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Doklady of the National Academy of Sciences of Belarus

Modeling of superradiance in a resonator under conditions of frequency drift caused by resonant nonlinearity

E. V. Timoshchenko, В. А. Юревич

Published May 4, 2026• 0 citations
Publisher

Abstract

Several modifications of the Maxwell–Bloch equations are presented for analyzing the emission characteristics of pulsed lasers. The analysis is performed under the condition of coherent interaction between light and a gain medium with resonant phase nonlinearity. For the first time, the interrelated factors of instability of the phase relationship of the light field and the response of the medium, caused by the dipole-dipole interaction and the contribution of quasi-resonant polarization, are taken into account. To describe the superradiance (SR) regime, semi-analytical expressions for the response variables in the Bloch vector formalism are refined. Various approximations of the original model are represented by systems of kinetic equations for the field and response variables of the medium, as well as a nonlinear oscillatory equation for the polar angle of the Bloch vector. Modeling of the coherent SR effect in a resonator showed that the temporal structure of SR is extremely sensitive to the resonant nonlinearity of the material response. It is shown that under nonlinear conditions, the typical nutational intensity structure of synchrotron radiation is transformed into a contrasting quasi-periodic modulation of the trailing edge of the main pulse in the subpicosecond range. A computational analysis of the synchrotron radiation process in a resonator is performed for the parameters of semiconductor quantum dot systems in nanoheterostructures. Such systems are considered promising for use in compact optical electronics and photonics devices.

DOI
10.29235/1561-8323-2026-70-2-108-118

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Several modifications of the Maxwell–Bloch equations are presented for analyzing the emission characteristics of pulsed lasers. The analysis is performed under the condition of coherent interaction between light and a gain medium with resonant phase nonlinearity. For the first time, the interrelated factors of instability of the phase relationship of the light field and the response of the medium, caused by the dipole-dipole interaction and the contribution of quasi-resonant polarization, are taken into account. To describe the superradiance (SR) regime, semi-analytical expressions for the response variables in the Bloch vector formalism are refined. Various approximations of the original model are represented by systems of kinetic equations for the field and response variables of the medium, as well as a nonlinear oscillatory equation for the polar angle of the Bloch vector. Modeling of the coherent SR effect in a resonator showed that the temporal structure of SR is extremely sensitive to the resonant nonlinearity of the material response. It is shown that under nonlinear conditions, the typical nutational intensity structure of synchrotron radiation is transformed into a contrasting quasi-periodic modulation of the trailing edge of the main pulse in the subpicosecond range. A computational analysis of the synchrotron radiation process in a resonator is performed for the parameters of semiconductor quantum dot systems in nanoheterostructures. Such systems are considered promising for use in compact optical electronics and photonics devices.
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 analogous 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.
Taking into account the ideas of the generalized two-level scheme, within the framework of the semiclassical approach to the consideration of the resonant interaction of the light field with matter, an analytical solution to the problem of the evolution of superradiance in a quasi-two-dimensional supercrystal formed by quantum dots is obtained. The calculation was carried out for the physical parameters of a semiconductor structure with quantum-well effects in the presence of resonant nonlinearity and intraband relaxation.
Active media are materials that consist of quantum systems, such as atoms, impurities, or quantum dots, and are characterized by strong resonant absorption and re-emission of radiation. In this article, we present a general framework for the numerical simulation and analysis of time-dependent radiation-induced phenomena in active media. The formulation used is based on the solution of semiclassical Maxwell–Bloch equations describing the evolution of each quantum element under the effect of external and re-emitted radiation. Within these Maxwell–Bloch equations, the coupling of quantum systems to classical Maxwellian fields poses computational challenges due to the strong nonlinearities involved. In contrast to traditional mesh-based solvers, we adopt an electric field integral-operator approach that can reliably account for near-field effects—including self-radiation—and is scalable to large systems. We then focus on media based on large numbers of quantum dots and demonstrate various physical effects arising from the near-field coupling, including polarization modulations and superradiance.
Abstract : The mathematical algorithms and programs for the study of the resonant light-matter interactions in the multi-component and multilevel media and photonic bandgap structures have been developed. The optimal component distribution in the two-component media have been found to get a pulse of a superradiative emission of the highest intensity. The mathematical algorithms and programs for the study of the femtosecond pulse propagation in an extended medium of the two-level atoms have developed. The regime of the inversionless superradiance in the two-component superradiative medium has been investigated. The theory of the superradiance by an ensemble of the two-level atoms embedded in the dielectric host was developed. It was shown that the near dipole-dipole interaction of dense collection of two-level atoms is enhanced by the presence of the host material, decreasing the pulse temporal width and increasing the peak pulse intensity of superradiative emission. The theory of nonlinear light-matter interaction in multidimensional resonant photonic crystals under Bragg diffraction condition has been developed. It was obtained the analytical and numerical solutions describing the novel kinds of nonlinear solitary waves: the Laue soliton, O-field, propagating and standing gap solitary waves. It has been described the spatio-temporal nonlinear dynamics of coherent field in periodic resonant structures with arbitrary modulation of atomic density and gain gratings.
A theoretical model for the propagation of coherent light pulses in resonant media where a large number of atoms cooperate in spontaneous emission (superradiance) is discussed. The medium is supposedly free of inhomogeneous broadening, and no lossy relaxation mechanisms are taken into account. The conditions for the emission of all spontaneous radiation in the direction of pulse propagation are described. A semi-classical model is used and, at each point in the medium, the propagation field and the spontaneous damping field are considered separately. The equation governing the evolution of a superradiant system in the presence of an applied pulse is derived. A mechanism of energy transfer from the traveling pulse to the medium is described which includes superradiant spontaneous emission effects. As a result of the neglect of all lossy relaxation processes, all energy stored in the medium is eventually returned to the pulse by coherent spontaneous emission. Therefore, in this theory, all pulses travel through the medium without energy loss. Numerical results for square input pulses are discussed which show two possible types of propagation behavior: (a) Low input intensities produce a negative tail to the input (positive) pulse and sharpening of the tail with the advance in the medium; (b) higher input intensities produce, after sufficient penetration, a steady-state pulse envelope somewhat similar to the $2\ensuremath{\pi}$ pulses of self-induced transparency. The steady-state solutions of the equations of motion are found numerically and the pulse shapes are computed for different degrees of superradiance. In the limit of strong superradiance, very asymmetric pulse envelopes of large area are found. For negligible superradiance, approximately $2\ensuremath{\pi}$ hyperbolic-secant pulses are obtained. The effects of inhomogeneous broadening are briefly considered, and the consequences of important superradiant damping in photon-echo experiments are qualitatively discussed.
The nonlinear optical properties of semiconductors near an excitonic resonance are investigated theoretically by using the macroscopic J model [\"Ostreich and Knorr, Phys. Rev. B 48, 17811 (1993); \"Ostreich and Knorr, Phys. Rev. B 50, 5717 (1994)] based on the microscopic semiconductor Bloch equations. These nonlinear properties cause modulational instability of long light pulses with large gain and give rise to a self-induced transmission of short light pulses in a semiconductor. By an example of the latter well-studied effect, the validity of the used macroscopic model is demonstrated, and good agreement is found with both existing theoretical and experimental results.