Unidirectional nonlinearPT-symmetric optical structures

Abstract

We show that non-linear optical structures involving a balanced gain-loss profile, can act as unidirectional optical valves. This is made possible by exploiting the interplay between the fundamental symmetries of parity (P) and time (T ), with optical nonlinear effects. This novel unidirectional dynamics is specifically demonstrated for the case of an integrable PT -symmetric nonlinear system.

PT-Symmetric Acoustics

“…However, when wave incidents come from the gain side, the nonlinearity kicks in and bends the "backbone" of resonance, resulting in strong asymmetric wave propagation and nonreciprocity at the same frequency without harmonic generation. Such asymmetric transport has already been demonstrated in electronics and optics [36][37][38][39][40]; however, acoustics remains an open area to be explored.…”

“…Several interesting physical features have been explored, such as power oscillations [28], unidirectional invisibility [29][30][31][32], the reconfigurable Talbot effect [33], and coherent perfect laser absorbers [34,35]. Moreover, in the nonlinear domain, PT symmetry has been used to realize potential optical isolators and circulators [36][37][38][39][40].…”

PT-symmetric dimer of coupled nonlinear oscillators

“…Here, in parallel to what is done in the PT -symmetric Schrödinger dimer typically [7,9,11], we have added a cubic onsite nonlinearity on each one of the nodes. For > 0, this nonlinearity is soft, imposing a finite (maximal energy) height type of potential, enabling the possibility of indefinite growth by means of the escape scenario considered earlier, e.g., in Ref.…”

“…However, one of the major milestones (and a principal thrust of recent activity) regarding the physical and experimental realizability of the corresponding Hamiltonians stemmed from progress in optics both at the theoretical [4,5] and at the experimental [6,7] levels. In particular, the realization that, in optics, the ubiquitous loss can be counteracted by an overwhelming gain in order to create a PT -symmetric setup, e.g., in a waveguide dimer [7], paved the way for numerous developments, especially so at the level of nonlinear systems, as several researchers studied nonlinear stationary states, stability, and dynamics of few site configurations [8][9][10][11][12][13][14][15][16] as well as of infinite lattices [17][18][19].…”

“…To provide an analytical insight into the above results, we use the rotating-wave approximation (RWA), which approximates the system by the corresponding nonlinear Schrödinger-type PT -symmetric dimer for which everything can be solved analytically, including the stationary states, the symmetry breaking bifurcations, and even the full dynamics [9,11,28,29]. A direct comparison of the RWA-derived Schrödinger dimer reveals natural similarities but also significant differences between the two models.…”