How Do the Purcell Factor, the Q‐Factor, and the Beta Factor Affect the Laser Threshold?

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 Fp. 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 Fp 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.

Ultralow-threshold laser using super-bound states in the continuum

“…5c). The estimated spontaneous emission factor is~0.01, which is smaller than the values of ultrasmall nanolasers 32 due to the relatively large mode volume [33][34][35] . Third, the interference images are measured in the spontaneous emission, amplified spontaneous emission, and lasing regions in the super-BIC laser (Fig.…”

Low-Threshold and Wavelength-Tunable InGaN Tubular WGM Laser Embedded in a Flexible Substrate

“…The Purcell effect describes the enhancement of spontaneous emission rate by the environment. In most cases, one can reduce the mode volume of a microcavity to lower the excitation threshold, which will also lead to an increase in the Purcell factor [37]. The effective mode volume of a microcavity is equal to the total electric field energy in the microcavity divided by the maximum electric field energy density.…”

Spaser and optical amplification conditions in graphene-coated active wires

“…The gain-loss compensation condition discussed in our work, also referenced as the gain threshold [26], does not necessarily mean that most emitted photons are the result of stimulated (coherent) emission, since, as calculations including saturation show, spontaneous (incoherent) emission can still be very important (especially if Purcell effects are relevant in the system studied). Requiring that most emitted photons come from spontaneous emission is a more strict condition that demands larger gain values than the ones informed here [32,33].…”