A Dynamical Model of Harmonic Generation in Centrosymmetric Semiconductors

We study second and third harmonic generation in centrosymmetric semiconductors at visible and UV wavelengths in bulk and cavity environments. Second harmonic generation is due to a combination of symmetry breaking, the magnetic portion of the Lorentz force, and quadrupolar contributions that impart peculiar features to the angular dependence of the generated signals, in analogy to what occurs in metals. The material is assumed to have a non-zero, third order nonlinearity that gives rise to most of the third harmonic signal. Using the parameters of bulk Silicon we predict that cavity environments can significantly modify second harmonic generation (390nm) with dramatic improvements for third harmonic generation (266nm). This occurs despite the fact that the harmonics may be tuned to a wavelength range where the dielectric function of the material is negative: a phase locking mechanism binds the pump to the generated signals and inhibits their absorption. These results point the way to novel uses and flexibility of materials like Silicon as nonlinear media in the visible and UV ranges

Transmission function properties for multi-layered structures: Application to super-resolution

We discuss the properties of the transmission function in the k-space for a generic multi-layered structure. In particular we analytically demonstrate that a transmission greater than one in the evanescent spectrum (amplification of the evanescent modes) can be directly linked to the guided modes supported by the structure. Moreover we show that the slope of the phase of the transmission function in the propagating spectrum is inversely proportional to the ability of the structure to compensate the diffraction of the propagating modes. We apply these findings to discuss several examples where super-resolution is achieved thanks to the simultaneous availability of the amplification of the evanescent modes and the diffraction compensation of the propagating modes

Optical Vortices during a Super-Resolution Process in a Metamaterial

We show that a super-resolution process with 100% visibility is characterized by the formation of a point of phase singularity in free space outside the lens in the form of a saddle with topological charge equal to -1. The saddle point is connected to two vortices at the end boundary of the lens, and the two vortices are in turn connected to another saddle point inside the lens. The structure saddle-vortices-saddle is topologically stable. The formation of the saddle point in free space explains also the negative flux of energy present in a certain region of space outside the lens. The circulation strength of the power flow can be controlled by varying the position of the object plane with respect to the lens