t o Ph o t on i cs" , Z ak opa n e 200 1 Sp on t an eou s Em ission b y A tom s in Sim p le En v iron m en ts W . `ak o w ic z I nst i t ut e of P h ysi cs, Po li sh Academ y of Sciences al .Lo tni k §w 32/ 46, 02-668 Warszawa , Po l andSpontan eous ra diation by ato ms in t he presence of the planar dielectri c{ v acuum interf ace, planar dielectri c w aveguides and cylindri cal dielectri c w aveguides are discussed in the frame of cavity quantum electro dynami cs in full analogy with that in free space.H owever, quanti zation of the electromagnetic Ùeld should be based on the mo des appropriate to the selected space structure.T hese quantizations are usuall y based on incoming w aves.H ow ever, the discussion of the angular intensity pattern of spontaneous emission can be simpli Ùed if the quantization is based on outgoing mo des.U sing these outgoing photons the angular emission radiatio n pattern has b een obtained from a straightf orw ard appli catio n of the p erturbativ e metho d of the quantum radiation theory .A dding a contribution of the w aveguiding photons attached to the w aveguides (w hen they are present ) the total emission of the spontaneous radiation and excitation decay rates of atoms radiatin g in these systems ha ve been derived.
t o Ph o t on i cs" , Z ak opa n e 200 1 Sp on t an eou s Em ission b y A tom s in Sim p le En v iron m en ts W . `ak o w ic z I nst i t ut e of P h ysi cs, Po li sh Academ y of Sciences al .Lo tni k §w 32/ 46, 02-668 Warszawa , Po l andSpontan eous ra diation by ato ms in t he presence of the planar dielectri c{ v acuum interf ace, planar dielectri c w aveguides and cylindri cal dielectri c w aveguides are discussed in the frame of cavity quantum electro dynami cs in full analogy with that in free space.H owever, quanti zation of the electromagnetic Ùeld should be based on the mo des appropriate to the selected space structure.T hese quantizations are usuall y based on incoming w aves.H ow ever, the discussion of the angular intensity pattern of spontaneous emission can be simpli Ùed if the quantization is based on outgoing mo des.U sing these outgoing photons the angular emission radiatio n pattern has b een obtained from a straightf orw ard appli catio n of the p erturbativ e metho d of the quantum radiation theory .A dding a contribution of the w aveguiding photons attached to the w aveguides (w hen they are present ) the total emission of the spontaneous radiation and excitation decay rates of atoms radiatin g in these systems ha ve been derived.
Spontaneous emission of photons by an atom placed near the dielectric waveguide is analyzed using global free electromagnetic modes, satisfying necessary continuity conditions at the waveguide boundaries 1. These modes include modes extended over the whole space (travelling) and modes trapped to the waveguide. To describe angular properties of the spontaneous emission, a parameterization of the travelling modes by the outgoing waves has been proposed. Otherwise, using a more common parameterization of these modes by the incoming waves, one has to take into account the interference of different reflected and transmitted waves accompanying photons incoming from both sides of the waveguide 2, what was overlooked in 3. Angular characteristics of the travelling photon emission (a), distributions of the trapped photon emission (b), as well as global decay rates (c), have been calculated using the quantum approach and standard perturbation theory. Enhancement and suppression of radiative decay rates in various configurations have been shown. A certain calculational error, in the treatment of the density of trapped states, in an earlier paper by Khosravi and Loudon 4, affecting emission rates for thin waveguides, has been corrected.
Introduction Ever since 1916/17 when Einstein argued [45] [46] that spontaneous emission must occur if matter and radiation are to achieve thermal equilibrium, physicists have believed that spontaneous emission is an inherent quantum mechanical property of atoms and that excited atoms inevitably radiate. This view, however, overlooks the fact that spontaneous emission is a consequence of the coupling of quantized energy states of atoms with the quantized radiation field, and is a manifestation of quantum noise or of emission ‘stimulated’ by ‘vacuum fluctuations’. An infinity of vacuum states is available to the photon radiated by an excited atom placed in free space, leading to the effective irreversibility of such emissions. If these vacuum states are modified, as for example by placing an excited atom between closely spaced mirrors or in a small cavity (essentially the Casimir effect), spontaneous emission can be greatly inhibited or enhanced or even made reversible. Recent advances in atomic and optical techniques have made it possible to control and manipulate spontaneous emission. A whole new branch of quantum optics called ‘cavity QED’ has developed since 1987 utilizing these dramatic changes in spontaneous emission rates in cavities to construct new kinds of microscopic masers or micromasers that operate with a single atom and a few photons or with photons emitted in pairs in a two-photon transition.
