Bound states in the continuum in a two-dimensional PT-symmetric system

Kartashov, Yaroslav V.; Milián, Carles; Torner, Lluís

doi:10.1364/ol.43.000575

Cited by 26 publications

(12 citation statements)

References 37 publications

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“…But since the real part of the eigenvalues for these states resides within the continuum, they have been interpreted in Refs. 30,56,79,80 as representing a quasi-bound state in continuum. This interpretation is consistent with the experimental study of defect states in a PT -symmetric optical lattice in Ref.…”

Section: Discussionmentioning

confidence: 99%

Reservoir-assisted symmetry breaking and coalesced zero-energy modes in an open PT-symmetric Su-Schrieffer-Heeger model

Garmon,

Noba

2021

Preprint

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We study a model consisting of a central PT -symmetric trimer with non-Hermitian strength parameter γ coupled to two semi-infinite Su-Schrieffer-Heeger (SSH) leads in order to demonstrate two qualitatively distinct types of PT -symmetry breaking. Within a subset of the parameter space corresponding to the topologically non-trivial phase of the SSH chains, we show that a gap opens within the broken PT regime of the discrete eigenvalue spectrum. For relatively smaller values of γ, the eigenvalues are embedded in the two SSH bands and hence become destabilized primarily due to the resonance interaction with the continuum. We refer to this as reservoir-assisted PT -symmetry breaking. As the value of γ is increased, the eigenvalues exit the two continuum bands and the discrete eigenstates become more strongly localized in the central trimer region. This approximate decoupling results in the discrete spectrum behaving more like the independent trimer, including both a region in which the PT -symmetry is restored (the gap) and a second region in which it is broken again. The second-order exceptional points (EP2s) associated with the PT -symmetry breaking thresholds form several two-dimensional exceptional surfaces in the parameter space of the model. For certain parameter values two of these surfaces intersect, forming a curve of fourth-order exceptional points (EP4s) along which the gap closes. Meanwhile, a second, qualitatively different scenario occurs in which the gap instead closes simultaneously along an extended domain of γ values.

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Section: Discussionmentioning

confidence: 99%

Reservoir-assisted symmetry breaking and coalesced zero-energy modes in an open PT-symmetric Su-Schrieffer-Heeger model

Garmon,

Noba

2021

Preprint

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“…Complex eigenfunctions associated with bifurcated eigenvalues are

L^{2}

‐integrable, and the real parts of these eigenvalues belong to the continuous spectrum. This enables a physical interpretation of such eigenfunctions in terms of non‐Hermitian generalizations 28,29 of bound states embedded in the continuum, well‐known in quantum mechanics, 30–33 optics, and other fields 34 . It should be noticed at the same time that most of the activity devoted to non‐Hermitian optical bound states in the continuum is being carried out for one‐dimensional systems.…”

Section: Introductionmentioning

confidence: 99%

“…It should be noticed at the same time that most of the activity devoted to non‐Hermitian optical bound states in the continuum is being carried out for one‐dimensional systems. For multidimensional geometries, most of the available results are numerical in nature 29 . From the practical point of view, it is also important that eigenfunctions associated with emerging from the essential spectrum eigenvalues are extremely weakly localized in the vicinity of the bifurcation, which hinders their efficient numerical evaluation.…”

Section: Introductionmentioning

confidence: 99%

Bifurcations of thresholds in essential spectra of elliptic operators under localized non‐Hermitian perturbations

2021

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We consider the operator H=scriptH′−∂2∂xd2onω×Rsubject to the Dirichlet or Robin condition, where a domain ω⊆double-struckRd−1 is bounded or unbounded. The symbol H′ stands for a second‐order self‐adjoint differential operator on ω such that the spectrum of the operator H′ contains several discrete eigenvalues Λj, j=1,…,m. These eigenvalues are thresholds in the essential spectrum of the operator scriptH. We study how these thresholds bifurcate once we add a small localized perturbation εL(ε) to the operator scriptH, where ε is a small positive parameter and L(ε) is an abstract, not necessarily symmetric operator. We show that these thresholds bifurcate into eigenvalues and resonances of the operator scriptH in the vicinity of Λj for sufficiently small ε. We prove effective simple conditions determining the existence of these resonances and eigenvalues and find the leading terms of their asymptotic expansions. Our analysis applies to generic nonself‐adjoint perturbations and, in particular, to perturbations characterized by the parity‐time (scriptPT) symmetry. Potential applications of our result embrace a broad class of physical systems governed by dispersive or diffractive effects. As a case example, we employ our findings to develop a scheme for a controllable generation of non‐Hermitian optical states with normalizable power and real part of the complex‐valued propagation constant lying in the continuum. The corresponding eigenfunctions can be interpreted as an optical generalization of bound states embedded in the continuum. For a particular example, the persistence of asymptotic expansions is confirmed with direct numerical evaluation of the perturbed spectrum .

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“…Recent achievements in the field of BIC are discussed in Refs. [17][18][19][20][21][22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Multipolar origin of bound states in the continuum

et al. 2019

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Metasurfaces based on resonant subwavelength photonic structures enable novel ways of wavefront control and light focusing, underpinning a new generation of flat-optics devices. Recently emerged all-dielectric metasurfaces exhibit high-quality resonances underpinned by the physics of bound states in the continuum that drives many interesting concepts in photonics. Here we suggest a novel approach to explain the physics of bound photonic states embedded into the radiation continuum. We study dielectric metasurfaces composed of planar periodic arrays of Mie-resonant nanoparticles ("meta-atoms") which support both symmetry protected and accidental bound states in the continuum, and employ the multipole decomposition approach to reveal the physical mechanism of the formation of such nonradiating states in terms of multipolar modes generated by isolated meta-atoms. Based on the symmetry of the vector spherical harmonics, we identify the conditions for the existence of bound states in the continuum originating from the symmetries of both the lattice and the unit cell. Using this formalism we predict that metasurfaces with strongly suppressed spatial dispersion can support the bound states in the continuum with the wavevectors forming a line in the reciprocal space. Our results provide a new way for designing high-quality resonant photonic systems based on the physics of bound states in the continuum.

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Bound states in the continuum in a two-dimensional PT-symmetric system

Cited by 26 publications

References 37 publications

Reservoir-assisted symmetry breaking and coalesced zero-energy modes in an open PT-symmetric Su-Schrieffer-Heeger model

Reservoir-assisted symmetry breaking and coalesced zero-energy modes in an open PT-symmetric Su-Schrieffer-Heeger model

Bifurcations of thresholds in essential spectra of elliptic operators under localized non‐Hermitian perturbations

Multipolar origin of bound states in the continuum

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