Controlling of blow-up responses by nonlinear PT -symmetric coupling

Abstract

We investigate the dynamics of a coupled waveguide system with competing linear and nonlinear loss-gain profiles which can facilitate power saturation. We show the usefulness of the model in achieving unidirectional beam propagation. In this regard, the considered type of coupled waveguide system has two drawbacks, (i) difficulty in achieving perfect isolation of light in a waveguide and (ii) existence of blow-up type behavior for certain input power situations. We here show a nonlinear PT symmetric coupling that helps to overcome these two drawbacks. Such a nonlinear coupling has close connection with the phenomenon of stimulated Raman scattering. In particular, we have elucidated the role of this nonlinear coupling using an integrable PT symmetric situation. In particular, using the integrals of motion, we have reduced this coupled waveguide problem to the problem of dynamics of a particle in a potential. With the latter picture, we have clearly illustrated the role of the considered nonlinear coupling. The above PT symmetric case corresponds to a limiting form of a general equation describing the phenomenon of stimulated Raman scattering. We also point out the ability to transport light unidirectionally even in this general case.

Integrability and trajectory confinement in -symmetric waveguide arrays

“…The model ( 15) includes our dimer (2) as a particular case with α = β = 0. However, the integrals of motion of ( 15) do not persist as β → 0; see Ref [19].…”

“…The literature suggests several recipes for preventing the blow-up in dimers, including linear vs nonlinear gain-loss competition [18,19] and nonlinear gain-loss saturation [12,20]. This paper explores cross-stimulation-an alternative mechanism that, in addition to ensuring nonsingular evolution, conserves the norm |u| 2 + |v| 2 (interpreted as the total power of light in the optical context).…”

Dissipative optical solitons in asymmetric Rosen-Morse potential

“…Many theoretical studies [11,12] and experimental realizations [13] have been reported in such systems. PT −symmetry breaking is also an important physical phenomenon because some of the desired properties are achieved at the point of symmetry breaking [14] and in the symmetry broken phase [15,16,17]. Theoretical studies on existence of stable soliton solutions in non−PT symmetric systems are also reported [18,19,20,21].…”

“…In nonlinear optical devices the complex refractive index constitutes the PT −symmetric potential which balances the loss and gain of optical pulse in the medium. PT −symmetry breaking is also an important physical phenomenon because some of the desired properties are achieved at the point of symmetry breaking [9,10] and in the symmetry broken phase [11][12][13][14]. PT −symmetry breaking exploited in many experiments [15][16][17][18].…”

Multifaceted dynamics and gap solitons in $\mathcal{PT}$-symmetric periodic structures

“…In the context of optics, the practicality of inherent loss in any functional device was not considered by the scientific community for many years [26]. But with the advent of parity-time (PT ) symmetry concept, these losses are no longer considered to be detrimental by virtue of the delicate balance between amplification and attenuation [27,28] in the system as in the case of PT -symmetric couplers [29,30], PT -metamaterials [31], PT -microring laser [32], PT -gratings [33,34], PT -laser cavities [35,36], etc. Though this notion traces its origin to the field of quantum mechanics way back in 1998 [37], the translation of the concept on to photonic platform paved the way for its major theoretical advancements [28,38,39] and the first experimental realization by Rütter et al on a LiNbO 3 waveguide [40].…”