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Physical Review Letters

Anomalous spontaneous–stimulated-decay phase transition and zero-threshold laser action in a microscopic cavity

F. De Martini, Gloria Regina Jacobovitz

Published Apr 25, 1988• 229 citations
Publisher

Abstract

In an active ``microcavity'' the condition of maximum ``enhancement'' of spontaneous emission corresponds to resonant coupling of atoms with a single field mode. We demonstrate that this exceptional condition results in the effective cancellation of spontaneous emission, in the onset of stimulated emission at exceedingly low excitation levels, and in an anomalously high stimulated-emission gain. In the context of phase-transition theory the active microcavity behaves as a statistical ensemble undergoing an order-disorder transition at an extremely high value of the critical temperature.

DOI
10.1103/physrevlett.60.1711

Related papers

ANOMALOUS PHASE-TRANSITION AND PHOTON-LOCALIZATION IN STIMULATD-EMISSION IN A MICROSCOPIC OPTICAL CAVITY

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In recent papers we have reported the first proposal and realization of the “microscopic cavity” (or “microcavity”) i.e. with relevant dimension d~d = (λ/2) where λ is the wavelength of the cavity-confined radiation (1). By this apparatus the Spontaneous-Emission (SE) inhibition-enhancement process in molecular physics (“Purcell effect”) has been demonstrated at optical frequencies (1). In the present work we report the demonstration that the phase of (SE) “enhancement” (i.e. d=d) is actually nonexistent in a microcavity as (SE) is overcome and merges into Stimulated-Emission (StE) at exceedingly low levels of molecular excitation, thus realizing, for the first time in Optics, a “Zero-Threshold-Laser” action. This is a direct consequence of the peculiar and novel condition of Quantutm-Statistical-Electrodynamics offered by the microcavity and consisiting of a resonant single-mode field-atom interaction. Assume that an atom or molecule with an homogeneous-broadened resonance at λ and linewidth Δλ = (λ·Δv/v), placed in a microcavity, emits a fluorescence photon at time t=to, and suppose that this is the only photon present in the cavity at that time.

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The quantum theory of the spontaneous emission (SpE) from an active microscopic cavity (microcavity) is given with emphasis on mirror separations of the order of the optical wavelength. The theory is based on a complete set of orthonormal-mode functions that include both transverse polarizations and span the infinite three dimensional space that pervades and surrounds the microcavity. SpE rates for different active-dipole orientations and cavity configurations are calculated. The SpE pulse shape detected outside the cavity is shown to be generally nonexponential. A detailed computer simulation of the process is presented on the basis of the given theory in the perspective of our experiment, for a cavity terminated by mirrors bearing either metal- or semiconductor-multilayered coatings. We then report an extensive experimental verification of the theory by adopting an Eu-dibenzoylmethane complex as active medium with SpE from the $^{5}$${\mathit{D}}_{0\mathrm{\ensuremath{-}}}^{7}$${\mathit{F}}_{2}$ line at \ensuremath{\lambda}=6111 \AA{}, under coherent uv excitation at ${\ensuremath{\lambda}}_{\mathit{p}}$=3547 \AA{}. The results show evidence of ``SpE inhibition'' and ``enhancement,'' of nonexponential decay of SpE signals, and of competition with superradiance and stimulated emission. Finally we report the results of an experimental test of the algorithm adopted in all computer calculations of the optical parameters of the multilayered structures used for cavity confinement.

