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Register a new userPT-symmetric coupler with a coupling defect: soliton interaction with exceptional point
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We study interaction of a soliton in a parity-time (PT) symmetric coupler which has local perturbation of the coupling constant. Such a defect does not change the PT-symmetry of the system, but locally can achieve the exceptional point. We found that the symmetric solitons after interaction with the defect either transform into breathers or blow up. The dynamics of anti-symmetric solitons is more complex, showing domains of successive broadening of the beam and of the beam splitting in two outwards propagating solitons, in addition to the single breather generation and blow up. All the effects are preserved when the coupling strength in the center of the defect deviates from the exceptional point. If the coupling is strong enough the only observable outcome of the soliton-defect interaction is the generation of the breather.
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We introduce the notion of a ${cal PT}$-symmetric dimer with a $chi^{(2)}$ nonlinearity. Similarly to the Kerr case, we argue that such a nonlinearity should be accessible in a pair of optical waveguides with quadratic nonlinearity and gain and loss, respectively. An interesting feature of the problem is that because of the two harmonics, there exist in general two distinct gain/loss parameters, different values of which are considered herein. We find a number of traits that appear to be absent in the more standard cubic case. For instance, bifurcations of nonlinear modes from the linear solutions occur in two different ways depending on whether the first or the second harmonic amplitude is vanishing in the underlying linear eigenvector. Moreover, a host of interesting bifurcation phenomena appear to occur including saddle-center and pitchfork bifurcations which our parametric variations elucidate. The existence and stability analysis of the stationary solutions is corroborated by numerical time-evolution simulations exploring the evolution of the different configurations, when unstable.
An experimental setup of three coupled $mathcal{PT}$-symmetric wave guides showing the characteristics of a third-order exceptional point (EP3) has been investigated in an idealized model of three delta-functions wave guides in W.~D. Heiss and G.~Wunner, J. Phys. A 49, 495303 (2016). Here we extend these investigations to realistic, extended wave guide systems. We place major focus on the strong parameter sensitivity rendering the discovery of an EP3 a challenging task. We also investigate the vicinity of the EP3 for further branch points of either cubic or square root type behavior.
Exceptional points in non-Hermitian systems have recently been shown to possess nontrivial topological properties, and to give rise to many exotic physical phenomena. However, most studies thus far have focused on isolated exceptional points or one-dimensional lines of exceptional points. Here, we substantially expand the space of exceptional systems by designing two-dimensional surfaces of exceptional points, and find that symmetries are a key element to protect such exceptional surfaces. We construct them using symmetry-preserving non-Hermitian deformations of topological nodal lines, and analyze the associated symmetry, topology, and physical consequences. As a potential realization, we simulate a parity-time-symmetric 3D photonic crystal and indeed find the emergence of exceptional surfaces. Our work paves the way for future explorations of systems of exceptional points in higher dimensions.
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William C. K. Mak
, Pak L. Chu (Optoelectronic Research Centre
, n Department of Electronic Engineering
2002
We study the interactions of a Bragg-grating soliton with a localized attractive defect which is a combined perturbation of the grating and refractive index. A family of exact analytical solutions for solitons trapped by the delta-like defect is found. Direct simulations demonstrate that, up to the numerical accuracy available, the trapped soliton is stable at a single value of its intrinsic parameter (mass). Trapped solitons with larger mass relax to the stable one through the emission of radiation, while the solitons with smaller mass decay. Depending on values of parameters, simulations of collisions between moving solitons and the defect show that the soliton can get captured, pass through, or even bounce from the defect. If the defect is strong and the soliton is heavy enough, it may split, as a result of the collision, into three fragments: trapped, transmitted, and reflected ones.
We theoretically demonstrate soliton steering in $mathcal{PT}$-symmetric coupled nonlinear dimers. We show that if the length of the $mathcal{PT}$-symmetric system is set to $2pi$ contrary to the conventional one which operates satisfactorily well only at the half-beat coupling length, the $mathcal{PT}$ dimer remarkably yields an ideal soliton switch exhibiting almost 99.99% energy efficiency with an ultra-low critical power.
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