Confined modes in two-dimensional tubes

Londergan, J. T.; Murdock, D. P.

doi:10.1119/1.4751875

Cited by 6 publications

(3 citation statements)

References 26 publications

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“…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

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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.

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Section: Introductionmentioning

confidence: 99%

Weakly bound states in heterogeneous waveguides

2016

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“…Such realizations are indeed susceptible of manipulations that produce partial isospectrality: we should bear in mind that the Dirichlet boundary value problem posed by bent waveguides leads to non-trivial behavior at high energies or frequencies, connecting the problem with wave-like manifestations of chaos [26]. However, at very low energies we can take advantage of trapped states at corners [14,[27][28][29][30] (in fact, only one bound state at a right bending angle), providing an exponentially evanescent coupling of two corners as a function of the distance between them. The idea then is to accommodate as many levels as necessary below the propagation threshold of the guide; this is done by adjusting the distances between the corners contained in the array; see figures 1, 6 and 7.…”

Section: Bent Waveguide Realizationsmentioning

confidence: 99%

Inverse lattice design and its application to bent waveguides

Rivera-Mociños¹,

Sadurní²

2016

J. Phys. A: Math. Theor.

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Abstract. This paper is divided in two parts. In the first part, the inverse spectral problem for tight-binding hamiltonians is studied. This problem is shown to have an infinite number of solutions for properly chosen energies. The space of such solutions is characterized by a hypersurface in the space of hopping amplitudes (i.e. couplings), whose dimension is half the number of sites in the array. Low dimensional examples for short chains are carefully studied and a table of exactly solvable inverse problems is provided in terms of Lie algebraic structures. With the aim of providing a method to generate lattice configurations, a set of equations for coupling constants in terms of energies is obtained; this is done by means of a new formula for the calculation of characteristic polynomials. Two examples with randomly generated spectra are studied numerically, leading to peaked distributions of couplings. In the second part of the paper, our results are applied to the design of bent waveguides, reproducing specific spectra below propagation threshold. As a demonstration, the Dirac and the finite oscillator are realized in this way. A few partially isospectral configurations are also presented.

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“…At low temperature and small electric bias, only the electrons near the Fermi energy contribute to the current. It has been shown that, under certain conditions, the propagation of ballistic electrons in semiconductor quantum wires, of electromagnetic waves in wave guides, of sound waves in pipes with different geometry, light propagation in optical fibres for photonic applications are all described by the same type of Helmholtz equation [9][10][11][12][13]. For the same boundary conditions this equation generates the same eigenvalue problem with the same solution.…”

Section: Introductionmentioning

confidence: 99%

Basic modelling of effects of geometry and magnetic field for quantum wires injecting electrons into a two-dimensional electron reservoir

Yakimenko

Yakimenko²,

Berggren³

2019

J. Phys.: Condens. Matter

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High-mobility two-dimensional electron gas (2DEG) which resides at the interface between GaAs and AlGaAs layered semiconductors has been used experimentally and theoretically to study ballistic electron transport. The present paper is motivated by recent experiments in magnetic electron focusing. The proposed device consists of two quantum point contacts (QPCs) serving as electron injector and collector which are placed in the same semiconductor GaAs/AlGaAs heterostructure. Here we focus on a theoretical study of the injection of electrons via a quantum wire/QPC into an open two-dimensional (2D) reservoir. The transport is considered for non-interacting electrons at different transmission regimes using the mode-matching technique. The proposed mode-matching technique has been implemented numerically. Electron flow through the quantum wire with hard-wall rectangular, conical and rounded openings has been studied. We have found for these three cases that the geometry of the opening does not play a crucial role for the electron propagation. When a perpendicular magnetic field is applied the electron paths in the 2D reservoir are curved. We analyse this case both classically and quantum-mechanically. The effect of spin-splitting due to exchange interactions on the electron flow is also considered. The effect is clearly present for realistic choices of device parameters and consistent with observations. The results of this study may be applied in designing magnetic focusing devices and spin separation.

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Confined modes in two-dimensional tubes

Cited by 6 publications

References 26 publications

Weakly bound states in heterogeneous waveguides

Weakly bound states in heterogeneous waveguides

Inverse lattice design and its application to bent waveguides

Basic modelling of effects of geometry and magnetic field for quantum wires injecting electrons into a two-dimensional electron reservoir

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