Heavily doped and positive biasing electric field above the threshold current can assure the radiations of random distributing radiative centers to interfere enhancement. Only particle quantity rollover, just the electronic quantity at high energy levels are much more, the chances of electron jump from a low level to a high energy level are greatly reduced. A lots of electronic radiation jumps are necessary for producing a superradiant output. The initial state of the evolution of a population inverted system to a superradiant state is satisfy spatial coherent condition.

Thanks for your reply!

But frankly speaking, I can't understand what you said. Could you put more detailed description about superradiance, particularly in gas medium?

As a literature said, "At first the system undergoes spontaneous emission in various directions at random times. Eventually a photon is emitted along the axis of the sample cell, leading to the excitation of one of the modes of the inverted medium." What do you think about this description?

Super-radiance is one mechanism by which coherent emission from an ensemble of emitters can be achieved- e.g. atoms. In a laser, spontaneous emission will accumulate in a specific spatial mode of the cavity and this will eventually stimulate emission from the population inversion and thus drive atoms into phase with each other and the laser mode. In super-radiance, closely spaced atoms tend to radiate together. This is because atoms are influenced by the radiation produced by their neighbors. Remarkably, even though this is a spontaneous process, the atoms can be driven into phase with each other because of their mutual proximity, which essentially needs to be much smaller than the wavelength of radiation being produced. As far as I know a population inversion is not absolutely necessary for this to occur as it is a spontaneous process. (The maths/physics for this is quite difficult to derive in all but the most simplified cases.) The requirement is for the density of excited emitters to be high. This leads to characteristic time scale over which the atoms can be driven in phase and this needs to be smaller than the radiative lifetime of individual atoms to get the super-radiant effect. I suggest you read the seminal work of Dicke on this. He worked with molecular emission at microwave frequencies where molecular density could be extremely large compared to the wavelength of the radiation.