Paraxial spin transport using the Dirac-like paraxial wave equation

Mehrafarin, Mohammad; Balajany, Hamideh

doi:10.1016/j.physleta.2010.01.067

Cited by 17 publications

(16 citation statements)

References 25 publications

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“…E bem sabido que aóptica e a mecânica quântica tem muito em comum [9][10][11][12][13][14][15][16][17][18][19][20][21] e as referências colocadas aqui nesse trabalho estão longe de encerrar todo o assunto. Do ponto de vista histórico uma formulação antiga baseada naóptica por Hamilton e Jacobi inspirou Erwin Schrödinger a escrever a versão ondulatória da mecânica quântica [8].…”

Section: Analogias Com a Mecânica Quânticáunclassified

Um breve tratado sobre a aproximação paraxial

Souza

Silveira²,

Nóbrega

et al. 2014

Rev. Bras. Ensino Fís.

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A equação de ondas paraxial emerge na descrição de diversos problemas em física e engenharia. Por exemplo, na mecânica quântica a equação de Schrödingeré uma aproximação paraxial da teoria relativística. Ela aparece também no estudo da propagação de ondas eletromagnéticas, nas mais variadas situações. Na presente contribuição apresentamos uma revisão geral da equação paraxial e sua obtenção em diversas situações importantes para a física e a engenharia. Analogias entre a equação paraxial no estudo de ondas eletromagnéticas e a equação de Schrödinger da mecânica quântica são discutidas, bem como a relação entre paraxialidade e transversalidade das ondas eletromagnéticas. Por fim, alguns exemplos interessantes de propagação de ondas no limite de paraxialidade são considerados. Palavras-chave: eletromagnéticas, equação paraxial, equação de Schrödinger.The paraxial wave equation describes many problems in Physics and Engineering. For instance, the Schrödin-ger equation describing non-relativistic particles can be considered as a paraxial approximation of the relativistic quantum mechanics. The paraxial equation also emerges in the study of the electromagnetic waves propagation in a large number of physical situations. In this contribution we present an overview of the paraxial wave equation and its derivation in relevant problems for Physics and Engineering. Analogies between the electromagnetic paraxial equation and the quantum mechanical Schrödinger equation are discussed, as well as the relationship between paraxiality and transversality of electromagnetic waves. Finally, a few interesting examples of wave propagation in the paraxial limit are considered. Keywords: electromagnetic waves, paraxial equation, Schrödinger equation. IntroduçãoAs equações de Maxwell descrevem todos os fenômenos eletromagnéticos conhecidos de modo bastante preciso, e quando são quantizadas apresentam concordância extraordinária entre teoria e dados experimentais. Na forma clássica e no mundo macroscópico, são dadas por [1] 2 . Todas as unidades utilizadas estão dadas no sistema internacional de medidas (SI). Para completar o conjunto das equações,é necessário conhecer as relações constitutivas dos meios, que descrevem a resposta dos meios materiaisà aplicação dos campos E e H. Restringindo a atenção ao caso de um meio material não-magnético isotrópico, de maior interesse para o momento, na presença de campos eletromagnéticos E(r, t) e H(r, t) que variam suavemente no espaço em comparação com a escala atômico-molecular, a resposta de um materialé dada pelas relações abaixo

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Section: Analogias Com a Mecânica Quânticáunclassified

Um breve tratado sobre a aproximação paraxial

Souza

Silveira²,

Nóbrega

et al. 2014

Rev. Bras. Ensino Fís.

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“…Historically, the analogy between Maxwell equations and those used in the relativistic electron theory has been discussed in different contexts and for various purposes (see, for example, 47,[92][93][94] ) since 1907 when Maxwell equations were reduced 95 to an alternative, more concise form by introducing a complex field F = E + iH:…”

Section: B Charge Transport In Disordered Graphenementioning

confidence: 99%

“…Indeed, many features of Anderson localization can be found in random graphene systems. It has been shown in 94 that although the wave functions of normally incident (θ = 0) particles are extended and belong to the continuous part of the spectrum, away from some vicinity of θ = 0, 1-D random graphene systems manifest all features of disorder-induced strong localization. In particular, for a long enough, disordered graphene superlattice the transmission coefficient, T , as a function of the angle of incidence, θ, (or of the energy E, if θ = 0 is fixed) has typical for Anderson localization shape, Fig.…”