Introduction The preceding chapters have focused on atomic transitions induced by applied radiation. That is, there is an optical field illuminating the atoms, and their response is calculated. It is implicitly assumed that an excited atom left alone will spontaneously return to the ground state, and conserve energy by emitting light that satisfies E 2 − E 1 = ħ ω 21 in accordance with the Planck and Bohr pictures. But this spontaneous emission process is not addressed quantitatively in these earlier chapters. Spontaneous emission is one of the most pervasive phenomena of atomic physics, and yet its origins remain among the least well-understood. The number of misconceptions is enormous, and they are to be found in textbooks, journal articles, and lecture notes. Because the natural decay of an excited atom adds energy to what is usually an empty mode of the electromagnetic field, the process is fundamentally quantum mechanical. Classical or even semi-classical descriptions cannot be assured to give correct answers. This is not to say that such discussion is to be avoided, but only that caution is needed in interpreting the results. Toward the end of the nineteenth century, many experimental results made it clear that classical mechanics needed to be supplemented by new theories. The first venture into the new physics was Planck's hypothesis that the energy of classical radiating oscillators like those discussed in Chap. 1 would have to be quantized into integer multiples of ħ ω. This notion led to his famous formula for the spectrum of thermal radiation from a non-reflective object (black body), and this formula describes a radiation field in thermodynamic equilibrium with its environment. The result of Planck's hypothesis in the context of thermal equilibrium plays a vital role in the discussion of spontaneous emission. Einstein A - and B -coefficients Soon after Bohr proposed a model of atomic structure consisting of discrete energy levels, connected by radiation whose energy satisfied Δ E = ħω when atoms made transition between them, Einstein published the first serious attempt to connect the absorption and emission processes. Absorption, he reasoned, could occur only in the presence of applied radiation, whereas spontaneous decay occurred without the application of any field.
The spontaneous emission of photons by an atom placed near the dielectric slab is analyzed using global free electromagnetic modes, satisfying necessary continuity conditions at the slab boundaries. These modes include the modes extended over the whole space (traveling) and the modes trapped to a waveguide formed by the slab (trapped). To describe angular properties of spontaneous emission a parametrization of the traveling modes by the outgoing waves has been proposed. Angular characteristics of the traveling photon emission, distributions of the trapped photon emission, as well as global decay rates have been calculated using the quantum approach and standard perturbation theory. Enhancement and suppression of radiative decay rates in various configurations have been shown. A certain calculational error in an earlier paper by Khosravi and Loudon [Proc. R. Soc. London Ser. A 436, 373 (1992)] affecting thin slabs and results near waveguide-mode thresholds has been improved.
We consider the spontaneous emission in an absorbing medium by calculating the quantum flow of energy from an emitting atom. For this purpose, we extend the analysis by Power and Thirunamachandran of quantized Maxwell fields in the vicinity of an atom in the free space to a situation where the emitter is in a dielectric medium. We represent the quantum flow in terms of the non-equal time commutators involving electric and magnetic fields, as well as the local displacement field. The commutators are calculated applying a previously developed microscopic theory of quantization of radiation in dielectrics. Consequently, we derive from first principles the rate of spontaneous emission in an absorbing medium containing local field factors and other refractive contributions. The results support the previous introduction of the (virtual cavity) local field correction by Barnett et al on a phenomenological basis, as well as our previous approach in which the spontaneous emission is considered as a resonance energy transfer to the far-zone atoms. A distinctive feature of the present formalism is that it deals with the spontaneous emission directly by calculating the quantum flow from the emitting atom. Therefore, the method is free from divergences appearing in other approaches analysing the spontaneous decay in absorbing media.
It is well known that spontaneous emission is not an intrinsic atomic property, but rather results from the coupling of the atom to the vacuum modes of the electromagnetic field. As such, it can be modified by tailoring the electromagnetic environment into which the atom can radiate. This was already realized by Purcell, who noted that the spontaneous emission rate can be enhanced if the atom placed inside a cavity is resonant with one of the cavity is resonant with one of the cavity modes, and by Kleppner, who discussed the opposite case of inhibited spontaneous emission. It has also been recognized that spontaneous emission need not be an irreversible process. Indeed, a system consisting of a single atom coupled to a single mode of the electromagnetic field undergoes a periodic exchange of excitation between the atom and the field. This periodic exchange remains dominant as long as the strength of the coupling between the atom and a cavity mode is itself dominant. 23 refs., 6 figs.