Trapped modes for off-centre structures in guides

Linton, C. M.; McIver, Maureen; McIver, P.; Ratcliffe, Keith; Zhang, J.

doi:10.1016/s0165-2125(02)00006-9

Cited by 47 publications

(21 citation statements)

References 14 publications

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“…These single-resonance parametric BICs can also exist in non-periodic structures, as shown theoretically in acoustic and water waveguides with an obstacle [143][144][145][146][147][148] , in quantum waveguides with impurities [149][150][151] or bends 95,152,153 , for mechanically coupled beads 29,30 and mechanical resonators 154 , and in optics for a low-index waveguide on a high-index membrane 155 .…”

Section: Single Resonancementioning

confidence: 79%

Bound states in the continuum

et al. 2016

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Bound states in the continuum are waves that, defying conventional wisdom, remain localized even though they coexist with a continuous spectrum of radiating waves that can carry energy away. Their existence was first proposed in quantum mechanics and, being a general wave phenomenon, later identified in electromagnetic, acoustic, and water waves. They have been studied in a wide variety of material systems such as photonic crystals, optical waveguides and fibers, piezoelectric materials, quantum dots, graphene, and topological insulators. This Review describes recent developments in this field with an emphasis on the physical mechanisms that lead to these unusual states across the seemingly very different platforms. We discuss recent experimental realizations, existing applications, and directions for future work.

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Section: Single Resonancementioning

confidence: 79%

Bound states in the continuum

et al. 2016

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“…In Linton et al (2002) acoustic resonances were found between the second and third cut-off's for wave propagation down a rigid waveguide containing an off-centre rigid plate aligned with the guide walls. The coupled waveguide problem under consideration here can be set up for energies between the second and third cut-offs, with three wave-like modes appearing in the region x < a and two propagating modes in the region x > a.…”

Section: Resultsmentioning

confidence: 98%

“…The ellipses are defined by two geometrical parameters a and b, say, where (x/a) 2 + (y/b) 2 = 1, and embedded trapped modes were found to exist for families of ellipses given by a = a(b), with the corresponding frequency being of the form k = k(b). Further examples of branches of embedded trapped modes in geometries defined by two geometrical parameters were computed in McIver, Linton, and Zhang (2002).…”

Section: Bound States Below the Second Cut-offmentioning

confidence: 99%

“…If one considers a geometry defined by a sufficient number of parameters then it may be possible to determine relationships between these parameters which lead to bound states. The numbers of parameters needed will depend on the energy band considered and the boundary conditions for the problem (see, e.g., Linton et al 2002).…”

Section: Bound States Below the Second Cut-offmentioning

confidence: 99%

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Bound states in coupled guides. I. Two dimensions

Linton

Ratcliffe

2004

Journal of Mathematical Physics

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Bound states in coupled guides. I. Two dimensions.C. M. Linton and K. RatcliffeBound states that can occur in coupled quantum wires are investigated. We consider a two-dimensional configuration in which two parallel waveguides (of different widths) are coupled laterally through a finite length window and construct modes which exist local to the window connecting the two guides. We study both modes above and below the first cut-off for energy propagation down the coupled guide. The main tool used in the analysis is the so-called residue calculus technique in which complex variable theory is used to solve a system of equations which is derived from a mode-matching approach. For bound states below the first cut-off a single existence condition is derived, but for modes above this cut-off (but below the second cut-off), two conditions must be satisfied simultaneously. A number of results have been presented which show how the bound-state energies vary with the other parameters in the problem.

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“…Precise estimations of the number of trapped modes versus the plate length were obtained for small lengths of the plate (8,9) and later for general lengths (10). Note that the existence of trapped mode about a plate is not systematic since if homogeneous Dirichlet conditions are considered on the channel walls, then no mode exists for a centred plate (at least below the cut-off frequency of antisymmetric modes of the duct (9,11,12)). …”

Section: Introductionmentioning

confidence: 99%

Resonances of an elastic plate in a compressible confined fluid

Dhia

Mercier

2007

The Quarterly Journal of Mechanics and Applied Mathematics

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SummaryWe present a theoretical study of the resonances of a fluid-structure problem, an elastic plate placed in a duct in the presence of a compressible fluid. The case of a rigid plate has been largely studied. Acoustic resonances are then associated to resonant modes trapped by the plate. Due to the elasticity of the plate we need to solve a quadratic eigenvalue problem in which the resonance frequencies k solve the equations γ(k) = k 2 where γ are the eigenvalues of a self-adjoint operator of the form A + kB. First we show how to study the eigenvalues located below the essential spectrum by using the Min-Max principle. Then we study the fixed-point equations. We establish sufficient conditions on the characteristics of the plate and of the fluid that ensure the existence of resonances. Such conditions are validated numerically.

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Trapped modes for off-centre structures in guides

Cited by 47 publications

References 14 publications

Bound states in the continuum

Bound states in the continuum

Bound states in coupled guides. I. Two dimensions

Resonances of an elastic plate in a compressible confined fluid

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