Section: B Charge Transport In Disordered Graphenementioning

confidence: 99%

Anderson localization in metamaterials and other complex media (Review Article)

Gredeskul

Kivshar

Asatryan

et al. 2012

Low Temperature Physics

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We review some recent (mostly ours) results on the Anderson localization of light and electron waves in complex disordered systems, including: (i) left-handed metamaterials, (ii) magneto-active optical structures, (iii) graphene superlattices, and (iv) nonlinear dielectric media. First, we demonstrate that left-handed metamaterials can significantly suppress localization of light and lead to an anomalously enhanced transmission. This suppression is essential at the long-wavelength limit in the case of normal incidence, at specific angles of oblique incidence (Brewster anomaly), and in the vicinity of the zero-ε or zero-µ frequencies for dispersive metamaterials. Remarkably, in disordered samples comprised of alternating normal and left-handed metamaterials, the reciprocal Lyapunov exponent and reciprocal transmittance increment can differ from each other. Second, we study magneto-active multilayered structures, which exhibit nonreciprocal localization of light depending on the direction of propagation and on the polarization. At resonant frequencies or realizations, such nonreciprocity results in effectively unidirectional transport of light. Third, we discuss the analogy between the wave propagation through multilayered samples with metamaterials and the charge transport in graphene, which enables a simple physical explanation of unusual conductive properties of disordered graphene superlatices. We predict disorder-induced resonances of the transmission coefficient at oblique incidence of the Dirac quasiparticles. Finally, we demonstrate that an interplay of nonlinearity and disorder in dielectric media can lead to bistability of individual localized states excited inside the medium at resonant frequencies. This results in nonreciprocity of the wave transmission and unidirectional transport of light.

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“…An "electric" field can be obtained through the definition E = −∇ ⊥ A 0 , making Eqs. (11) and (12) resemble Newton's second law for a "charged" particle, as follows:…”

Section: "Gauge" Symmetries Of the Optical Fieldsmentioning

confidence: 99%

“…In another research direction, the similarity of equations describing electromagnetic field propagation in optical frequencies with their analog of quantum mechanics suggests use of the former to simulate the behavior of the latter in a more or less classical way. For instance, one can consider M. Mehrafarin and H. Balajany, who showed that Maxwell's * cadartora@eletrica.ufpr.br equations assume a Dirac-like form, making the study of paraxial propagation easier in a weakly inhomogeneous medium [11].…”

Section: Introductionmentioning

confidence: 99%

Lagrangian-Hamiltonian formulation of paraxial optics and applications: Study of gauge symmetries and the optical spin Hall effect

et al. 2011

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In the context of the paraxial regime, usually valid for optical frequencies and also in the microwave spectrum of guided waves, the propagation of electromagnetic fields can be analyzed through a paraxial wave equation, which is analogous to the nonrelativistic Schrödinger equation of quantum mechanics but replacing time t with spatial coordinate z. Considering that, here it is shown that for lossless media in optical frequencies it is possible to construct a Lagrangian operator with an one-to-one correspondence with nonrelativistic quantum mechanics, which allows someone to use the same mathematical methods and techniques for solving problems. To demonstrate that, we explore a few applications in optics with increasing levels of complexity. In the spirit of a Hamiltonian formulation, the ray-tracing trajectories of geometric optics in paraxial regime are obtained in a clear manner. Following that, the gauge symmetries of the optical-field Lagrangian density is discussed in a detailed way, leading to the general form of the interaction Hamiltonian. Through the use of perturbation theory, we discuss a classical analog for a quantum NOT gate, making use of mode coupling in an isotropic chiral medium. At last, we explore the optical spin Hall effect and its possible applications using an effective geometric optics equation derived from an interaction Hamiltonian for the optical fields. We also predict within the framework of paraxial optics a spin Hall effect of light induced by gravitational fields.

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Paraxial spin transport using the Dirac-like paraxial wave equation

Cited by 17 publications

References 25 publications

Um breve tratado sobre a aproximação paraxial

Um breve tratado sobre a aproximação paraxial

Anderson localization in metamaterials and other complex media (Review Article)

Lagrangian-Hamiltonian formulation of paraxial optics and applications: Study of gauge symmetries and the optical spin Hall effect

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