Quantum Theory of a Dielectric-vacuum Interface in One Dimension

Barnett, Stephen M.; Matloob, Reza; Loudon, R.

doi:10.1080/09500349514551011

Cited by 52 publications

(38 citation statements)

References 7 publications

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“…The presence of absorption greatly complicates the theory since, in addition to the complex nature of the dielectric function, it also introduces unavoidable noise sources in the dielectric media, and these matters will be treated in subsequent publications [21,22). The refractive index is an even function, il(co) = i)(co), and (Al) can therefore be written g f dcog"*(z', co)g"(z,co) =I+I*, 0 where I = dc' exp[icosi(co)~zz'~/ c] 1~~exp(ik zz'~) 2~2 2 2 2 00 4mc ri( co ) 4m i -~-~k cco ri(co) (A3)…”

Section: Cgnci Usi(onsmentioning

confidence: 99%

“…Craps then appear in the ranges of integration along the real frequency axis, and the results given above are not strictly justified. It can, however, be shown that these results are in fact correct for a more realistic model that takes account of the inevitable imaginary part of the dielectric function, as in [8], and the generalizations to inhomogeneous dielectric media [21,22].…”

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confidence: 93%

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Electromagnetic-field quantization in inhomogeneous and dispersive one-dimensional systems

Santos

Loudon

1995

Phys. Rev. A

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The electromagnetic field is quantized in a material whose dielectric function varies with frequency and one spatial dimension. The dielectric function is assumed to have a known form and to be real over the range of frequencies important for a particular application, for example the propagation of an optical signal. General properties of the mode functions are derived and employed in the quantization procedure. Expressions are obtained for the energy and momentum density and current operators, and these are shown to satisfy the appropriate conservation and continuity relations. The general formalism is illustrated by application to the examples of a homogeneous dielectric and two di8'erent dielectrics with a sharp interface. PACS number(s): 42.50.p, 12.20.m

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Section: Cgnci Usi(onsmentioning

confidence: 99%

mentioning

confidence: 93%

Electromagnetic-field quantization in inhomogeneous and dispersive one-dimensional systems

Santos

Loudon

1995

Phys. Rev. A

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“…This method has been used to calculate the vacuum eld uctuations in absorbing dielectrics [2], and hence to obtain the spontaneous emission rate for an excited atom embedded in an in nite absorbing dielectric medium. Various quantization schemes have been proposed in order to resolve the problem of describing the eå ects of dispersive and absorptive linear dielectric devices on quantized radiation [3][4][5][6][7][8][9][10][11][12][13]. An interesting approach to the problem of quantization in lossy dielectrics uses Langevin forces to represent the noise [10][11][12][13], and has been applied to the calculation of quantum-optical processes in dielectric slabs with local susceptibility [9,11] and to the calculation of Casimir eå ects in absorbing dielectrics [8].…”

Section: Introductionmentioning

confidence: 99%

Mode expansion and photon operators in dispersive and absorbing dielectrics

Stefano¹,

Savasta²,

Girlanda³

2001

Journal of Modern Optics

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We present a one-dimensional quantization scheme for the electromagnetic eld in arbitrary planar absorbing and dispersive dielectrics, taking into account explicitly the nite extent of media. The complete form of the electric eld operator includes a part that corresponds to the free elds incident from the vacuum towards the medium and a particular solution which can be expressed by using the classical Green-function integral representation of the electromagnetic eld. By expressing the classical Green function in terms of the light modes of the dielectric structure, we obtain a natural generalization to absorbing media of the familiar method of mode expansion which strictly applies to non-absorbing media. As an application of our mode expansion, we obtain general quantum-optical input-output relations relating the output photon operators in vacuum to the input photon operators and to the reservoir noise operators. The input-output relations obtained are uniquely determined by the knowledge of the classical light modes of the planar system. We nally show that our quantization scheme for arbitrary planar dielectrics satis es the prescribed equal-time commutation relations of QED.

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“…Recently the electromagnetic field is quantized in dielectric media that show both loss and dispersion using the Green function tensor and introducing the notion of the noise current density operator [8][9][10][11][12][13][14]. This is in some sense, at least in its one-dimensional form, a mathematically well-established development to the beam splitter technique [15].…”

Section: Introductionmentioning

confidence: 99%

Electromagnetic field quantization in a linear isotropic dielectric

Matloob

2004

Phys. Rev. A

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A macroscopic electromagnetic field is quantized in a linear isotropic dielectric by the association of a damped quantum-mechanical harmonic oscillator with each mode of the radiation field. The macroscopic Langevin equation is used to describe the motion of a damped oscillator. We discuss a fully canonical approach for the quantization of a harmonic oscillator with damping subjected to a Langevin force operator. The conjugate momentum is defined in the usual way and the quantum-mechanical Hamiltonian is introduced. This provides us with a direct method for the quantization of the radiation field in a dielectric material. Special attention is paid to the decomposition of the radiation field into transverse and longitudinal parts and their difference is elucidated by this approach.

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Quantum Theory of a Dielectric-vacuum Interface in One Dimension

Cited by 52 publications

References 7 publications

Electromagnetic-field quantization in inhomogeneous and dispersive one-dimensional systems

Electromagnetic-field quantization in inhomogeneous and dispersive one-dimensional systems

Mode expansion and photon operators in dispersive and absorbing dielectrics

Electromagnetic field quantization in a linear isotropic dielectric

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