Waves in locally periodic media

Griffiths, David J.; Steinke, Carl A.

doi:10.1119/1.1308266

Cited by 211 publications

(205 citation statements)

References 59 publications

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“…Consider the case that v 0 (x) = 0 and the perturbation involves an array of Dirac delta-functions [13][14][15][16]:…”

Section: Array Of Complex Delta-function Potentialsmentioning

confidence: 99%

Perturbative analysis of spectral singularities and their optical realizations

Mostafazadeh¹,

Rostamzadeh²

2012

Phys. Rev. A

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We develop a perturbative method of computing spectral singularities of a Schrödinger operator defined by a general complex potential that vanishes outside a closed interval. These can be realized as zero-width resonances in optical gain media and correspond to a lasing effect that occurs at the threshold gain. Their time-reversed copies yield coherent perfect absorption of light that is also known as antilasering. We use our general results to establish the exactness of the n-th order perturbation theory for an arbitrary complex potential consisting of n delta-functions, obtain an exact expression for the transfer matrix of these potentials, and examine spectral singularities of complex barrier potentials of arbitrary shape. In the context of optical spectral singularities, these correspond to inhomogeneous gain media.

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“…Consider the case that v 0 (x) = 0 and the perturbation involves an array of Dirac delta-functions [13][14][15][16]:…”

Section: Array Of Complex Delta-function Potentialsmentioning

confidence: 99%

Perturbative analysis of spectral singularities and their optical realizations

Mostafazadeh¹,

Rostamzadeh²

2012

Phys. Rev. A

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“…[2][3][4][5] In this way, the transfer matrix formalism provides a simple mathematical tool allowing for a unified treatment of such diverse problems as electron or phonon dynamics in both periodic and aperiodic lattices, [6][7][8][9][10][11][12][13][14][15][16] optical properties of dielectric multilayers, [17][18][19][20][21] the propagation of acoustic waves in semiconductor heterostructures and metallic superlattices, [22][23][24] localization of elastic waves in heterogeneous media, 25 or charge transport through DNA chains. [26][27][28][29][30] A significant number of works have focused on the study of systems based on two simple kinds of transfer matrices, namely, the so-called on-site and transfer models.…”

Section: ͑3͒mentioning

confidence: 99%

Renormalization transformation of periodic and aperiodic lattices

Maciá

Rodríguez-Oliveros

2006

Phys. Rev. B

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In this work we introduce a similarity transformation acting on transfer matrices describing the propagation of elementary excitations through either periodic or Fibonacci lattices. The proposed transformation can act at two different scale lengths. At the atomic scale the transformation allows one to express the systems' global transfer matrix in terms of an equivalent on-site model one. Correlation effects among different hopping terms are described by a series of local phase factors in that case. When acting on larger scale lengths, corresponding to short segments of the original lattice, the similarity transformation can be properly regarded as describing an effective renormalization of the chain. The nature of the resulting renormalized lattice significantly depends on the kind of order ͑i.e., periodic or quasiperiodic͒ of the original lattice, expressing a delicate balance between chemical complexity and topological order as a consequence of the renormalization process.

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“…On the other hand, in a series of works devoted to the study of periodic superlattices it was reported that Chebyshev polynomials play, for finite systems, a similar role to the one played by the Bloch functions in the description of transport properties of infinite periodic systems. [40][41][42] In addition, the ability of these polynomials to properly describe the propagation of both quantum and classical waves in locally periodic media ͑namely, systems having only a relatively small number of repeating elements͒ in a compact way has been recently illustrated, 43 as well as their convenience when describing the presence of extended states in correlated random systems. 44,45 …”

Section: Introductionmentioning

confidence: 99%

Hierarchical description of phonon dynamics on finite Fibonacci superlattices

Maciá

2006

Phys. Rev. B

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We study the phonon dynamics of Fibonacci heterostructures where two kinds of order ͑namely, periodic and quasiperiodic͒ coexist in the same sample at different length scales. We derive analytical expressions describing the dispersion relation of finite Fibonacci superlattices in terms of nested Chebyshev polynomials of the first and second kinds. In this way, we introduce a unified description of the phonon dynamics of Fibonacci heterostructures, able to exploit their characteristic hierarchical structure in a natural way.

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Waves in locally periodic media

Cited by 211 publications

References 59 publications

Perturbative analysis of spectral singularities and their optical realizations

Perturbative analysis of spectral singularities and their optical realizations

Renormalization transformation of periodic and aperiodic lattices

Hierarchical description of phonon dynamics on finite Fibonacci superlattices

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