How Do the Purcell Factor, the <i>Q</i>‐Factor, and the Beta Factor Affect the Laser Threshold?
Jacob B. Khurgin, M. A. Noginov
Abstract
Abstract As lasers get more and more miniaturized and their dimensions become comparable to the wavelength, two interconnected phenomena take place: the fraction of spontaneous radiation going into a specific laser mode ( β ‐factor) increases and can ultimately reach unity, while the radiative lifetime gets shortened by the Purcell factor F p . Often it is assumed that an increase of these two factors, along with the quality factor ( Q ‐factor), almost invariably causes reduction of the lasing threshold. This assumption is tested on various photonic and plasmonic lasers, demonstrating that, while there is obvious correlation between the aforementioned factors and the laser threshold, the dependence is far from being straightforward and omnipresent. Depending on specific laser material and geometry, the threshold can decrease, increase, or stay unchanged when β ‐factor, Q ‐factor, and F p increase. For the most part, the reduction of threshold is achieved simply by reducing the laser volume and this volume reduction can concurrently cause the increase in β ‐factor and/or Purcell factor, but it would be imprudent to say that the increase in either of these factors is the cause of the threshold reduction.