There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

1. Introduction 2. Theoretical foundations 3. Propagation and focusing of optical fields 4. Spatial resolution and position accuracy 5. Nanoscale optical microscopy 6. Near-field optical probes 7. Probe-sample distance control 8. Light emission and optical interaction in nanoscale environments 9. Quantum emitters 10. Dipole emission near planar interfaces 11. Photonic crystals and resonators 12. Surface plasmons 13. Forces in confined fields 14. Fluctuation-induced phenomena 15. Theoretical methods in nano-optics Appendices Index.

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Principles of nano-optics

Bose-Einstein condensation (BEC) has been observed in a dilute gas of sodium atoms. A Bose-Einstein condensate consists of a macroscopic population of the ground state of the system, and is a coherent state of matter. In an ideal gas, this phase transition is purely quantum-statistical. The study of BEC in weakly interacting systems which can be controlled and observed with precision holds the promise of revealing new macroscopic quantum phenomena that can be understood from first principles.

Bose-Einstein condensation in a gas of sodium atoms

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Principles Of Fluorescence Spectroscopy

To say that this is the best book on the quantum theory of fields is no praise, since to my knowledge it is the only book on this subject But it is a very good and most useful book The original was written in German and appeared in 1942 This is a translation with some minor changes A few remarks have been added, concerning meson theory and nuclear forces, also footnotes referring to modern work in this field, and finally an appendix on the symmetrization of the energy momentum tensor according to Belinfante Quantum Theory of Fields Prof Gregor Wentzel Translated from the German by Charlotte Houtermans and J M Jauch Pp ix + 224, (New York and London: Interscience Publishers, Inc, 1949) 36s

Quantum Theory of Fields

VIII. IX. Introduction Quantum Uncertainty and Probability Considerations A. Energy-Time Uncertainty and Synergistic Ab korption 1. Cooperative Absorption Mechanism 2. Distributive Absorption Mechanism B. Probability Considerations Selection Rules Classification of Synergistic Two-Photon Processet, A. Single-Frequency Excitation B. Two-Frequency Excitation Quantum Electrodynamics A. Hamiltonian Representation B. Time-Dependent Perturbation Theory C. Tensor Formulation Rate Equations for Rigidly Oriented Systems A. Single-Frequency Cooperative Two-Photon Absorption B. Single-Frequency Distributive Two-Photon Absorption C. Two-Frequency Cooperative Two-Photon Absorption D. Two-Frequency Distributive Two-Photon Absorption Rate Equations for Fluid Media A. Single-Frequency Cooperative Two-Photon P bsorption B. Single-Frequency Distributive Two-Photon Absorption C. Two-Frequency Cooperative Two-Photon A t sorption D. Two-Frequency Distributive Two-Photon Absorption Range-Dependence Polarization Dependence A. Single-Beam Polarization Parameters

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Synergistic Effects in Two-Photon Absorption: the Quantum Electrodynamics of Bimolecular Mean-Frequency Absorption

We propose a scheme for a viable and highly flexible all-optical atomic cooling and trapping using twisted light. In particular, we explain how one-dimensional twisted optical molasses should lead to a microscale atomic ring or a picoampere ionic current. Two-dimensional and three-dimensional molasses lead, respectively, to the creation of atom or ion loops and discrete atom clusters positioned at the eight corners of a microcube. These features at the microscale should find applications in physics and in quantum information processing using optically trapped atoms and ions.

Generation of microscale current loops, atom rings, and cubic clusters using twisted optical molasses

The spatial variation in phase and the propagating wave-front of plane wave electromagnetic radiation are widely familiar text-book territory. In contrast, the developing amplitude and phase of radiation emitted by a dipole or multipole source generally receive less attention, despite the prevalence of these systems. There is additional complexity in such cases where, in consequence of retardation, the character and features significantly and progressively change as radiation propagates onwards, from the near-field and out towards the wave-zone. Readily developed analytical representations of the electric field, cast as a function of distance from the source, provide illuminating insights into the most prominent and distinctive properties of radiant electromagnetic emission. Graphical implementations and animations of the results prove particularly instructive in revealing the spatial form and temporal evolution of the emergent electromagnetic fields.

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Identifying the development in phase and amplitude of dipole and multipole radiation

In the analysis of molecular structure and local order in heterogeneous samples, multiphoton excitation of fluorescence affords chemically specific information and high-resolution imaging. This report presents the results of an investigation that secures a detailed theoretical representation of the fluorescence polarization produced by one-, two-, and three-photon excitations, with orientational averaging procedures being deployed to deliver the fully disordered limits. The equations determining multiphoton fluorescence response prove to be expressible in a relatively simple, generic form, and graphs exhibit the functional form of the multiphoton fluorescence polarization. Amongst other features, the results lead to the identification of a condition under which the fluorescence produced through the concerted absorption of any number of photons becomes completely unpolarized. It is also shown that the angular variation of fluorescence intensities is reliable indicator of orientational disorder.

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A molecular theory for two-photon and three-photon fluorescence polarization

In the circular differential Raman scattering observed in biological and other large polyfunctional molecules, many spectral features may be attributed to conferred chirality, in the following sense. Although a given vibrational transition may occur within a group in an intrinsically achiral local environment, it is coupling with another achiral but dissymmetrically placed group that generates the chiral response. Where two groups so coupled are chemically dissimilar, the effect originates in interference between one- and two-centre scattering mechanisms. The one-centre mechanism entails vibrational transition by a group as it undergoes conventional Raman scattering. The two-centre mechanism involves mediation of the chiral influence of a second group on this transition by Forster-type radiationless energy transfer. Where quantum-mechanical interference generates a differential Raman signal, the circular intensity differential depends on the inverse square of the distance between the groups so coupled. This distance dependence may be understood as originating from a combination of two factors. One is the linear distance dependence characterising Raman optical activity due to direct interference between transitions at distinct sites, which arises in the case of chemically identical groups. The other is the inverse cubic distance dependence associated with the probability amplitude for Forster energy migration. The Raman optical activity of any group with no chemical equivalents in its vicinity should thus be interpreted as resulting from a sum of inverse-square couplings with other chromophores. The two-group model for Raman optical activity is critically assessed, possible ways to improve upon the model are considered, and the result for the differential scattering intensity is recast in a new form that is more general and also more consise than has hitherto been presented.

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David L. Andrews

Papers

Synergistic Effects in Two-Photon Absorption: the Quantum Electrodynamics of Bimolecular Mean-Frequency Absorption

Generation of microscale current loops, atom rings, and cubic clusters using twisted optical molasses

Identifying the development in phase and amplitude of dipole and multipole radiation

A molecular theory for two-photon and three-photon fluorescence polarization

Two-group Raman optical activity revisited