The classical limit of the quantum mechanical Kepler problem is derived by using a simple mathematical procedure recently proposed. The method is based both on Bohr’s correspondence principle and the local averages of the quantum probability distribution. We illustrate in a clear fashion the difference between Planck’s limit and Bohr’s correspondence principle. We discuss the confinement effect in macroscopic systems.

In this paper we introduce a simple procedure for computing the macroscopic quantum behaviour of periodic quantum systems in the high energy regime. The macroscopic quantum coherence is ascribed to a one-particle state, not to a condensate of a many-particle system; and we are referring to a system of high energy but with few degrees of freedom. We show that, in the first order of approximation, the quantum probability distributions converge to its classical counterparts in a clear fashion, and that the interference effects are strongly suppressed. The harmonic oscillator provides a testing ground for these ideas and yields excellent results.

Elementary long-range plasmon modes are described assuming an exponential dependence of the refractive index in the neighbourhood of the interface dielectric-metal thin film. The study is performed using coupling mode theory. The interference between two longrange plasmon modes generated that way allows the synthesis of surface sinusoidal plasmon modes, which can be considered as completely coherent generalized plasmon modes. These sinusoidal plasmon modes are used for the synthesis of new partially coherent surface plasmon modes, which are obtained by means of an incoherent superposition of sinusoidal plasmon modes where the period of each one is considered as a random variable. The kinds of surface modes generated have an easily tuneable profile controlled by means of the probability density function associated to the period. We show that partially coherent plasmon modes have the remarkable property to control the length of propagation which is a notable feature respect to the completely coherent surface plasmon mode. The numerical simulation for sinusoidal, Bessel, Gaussian and Dark Hollow plasmon modes are presented.

In this Letter, we describe the optical field associated with transmittances characterized by a slit-shaped curve. The influence of the curvature is that the diffraction field generates focusing regions. The focusing geometry corresponds to the geometry of the transmittance curve, except for scaling, rotations or translations. A relevant point is that the changes in the morphology of the diffraction field are bounded by the focusing regions. Our experimental and computational results are in good agreement with the theoretical predictions.

An alternative method to generate J(0) Bessel beams with controlled spatial partial coherence properties is introduced. Far field diffraction from a discrete number of source points on an annular region is calculated. The average for different diffracted fields produced at several rotation angles is numerically calculated and experimentally detected. Theoretical and experimental results show that for this particular case, the J(0) Bessel beam is a limit when the number of points tends towards infinity and the associated complex degree of coherence is also a function of the number of points.