Ole Keller

Configurational Resonances in Optical Near-Field Microscopy: A Rigorous Point-Dipole Approach

Abstract A theoretical analysis of the framework for near-field microscopy based on a microscopic description of the interaction between the dielectric probe and the surface is presented. The probe tip is assumed to be a point-like sphere and the surface (selvedge) is represented by point-like spheres placed on a two-dimensional lattice. The bulk is treated as a homogeneous continuum. Using a Greens function formalism we have established a set of self-consistent algebraic equations to describe the local field at the sites of the probe tip and the selvedge. All contributions including bulk reflection and many-body interactions have been taken into account. By means of a point-dipole approach we have for N dipoles solved the 3 N × 3 N linear algebraic equations exactly. The results have been compared with approximate solutions obtained by a Born series expansion. We have found that the approximate solutions are very different from the exact solution in the case of strong interaction. The approximate solutions tend to infinity only when the tip-surface distance decreases to zero, and the results depend strongly on the number of Born iterations performed. However, for the exact solution it is shown that there are regions close to the surface where an enhanced field can be induced by the probe, while, when the tip-surface distance decreases to zero the self-consistent field tends to zero. Thus, we have found resonance interactions between the probe tip and the surface. These resonances are referred to as configurational ones, since, for any given dipole polarizabilities, the system can be adjusted to resonance by varying the distances between the dipoles. The resonance conditions for some simple systems are presented in an explicit form. It is demonstrated that the resonance coupling of the field component perpendicular to the surface occurs at a bigger distance of the tip dipole from the surface than that of the parallel components. The relation between the polarizability of the probe tip and the resonance positions is considered. It is shown that in the absence of retardation and damping the resolution of the system can be as close to infinity as the tip-surface distance is close to the resonance value. The self-consistent field at the site of the probe is calculated for different distances between the tip and the surface and as a function of the position of the tip along the surface.

Local fields in the electrodynamics of mesoscopic media

Abstract To understand the electrodynamics of mesoscopic media it is in general necessary to take into account local-field effects. This article presents a review of the role played by local fields in the high-frequency electrodynamics of systems exhibiting essential quantum confinement of the electron motion. In Part A, the fundamental local-field theory is described. By combining an electromagnetic propagator formalism with a microscopic linear and nonlocal response theory the basic loop equation for the local field is established and some of its implications studied. Various kinds of local-field calculations are presented and the underlying physical interpretations discussed. In Part B, the basic theory is used to study the linear local-field electrodynamics of a few, but representative and varied, mesoscopic systems. Special emphasis is devoted to investigations of the local-field phenomena in quantum wells and small particles (quantum dots), and to studies of optical near-field electrodynamics and surface dressing of charged wave packets in motion. In Part C, important features of the nonlinear local-field electrodynamics of mesoscopic media are described on the basis of selected examples. Thus, a description of optical second-harmonic generation in quantum wells is followed by a discussion of the photon-drag effect in one- and two-level quantum wells, and in mesoscopic metallic and semiconducting rings. Finally, a local-field study of the optical phase conjugation of the field radiated by a mesoscopic particle is undertaken, and a new route leading to confinement of electromagnetic fields into the so-called quantum dots of light is presented.

External-reflection near-field optical microscope with cross-polarized detection

An external-reflection scanning near-field optical microscope with the detected light polarized perpendicular to the polarization of the light coupled into the fiber is presented. When various metallic gratings are scanned, it is shown that the lateral and the depth resolutions of this microscope are better than 100 and 10 nm, respectively.

Attached and Radiated Electromagnetic Fields of an Electric Point Dipole

The standard dyadic Green function description of the electromagnetic field generated by an electric point dipole is modified (and corrected) so that a rigorous classical theory for the attached and radiated parts of the near field appears. The present propagator formalism follows from analysis of the transverse and longitudinal dipole electrodynamics. Elimination of both the transverse and the longitudinal self-fields leads to a description of the radiated dipole field that enables one to obtain the associated energy flux in the near- and mid-field zones also and that is correctly retarded (with the vacuum speed of light) everywhere in space. The related retarded transverse propagator exists in the time (space) domain, whereas the standard propagator exists only in the frequency (space) domain. As a forerunner to an analysis of the Weyl expansions for the standard, longitudinal self-field and retarded transverse propagators, the plane-wave mode expansions of these propagators are investigated, and contour integrations are specified in such a manner that the rigorous Green function description is regained. It is found that, in order for the retarded transverse propagator description to be consistent in the near-field zone, the Weyl expansion for this propagator has to contain evanescent components not only for wave numbers larger than the vacuum wave number but in the entire angular spectrum. The present theory may influence our view of optical near-field phenomena and (classical) photon tunneling because in both of these fields a proper identification of attached and radiated fields seems needed.

