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Soviet Journal of Quantum Electronics

Spontaneous emission from a medium with a band spectrum

Vladimir P Bykov

Published Jul 31, 1975• 239 citations
Publisher

Abstract

A theoretical analysis is made of the spontaneous emission from an excited atom or a molecule in a one-dimensional periodic structure formed by a screened two-conductor line filled with periodically distributed dielectric disks. It is shown that when the transition frequency lies within or close to the forbidden band of the periodic structure, the decay of an excited state of an atom or a molecule produces a characteristic long-lived dynamic state. This dynamic state is a superposition of the excited and ground states with an admixture of a photon "cloud," which surrounds the atom or molecule. A study is made of the distribution of the electromagnetic energy of the dynamic state. The energy and the decay law of the excited state are obtained and the spectrum of the emission which accompanies this decay is obtained. It is shown that the spontaneous emission can be suppressed strongly in volumes much greater than the wavelength. The possibility of the suppression of spontaneous emission from lasers is discussed.

DOI
10.1070/qe1975v004n07abeh009654

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Annual Meeting Optical Society of America•Jan 1, 1992•1 citation
A theoretical analysis is made of the spontaneous emission from an excited atom or a molecule in a one-dimensional periodic structure formed by a screened two-conductor line filled with periodically distributed dielectric disks. It is shown that when the transition frequency lies within or close to the forbidden band of the periodic structure, the decay of an excited state of an atom or a molecule produces a characteristic long-lived dynamic state. This dynamic state is a superposition of the excited and ground states with an admixture of a photon "cloud," which surrounds the atom or molecule. A study is made of the distribution of the electromagnetic energy of the dynamic state. The energy and the decay law of the excited state are obtained and the spectrum of the emission which accompanies this decay is obtained. It is shown that the spontaneous emission can be suppressed strongly in volumes much greater than the wavelength. The possibility of the suppression of spontaneous emission from lasers is discussed.
The spontaneous emission field and spectrum of a two-level atom, located in an isotropic photonic crystal with dynamic band edges, are investigated by means of numeric calculation. The investigation is expected to help comprehend the characteristics of the atomic spontaneous emission in the dynamic photonic crystal, and provide a possible way to control dynamically the spontaneous emission in photonic crystal. The expression of the spontaneous radiation field is obtained without using the far-zone approximation and the Weisskopf-Wigner approximation, and expected to be applicable in other relevant researches. In the investigation, the spontaneous radiation field and spectrum are calculated when the band edge frequency is unmodulated, or modulated by a step function or triangle function. In the unmodulated situation, the radiation field intensity tends to a constant which is equal to the intensity of the localized field component. The radiation field pulse presents a wave packet behavior as propagation distance increases. The components of the radiation field correspond one-to-one to the peaks in the spontaneous radiation spectrum. When the band edge frequency is modulated by step function, the radiation field intensity tends to a steady-state value after the modulation has happened. And the steady-state intensity is affected by the time when the modulation happens. The components of the non-localized field and the frequency of the localized field after modulation depend on the atomic transition frequency and the band edge frequency, and are identical to those in the unmodulated situation with the same parameters. When the band edge frequency is modulated by a triangle function, the field intensity presents a decaying quasi-periodic oscillation after a long enough time. The modulation frequency determines the frequency of the oscillation, and influences the decay rate. The radiation energy becomes sharp peaks around a set of the discrete frequencies which are evenly spaced with the modulation frequency. The central frequency of these frequencies depends on the atomic transition frequency and the value range of the band edge frequency. The modulation initial phase affects the intensity of the radiation field emitted in an initial period of time.
Spontaneous emission can be modified if the atom is driven by an external coherent field. Such modification include the three-peak spectrum of resonance fluorescence from a two level atom. The spectral line elimination and cancellation of spontaneous emission is possible under conditions that the spontaneous emission from an excited atom can be trapped in the upper states without decaying. The amount of fluorescence in this case as well as the population of the upper levels can be controlled. If spontaneous emission along with atomic transition is suppressed, it is possible to create a population in version on this transition by using a very weak incoherent pumping.
We consider the process of spontaneous emission of a two-level atom embedded into a periodic layered dielectric structure. When the resonant atomic frequency lies within the photon-density-of-states gap, of width \ensuremath{\Gamma}, the atom emits light during a time interval t\ensuremath{\Gamma}\ensuremath{\ll}1 until the spontaneous emission becomes fully inhibited. We discuss the enhancing of spontaneous emission by tuning the atomic resonance with a one-mode microcavity. In the \ensuremath{\lambda}/4-shifted distributed feedback microcavities which possess the \ensuremath{\delta}-function-like density of states, in the middle of the gap, the process of spontaneous emission has damped Rabi oscillation behavior; the damping depends on the width of the gap and the height of its walls. A profile of the density-of-states gap can be determined from the experimental data on the temporal behavior of the atomic spontaneous decay.
We study the spontaneous emission of an atom embedded in a one-dimensional photonic crystal or superlattice using a classical electrodynamic theory of radiation. The rate of emission is a function of the frequency of the emitted photon, the dipole's position and orientation, as well as the geometric and material parameters of the superlattice. The emission spectrum shows an oscillatory behavior which follows the photonic band structure. For TE modes, there are frequency regions where radiative emission is completely prohibited due to the absence of modes with k//>omega/c; the radiation is then TM polarized. In addition to the radiative modes, there are always evanescent modes with k//>omega/c which are waveguided by the dielectric layers. The evanescent contribution to the spontaneous emission is dominant if a dielectric layer is in the near field region of the dipole. For TM modes, emission rates greatly vary for parallel and perpendicular dipole moments. In a photonic crystal with a high filling fraction of the dielectric and perpendicular dipoles located in the low-index layer, the decay rate can be as much as 76 times the free space value for a single atom and 50 times for a gas of atoms. We also find that the rate of emission presents a strong dependence on the atom's position.
Decay of an excited molecule ~atom! has been considered in an absorbing dielectric. The decay rate has been derived calculating the total rate of excitation transfer to the surrounding species. The contribution due to the far-zone energy transfer yields the rate of photon emission in the absorbing medium. The analysis is based on a microscopic QED theory of energy transfer in condensed phases. As a result, effects due to discreteness of the medium ~such as the local field effects! are reflected intrinsically in the decay rates. The microscopic approach supports the previous introduction of the local field factors on a phenomenological basis.
We consider the dynamics of the spontaneous emission of a two-level atom embedded into a periodic layered dielectric structure. When the resonant atomic frequency lies within the photon-density-of-states gap (DOS) of width Γ, the atom spontaneous emission becomes fully inhibited for times tΓ ≥ 1. We discuss its enhancing by tuning the atomic resonance with a one mode microcavity. In the λ/4 shifted distributed feedback microcavities, which possess a δ function in the DOS, the spontaneous emission has damped Rabi oscillations and the damping depends on r and the gap depth.