Nonlinearly<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="script">PT</mml:mi></mml:math>-symmetric systems: Spontaneous symmetry breaking and transmission resonances

Abstract

We consider a class of $\mathcal{PT}$-symmetric systems which include mutually matched nonlinear loss and gain (in other words, a class of $\mathcal{PT}$-invariant Hamiltonians in which both the harmonic and anharmonic parts are non-Hermitian). For a basic system in the form of a dimer, symmetric and asymmetric eigenstates, including multistable ones, are found analytically. We demonstrate that, if coupled to a linear chain, such a nonlinear $\mathcal{PT}$-symmetric dimer generates previously unexplored types of nonlinear Fano resonances, with completely suppressed or greatly amplified transmission, as well as a regime similar to the electromagnetically induced transparency. The implementation of the systems is possible in various media admitting controllable linear and nonlinear amplification of waves.