Field quantization and spontaneous emission in lossless dielectric multilayer structures

A complete set of cavity modes in planar dielectric multilayer structures is presented which naturally includes the guided modes. We show that most of these orthonormal fields can be derived from a coherent superposition of plane waves incident on the stack from the air and from the substrate. Using this set of cavity modes, we present a quantization scheme in idealized lossless stratified dielectric structures. This enables us to discuss the vacuum quantum fluctuations of the fields within the multilayer stack. The spontaneous emission of photons by a two-level atom located at any position inside the stratified planar structure is derived using the quantum approach and standard perturbation theory. The spontaneous emission rate as well as the radiation pattern in the air, in the substrate and in the guided mode are presented. Finally, a numerical analysis of the radiative properties of an erbium atom located in an asymmetrical Fabry - Perot multilayer structure is investigated. We show that a large part of the emitted power is directed in one half-space although a significant amount of light remains trapped in the guided modes of the structure.

[1]  J. Jauch,et al.  Phenomenological Quantum-Electrodynamics , 1948 .

[2]  Polman,et al.  Measuring and modifying the spontaneous emission rate of erbium near an interface. , 1995, Physical review letters.

[3]  G. Kurizki,et al.  Spontaneous and induced atomic decay in photonic band structures , 1994 .

[4]  Rigneault,et al.  Modal analysis of spontaneous emission in a planar microcavity. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[5]  D. Marcuse.  Theory of dielectric optical waveguides , 1974 .

[6]  S. Machida,et al.  Photon Number Squeezed States in Semiconductor Lasers , 1992, Science.

[7]  C. cohen-tannoudji,et al.  Vacuum fluctuations and radiation reaction : identification of their respective contributions , 1982 .

[8]  C. K. Carniglia,et al.  Quantization of Evanescent Electromagnetic Waves , 1971 .

[9]  Deng,et al.  Spontaneous-emission coupling from multiemitters to the quasimode of a Fabry-Pérot microcavity. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[10]  S. Ho,et al.  Spontaneous emission from excitons in thin dielectric layers. , 1993, Optics letters.

[11]  E. Purcell,et al.  Resonance Absorption by Nuclear Magnetic Moments in a Solid , 1946 .

[12]  Meschede,et al.  Suppression of spontaneous decay at optical frequencies: Test of vacuum-field anisotropy in confined space. , 1987, Physical review letters.

[13]  J. Oudar,et al.  NONGUIDING HALF-WAVE SEMICONDUCTOR MICROCAVITIES DISPLAYING THE EXCITON-PHOTON MODE SPLITTING , 1994 .

[14]  Erich P. Ippen,et al.  Spontaneous emission rate alteration in optical waveguide structures , 1990 .

[15]  Kim,et al.  Quantization of electromagnetic fields in cavities and spontaneous emission. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[16]  Daniel Kleppner,et al.  Cavity quantum electrodynamics , 1986 .

[17]  H. Yokoyama,et al.  Physics and Device Applications of Optical Microcavities , 1992, Science.

[18]  Hans Kuhn,et al.  Classical Aspects of Energy Transfer in Molecular Systems , 1970 .

[19]  Pierre Benech,et al.  An exact simplified method for the normalization of radiation modes in planar multilayer structures , 1992 .

[20]  Diana L. Huffaker,et al.  Spontaneous Emission from Planar Microstructures , 1994 .

[21]  P. Benech,et al.  A simple method for the determination of orthogonal radiation modes in planar multilayer structures , 1994 .

[22]  R. Loudon,et al.  Quantum theory of high-resolution length measurement with a Fabry-Perot interferometer , 1987 .

[23]  Hervé Rigneault,et al.  Radiative and guided wave emission of Er 3+ satoms located in planar multidielectric structures , 1997 .

[24]  Feng,et al.  Quantum theory of spontaneous emission in a one-dimensional optical cavity with two-side output coupling. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[25]  Hiroyuki Yokoyama,et al.  Enhanced spontaneous emission from GaAs quantum wells in monolithic microcavities , 1990 .

[26]  P. Mataloni,et al.  Anomalous spontaneous emission time in a microscopic optical cavity. , 1987, Physical review letters.

[27]  E. Yablonovitch,et al.  Inhibited spontaneous emission in solid-state physics and electronics. , 1987, Physical review letters.

[28]  Daniel Kleppner,et al.  Inhibited Spontaneous Emission , 1981 .

[29]  H. Rigneault,et al.  Fluorescence of Ta(2)O(5) thin films doped by kilo-electron-volt Er implantation: application to microcavities. , 1996, Applied optics.

[30]  R. Glauber,et al.  Quantum optics of dielectric media. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[31]  Meschede,et al.  One-atom maser. , 1985, Physical review letters.

[32]  K. Ujihara,et al.  ANALYSIS OF SPONTANEOUS EMISSION FROM A PLANAR MICROCAVITY-DEPENDENCE ON THE REFRACTIVE INDEX OF THE CAVITY REGION AND ATOMIC LOCATION , 1994 .

[33]  Oliver King,et al.  Directional, enhanced fluorescence from molecules near a periodic surface. , 1994, Applied optics.

[34]  C. Weisbuch,et al.  Observation of the coupled exciton-photon mode splitting in a semiconductor quantum microcavity. , 1992, Physical review letters.

[35]  C. Amra.  First-order vector theory of bulk scattering in optical multilayers , 1993 .

[36]  Richart E. Slusher,et al.  Optical Processes in Microcavities , 1993 .

[37]  Machida,et al.  Modification of spontaneous emission rate in planar dielectric microcavity structures. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[38]  D. J. Bradley.  Progress in Optics, Vol. XII , 1976 .

[39]  Hiroyuki Yokoyama,et al.  Spontaneous emission and laser oscillation properties of microcavities containing a dye solution , 1991 .

[40]  Ian J. Hodgkinson,et al.  Thin-films field-transfer matrix theory of planar multilayer waveguides and reflection from prism-loaded waveguides , 1984 .

[41]  David G. Voelz,et al.  Nonconventional Laser Imaging Using Sampled-Aperture Receivers , 1992 .

[42]  Knight,et al.  Field quantization in dielectric media and the generalized multipolar Hamiltonian. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[43]  Loudon,et al.  Spontaneous emission in the optical microscopic cavity. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[44]  De Martini F,et al.  Single-mode generation of quantum photon states by excited single molecules in a microcavity trap. , 1996, Physical review letters.

[45]  K. Tews.  On the variation of luminescence lifetimes. The approximations of the approximative methods , 1974 .

[46]  E. Yablonovitch.  Photonic band-gap structures , 1993 .

[47]  Dennis G. Deppe,et al.  Spontaneous emission from a dipole in a semiconductor microcavity , 1991 .

[48]  Vogel,et al.  Action of passive, lossless optical systems in quantum optics. , 1987, Physical review. A, General physics.

[49]  Lin,et al.  Cavity quantum electrodynamic enhancement of stimulated emission in microdroplets. , 1991, Physical review letters.

[50]  J. Raimond,et al.  Observation of cavity-enhanced single-atom spontaneous emission , 1983 .