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arXiv:quant-ph/0303021 · Physical Review A

Input-output relations at dispersing and absorbing planar multilayers for the quantized electromagnetic field containing evanescent components

M. Khanbekyan, L. Knöll, Dirk‐Gunnar Welsch

Published Jun 24, 2003• 18 citations
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Abstract

By using the Green-function concept of quantization of the electromagnetic field in dispersing and absorbing media, the quantized field in the presence of a dispersing and absorbing dielectric multilayer plate is studied. Three-dimensional input-output relations are derived for both amplitude operators in the $\mathbf{k}$ space and the field operators in the coordinate space. The conditions are discussed, under which the input-output relations can be expressed in terms of bosonic operators. The theory applies to both (effectively) free fields and fields, created by active atomic sources inside and/or outside the plate, including also evanescent-field components.

DOI
10.1103/physreva.67.063812

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By using the Green-function concept of quantization of the electromagnetic field in dispersing and absorbing media, the quantized field in the presence of a dispersing and absorbing dielectric multilayer plate is studied. Three-dimensional input-output relations are derived for both amplitude operators in the k\mathbf{k}k space and the field operators in the coordinate space. The conditions are discussed, under which the input-output relations can be expressed in terms of bosonic operators. The theory applies to both (effectively) free fields and fields, created by active atomic sources inside and/or outside the plate, including also evanescent-field components.
The theory developed by Gruner and Welsch [Phys. Rev. A 54, 1661 (1996)] for calculating the 1D input-output relations of the quantized electromagnetic field at dispersing and absorbing dielectric (multilayer) plates is generalized to the three-dimensional case. First a general recipe for the derivation of the reflection and transmission coefficients at an arbitrary body that separates two half spaces from each other is presented. The general theory is then applied to the case of planar multilayer structures, for which the Green tensor is well-known.
Using the Green-function approach to the problem of quantization of the phenomenological Maxwell theory, the propagation of quantized radiation through dispersive and absorptive multilayer dielectric plates is studied. Input-output relations are derived, with special emphasis on the determination of the quantum noise generators associated with the absorption of radiation inside the dielectric matter. The input-output relations are used to express arbitrary correlation functions of the outgoing field in terms of correlation functions of the incoming field and those of the noise generators. To illustrate the theory, photons at dielectric tunneling barriers are considered. It is shown that inclusion in the calculations of losses in the photonic band gaps may substantially change the barrier traversal times. \textcopyright{} 1996 The American Physical Society.
Using the Green function approach to the problem of quantization of the phenomenological Maxwell theory, the propagation of quantized radiation through dispersive and absorptive multilayer dielectric plates is studied. Input--output relations are derived, with special emphasis on the determination of the quantum noise generators associated with the absorption of radiation inside the dielectric matter. The input--output relations are used to express arbitrary correlation functions of the outgoing field in terms of correlation functions of the incoming field and those of the noise generators. To illustrate the theory, the effect of a single-slab plate on the mean photon-number densities in the frequency domain is discussed in more detail.
We present a one-dimensional quantization scheme for the electromagnetic field in arbitrary planar absorbing and dispersive dielectrics, taking into account explicitly the finite extent of media. The complete form of the electric field operator includes a part that corresponds to the free fields 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 field. 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 finally show that our quantization scheme for arbitrary planar dielectrics satisfies the prescribed equal-time commutation relations of QED.
A general theory of the interaction of the quantized electromagnetic field with atoms, in the presence of dispersing and absorbing dielectric bodies of given Kramers-Kronig consistent permittivities, is developed. It is based on a source-quantity representation of the electromagnetic field, in which the electromagnetic-field operators are expressed in terms of a continuous set of fundamental bosonic fields via the Green tensor of the classical problem. Introducing scalar and vector potentials, the formalism is extended to include in the theory the interaction of the quantized electromagnetic field with additional atoms. Both the minimal-coupling scheme and the multipolar-coupling scheme are considered. The theory replaces the standard concept of mode decomposition, which fails for complex permittivities. It enables us to treat the effects of dispersion and absorption in a consistent way and to give a unified approach to the atom-field interaction, without any restriction to a particular interaction regime in a particular frequency range. All relevant information about the dielectric bodies, such as form and intrinsic dispersion and absorption, is contained in the Green tensor. The application of the theory to the spontaneous decay of an excited atom in the presence of dispersing and absorbing bodies is addressed.