Phase conjugation of an optical near field

Using degenerate four-wave mixing in an Fe:LiNbO(3) 0.04-wt. % crystal and an external-reflection near-field optical microscope, we have achieved phase conjugation of light emitted by a fiber tip. We observe that the phase-conjugated light at a wavelength of 633 nm can reach a power of ~0.1 nW and produce a 180-nm-wide spot image in the near-field microscope. This is the first direct demonstration, to our knowledge, of the phase conjugation of near-field components of optical fields.

Control of the tip–surface distance in near-field optical microscopy

An experimental technique that makes use of the intensity of the interference pattern formed by light that propagates directly from the single-mode fiber tip and light that is reflected by the surface under anoblique angle of incidence is developed to control the tip-surface distance in near-field opticalmicroscopy. It is shown that by using another fiber as a detector with a polished edge placed at the surface near the fiber tip one can determine the tip-surface separation with an accuracy better than 15 nm at distances less than 1 µm. The technique proposed is used to investigate the influence of the shape of the tip in near-field measurements.

Correlation between optical and topographical images from an external reflection near-field microscope with shear force feedback

An external reflection scanning near-field optical microscope with shear force regulation of the tip-surface distance is described. Near-field optical and shear force topographical images are compared for various samples. It is shown that the most important correlative relationships between these images can be deduced from symmetry considerations. The possibility of extracting additional information from the optical images is demonstrated on images of human blood cells.

Numerical study of configurational resonances in near-field optical microscopy with a mesoscopic metallic probe

In Scanning Near-field Optical Microscopy (SNOM), the case, where the probe is represented by a small metallic sphere, is studied using a microscopic description of the interaction between the probe tip and the surface. A newly established integral expression for the polarizability of a mesoscopic metallic sphere is employed to investigate the conditions for obtaining configurational resonances and to calculate the resolution of the system near the resonance. Both the frequency of light and the probe size are found to be critical for observing the configurational resonances. The width of the resonance peak and the smallest object for which the resonance condition still can be fulfilled (aspects that are relevant to the resolution) are considered for various probe sizes. The influence of the fine structure in the polarizability of the metallic sphere on the resonance distance between two identical spheres is finally discussed.

Optical diamagnetic polarizability of a mesoscopic metallic sphere: transverse self-field approach

Abstract The optical electric-dipole polarizability of a small (diameter less than 100 A) metallic sphere is calculated in the case where the optical diamagnetic response dominates the particle-field interaction. The smallness of the particle makes it feasible to retain only the transverse self-field part of the electromagnetic propagator where determining the local field inside the particle. By assuming the conduction electrons to be confined in the constant potential of a spherical quantum well with infinitely high barriers the height and halfwidth of the particle frequency resonance peak is calculated for different particle radii, taking Au as an example. Quantum-size effects are clearly displayed and qualitative agreement is obtained with the available experimental data of Kreibig [J. Physique 38 (1977) C2-97].

Quantum-well enhancement of the Goos–Hänchen shift for p-polarized beams in a two-prism configuration

It is predicted that the Goos-Hänchen effect can be resonantly enhanced by placing a metallic quantum well (ultrathin film) at the dielectric-vacuum (air) interface. We study the enhancement of the phenomenon, as it appears in frustrated total internal reflection with p-polarized light, both theoretically and numerically. Starting from boundary conditions for the electromagnetic field, which in a self-consistent manner take into account the quantum-well dynamics, we derive new expressions for the amplitude reflection and transmission coefficients of light, and from these the stationary phase approximation to the Goos-Hänchen shifts is obtained. It is shown that large peaks appear in the Goos-Hänchen shift below the critical angle in reflection, and these are located at the minima for the energy reflection coefficient. Both positive and negative shifts may occur, and the number of peaks depends on the gap width. To determine the accuracy of the simple stationary phase approximation, we carry out a rigorous stationary energy-transport calculation of the Goos-Hänchen shift. Although the overall agreement between the two approaches is good, the stationary phase approach mostly overestimates the peak heights. For a Gaussian incident beam, the resonance displacement of the reflected beam can be as large as the Gaussian width parameter. It is suggested that the possible relation between the Goos-Hänchen effect and the optical tunneling phenomenon in the two-prism configuration should be reinvestigated by depositing quantum wells on the glass-vacuum interfaces to obtain a better spatial photon localization.