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Physical Review A

Parametric fluorescence and second-harmonic generation in a planar Fabry-Perot microcavity

Andrea Aiello, Daniele Fargion, Elena Cianci

Published Sep 1, 1998• 10 citations
Publisher

Abstract

In this work we develop a quantum theory of second-order nonlinear optical processes such as parametric fluorescence and second-harmonic generation (SHG), generated by a strong electromagnetic field in an active medium placed in a microcavity. Fields are quantized and expanded in terms of a suitable set of cavity normal modes. In the first part of this work we consider a single many-level quantum system (an atom or molecule), which interacts with all the radiation field modes (spontaneous emission). We show how vacuum fluctuations affect both SHG and parametric processes. For SHG, we demonstrate that the presence of the microcavity allows the introduction of the concept of coherence length, even for a medium made of a single molecule. In the second part of this paper we discuss the case of a uniform distribution of emitting dipoles. For this configuration we calculate the differential extinction coefficient, and discuss the dependence of the emitting power on the microcavity's parameters. Finally we suggest the possibility of realizing a micro-optical parametric oscillator.

DOI
10.1103/physreva.58.2446

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In this work we develop a quantum theory of second-order nonlinear optical processes such as parametric fluorescence and second-harmonic generation (SHG), generated by a strong electromagnetic field in an active medium placed in a microcavity. Fields are quantized and expanded in terms of a suitable set of cavity normal modes. In the first part of this work we consider a single many-level quantum system (an atom or molecule), which interacts with all the radiation field modes (spontaneous emission). We show how vacuum fluctuations affect both SHG and parametric processes. For SHG, we demonstrate that the presence of the microcavity allows the introduction of the concept of coherence length, even for a medium made of a single molecule. In the second part of this paper we discuss the case of a uniform distribution of emitting dipoles. For this configuration we calculate the differential extinction coefficient, and discuss the dependence of the emitting power on the microcavity's parameters. Finally we suggest the possibility of realizing a micro-optical parametric oscillator.
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The process of generation of non-classical radiation in an active Fabry-Perot dye microcavity, under femtosecond excitation, has been investigated. Single photon states, with a non-classical sub-Poissonian distribution have been generated after the excitation of a small number of active molecules, located between the two mirrors. By multiple excitation of the active medium, collective emission phenomena are expected because of the strong superradiant coupling occurring within the transverse coherence area of the microcavity. In particular, we have experimentally verified the principle of relativistic causality within the process of two-dipole superradiance by transverse interaction, in condition of strong microcavity confinement.
A complete set of cavity modes in planar dielectric microcavities is presented which naturally includes guided modes. We show that most of these orthonormal fields can be derived from a coherent superposition of plane waves incoming on the stack from the air and from the substrate. Spontaneous emission of a dipole located inside the microcavity is analyzed, in terms of cavity modes. Derivation of the radiation pattern in the air and in the substrate is presented. The power emitted into the guided modes is also determined. Finally, a numerical analysis of the radiative properties of an erbium atom located in a Fabry-P\'erot multilayer dielectric microcavity is investigated. We show that a large amount of light is emitted into the guided modes of the structure, in spite of the Fabry-P\'erot resonance, which increases the spontaneous emission rate in a normal direction. \textcopyright{} 1996 The American Physical Society.
A three-dimensional quantum nonperturbative theory of spontaneous emission in a planar microcavity is developed on the basis of a complete set of orthogonal standing-wave mode functions. Earlier results on the spontaneous decay rate and far-field emission pattern which have been obtained in a perturbative fashion are shown to be contained in our theory. Time evolution of the initially excited atomic state is considered and comparison with perturbative results is given. It is found that though the Fabry-Perot cavity is of an open type, vacuum-field Rabi oscillations are still possible. Conditions that are favorable for this strong coupling regime are discussed. The near-field spontaneous-emission pattern and the transition from the near field to the far field are investigated. For moderate mirror reflectivities, the spread in the near-field emission pattern is found to be in good agreement with the effective mode radius concept. When the mirror reflectivity increases, however, one has a strong coupling regime and together with it, multiple reabsorptions and reemissions of the photon may occur, leading to a better localization of the photon around the atomic position. These considerations may be useful in designing microlasers of the planar type.
We study the spontaneous-emission of a single atom located between two parallel infinite plates where one of the plates is partially reflective and the plate separation is of the order of the wavelength of the atomic transition. We pay particular attention to the nature of the field modes in such a finite finesse cavity, including the full three-dimensional nature of the field. We then compute the decay rate of an excited atom placed inside such a cavity. The angular distributions of the spontaneous-emission and of the cavity field vacuum fluctuation variances are investigated. Finally, we examine the output field from an atom inside a finite finesse microcavity. We show that the radiation transmitted outside such microcavity forms a nondiffracting Bessel beam. \textcopyright{} 1996 The American Physical Society.
This work presents a quantum theory of the nonlinear optical process of second-harmonic generation (SHG) in one-dimensional microresonators. More specifically, we show how the manipulation of vacuum field fluctuations in high-confinement systems, leading to a spectrally (and spatially) modulated commutation relation for the photon's generalized formulations of their creation and annihilation operators, deeply affects SHG behavior and gives rise to a threshold level. The two main effects the modulated commutator has on this optical process are an inhibition of the SHG process at low pumping level and a significant (cubic) amplification of the second-harmonic signal production rate once the threshold is overcome (finally reaching the usual quadratic dependence at sufficiently high pumping level). Our predictions, which represent a concrete picture of a fractional quantum system, could be used to probe vacuum field fluctuations present in high-confinement microresonators and emphasize the fundamental importance of vacuum field fluctuations.