We performed a numerical investigation of the dynamics of the Bloch equations, extended for dense media (media having many atoms within a cubic resonance wavelength), for optical pulses whose duration is much less than an induced-dipole dephasing time. We find a signature of near dipole-dipole interaction which may provide a useful method for validating the first-principles model, for measuring the strength of the interaction, and for coherent pumping. Further, we demonstrate a new and unique optical switching mechanism which may lead to the development of important devices.PACS numbers: 42.65.Pc, 42.50.Hz, 42.79.Ta In dense media, of densities such that there are many atoms within a cubic atomic resonance wavelength, induced near dipole-dipole (NDD) interactions can cause a dynamic frequency chirp in the system [l-4]. In the steady-state limit, NDD interactions may cause bistability that is intrinsic to the material and does not require an external feedback mechanism [I]. Intrinsic optical bistability (IOB) can have important device applications in optical computing and optical data processing [5]. Other effects of NDD interactions which have been analyzed include conditions for self-induced transparency (SIT) in isotropic, homogeneously broadened media [2], and selfphase modulation in SIT [3], as well as linear and nonlinear shifts in the absorption spectrum [4]. Both linear and nonlinear spectral effects due to NDD interactions have recently been observed in reAectivity spectrum measurements using a sapphire window to form an interface with a dense potassium vapor [6].In this Letter, we consider optical pulses, whose temporal duration is assumed to be much less than an induced-dipole dephasing time, incident upon a thin film of homogeneously broadened material composed of twolevel atoms with NDD interactions.In this limit, the induced-dipole dephasing time and the population-decay time can be neglected. We consider the film thickness in the propagation direction to be much smaller than the atomic resonance wavelength so that propagation effects may be neglected.Under these conditions, we find that the inversion w that remains after a pulse has passed has a nearly stepfunction response to the peak value of the time-varying field, largely independent of the pulse shape and pulse area. A peak Rabi frequency, Ao=pEo/h, is associated with the peak amplitude Fo of the field envelope, where p is the matrix element of the transition dipole moment.The system, initially in the ground state, w = -I, is always returned to the ground state when the peak Rabi frequency is less than the strength of the NDD interaction~. However, the final state of the inversion is the fully excited state, w =1, when Qo is nearly equal to e. This suggests that the strength of the NDD interaction can be measured by increasing the field amplitude and interrogating the system after the pulse has passed, in a pulseprobe scenario, to determine whether the system is in the ground or excited state. Furthermore, the nearly stepfunction response of...

The local-field renormalization of the spontaneous emission rate in a dielectric is explicitly obtained from a fully microscopic quantum-electrodynamical, many-body derivation of Langevin-Bloch operator equations for two-level atoms embedded in an absorptive and dispersive, linear dielectric host. We find that the dielectric local-field enhancement of the spontaneous emission rate is smaller than indicated by previous studies.In the formative period of nonlinear optics, Bloembergen taught us that the nonlinear optical effects of a dilute collection of atoms that are embedded in a dielectric host are enhanced by local-field effects [1]. Now, in the era of quantum optics, researchers are again looking at the interaction of dielectric materials, the radiation field, and resonant atoms. Central to these investigations are efforts to quantize the electromagnetic field in dielectrics. One widely used technique is to quantize the macroscopic Maxwell equations in which the classical constitutive relations have been assumed [2][3][4][5][6][7]. In the microscopic approach, a generalized Hopfield transformation, based on Fano diagonalization, is used to obtain the coupled polariton modes of the coupled field-oscillator system [8][9][10]. These quantization methods are well-established for dielectrics with negligible absorption and techniques to deal with the special requirements of quantizing the electromagnetic field in absorbing dielectrics are beginning to emerge [5][6][7]9,10].Since Purcell first predicted the alteration of the emission rate of an excited atom due to an optical cavity [11], it has become well known that the observed spontaneous emission rate of an atom depends on its environment. When the quantized coupled field-dielectric theories are applied to the spontaneous emission of a two-level atom embedded in an absorptionless dielectric, the relationis obtained [3,4,7,8,10]. Here, n is the linear index of refraction and ℓ is the dielectric local-field enhancement factor, Γ 0 is the vacuum spontaneous emission rate, and Γ diel SE is the enhanced spontaneous emission rate in the dielectric. Both the Lorentz virtual-cavity model ℓ = (n 2 + 2)/3 and the Onsanger real-cavity model ℓ = 3n 2 /(2n 2 + 1) have been utilized in various studies of local-field effects on spontaneous emission.One of the key features of these approaches of applying the quantization of fields in dielectrics to spontaneous emission is that the oscillators that comprise the dielectric host are assumed to be unaffected by the presence of the embedded atom. The dielectric medium, as well as the field, is treated as a local condition at the site of a resonant atom such that the atom interacts with an all-pervasive, nonlocal, quantized effective field, the vacuum polariton modes, rather than the local vacuum radiation field modes and the oscillators. Because the near-dipole-dipole interaction is the fundamental interaction underlying the Lorentz local field, a many-body approach that explicitly deals with the vacuum radiation field modes and the...

