Henk F. Arnoldus

Conditions for sub-poissonian photon statistics and squeezed states in resonance fluorescence

We study the conditions for sub-poissonian photon statistics and squeezed states in the field of resonance fluorescence of a two-state atom. These conditions as a function of the detuning from resonance, the linewidth and the Rabi frequency have some overlap, but they are largely complementary. Super-poissonian statistics arise for small linewidths and large detunings, irrespective of the Rabi frequency. Squeezed states require small linewidths and either low or moderate Rabi frequencies, or large detunings from resonance.

Spatial separation of the traveling and evanescent parts of dipole radiation.

Electric dipole radiation consists of traveling and evanescent plane waves. When radiation is detected in the far field, only the traveling waves will contribute to the intensity distribution, as the evanescent waves decay exponentially. We propose a method to spatially separate the traveling and evanescent waves before detection. It is shown that when the radiation passes through an interface, evanescent waves can be converted into traveling waves and can subsequently be observed in the far field. Let the radiation be observed under angle theta(t) with the normal. Then there exists an angle theta(ac) such that for 0 < or = theta(t) < theta(ac) all intensity originates in traveling waves, whereas for theta(ac) < theta(t) < pi/2 only evanescent waves contribute. It is shown that with this technique and under the appropriate conditions almost all far-field power can be provided by evanescent waves.

Energy flow lines for the radiation emitted by a dipole

An oscillating electric dipole emits radiation, and the flow of energy in the electromagnetic field is represented by the field lines of the Poynting vector. In the most general state of oscillation the dipole moment vector traces out an ellipse. We have evaluated analytically the field lines of the Poynting vector for the emitted light, and it appears that each field line lies on a cone, which has its axis perpendicular to the plane of the ellipse. The field lines exhibit a vortex structure near the location of the dipole, and they approach a straight line in the far field. It is shown that due to the spiraling of the field lines near the source, the asymptotic limit of a field line is displaced as compared to a ray which would come directly out of the source. Both the spatial extent of the vortex in the near field and the magnitude of the displacement of the image in the far field are of nanoscale dimension.

Subwavelength displacement of the far-field image of a radiating dipole

The field lines of the Poynting vector for light emitted by a dipole with a rotating dipole moment show a vortex pattern near the location of the dipole. In the far field, each field line approaches a straight line, but this line does not appear to come exactly from the location of the dipole. As a result, the image of the dipole in its plane of rotation seems displaced. Secondly, the image in the far field is displaced as compared with the image of a source for which the field lines run radially outward. It turns out that both image displacements are the same. The displacements are of subwavelength scale, and they depend on the angles of observation. The maximum displacement occurs for observation in the plane of rotation and equals lambda/pi, where lambda is the wavelength of the light.

Traveling and evanescent parts of the electromagnetic Green’s tensor

The angular spectrum representation of the electromagnetic Greens tensor has a part that is a superposition of exponentially decaying waves in the +z and -z directions (evanescent part) and a part that is a superposition of traveling waves, both of which are defined by integral representations. We have derived an asymptotic expansion for the z dependence of the evanescent part of the Greens tensor and obtained a closed-form solution in terms of the Lommel functions, which holds in all space. We have shown that the traveling part can be extracted from the Greens tensor by means of a filter operation on the tensor, without regard to the angular spectrum integral representation of this part. We also show that the so-called self-field part of the tensor is properly included in the integral representation, and we were able to identify this part explicitly.

Representation of the near-field, middle-field, and far-field electromagnetic Green’s functions in reciprocal space

The electromagnetic field, generated by a source, has four typical components: the far field, the middle field, the near field, and the self-field. This decomposition is studied with the help of the dyadic Green’s function for the electric field and its representation in reciprocal (k) space. The representations in k space involve three universal functions, which we call the T(q) functions. Various representations of these functions are presented, and an interesting sum rule is derived. It is shown that the magnetic field can be split in a similar way, leading to a middle field and a far field only.

Travelling and evanescent parts of the optical near field

Abstract The optical near field of a localized source has been studied by means of the angular spectrum representation of the electromagnetic Greens tensor. This Greens tensor can be expressed in terms of four auxiliary functions, which depend on the field point through the dimensionless radial distance q to the source, or origin of coordinates, and the polar angle ρ with the z axis. Each function separates into a part containing travelling (radiative) waves and a part which is a superposition of evanescent (decaying) waves. We have derived series expansions in q of the four functions, both for the travelling and for the evanescent parts. It is shown that the travelling waves are finite at the origin of coordinates, and that all singular behaviour of the radiation field is governed by the evanescent waves. It is illustrated numerically that the series expansions are applicable up to about five wavelengths from the origin. In order to extend the range to also cover larger values of q, we have derived series expansions of the auxiliary functions which converge rapidly near the x-y plane, and a full asymptotic expansion with the z coordinate as the large variable. Finally, from the properties of the Taylor coefficients we have derived simple new integral representations for the auxiliary functions.

Density matrix for photons in a cavity

The transient behavior of the density operator for radiation in a single-mode cavity at a finite temperature is considered. Any initial state will evolve toward thermal equilibrium because of the interaction with the mirrors. This steady state is determined uniquely by the temperature, but the transient state depends on the initial conditions. The equation of motion for the matrix elements of the density operator is solved analytically, given an arbitrary initial state. The factorial moments, the generating function, and the time-dependent spectral distribution are also obtained. The results yield known expressions in the appropriate limits.

Nanoscale shift of the intensity distribution of dipole radiation

The energy flow lines (field lines of the Poynting vector) for radiation emitted by a dipole are in general curves, rather than straight lines. For a linear dipole the field lines are straight, but when the dipole moment of a source rotates, the field lines wind numerous times around an axis, which is perpendicular to the plane of rotation, before asymptotically approaching a straight line. We consider an elliptical dipole moment, representing the most general state of oscillation, and this includes the linear dipole as a special case. Due to the spiraling near the source, for the case of a rotating dipole moment, the field lines in the far field are displaced with respect to the outward radial direction, and this leads to a shift of the intensity distribution of the radiation in the far field. This shift is shown to be independent of the distance to the source and, although of nanoscale dimension, should be experimentally observable.

Photon Statistics of Fluorescence Radiation

We study the general properties of the photon statistics of fluorescence radiation, emitted by a two-level atom in a strong laser field and a perturber bath. We investigate the deviation of the factorial moments from a Poisson distribution, and we show that for long counting times the lowest-order correction can be expressed entirely by the quantity Q, which represents the deviation of the variance from the average. We introduce and evaluate the quantities gn(t), which serve as a measure for the deviation of the higher-order statistics from Poissonian statistics. Subsequently we obtain explicit expressions for the average waiting time for the appearance of the n th photon, after an arbitrary initialization of the counting process. It turns out that the average time delay is again determined by Q. Hence this parameter can be measured in a photon-counting experiment, which involves only the observation of a single photon, rather than an (in principle) infinite number of photons.