Exact control of parity-time symmetry in periodically modulated nonlinear optical couplers

Abstract

We propose a mechanism for realization of exact control of parity-time (PT ) symmetry by using a periodically modulated nonlinear optical coupler with balanced gain and loss. It is shown that for certain appropriately chosen values of the modulation parameters, we can construct a family of exact analytical solutions for the two-mode equations describing the dynamics of such nonlinear couplers. These exact solutions give explicit examples that allow us to precisely manipulate the system from nonlinearity-induced symmetry breaking to PT symmetry, thus providing an analytical approach to the all-optical signal control in nonlinear PT -symmetric structures. PACS numbers: 42.25.Bs, 11.30.Er, 42.82.Et II. EXACT ANALYTICAL SOLUTIONS AND STABILITY ANALYSIS A. Model and PT -symmetry propertiesWe consider the simplest possible arrangement which consists of two coupled PT -symmetric waveguides with Kerr nonlinearity and with the linear refractive index periodically modulated along the propagation direction. Under coupled-mode theory, the two modal field ampli-

Analytical results for a parity-time-symmetric two-level system under synchronous combined modulations

“…4(a), which are directly obtained from Eqs. (30)(the n = 0 case), (33) and (36). As an example, in Fig.…”

“…4(b), we select R = 1.5 and the pulse area 2A = arccoshR/ √ R 2 − 1 given by Eq. (36) to show the numerical results for time evolutions of the population distributions with the initial state (25).…”

“…A surprising finding of such PT -symmetric non-Hermitian Hamiltonian systems is phase transition, where the spectrum changes from all real to complex when the gain-loss parameter exceeds a certain threshold. It has been widely demonstrated that external driving fields can be effectively used for implementing coherent controls of PT symmetry, and extension of driven two-level systems to non-Hermitian case is currently of broad interest [30]- [36]. For the proper control of the PT -symmetric two-level system, different analytic methods are required.…”

Variational approach to study solitary waves in $\mathcal{PT}$-symmetric nonlinear couplers

“…This phase difference in E 1,2 can also be evident from Eqs. ( 13) and (14), where the back and forth energy oscillations between the two channels are π phase apart when Γ = 0. However, Γ introduces an additional phase, as shown in the PT -symmetric case.…”

“…Since the landmark experiment [6] on the PT -symmetric coupler was carried out, the area virtually got exploded with research from various perspectives. In particular, nonlinear PT -symmetric coupler and its variants have been studied quite extensively [11][12][13][14]. In this context, various solitary wave solutions to the PT -symmetric coupled nonlinear Schrödinger equations (NLSEs), that describe pulse propagation in a nonlinear PT -symmetric coupler has been investigated by many research groups.…”