Peter Walden Milonni

Despite their great variety and range of size, power, wavelength, and temporal, spatial, and polarization characteristics, all lasers involve certain basic concepts, such as gain, threshold, and electromagnetic modes of oscillation 1 ; 2 ; 3 ; 4 ; 5 ; 6 . In addition to these universal characteristics are features, such as Gaussian beam modes, that are important to such a wide class of devices and must be included in any reasonable compendium of important laser concepts and formulas. We have, therefore, included here both generally applicable results as well as some more specific but widely applicable ones.

An expression is derived for the momentum diffusion constant due to photon scattering of a small polarizable particle in blackbody radiation, and is shown to be related to the long-wavelength collisional decoherence rate for such a particle in a thermal environment. We show how this diffusion constant appears in the steady-state photon emission rate of two dipoles induced by blackbody radiation. We consider in addition the Einstein-Hopf drag force on a small polarizable particle moving in a blackbody field, and derive its relativistic form from the Lorentz transformation of forces. We obtain an expression for the rate of change of the field energy density associated with changes in the particles' kinetic energies and relate it to the Kompaneets equation for the case of Compton scattering by thermalized electrons.

An isotropic electromagnetic field in a plasma of thermalized electrons undergoes changes in energy as a result of Compton scattering and an Einstein-Hopf drag force on the electrons, eventually approaching a Bose-Einstein photon distribution at the electron temperature. The rate of change of field energy due to the combined effects of Compton scattering and the drag force is shown to be described by the Kompaneets equation for photon diffusion in frequency space. A similarity is noted between this approach and Einstein's derivation of the Planck spectrum based on the recoil of atoms as they absorb and emit radiation.

A proposed experiment to test whether space is discretized [J. D. Bekenstein, Phys. Rev. D 86, 124040 (2012); Found. Phys. 44, 452 (2014)] is based on the supposed impossibility of an incident photon causing a displacement of a transparent block by less than the Planck length. An analysis of the quantum and thermal jitter of the block shows that it greatly diminishes the possibility that the experiment could reveal Planck-scale signals.

Using two crystals for spontaneous parametric down-conversion in a parallel setup, we observe two-photon interference with high visibility. The high visibility is consistent with complementarity and the absence of which-path information. The observations are explained as the effects of entanglement or equivalently in terms of interfering probability amplitudes and also by the calculation of a second-order field correlation function in the Heisenberg picture. The latter approach brings out explicitly the role of the vacuum fields in the down-conversion at the crystals and in the photon coincidence counting. For comparison, we show that the Hong-Ou-Mandel dip can be explained by the same approach in which the role of the vacuum signal and idler fields, as opposed to entanglement involving vacuum states, is emphasized. We discuss the fundamental limitations of a theory in which these vacuum fields are treated as classical, stochastic fields.

We describe how Fourier signal processing techniques can be generalized to partially coherent fields. Using standard coherence theory, we first show that focusing of a partially coherent beam by a lens modifies its coherence properties. We then consider a 4f imaging system composed of two lenses and discuss how spatial filtering in the Fourier plane allows one to tune the coherence properties of the beam. This, in turn, provides control over the beam's directionality, spectrum, and degree of polarization. (C) 2017 Optical Society of America

We present a Heisenberg-picture approach to the electric dipole interaction of two generally nonidentical atoms, one of which is initially excited, and address the question of whether the dependence of the interaction energy on the interatomic separation r is purely monotonic or is sinusoidally modulated as it falls off with r. We derive energies of both types and associate them with different model assumptions and physical effects. The sinusoidally modulated form is the interaction energy involved in reversible exchange of excitation ("pendulation"). The monotonic form characterizes an energy shift associated with effectively irreversible (Forster) excitation transfer.

Coherence can be induced or stimulated in parametric down-conversion using two or three crystals when, for example, the idler modes of the crystals are aligned. Previous experiments with induced coherence [Phys. Rev. Lett. 114, 053601 (2015)] focused on which-path information and the role of vacuum fields in realizing complementarity via reduced visibility in single-photon interference. Here we describe experiments comparing induced and stimulated coherence. Different single-photon interference experiments were performed by blocking one of the pump beams in a three-crystal setup. Each counted photon is emitted from one of two crystals and which-way information may or not be available, depending on the setup. Distinctly different results are obtained in the induced and stimulated cases, especially when a variable transmission filter is inserted between the crystals. A simplified theoretical model accounts for all the experimental results and is also used to address the question of whether the phases of the signal and idler fields in parametric down-conversion are correlated.