A classical analog of the quantum Zeeman effect.

We extend a recent classical mechanical analog of Bohr's atom consisting of a scalar field coupled to a massive point-like particle [P. Jamet and A. Drezet, "A mechanical analog of Bohr's atom based on de Broglie's double-solution approach," Chaos 31, 103120 (2021)] by adding and studying the contribution of a uniform weak magnetic field on their dynamics. In doing so, we are able to recover the splitting of the energy levels of the atom called Zeeman's effect within the constraints of our model and in agreement with the semiclassical theory of Sommerfeld. This result is obtained using Larmor's theorem for both the field and the particle, associating magnetic effects with inertial Coriolis forces in a rotating frame of reference. Our work, based on the old "double solution" theory of de Broglie, shows that a dualistic model involving a particle guided by a scalar field can reproduce the normal Zeeman effect.

A mechanical analog of Bohr's atom based on de Broglie's double-solution approach.

Motivated by recent developments of hydrodynamical quantum mechanical analogs [J. W. M. Bush, Annu. Rev. Fluid Mech. 47, 269-292 (2015)], we provide a relativistic model for a classical particle coupled to a scalar wave field through a holonomic constraint. In the presence of an external Coulomb field, we define a regime where the particle is guided by the wave in a way similar to the old de Broglie phase-wave proposal. Moreover, this dualistic mechanical analog of the quantum theory is reminiscent of the double-solution approach suggested by de Broglie in 1927 and is able to reproduce the Bohr-Sommerfeld semiclassical quantization formula for an electron moving in an atom.

Plasmon scattering from holes: from single hole scattering to Young's experiment.

In this paper, the scattering of surface plasmon polaritons (SPPs) into photons at holes is investigated. A local, electrically excited source of SPPs using a scanning tunneling microscope (STM) produces an outgoing circular plasmon wave on a thick (200 nm) gold film on glass containing holes of 250, 500 and 1000 nm diameter. Fourier plane images of the photons from hole-scattered plasmons show that the larger the hole diameter, the more directional the scattered radiation. These results are confirmed by a model where the hole is considered as a distribution of horizontal dipoles whose relative amplitudes, directions, and phases depend linearly on the local SPP electric field. An SPP-Young's experiment is also performed, where the STM-excited SPP wave is incident on a pair of 1 µm diameter holes in the thick gold film. The visibility of the resulting fringes in the Fourier plane is analyzed to show that the polarization of the electric field is maintained when SPPs scatter into photons. From this SPP-Young's experiment, an upper bound of ≈200 nm for the radius of this STM-excited source of surface plasmon polaritons is determined.

Surface plasmon leakage radiation microscopy at the diffraction limit.

This paper describes the image formation process in optical leakage radiation microscopy of surface plasmon-polaritons with diffraction limited spatial resolution. The comparison of experimentally recorded images with simulations of point-like surface plasmon-polariton emitters allows for an assignment of the observed fringe patterns. A simple formula for the prediction of the fringe periodicity is presented and practically relevant effects of abberations in the imaging system are discussed.

Large variation in the boundary-condition slippage for a rarefied gas flowing between two surfaces.

We study the slippage of a gas along mobile rigid walls in the sphere-plane confined geometry and find that it varies considerably with pressure. The classical no-slip boundary condition valid at ambient pressure changes continuously to an almost perfect slip condition in a primary vacuum. Our study emphasizes the key role played by the mean free path of the gas molecules on the interaction between a confined fluid and solid surfaces and further demonstrates that the macroscopic hydrodynamics approach can be used with confidence even in a primary vacuum environment where it is intuitively expected to fail.

Surface plasmon mediated near-field imaging and optical addressing in nanoscience.

We present an overview of recent progress in "plasmonics". We focus our study on the observation and excitation of surface plasmon polaritons (SPPs) with optical near-field microscopy. We discuss in particular recent applications of photon scanning tunnelling microscope (PSTM) for imaging of SPP propagating in metal and dielectric wave guides. We show how near-field scanning optical microscopy (NSOM) can be used to optically and actively address remote nano objects such as quantum dots. Additionally we compare results obtained with near-field microcopy to those obtained with other optical far-field methods of analysis such as leakage radiation microscopy (LRM).

Near-field microscopy with a scanning nitrogen-vacancy color center in a diamond nanocrystal: A brief review.

We review our recent developments of near-field scanning optical microscopy (NSOM) that uses an active tip made of a single fluorescent nanodiamond (ND) grafted onto the apex of a substrate fiber tip. The ND hosting a limited number of nitrogen-vacancy (NV) color centers, such a tip is a scanning quantum source of light. The method for preparing the ND-based tips and their basic properties are summarized. Then we discuss theoretically the concept of spatial resolution that is achievable in this special NSOM configuration and find it to be only limited by the scan height over the imaged system, in contrast with the standard aperture-tip NSOM whose resolution depends critically on both the scan height and aperture diameter. Finally, we describe a scheme we have introduced recently for high-resolution imaging of nanoplasmonic structures with ND-based tips that is capable of approaching the ultimate resolution anticipated by theory.

Diffraction by a small aperture in conical geometry: application to metal-coated tips used in near-field scanning optical microscopy.

Light diffraction through a subwavelength aperture located at the apex of a metallic screen with conical geometry is investigated theoretically. A method based on a multipole field expansion is developed to solve Maxwell's equations analytically using boundary conditions adapted both for the conical geometry and for the finite conductivity of a real metal. The topological properties of the diffracted field are discussed in detail and compared to those of the field diffracted through a small aperture in a flat screen, i.e., the Bethe problem. The model is applied to coated, conically tapered optical fiber tips that are used in near-field scanning optical microscopy. It is demonstrated that such tips behave over a large portion of space like a simple combination of two effective dipoles located in the apex plane (an electric dipole and a magnetic dipole parallel to the incident fields at the apex) whose exact expressions are determined. However, the large "backward" emission in the P plane--a salient experimental fact that has remained unexplained so far--is recovered in our analysis, which goes beyond the two-dipole approximation.

Viscous cavity damping of a microlever in a simple fluid.

We consider the problem of oscillation damping in air of a thermally actuated microlever as it gradually approaches an infinite wall in parallel geometry. As the gap is decreased from 20 microm down to 400 nm, we observe the increasing damping of the lever Brownian motion in the fluid laminar regime. This manifests itself as a linear decrease in the lever quality factor accompanied by a dramatic softening of its resonance, and eventually leads to the freezing of the CL oscillation. We are able to quantitatively explain this behavior by analytically solving the Navier-Stokes equation with perfect slip boundary conditions. Our findings may have implications for microfluidics and micro- and nanoelectromechanical applications.

Plasmonic crystal demultiplexer and multiports.

We report the realization of two-dimensional optical wavelength demultiplexers and multiports for surface plasmons polaritons (SPPs) based on plasmonic crystals, i.e., photonic crystals for SPPs. These SPP elements are built up of lithographically fabricated gold nanostructures on gold thin films. We show by direct imaging of laterally confined SPP beams in the visible spectral range by leakage radiation microscopy that SPPs of different wavelengths are efficiently rerouted into different directions. In addition we demonstrate the generation of three output SPP beams from one input beam.

Far-field emission of a tapered optical fibre tip: a theoretical analysis.

The far-field transmission pattern of a tapered optical tip with small aperture (radius approximately < 40 nm) is modelled by solving Maxwell's equations in the radiation zone with boundary conditions appropriate to the conical geometry. The model is able to reproduce the large differences between the S and P polarizations observed previously in the emission profile of such a tip [Obermüller and Karrai. Appl. Phys. Lett. (1995) 67, 3408].