The problem of finding a semiclassical spectrum of an Andreev billiard (ballistic chaotic cavity coupled to superconductor by an N-mode construction) is considered. We identify the time T between Andreev reflections as a classical adiabatic invariant. Quantization of the adiabatically invariant torus in phase space gives a discrete set of periods Tn, which in turn generate a ladder of excited states. The largest quantized period is given be the Ehrenfest time, proportional to the logarithm of the Plank constant. The wave functions of Andreev levels fill the cavity in a highly nonuniform "squeezed" way, which has no counterpart in normal state chaotic or regular billiards. The theory is applied to the problems of calculating a hard gap in the semiclassical spectrum and crossover between semiclassical and random matrix description of Andreev billiards. Similar ideas may be used for the description of classical to quantum crossover in shot noise in a ballistic quantum dot.

Bell's theorem is a statement that quantum mechanics produces special (entangled) states that have correlations that no local, realistic theory can possible reproduce. Both experimental and theoretical works on Bell's theorem proceed from the idea that the two entangled states are produced by the decay of a single central particle into two particles. But there is a new way to produce entangled states that originates from two independent pairs of particles, and which is exceedingly hard to get a handle on classically. I will discuss the background of the subject, and the new information provided by these new experiments

The optical response of the nanostructured metallic composite could be dramatically different from the response of bulk metal due to resonant excitation of plasmon polariton modes. The spectral characteristics of these modes are strongly affected by the geometry of composite.

In random metal-dielectric percolation films plasmon modes are localized in subwavelength areas with spatial dimensions about 100 nm, so-called "hot spots". Resonant excitation of such localized modes leads to huge enhancements of local linear and nonlinear fields. Due to random structure of the percolation composite, such field enhancement exists in the broad spectrum range, from near UV to mid-infrared, opening a way to the important applications in spectroscopy, biophysics and related areas.

Excitation of polariton modes in composite of metal nanowire pairs, leads to the possibility of construction of left-handed media in the optical and near IF frequency range. One of the most promising applications is the construction of "perfect" lens with subwavelength resolution in the far field.

Dielectric cavities can support long-lived resonant states of the electromagnetic field. These resonances correspond to ray trajectories, which are trapped inside the cavity by internal reflection, as e.g. in "whispering gallery" resonances of microspheres and microcylinders. When such cavities are deformed from their symmetric shapes, the dynamics of the corresponding ray trajectories undergoes a transition from integrability to chaos. This transition has a dramatic effect on the properties of the high-Q resonances.

Microcylinder lasers based on such asymmetric resonators, show strongly directional light emission and high power output (with several orders of magnitude enhancement compared to standard microdisc lasers). Measurements of the optical spectra in these novel semiconductor devices show direct signatures of the classical Kolmogorov-Arnold-Moser transition from integrability to chaos, chaos-assisted tunneling, dynamical Anderson localization and a laser action on "scar"-modes.