Doppler shift on local density of states and local impurity scattering in the vortex state

AbstractWe study discrete random Schrödinger operators via the supersymmetric formalism. We develop a cluster expansion that converges at both strong and weak disorder. We prove the exponential decay of the disorder-averaged Green’s function and the smoothness of the local density of states either at weak disorder and at energies in proximity of the unperturbed spectrum or at strong disorder and at any energy. As an application, we establish Lifshitz-tail-type estimates for the local density of states and thus localization at weak disorder.

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Near-Field Excitation of Bound States in the Continuum in All-Dielectric Metasurfaces through a Coupled Electric/Magnetic Dipole Model

Nanomaterials ◽

10.3390/nano11040998 ◽

2021 ◽

Vol 11 (4) ◽

pp. 998

Author(s):

Diego R. Abujetas ◽

José A. Sánchez-Gil

Keyword(s):

Magnetic Dipole ◽

Density Of States ◽

Bound States ◽

Local Density ◽

Near Field ◽

Field Pattern ◽

Local Density Of States ◽

Optical Modes ◽

Source Excitation ◽

The Continuum

Resonant optical modes arising in all-dielectric metasurfaces have attracted much attention in recent years, especially when so-called bound states in the continuum (BICs) with diverging lifetimes are supported. With the aim of studying theoretically the emergence of BICs, we extend a coupled electric and magnetic dipole analytical formulation to deal with the proper metasurface Green function for the infinite lattice. Thereby, we show how to excite metasurface BICs, being able to address their near-field pattern through point-source excitation and their local density of states. We apply this formulation to fully characterize symmetry-protected BICs arising in all-dielectric metasurfaces made of Si nanospheres, revealing their near-field pattern and local density of states, and, thus, the mechanisms precluding their radiation into the continuum. This formulation provides, in turn, an insightful and fast tool to characterize BICs (and any other leaky/guided mode) near fields in all-dielectric (and also plasmonic) metasurfaces, which might be especially useful for the design of planar nanophotonic devices based on such resonant modes.

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MODIFICATION OF CASIMIR FORCES DUE TO BAND GAPS IN PERIODIC STRUCTURES

International Journal of Modern Physics A ◽

10.1142/s0217751x02010145 ◽

2002 ◽

Vol 17 (06n07) ◽

pp. 798-803 ◽

Cited By ~ 7

Author(s):

C. VILLARREAL ◽

R. ESQUIVEL-SIRVENT ◽

G. H. COCOLETZI

Keyword(s):

Density Of States ◽

Casimir Force ◽

Periodic Structures ◽

Local Density ◽

Band Gaps ◽

Basic Unit ◽

Local Density Of States ◽

Casimir Forces ◽

Unit Cells ◽

The Difference

The Casimir force between inhomogeneous slabs that exhibit a band-like structure is calculated. The slabs are made of basic unit cells each made of two layers of different materials. As the number of unit cells increases the Casimir force between the slabs changes, since the reflectivity develops a band-like structure characterized by frequency regions of high reflectivity. This is also evident in the difference of the local density of states between free and boundary distorted vacuum, that becomes maximum at frequencies corresponding to the band gaps. The calculations are restricted to vacuum modes with wave vectors perpendicular to the slabs.

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