The macroscopic quantum theory of the electromagnetic field in a dielectric medium interacting with a dense collection of embedded two-level atoms fails to reproduce a result that is obtained from an application of the classical Lorentz local-field condition. Specifically, macroscopic quantum electrodynamics predicts that the Lorentz redshift of the resonance frequency of the atoms will be enhanced by a factor of the refractive index n of the host medium. However, an enhancement factor of (n 2 + 2)/3 is derived using the Bloembergen procedure in which the classical Lorentz local-field condition is applied to the optical Bloch equations. Both derivations are short and uncomplicated and are based on well-established physical theories, yet lead to contradictory results. Microscopic quantum electrodynamics confirms the classical local-field-based results. Then the application of macroscopic quantum electrodynamic theory to embedded atoms is proved false by a specific example in which both the correspondence principle and microscopic theory of quantum electrodynamics are violated.

The total momentum of a thermodynamically closed system is unique, as is the total energy. Nevertheless, there is continuing confusion concerning the correct form of the momentum and the energy-momentum tensor for an electromagnetic field interacting with a linear dielectric medium. Rather than construct a total momentum from the Abraham momentum or the Minkowski momentum, we define a thermodynamically closed system consisting of a propagating electromagnetic field and a negligibly reflecting dielectric and we identify the Gordon momentum as the conserved total momentum by the fact that it is invariant in time. In the formalism of classical continuum electrodynamics, the Gordon momentum is therefore the unique representation of the total momentum in terms of the macroscopic electromagnetic fields and the macroscopic refractive index that characterizes the material. We also construct continuity equations for the energy and the Gordon momentum, noting that a time variable transformation is necessary to write the continuity equations in terms of the densities of conserved quantities. Finally, we use the continuity equations and the time-coordinate transformation to construct an array that has the properties of a traceless, symmetric energy-momentum tensor.

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In a continuum setting, the energy-momentum tensor embodies the relations between conservation of energy, conservation of linear momentum, and conservation of angular momentum. The welldefined total energy and the well-defined total momentum in a thermodynamically closed system with complete equations of motion are used to construct the total energy-momentum tensor for a stationary simple linear material with both magnetic and dielectric properties illuminated by a quasimonochromatic pulse of light through a gradient-index antireflection coating. The perplexing issues surrounding the Abraham and Minkowski momentums are bypassed by working entirely with conservation principles, the total energy, and the total momentum. We derive electromagnetic continuity equations and equations of motion for the macroscopic fields based on the material fourdivergence of the traceless, symmetric total energy-momentum tensor. We identify contradictions between the macroscopic Maxwell equations and the continuum form of the conservation principles. We resolve the contradictions, which are the actual fundamental issues underlying the AbrahamMinkowski controversy, by constructing a unified version of continuum electrodynamics that is based on establishing consistency between the three-dimensional Maxwell equations for macroscopic fields, the electromagnetic continuity equations, the four-divergence of the total energy-momentum tensor, and a four-dimensional tensor formulation of electrodynamics for macroscopic fields in a simple linear medium.

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In a previous work, Optics Communications 284 (2011) 2460-2465, we considered a dielectric medium with an anti-reflection coating and a spatially uniform index of refraction illuminated at normal incidence by a quasimonochromatic field. Using the continuity equations for the electromagnetic energy density and the Gordon momentum density, we constructed a traceless, symmetric energy-momentum tensor for the closed system. In this work, we relax the condition of a uniform index of refraction and consider a dielectric medium with a spatially varying index of refraction that is independent of time, which essentially represents a mechanically rigid dielectric medium due to external constraints. Using continuity equations for energy density and for Gordon momentum density, we construct a symmetric energy-momentum matrix, whose four-divergence is equal to a generalized Helmholtz force density four-vector. Assuming that the energy-momentum matrix has tensor transformation properties under a symmetry group of space-time coordinate transformations, we derive the global conservation laws for the total energy, momentum, and angular momentum.