<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="script">PT</mml:mi></mml:math> symmetry breaking in multilayers with resonant loss and gain locks light propagation direction

Abstract

Using the Maxwell-Bloch equations for resonantly absorbing and amplifying media, we study the temporal dynamics of light propagation through the $\mathcal{PT}$-symmetric structures with alternating loss and gain layers. This approach allows us to precisely describe the response of the structure near the exceptional points of $\mathcal{PT}$ symmetry breaking phase transition and, in particular, take into account the nonlinear effect of loss and gain saturation in the $\mathcal{PT}$ symmetry broken state. We reveal that in this latter state the multilayer system possesses a lasinglike behavior, releasing the pumped energy in the form of powerful pulses. We predict locking of pulse direction due to the $\mathcal{PT}$ symmetry breaking, as well as saturation-induced irreversibility of phase transition and nonreciprocal transmission.