Universal lasing condition

Usually, the cavity is considered an intrinsic part of laser design to enable coherent emission. For different types of cavities, it is assumed that the light coherence is achieved by different ways. We show that regardless of the type of cavity, the lasing condition is universal and is determined by the ratio of the width of the atomic spectrum to the product of the number of atoms and the spontaneous radiation rate in the laser structure. We demonstrate that cavity does not play a crucial role in lasing since it merely decreases the threshold by increasing the photon emission rate thanks to the Purcell effect. A threshold reduction can be achieved in a cavity-free structure by tuning the local density of states of the electromagnetic field. This paves the way for the design of laser devices based on cavity-free systems.