Topological description for gaps of one-dimensional symmetric all-dielectric photonic crystals

Xi, Sichuan; Xue, Chunhua; Jiang, Haitao; Chen, Hong

doi:10.1364/oe.24.018580

Cited by 35 publications

(32 citation statements)

References 19 publications

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“…The scattering matrix, or S-matrix, approach is a useful method to find bound states and their properties in open systems [48,49]. This approach has been of importance in the understanding of superconducting junctions [50][51][52][53][54], and has also been utilised in the context of photonic crystals [55][56][57], the calculation of topological invariants [58] and the topic of quantum chaos in billiards [59,60]. Recently, the S-matrix method was used to solve for the Zak phase in one-dimensional tight-binding models [61], bringing it closer to the models we will consider in this work.…”

Section: Introductionmentioning

confidence: 99%

Exact edge, bulk, and bound states of finite topological systems

2018

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Finite topologically non-trivial systems are characterised, among many other unique properties, by the presence of bound states at their physical edges. These topological edge modes can be distinguished from usual Shockley waves energetically, as their energies remain finite and in-gap even when the boundaries of the system represent an effectively infinite and sharp energetic barrier. Theoretically, the existence of topological edge modes can be shown by means of the bulkedge correspondence and topological invariants. On a clean one-dimensional lattice and reducible two-dimensional models, in either the commensurate or semi-infinite case, the edge modes can be essentially obtained analytically, as shown in [Phys. Rev. Lett. 71, 3697 (1993)] and [Phys. Rev. A 89, 023619 (2014)]. In this work, we put forward a method for obtaining the spectrum and wave functions of topological edge modes for arbitrary finite lattices, including the incommensurate case. A small number of parameters are easily determined numerically, with the form of the eigenstates remaining fully analytical. We also obtain the bulk modes in the finite system analytically and their associated eigenenergies, which lie within the infinite-size limit continuum. Our method is general and can be easily applied to obtain the properties of non-topological models and/or extended to include impurities. As an example, we consider a relevant case of an impurity located next to one edge of a one-dimensional system, equivalent to a softened boundary in a separable two-dimensional model. We show that a localised impurity can have a drastic effect on the original topological edge modes of the system. Using the periodic Harper and Hofstadter models to illustrate our method, we find that, on increasing the impurity strength, edge states can enter or exit the continuum, and a trivial Shockley state bound to the impurity may appear. The fate of the topological edge modes in the presence of impurities can be addressed by quenching the impurity strength. We find that at certain critical impurity strengths, the transition probability for a particle initially prepared in an edge mode to decay into the bulk exhibits discontinuities that mark the entry and exit points of edge modes from and into the bulk spectrum.

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Section: Introductionmentioning

confidence: 99%

Exact edge, bulk, and bound states of finite topological systems

2018

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“…In these systems, where timereversal (TR) symmetry is not broken [13,14,15,16], crystalline or intrinsic symmetries of the wave fields and differing topology of bulk bands give rise to wavevector-locked states at the interface [12]. Analogously, opposite single-negative bulk materials [17] support bound states that exhibit a similar though limited robustness [18,19,20]. In addition, trivial structures such as nanofibers and glide-plane PC waveguides [21], where light is tightly confined with evanescent wave on their interface, can exhibit direction-dependent polarizations [22].…”

mentioning

confidence: 99%

“…inversion-symmetry [41,42]. Note that a single PEC-PMC interface is sufficient to partially bound energy due to ε -negative and μ -negative materials possessing different topological orders when considering a fixed wave polarization [18,19,20]. As the new decoupled interface modes form a hybrid of magnetic and electric modes with a specific phase relationship, they possess conserved pseudo-spin values [43,36].…”

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confidence: 99%

Guiding Waves Along an Infinitesimal Line between Impedance Surfaces

Bisharat

Sievenpiper

2017

Phys. Rev. Lett.

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“…Therefore the two kinds of single negative band gap of figures 5(a) and (c) belong to different topological phases, respectively. The topological phase transition can take place when the system converts from effective elasticity negative (ENG) to effective mass negative (MNG), which is similar to the topological change between ENG (ò negative) and MNG (μ negative) in electromagnetism [51][52][53][54].…”

Section: Band Inversion and Zak Phasesmentioning

confidence: 99%

Dark state, zero-index and topology in phononic metamaterials with negative mass and negative coupling

et al. 2019

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Phononic metamaterials have attracted extensive attention since they are flexibly adjustable to control the transmission. Here we study a one-dimensional phononic metamaterial with negative mass and negative coupling, made of resonant oscillators and chiral couplings. At the frequency where the effective mass and coupling are both infinite, a flat band emerges that induces a sharply high density of states, reminiscent of the phononic dark states. At the critical point of band degeneracy, a phononic Dirac-like point emerges where both the effective mass and the inverse of effective coupling are simultaneously zero, so that zero-index is realized for phonons. Moreover, the phononic topological phase transition is observed when the phononic band gap switches between single mass-negative and single coupling-negative regimes. When these two distinct single negative phononic metamaterials are connected to each other, a phononic topological interface state is identified within the gap, manifested as the phononic counterpart of the topological Jackiw-Rebbi solution.

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Topological description for gaps of one-dimensional symmetric all-dielectric photonic crystals

Cited by 35 publications

References 19 publications

Exact edge, bulk, and bound states of finite topological systems

Exact edge, bulk, and bound states of finite topological systems

Guiding Waves Along an Infinitesimal Line between Impedance Surfaces

Dark state, zero-index and topology in phononic metamaterials with negative mass and negative coupling

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