It is shown that the concept of topological phase transitions can be used to design nonlinear photonic structures exhibiting power thresholds and discontinuities in their transmittance. This provides a novel route to devising nonlinear optical isolators. We study three representative designs: (i) a waveguide array implementing a nonlinear 1D Su-Schrieffer-Heeger model, (ii) a waveguide array implementing a nonlinear 2D Haldane model, and (iii) a 2D lattice of coupled-ring waveguides. In the first two cases, we find a correspondence between the topological transition of the underlying linear lattice and the power threshold of the transmittance, and show that the transmission behavior is attributable to the emergence of a self-induced topological soliton. In the third case, we show that the topological transition produces a discontinuity in the transmittance curve, which can be exploited to achieve sharp jumps in the power-dependent isolation ratio. particularly pressing problem due to the absence of strong magneto-optic effects [2][3][4]. Our goal is to obtain a conceptual understanding of the features and limitations of these novel isolation schemes; as such, we will make use of simplified models, based on the coupled-mode theory and transfer matrix frameworks, capturing just the essentials of nonlinearity and bandstructure topology. In particular, we will not attempt to study the actual device geometries and material nonlinearities needed to achieve the nonlinear lattice parameters appearing in our models, nor to optimize our designs to maximize their performance.The first type of structure we will study is an array of coupled optical waveguides, where light is guided ('evolves') either forward or backward along each waveguide, and can hop between adjacent waveguides via evanescent coupling. We begin with an exemplary waveguide array corresponding to a 1D Su-Schrieffer-Heeger (SSH) model [27], with Kerr-like nonlinearities added to the inter-waveguide coupling strengths. Hadad, Khanikaev, and Alù have shown that such a model can exhibit a self-induced topological transition [42], in which the nonlinearity drives a local region of the lattice into a different topological phase, giving rise to selftrapped soliton-like edge states. These nonlinear edge states allow a high-intensity signal injected in a edge waveguide to resist diffraction into the rest of the lattice. We show that when such a lattice has asymmetric input and output coupling losses, it can function as an efficient optical isolator. Light is injected into one port of an edge waveguide, evolves through a fixed distance, and leaves at the other end of the same waveguide. With appropriately-chosen system parameters, the forward transmittance (via a self-induced topological edge state) is of order unity, while the backward transmittance (without an edge state) is suppressed by several orders of magnitude.The isolator relies on the fact that the self-induced topological transition has a power threshold-i.e., the soliton-like edge state appears only above ...

We perform a theoretical study of the nonlinear dynamics of nonlinear optical isolator devices based on coupled microcavities with gain and loss. This reveals a correspondence between the boundary of asymptotic stability in the nonlinear regime, where gain saturation is present, and the PT -breaking transition in the underlying linear system. For zero detuning and weak input intensity, the onset of optical isolation can be rigorously derived, and corresponds precisely to the transition into the PT -broken phase of the linear system. When the couplings to the external ports are unequal, the isolation ratio exhibits an abrupt jump at the transition point, whose magnitude is given by the ratio of the couplings. This phenomenon could be exploited to realize an actively controlled nonlinear optical isolator, in which strong optical isolation can be turned on and off by tiny variations in the inter-resonator separation.

Abstractα-Synuclein (α-syn) is the main protein component of Lewy bodies, the major pathological hallmarks of Parkinson’s disease (PD). C-terminally truncated α-syn is found in the brain of PD patients, reduces cell viability and tends to form fibrils. Nevertheless, little is known about the mechanisms underlying the role of C-terminal truncation on the cytotoxicity and aggregation of α-syn. Here, we use nuclear magnetic resonance spectroscopy to show that the truncation alters α-syn conformation, resulting in an attractive interaction of the N-terminus with membranes and molecular chaperone, protein disulfide isomerase (PDI). The truncated protein is more toxic to mitochondria than full-length protein and diminishes the effect of PDI on α-syn fibrillation. Our findings reveal a modulatory role for the C-terminus in the cytotoxicity and aggregation of α-syn by interfering with the N-terminus binding to membranes and chaperone, and provide a molecular basis for the pathological role of C-terminal truncation in PD pathogenesis.