Multiple bound states in sharply bent waveguides

Carini, John P.; Londergan, J. T.; Mullen, Kieran; Murdock, D. P.

doi:10.1103/physrevb.48.4503

Cited by 78 publications

(84 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In particular, Exner and Seba [5] have proved that the existence of a bound state for an electron confined to a planar waveguide, with curvature decaying at infinity and obeying Dirichlet boundary conditions at the border; Goldstone and Jaffe [6] have proved that an electron confined to an infinite tube of constant cross section, in two or more dimensions, has always a bound state, when the tube is not perfectly straight. The effect of bound states in infinite non-straight waveguides has been studied in [7,8,9,10,11,12]. It is worth mentioning a recent pedagogical article by Londergan and Murdock [13], that illustrates different numerical methods for the solutions of confined systems, in particular two-dimensional waveguides.…”

Section: Introductionmentioning

confidence: 99%

Weakly bound states in heterogeneous waveguides

2016

View full text Add to dashboard Cite

Abstract. We study the spectrum of the Helmholtz equation in a two-dimensional infinite waveguide, containing a weak heterogeneity localized at an internal point, and obeying Dirichlet boundary conditions at its border. We prove that, when the heterogeneity corresponds to a locally denser material, the lowest eigenvalue of the spectrum falls below the continuum threshold and a bound state appears, localized at the heterogeneity. We devise a rigorous perturbation scheme and derive the exact expression for the energy to third order in the heterogeneity.

show abstract

Section: Introductionmentioning

confidence: 99%

Weakly bound states in heterogeneous waveguides

2016

View full text Add to dashboard Cite

show abstract

“…For an arbitrary angle [3] provides an asymptotics of the lowest eigenvalues when the angle goes to π/2. The regime with small angle limit has been studied in [5] and more recently in [10,11]. The question of waveguides with corner arises naturally because it is studied for smooth waveguides in [13,6,7] where we learn, among other things, that curvature induces bound states below the essential spectrum.…”

Section: Motivations and Related Questionsmentioning

confidence: 99%

Dirichlet eigenvalues of cones in the small aperture limit

Ourmières-Bonafos¹

2014

J. Spectr. Theory

View full text Add to dashboard Cite

We are interested in finite cones of fixed height 1 parametrized by their opening angle. We study the eigenpairs of the Dirichlet Laplacian in such domains when their apertures tend to 0. We provide multi-scale asymptotics for eigenpairs associated with the lowest eigenvalues of each fiber of the Dirichlet Laplacian. In order to do this, we investigate the family of their one-dimensional Born-Oppenheimer approximations. The eigenvalue asymptotics involves powers of the cube root of the aperture, while the eigenfunctions include simultaneously two scales.

show abstract

“…Remembering the exact analogy between tubes and waveguides, this also implies that bent waveguides will possess a confined mode below the cutoff frequency. Carini et al 16,17 demonstrated that a waveguide in the form of an L-shaped tube possessed a confined mode below the cutoff frequency, at just the location predicted by numerical calculations.…”

Section: Solutions For Modes In a Two-dimensional Tubementioning

confidence: 99%

Confined modes in two-dimensional tubes

Londergan

Murdock

2012

American Journal of Physics

Self Cite

View full text Add to dashboard Cite

On the Aharonov-Casher system and the Landau-Aharonov-Casher system confined to a two-dimensional quantum ring J. Math. Phys. 53, 023514 (2012) We survey various numerical methods for finding solutions of quantum confined states. We especially consider states in two-dimensional (2D) tubes, or 2D surfaces that are confined in the transverse direction but are unconfined in the longitudinal direction. We first review existence proofs for bound states in long 2-D tubes. We then review various methods for finding such states and we discuss the significance of these eigenstates.

show abstract

Multiple bound states in sharply bent waveguides

Cited by 78 publications

References 18 publications

Weakly bound states in heterogeneous waveguides

Weakly bound states in heterogeneous waveguides

Dirichlet eigenvalues of cones in the small aperture limit

Confined modes in two-dimensional tubes

Contact Info

Product

Resources

About