On Solving the Problem of Quasi-Two-Dimensional Supercrystal Nonlinear Resonance Response

Abstract

Taking into account the foundations of the generalized two-level scheme, an analytical solution to the problem of the evolution of superradiance in a quasi-two-dimensional supercrystal formed by quantum dots is obtained under homogeneous lasing field assumption in the resonant medium of the quasicrystal. The calculation was performed for the physical parameters of a semiconductor structure with quantum-well effects in the presence of resonant nonlinearity and intraband relaxation. We use the generalized two-level scheme, which allows us to take into account the self-modulating spectral broadening of the light field due to the absorption of radiation in quasi-resonant transitions in the quantum mechanical material equations, which are solved together with the field coupling equations. A relation is formulated that is analo-gous to the law of conservation of the polar angle of the Bloch vector for the more general case of interaction under consideration, in which, along with the phase nonlinearity of the response, the spread rate of active dipoles within the spectral line width is taken into account (i.e., the finiteness of the phase relaxation time of elementary emitters). The use of the Bloch vector formalism in this case makes it possible to obtain an analytical solution of the original modification of the nonlinear system of equations for the semiconductor supercrystals response variables and to calculate the shape of the superradiance pulses. The calculations predict the pronounced asymmetry of the pulses emitted by the semiconductor supercrystals. The calculated estimates of the time dynamics of the superradiance process, taking into account the nonlinearities typical for the resonant response, can be used in the development of methods for obtaining and profiling optical pulses in the sub-picosecond range of durations in modern compact nanophotonics devices.