Semiclassical wave functions for open quantum billiards

Lackner, Fabian; Březinová, Iva; Burgdörfer, Joachim; Libisch, Florian

doi:10.1103/physreve.88.022916

Cited by 12 publications

(6 citation statements)

References 62 publications

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“…2 (d) shows an important distinction to the selfintersecting orbits: as increases, the corners of the waveguide aperture encroach on the orbit and eventually touch it. The resulting corner diffraction [25] will degrade the lifetime of any modes based on this orbit. The numerical computations to be described in section III have revealed high-Q modes in cavities of the shape (2), that do show enhanced intensity near the rectangle orbit, but never exclusively on that orbit.…”

Section: Cavity Shape and Ray Phase Spacementioning

confidence: 99%

Folded chaotic whispering-gallery modes in nonconvex, waveguide-coupled planar optical microresonators

Burke¹,

Nöckel²

2019

Phys. Rev. A

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Chaotic whispering-gallery modes have significance both for optical applications and for our understanding of the interplay between wave phenomena and the classical ray limit in the presence of chaotic dynamics and openness. In strongly non-convex geometries, a theorem by Mather rules out the existence of invariant curves in phase space corresponding to rays circulating in whispering-gallery patterns, so that no corresponding modes of this type are expected. Here we discuss numerical computations of the electromagnetic fields in planar dielectric cavities that are strongly non-convex because they are coupled to waveguides. We find a family of special states which retains many features of the chaotic whispering-gallery modes known from convex shapes: an intensity pattern corresponding to near-grazing incidence along extended parts of the boundary, and comparatively high cavity Q factors. The modes are folded into a figure-eight pattern, so overlap with the boundary is reduced in the region of self-intersection. The modes combine the phenomenology of chaotic whispering-gallery modes with an important technological advantage: the ability to directly attach waveguides without spoiling the Q factor of the folded mode. Using both a boundary-integral method and the finite-difference time domain technique, we explore the dependence of the phenomenon on wavelength in relation to cavity size, refractive-index contrast to the surrounding medium, and the degree of shape deformation. A novel feature that distinguishes folded from regular whispering gallery modes is that a given shape will support high-Q folded chaotic whispering gallery modes only in certain wavelength windows.

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Section: Cavity Shape and Ray Phase Spacementioning

confidence: 99%

Folded chaotic whispering-gallery modes in nonconvex, waveguide-coupled planar optical microresonators

Burke¹,

Nöckel²

2019

Phys. Rev. A

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“…Moreover, numerous results of research [18][19][20] also reveal that external parameters such as the driven source and measuring device can cause the resonant modes to display various eigenmode-mixing phenomena. Scattering theory [21,22] has been used to study the frequency spectra and spatial patterns in microwave cavities because the entering and measuring antennas take the role of the scattering channels. However, for other experimental systems such as laser resonators and vibrating plates, the spatial patterns of resonant modes can be measured with the straightforward imaging method instead of the invasive scattering process.…”

Section: Introductionmentioning

confidence: 99%

Exploring the distinction between experimental resonant modes and theoretical eigenmodes: From vibrating plates to laser cavities

Tuan

Wen

et al. 2014

Phys. Rev. E

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Experimentally resonant modes are commonly presumed to correspond to eigenmodes in the same bounded domain. However, the one-to-one correspondence between theoretical eigenmodes and experimental observations is never reached. Theoretically, eigenmodes in numerous classical and quantum systems are the solutions of the homogeneous Helmholtz equation, whereas resonant modes should be solved from the inhomogeneous Helmholtz equation. In the present paper we employ the eigenmode expansion method to derive the wave functions for manifesting the distinction between eigenmodes and resonant modes. The derived wave functions are successfully used to reconstruct a variety of experimental results including Chladni figures generated from the vibrating plate, resonant patterns excited from microwave cavities, and lasing modes emitted from the vertical cavity.

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“…The approach used by Bøggild et al for large-scale electron transport simulations is purely semiclassical and belongs to a broadly used class of simulation known as billiard models. In the last few years these models have proven to successfully provide insights on the overall magneto-transport characteristics of graphene [7][8][9][10] and other large-scale ballistic devices in the mesoscopic limit [11].…”

Section: Introductionmentioning

confidence: 99%

Large-scale tight-binding simulations of quantum transport in ballistic graphene

Calogero¹,

Papior²,

Bøggild³

et al. 2018

J. Phys.: Condens. Matter

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Graphene has proven to host outstanding mesoscopic effects involving massless Dirac quasiparticles travelling ballistically resulting in the current flow exhibiting light-like behaviour. A new branch of 2D electronics inspired by the standard principles of optics is rapidly evolving, calling for a deeper understanding of transport in large-scale devices at a quantum level. Here we perform large-scale quantum transport calculations based on a tight-binding model of graphene and the non-equilibrium Green's function method and include the effects of p-n junctions of different shape, magnetic field, and absorptive regions acting as drains for current. We stress the importance of choosing absorbing boundary conditions in the calculations to correctly capture how current flows in the limit of infinite devices. As a specific application we present a fully quantum-mechanical framework for the '2D Dirac fermion microscope' recently proposed by Bøggild et al (2017 Nat. Commun. 8 10.1038), tackling several key electron-optical effects therein predicted via semiclassical trajectory simulations, such as electron beam collimation, deflection and scattering off Veselago dots. Our results confirm that a semiclassical approach to a large extend is sufficient to capture the main transport features in the mesoscopic limit and the optical regime, but also that a richer electron-optical landscape is to be expected when coherence or other purely quantum effects are accounted for in the simulations.

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Semiclassical wave functions for open quantum billiards

Cited by 12 publications

References 62 publications

Folded chaotic whispering-gallery modes in nonconvex, waveguide-coupled planar optical microresonators

Folded chaotic whispering-gallery modes in nonconvex, waveguide-coupled planar optical microresonators

Exploring the distinction between experimental resonant modes and theoretical eigenmodes: From vibrating plates to laser cavities

Large-scale tight-binding simulations of quantum transport in ballistic graphene

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