1287 ISSN 1063-7826, Semiconductors, 2019, Vol. 53, No. 10, pp. 1287–1294. © Pleiades Publishing, Ltd., 2019. Russian Text © The Author(s), 2019, published in Fizika i Tekhnika Poluprovodnikov, 2019, Vol. 53, No. 10, pp. 1321–1328. On the Asymmetric Generation of a Superradiant Laser with a Symmetric Low-Q Cavity Vl. V. Kocharovsky a , V. A. Kukushkin a , S. V. Tarasov a , E. R. Kocharovskaya a, *, and V. V. Kocharovsky a,b a Institute of Applied Physics, Russian Academy of Sciences, Nizhny Novgorod, 603950 Russia b Texas A and M University, College Station, 77843 USA *e-mail: katya@appl.sci-nnov.ru Received April 24, 2019; revised April 29, 2019; accepted April 29, 2019 Abstract—On the basis of numerical solution to the Maxwell–Bloch equations within the one-dimensional two-level model of a superradiant laser with a symmetric cavity in which the photon lifetime is less than the incoherent relaxation time of the optical-dipole oscillations of active centers, the phenomenon of the spon- taneous asymmetric generation of counter-propagating waves under continuous uniform pumping of the active medium is revealed. It is shown that the observed symmetry breaking of the spatial profiles of counter- propagating waves of the electromagnetic field and, the polarization and inversion of the population of active- medium levels in the case of a small inhomogeneous broadening of the spectral line of its working transition occurs due to the asymmetric half-wave nonlinear grating of inversion of the energy-level population pro- duced by these waves. Keywords: superradiant semiconductor laser, asymmetric generation DOI: 10.1134/S1063782619100105 1. INTRODUCTION In conventional lasers with symmetric high-Q Fabry–Perot cavities (including those combined with the distributed feedback of counter-propagating waves), where the lifetime T E of photons is large as compared with the polarization (optical-dipole oscil- lations) lifetime T 2 of the active centers, the steady- state single-mode generation corresponds to symmet- rical field distribution. In this case, the inversion grat- ing of the population of levels of the working transition formed by waves of the electromagnetic field and the polarization field of the active medium affects only slightly the mode structure and simply leads to a small additional field inhomogeneity along the cavity axis z without symmetry breaking of counter-propagating waves at the uniform or, in general, symmetric distri- bution of the active medium and pumping inverting the population of its working levels. For nonstation- ary, including multimode, generation, the distribution of the field in individual modes and that of the total field on average are also usually symmetric if no spe- cial mode phasing is facilitated, for example, by the methods of passive or active mode-locking leading to the formation of a pulse running ground the cavity (see [1–8]). However, according to [9], in superradiant lasers with low-Q symmetric cavities (Fig. 1), where the photon lifetime is small as compared with the polar- ization lifetime of the active centers, T E < T 2 , for steady lasing with continuous pumping in a wide range of values including the vicinity of the nonstationary- generation threshold, spontaneous symmetry break- ing of the counter-propagating waves is typical. This phenomenon is expected in all steady lasing regimes, including the quasi-stationary, self-modulation and pulsed ones. In principle, this is possible in different (including semiconductor) lasers with not high inho- mogeneous broadening of the spectral line of active centers, the role of which can be played by, for exam- ple, impurities, excitons, or even electrons and holes in strongly magnetized quantum wells (see, for exam- ple, [10–21]). The most pronounced predicted phenomenon associated with the inversion grating of populations of working-transition levels created by the beats of counter-propagating waves is expected for dense active media with a weak inhomogeneous broadening of the spectral line, which is much smaller than the spectral width 2/T E of cavity modes and the so-called cooper- ative frequency of an inverted two-level laser medium, where d is the dipole moment of the active centers at the operating-transition frequency ω 21 , and N 0 is the 2 21 0 0 2 , c d N π ω ν = ε Γ ɶ ℏ XXIII INTERNATIONAL SYMPOSIUM “NANOPHYSICS AND NANOELECTRONICS”, NIZHNY NOVGOROD, MARCH 11–14, 2019