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z-arcs in the thirty degrees sector

Movshovich Yevgenya

Journal of Applied Analysis

2021

Vol. 27, nr 2

299--320

In this detailed study of 3-segment non-convex simple arcs inscribed in the 30∘ sector, we show that each such arc of length one fits in the interior of the sector of radius one with the prescribed embedding. We discuss implications of this study for covering problems involving triangular covers and for the worm problem of Leo Moser.

Electromagnetically induced transparency for A-like systems with degenerate autoionizing levels and a broadband coupling laser

Khoa D. Q., Van C. L., Lanh C. V., Phuc H. V.

Optica Applicata

2016

Vol. 46, nr 1

93--102

In our previous paper (DOAN QUOC K. et al., Physica Scripta T147, 2012, article 014008), electromagnetically induced transparency for A-like systems consisting of two lower bound states and a flat continuum coupled to an autoionization state embedded in it has been considered, in which the laser coupling light is modeled by white noise. In this paper, we investigate a similar scheme, where the continuum involved in the problem is replaced by one with so-called the double-A system, when instead of one autoionization state we have two autoionization states of the same energy embedded in the continuum. For such a system containing degenerate autoionization levels we derive a set of coupled stochastic integro-differential equations which can be averaged exactly. This leads to the exact formula determining the stationary solution for the electric susceptibility. Dispersion and absorption spectra for electromagnetically induced transparency are found and compared with those obtained previously by us and other authors.

Electromagnetically induced transparency in systems with degenerate autoionizing levels in Λ-configuration

Dinh T. B., Leoński W., Perina J., Long V. C.

Optica Applicata

2013

Vol. 43, nr 3

471--484

We discuss a Λ-like model of atomic levels involving two autoionizing (AI) states of the same energy. The system is irradiated by two external electromagnetic fields (strong – driving and weak – probing). For such a system containing degenerate AI levels we derive the analytical formula describing the medium susceptibility. We show that the presence of the second AI level leads to the additional electromagnetically induced transparency (EIT) window appearance. We show that the characteristics of this window can be manipulated by changes of the parameters describing the interactions of AI levels with other ones. This is a new mechanism which leads to additional transparency windows in EIT model, that differs from the mechanism where a bigger number of Zeeman sublevels is taken into account.