Physical Review A•Mar 1, 1991•231 citations
In an active microcavity'' the condition of maximum enhancement'' of spontaneous emission corresponds to resonant coupling of atoms with a single field mode. We demonstrate that this exceptional condition results in the effective cancellation of spontaneous emission, in the onset of stimulated emission at exceedingly low excitation levels, and in an anomalously high stimulated-emission gain. In the context of phase-transition theory the active microcavity behaves as a statistical ensemble undergoing an order-disorder transition at an extremely high value of the critical temperature.
In recent papers we have reported the first proposal and realization of the “microscopic cavity” (or “microcavity”) i.e. with relevant dimension d~d = (λ/2) where λ is the wavelength of the cavity-confined radiation (1). By this apparatus the Spontaneous-Emission (SE) inhibition-enhancement process in molecular physics (“Purcell effect”) has been demonstrated at optical frequencies (1). In the present work we report the demonstration that the phase of (SE) “enhancement” (i.e. d=d) is actually nonexistent in a microcavity as (SE) is overcome and merges into Stimulated-Emission (StE) at exceedingly low levels of molecular excitation, thus realizing, for the first time in Optics, a “Zero-Threshold-Laser” action. This is a direct consequence of the peculiar and novel condition of Quantutm-Statistical-Electrodynamics offered by the microcavity and consisiting of a resonant single-mode field-atom interaction. Assume that an atom or molecule with an homogeneous-broadened resonance at λ and linewidth Δλ = (λ·Δv/v), placed in a microcavity, emits a fluorescence photon at time t=to, and suppose that this is the only photon present in the cavity at that time.
Several experimental schemes of vacuum-confinement in electromagnetic-bounded structures are presented together with related results involving Spontaneously Emitting (SE) molecules. Striking anomalies in the SE spatial-distribution and decay-times are detected. In addition, an anomalous "zero-threshold-laser" behaviour of molecular Stimulated Emission (StE) in a single-mode Casimir-type microscopic cavity is reported. This novel effect is due to an unexpected collective molecular process taking place at an exceedingly low excitation level in the optical-pumping scheme. In the framework of "Phase-transition" theory this effect corresponds to an order-disorder transition taking place at a critical-temperature T c which is virtually infinite.
High gain and virtual zero threshold have been recognized to be distinctive properties of the microlaser since its original proposal and realization by our laboratory in 1988. These properties are investigated both theoretically and experimentally. They are found to be determined by the synergy of several quantum-statistical processes that take place in the condition of extreme field confinement provided by the peculiar Casimir-type topology of the optical microcavity. The determination of the microcavity mode structure leads to a detailed study of the process of spontaneous emission (SpE), its merging with stimulated emission, and the consequent anomalous onset of the collective atomic behavior at low excitation levels. A microlaser excitation threshold of ~50 pJ has been determined experimentally with a molecular Oxazine microlaser excited by a femtosecond source. The relevance in atomic dynamics of the processes of SpE inhibition—enhancement, mode competition, fluorescence loss, interatomic transverse Bose correlations, and periodic excitation—is investigated both theoretically and experimentally. A discussion of the overall process in terms of a second-order phase transition in a nonequilibrium statistical problem is given. The extension of the microlaser dynamics to other quantum systems, such as the microscopic parametric oscillator, and to Raman and Compton scattering is considered.
The near-zero threshold and the very high gain of the active optical microlaser are investigated both theoretically and experimentally. These properties are found to be determined by the synergy of several quantum-statistical processes taking place in the condition of extreme field confinement provided by the peculiar Casimir-type topology of the optical microcavity. The determination of the microcavity mode structure leads to a detailed study of the process of merging of the spontaneous emission with stimulated emission (StE) and of the consequent anomalous onset of the collective atomic behavior at very low excitation levels. An excitation threshold of about 50 pJ has been determined experimentally with a molecular oxazine microlaser excited by a femtosecond-pulse source. The relevance within the overall StE dynamics of the processes of mode-competition fluorescence loss, interatom transverse Bose correlations, and periodic excitation are investigated both theoretically and experimentally. A discussion of the overall process in terms of a second-order phase transition in a nonequilibrium statistical problem is given. The extension of the microcavity dynamics to quantum-dynamical systems such as the ``microscopic'' parametric oscillator and to Raman and Compton scattering is also considered.
A description is given of several novel experimental methods for quantum-electrodynamic vacuum confinement of emission modes close to a single electromagnetic boundary and in a microscopic Fabry–Perot optical cavity of length of the same order of magnitude as the wavelength of the recorded radiation. Strong anomalies (Purcell effect) of the spontaneous emission process and of a phase transition with spontaneous–stimulated decay of states in the stimulated emission process are demonstrated experimentally. It is shown that in the context of the phase transition theory an active microscopic cavity behaves as a superconductor with an extremely high critical transition temperature. This unusual behavior can be interpreted as a manifestation of a perturbation induced in a quantum system by "measurement apparatus" of dimensions comparable with the de Broglie wavelength of a test particle.
The quantum theory of the spontaneous emission (SpE) from an active microscopic cavity (microcavity) is given with emphasis on mirror separations of the order of the optical wavelength. The theory is based on a complete set of orthonormal-mode functions that include both transverse polarizations and span the infinite three dimensional space that pervades and surrounds the microcavity. SpE rates for different active-dipole orientations and cavity configurations are calculated. The SpE pulse shape detected outside the cavity is shown to be generally nonexponential. A detailed computer simulation of the process is presented on the basis of the given theory in the perspective of our experiment, for a cavity terminated by mirrors bearing either metal- or semiconductor-multilayered coatings. We then report an extensive experimental verification of the theory by adopting an Eu-dibenzoylmethane complex as active medium with SpE from the 5^{5}5${\mathit{D}}_{0\mathrm{\ensuremath{-}}}^{7}$F2{\mathit{F}}_{2}F2​ line at \ensuremath{\lambda}=6111 \AA{}, under coherent uv excitation at ${\ensuremath{\lambda}}_{\mathit{p}}$=3547 \AA{}. The results show evidence of ``SpE inhibition'' and ``enhancement,'' of nonexponential decay of SpE signals, and of competition with superradiance and stimulated emission. Finally we report the results of an experimental test of the algorithm adopted in all computer calculations of the optical parameters of the multilayered structures used for cavity confinement.