Bound states in the continuum in open Aharonov-Bohm rings

Bulgakov, Evgeny N.; Pichugin, K. N.; Sadreev, Almas F.; Rotter, I.

doi:10.1134/s0021364006200057

Cited by 62 publications

(89 citation statements)

References 34 publications

(71 reference statements)

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“…Analytical expression for the resonant width can be derived following Refs. [77,78]. Thus we have slowly decaying quasi BSC modes above the light cone similar to those considered in Ref.…”

Section: Scattering Of Plane Waves In the Vicinity Of The Quasi-bscs mentioning

confidence: 80%

“…This equation manifests one remarkable as well as important for applications property of the BSCs to enormously enhance the incident wave Ψ inc by the factor 1/L c [52,77,78].…”

Section: Emergence Of the Bsc In Scatteringmentioning

confidence: 99%

“…Also the BSC is unique by that the solution of the scattering problem becomes ambiguous [25] and can be written as superposition of particular scattering state and the BSC [77,78].…”

Section: Emergence Of the Bsc In Scatteringmentioning

confidence: 99%

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Light Trapping above the Light Cone in One-Dimensional Arrays of Dielectric Spheres

2017

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Abstract:We demonstrate bound states in the radiation continuum (BSC) in a linear periodic array of dielectric spheres in air above the light cone. We classify the BSCs by orbital angular momentum m = 0, ±1, ±2 according to the rotational symmetry of the array, Bloch wave vector β directed along the array according to the translational symmetry, and polarization. The most simple symmetry protected BSCs have m = 0, β = 0 and occur in a wide range of the radius of the spheres and dielectric constant. More sophisticated BSCs with m = 0, β = 0 exist only for a selected radius of spheres at fixed dielectric constant. We also find robust Bloch BSCs with β = 0, m = 0. All BSCs reside within the first but below the other diffraction continua. We show that the BSCs can be easily detected by bright features in scattering of different plane waves by the array as dependent on type of the BSC. The symmetry protected TE/TM BSCs can be traced by collapsing Fano resonance in cross-sections of normally incident TE/TM plane waves. When plane wave with circular polarization with frequency tuned to the bound states with OAM illuminates the array the spin angular momentum of the incident wave transfers into the orbital angular momentum of the BSC. This, in turn, gives rise to giant vortical power currents rotating around the array. Incident wave with linear polarization with frequency tuned to the Bloch bound state in the continuum induces giant laminar power currents. At last, the plane wave with linear polarization incident under tilt relative to the axis of array excites Poynting currents spiralling around the array. It is demonstrated numerically that quasi-bound leaky modes of the array can propagate both stationary waves and light pulses to a distance of 60 wavelengths at the frequencies close to the bound states in the radiation continuum. A semi-analytical estimate for decay rates of the guided waves is found to match the numerical data to a good accuracy.

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“…Analytical expression for the resonant width can be derived following Refs. [77,78]. Thus we have slowly decaying quasi BSC modes above the light cone similar to those considered in Ref.…”

Section: Scattering Of Plane Waves In the Vicinity Of The Quasi-bscs mentioning

confidence: 80%

“…This equation manifests one remarkable as well as important for applications property of the BSCs to enormously enhance the incident wave Ψ inc by the factor 1/L c [52,77,78].…”

Section: Emergence Of the Bsc In Scatteringmentioning

confidence: 99%

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Light Trapping above the Light Cone in One-Dimensional Arrays of Dielectric Spheres

2017

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“…There is however a unique case when the solution of linear equation (1) is not unambiguous [37] when the inverse of the matrix L does not exists for Det( L) = 0 [38,39]. That occurs if one of complex eigenvalues of L turns to zero giving rise to the BSC as a null eigenvector of L…”

Section: Basic Equations For Em Wave Scattering By a Linear Array Of mentioning

confidence: 99%

“…Then the solution of Eq. (7) can be presented as linear superposition of the BSC and the particular solution [38,39] …”

Section: Basic Equations For Em Wave Scattering By a Linear Array Of mentioning

confidence: 99%

Trapping of light with angular orbital momentum above the light cone

Bulgakov¹,

Sadreev

2017

AEM

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We consider bound states in the radiation continuum (BSC) above the light cone in an one-dimensional periodic array of dielectric spheres in air. The BSCs are classified by orbital angular momentum m, Bloch wave vector β directed along the array, and polarization. The most simple symmetry protected BSCs have m = 0, β = 0 and occur in a wide range of the radius of spheres and dielectric constant. More sophisticated BSCs with m ̸ = 0, β = 0 exist only for a selected radius of the spheres at a fixed dielectric constant. We also show the existence of robust Bloch BSCs with β ̸ = 0, m = 0. The BSCs with m = 0 can be easily detected by the collapse of Fano resonance in scattering of a plane wave. In response to a plane wave with circular polarization the BSCs with m ̸ = 0 give rise to Poynting vector spiralling around the array.

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Light-Induced Breaking of Symmetry in Photonic Crystal Waveguides with Nonlinear Defects as a Key for All-Optical Switching Circuits

Bulgakov

Sadreev

Pichugin

2012

Progress in Optical Science and Photonics

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We consider light transmission in 2D photonic crystal waveguide coupled with two identical nonlinear defects positioned symmetrically aside the waveguide. We show that with growth of injected light power there is a breaking of symmetry by two ways. In the first way the symmetry is broken because of different light intensities at the defects. In the second way the intensities at the defects are equaled but phases of complex amplitudes are different. That results in a vortical power flow between the defects similar to the DC Josephson effect if the input power over the waveguide is applied and the defects are coupled. As application of these phenomena we consider the symmetry breaking for the light transmission in a T-shaped photonic waveguide with two nonlinear defects. We demonstrate as this phenomenon can be explored for all-optical switching of light transmission from the left output waveguide to the right one by application of input pulses. Finally we consider the symmetry breaking in the waveguide coupled with single defect presented however by two dipole modes.

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Bound states in the continuum in open Aharonov-Bohm rings

Cited by 62 publications

References 34 publications

Light Trapping above the Light Cone in One-Dimensional Arrays of Dielectric Spheres

Light Trapping above the Light Cone in One-Dimensional Arrays of Dielectric Spheres

Trapping of light with angular orbital momentum above the light cone

Light-Induced Breaking of Symmetry in Photonic Crystal Waveguides with Nonlinear Defects as a Key for All-Optical Switching Circuits

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