The topological nature of this localized mode means that it is insensitive to off-diagonal perturbations that alter the coupling coefficients, as long as they do not close the bandgap. While an infinite SSH array exhibits two bands that are separated by a bandgap, 16 a semi-infinite SSH array that is terminated at the weak coupling bond can support a topological mid-gap defect state, which is localized at the edge. In particular, we considered a special class of 1D photonic systems that emulate the so-called Su-Schrieffer-Heeger (SSH) Hamiltonian 16 (shown schematically in Figure 2) and thus possess a non-trivial topological order. Progress such as this is crucial in the development of next-generation photonic chips that operate at ultra-high speeds. The results of our work indicate that the proposed device can exhibit large bandwidth and a high isolation ratio (the ratio between backward and forward transmission). In a recent study, 15 we conducted theoretical and numerical investigations that showed it is possible to use a special type of 1D topological waveguide array to design and build on-chip optical diodes. Conversely, neither the sphere nor the ellipsoid are equivalent to a torus. A sphere and an ellipsoid are topologically equivalent since they can be deformed into one another without tearing or gluing. On the other hand, a sphere and a torus are topologically different (see Figure 1).įigure 1. 14 For example, a sphere and an ellipsoid are topologically equivalent because they can be deformed smoothly into one another without tearing or gluing. Topology is a branch of mathematics that deals with the global features of objects rather than their geometrical details. 8–13 These topological photonic arrangements can support defect states that are protected against certain types of disorder. Inspired by some recent progress in condensed matter physics, photonic structures with eigenspectra that exhibit topological properties have lately attracted considerable attention. 1 Although several novel concepts have been proposed for building integrated photonic isolators, 2–7 a practical implementation that meets market standards is still elusive. Commercial optical isolators that rely on the Faraday rotation effect, however, are bulky and incompatible with on-chip integration. 1 Such devices are indispensable tools in all laser systems because any feedback from the laser output can cause damage or lead to emission instabilities. Optical diodes (or isolators) are devices that allow light to propagate in only one direction and block light propagation in the opposite direction.
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