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

Second and Third Harmonic Generation in Metal-Based Nanostructures

We present a new theoretical approach to the study of second and third harmonic generation from metallic nanostructures and nanocavities filled with a nonlinear material, in the ultrashort pulse regime. We model the metal as a two-component medium, using the hydrodynamic model to describe free electrons, and Lorentz oscillators to account for core electron contributions to both the linear dielectric constant and to harmonic generation. The active nonlinear medium that may fill a metallic nanocavity, or be positioned between metallic layers in a stack, is also modeled using Lorentz oscillators and surface phenomena due to symmetry breaking are taken into account. We study the effects of incident TE- and TM-polarized fields and show that a simple re-examination of the basic equations reveals additional exploitable dynamical features of nonlinear frequency conversion in plasmonic nanostructures.Comment: 33 pages, including 11 figures and 74 references; corrected affiliations and some typo

Gap solitons in a nonlinear quadratic negative index cavity

By integrating the full Maxwell's equations we predict the existence of gap solitons in a quadratic, Fabry-Perot negative index cavity. An intense, fundamental pump pulse shifts the band structure that forms when magnetic and electric plasma frequencies are different so that a weak, second harmonic pulse initially tuned inside the gap is almost entirely transmitted. The process is due cascading, which occurs far from phase matching conditions, and causes pulse compression. A nonlinear polarization spawns a dark soliton, while a nonlinear magnetization produces a bright soliton

Extraordinary Transmission in the UV Range from Sub-wavelength Slits on Semiconductors

In this paper we describe a way to achieve the extraordinary transmission regime from sub-wavelength slits carved on semiconductor substrates. Unlike metals, the dielectric permittivity of typical semiconductors like GaAs or GaP is negative beginning in the extreme UV range (lambda <= 270nm). We show that the metal-like response of bulk semiconductors exhibits surface plasmon waves that lead to extraordinary transmission in the UV and soft X-ray ranges. The importance of realistic material response versus perfect conductors is also discussed. These findings may be important in high resolution photo-lithography, near field optical devices and ultra high density optical storage

Reevaluation of radiation reaction and consequences for light-matter interactions at the nanoscale

In the context of electromagnetism and nonlinear optical interactions damping is generally introduced as a phenomenological, viscous term that dissipates energy, proportional to the temporal derivative of the polarization. Here, we follow the radiation reaction method presented in [G. W. Ford and R. F. O'Connell, Phys. Lett. A, 157, 217 (1991)], which applies to non-relativistic electrons of finite size, to introduce an explicit reaction force in the Newtonian equation of motion, and derive a hydrodynamic equation that offers new insight on the influence of damping in generic plasmas, metal-based and/or dielectric structures. In these settings, we find new damping-dependent linear and nonlinear source terms that suggest the damping coefficient is proportional to the local charge density, and nonlocal contributions that stem from the spatial derivative of the magnetic field and discuss the conditions that could modify both linear and nonlinear electromagnetic responses.Comment: 11 pages, 1 figure, 19 reference

Reevaluation of radiation reaction and consequences for light-matter interactions at the nanoscale

In the context of electromagnetism and nonlinear optical interactions damping is generally introduced as a phenomenological, viscous term that dissipates energy, proportional to the temporal derivative of the polarization. Here, we follow the radiation reaction method presented in [G. W. Ford and R. F. O'Connell, Phys. Lett. A, 157, 217 (1991)], which applies to non-relativistic electrons of finite size, to introduce an explicit reaction force in the Newtonian equation of motion, and derive a hydrodynamic equation that offers new insight on the influence of damping in generic plasmas, metal-based and/or dielectric structures. In these settings, we find new damping-dependent linear and nonlinear source terms that suggest the damping coefficient is proportional to the local charge density, and nonlocal contributions that stem from the spatial derivative of the magnetic field and discuss the conditions that could modify both linear and nonlinear electromagnetic responses.Comment: 11 pages, 1 figure, 19 reference

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