33,34,35]. The power efficiency of state-of-the-art SPLs is almost an order of magnitude lower[33,34,35] This is due to the fact that lasers, especially BPLs, are subject to two competitive processes: the absorption of the pump in the gain media and the losses at the lasing wavelength, which scale simultaneously with the mode volume. The critical parameter for power efficiency would be paving the way to overcome this constrain in practical conditions via intelligent design of a sensitizer[37]
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