Nonlinear reversal of thePT-symmetric phase transition in a system of coupled semiconductor microring resonators

Abstract

A system of two coupled semiconductor-based resonators is studied when lasing around an exceptional point. We show that the presence of nonlinear saturation effects can have important ramifications on the transition behavior of this system. In sharp contrast with linear PT-symmetric configurations, nonlinear processes are capable of reversing the order in which the symmetry breaking occurs. Yet, even in the nonlinear regime, the resulting non-Hermitian states still retain the structural form of the corresponding linear eigenvectors expected above and below the phase transition point. The conclusions of our analysis are in agreement with experimental data.

Integrable nonlinear parity-time-symmetric optical oscillator

“…This is in contrast to a linear PT -symmetric coupler where the transition occurs instead at g = 1. Although nonlinear saturation effects tend to modify the location of this transition in the parameter space, the order in which it takes place is not affected -unlike in other nonlinear PT -symmetric settings [25]. Finally, an interesting feature associated with this oscillator is the fact that within the exact PT -symmetry domain, as the system gets close to the nonlinear phase transition point, the period of oscillations tends to approach infinity.…”

“…In a temporal representation involving a coupled micro-ring configuration, κ is of the order 10 11 s −1 . Gain and loss in the presence and absence of pump light respectively, are also of the same order [25]. In what follows we determine the critical points of this nonlinear system and through the use of Stokes parameters, identify conservation laws and regimes of oscillatory and stationary responses.…”

“…Under these considerations, balancing field amplification and decay in an evanescently coupled structure composed of two identical elements, renders the system PT -symmetric. In this respect, the optical/electrical pumping level in typi-cal designs based on semiconductor quantum wells allows control over the values of both the gain and loss [15,25], whereas the spatial separation between the components of the dimer determines the respective coupling strength.…”

“…Yet, in many optical realizations, nonlinearity is not only unavoidable but also often prevalent. This is particularly true in semiconductor-based systems where saturation effects strongly influence both gain and loss, to the point that a reversal in PT -symmetry breaking can occur [25]. Clearly, of importance will be to understand at a fundamental level, the role such nonlinear processes play in the dynamics of PT -symmetric arrangements [26][27][28].…”

Highly amplified light transmission in a parity-time symmetric multilayered structure

“…Since then, numerous phenomena have been reported in the field of parity time symmetric optics. To cite, some of them include: onset of chaos in optomechanical systems [5], optical mesh lattices [6][7][8], modulational invisibility in complex media [9], Peregrine soliton dynamics [10], plasmon excitation [11,12], unidirectional reflectionlessness, invisibility and non-reciprocity in periodic structures [13][14][15][16][17], whispering gallery modes [18], microring resonators [19][20][21], optical oligomers [22][23][24][25] and so on.…”