Theory of Mirrorless Lasing and Backward Emission from an Amplifying Layer: Analysis based on Macroscopic Electromagnetism

We study the phenomenon of mirrorless lasing and backward emission from the viewpoint of macroscopic electromagnetism by assigning complex permittivity to a light-emitting or amplifying layer. The amplifying medium is described using complex permittivity without detailing the micro-processes in it. The analysis is performed using the well-known Airy formulas for the plane wave normal incidence on a homogeneous dielectric layer. Giant reflection and transmission corresponding to the lasing threshold are obtained by increasing the layer thickness at the fixed value of imaginary part of the layer's permittivity corresponding to gain in it. This result is inherently independent from the incident wave amplitude and denotes the lasing from the both interfaces of the layer (forward and backward emission). At the further increase of the layer's thickness only strong backward emission is observed. The socalled phenomenon of mirrorless lasing is owing to the discontinuation of gain at the boarders of the amplifying layer with surrounding passive media. The backward emission is observed for layers with the gain at the thicknesses longer than that necessary for lasing. The length of the amplifying layer required for the lasing initiation strongly depends on the value of the gain.