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Recent years have witnessed significant developments in the study of nonlinear properties of various optical materials at the nanoscale. However, in most cases experimental results on harmonic generation from nanostructured materials are reported without the benefit of suitable theoretical models and appropriate comparisons to assess enhancement of conversion efficiencies compared to the intrinsic properties of a given material. Here, we report experimental observations of even and odd optical harmonics generated from a suspended subwavelength silicon film, a dielectric membrane, up to the 7th harmonic tuned deep in the UV range at 210nm, which is the current limit of our detection system, using peak power densities of order 3TW/cm^2. We explain the experimental data with a time domain, hydrodynamic-Maxwell approach broadly applicable to most materials. Our approach accounts simultaneously for surface and magnetic nonlinearities that generate even optical harmonics, as well as linear and nonlinear material dispersions beyond the third order to account for odd optical harmonics, plasma formation, and a phase locking mechanism that makes the generation of high harmonics possible deep into the UV range, where semiconductors like silicon start operating in a metallic regime.

By uncovering novel aspects of second harmonic generation in aluminum we show that there are unusual and remarkable consequences of resonant absorption, namely an unexpectedly critical role that bound electrons play for light-matter interactions across the optical spectrum, suggesting that a different basic approach is required to fully explain the physics of surfaces. We tackle an issue that is never under consideration given the generic hostile conditions to the propagation of light under resonant absorption. Unlike most noble metals, aluminum displays Lorentz-like behavior and interband transitions centered near 810 nm, thus splitting the plasmonic range in an atypical manner and setting its linear and nonlinear optical properties apart. Studies of aluminum nanostructures having complex topologies abound, as do reported inconsistencies in the linear spectral response of surface plasmons and harmonic generation. Our experimental observations of second harmonic generation from aluminum nanolayers show that bound electrons are responsible for a unique signature neither predicted nor observed previously: a hole in the second harmonic spectrum. A hydrodynamic-Maxwell theory explains these findings exceptionally well and becomes the basis for renewed studies of surface physics., Comment: 8 pages, 5 figures

Notwithstanding its long history, the study of nonlinear optics from metal surfaces is still an active field of research. For instance, in view of the presence of absorption questions remain concerning the possibility of significantly enhancing harmonic conversion efficiencies in the visible and UV ranges. While to many it may seem that metals do not easily lend themselves to that purpose, they are nevertheless crucial materials in the development of nanophotonics, and more generally, to electromagnetism at the nanoscale. Here, we report our experimental observations and numerical simulations of second and third harmonic generation from a gold nanograting, which exhibits a plasmonic resonance whose spectral position depends on incident angle. All things being equal, the enhancement of nonlinear optical processes from the UV to the near IR range manifests itself in dramatic manner: second harmonic generation conversion efficiencies increase more than three orders of magnitude compared to a flat gold mirror, while third harmonic generation conversion efficiency increases by nearly four orders of magnitude, both in excellent agreement with predictions. The clear inferences one may draw from our results are that our model describes the dynamics with unprecedented accuracy, and that much remains to be revealed in the development of nonlinear optics of metals at the nanoscale.

The predominant methods currently used to determine nonlinear optical constants like the nonlinear refractive index n2 or chi3 rely mostly on experimental, open and closed z-scan techniques and beam deflection methods. While these methods work well when the linear absorption is relatively small or negligible, the retrieval process is more complicated for a strongly scattering, dispersive or absorbing medium. The study of optics at the nanoscale in the ps or fs regimes demands the development of new theoretical tools experimental approaches, to extract and verify both linear and nonlinear optical dispersions exhibited by matter, especially when material constituents are fashioned into nanostructures of arbitrary shape. We present a practical, combined experimental and theoretical approach based on a hydrodynamic model that uses experimental results of harmonic generation conversion efficiencies to retrieve complex, nonlinear dispersion curves, not necessarily only for third order processes. We provide examples for materials that are of special interest to nanophotonics, silicon, gold, and indium tin oxide, which displays nonlocal effects and a zero-crossing of the real part of the dielectric constant. The results for silicon and gold compare well with analytical predictions based on the nonlinear oscillator model. Based on our assessment of THG conversion efficiencies in silicon, we predict chi3(w) and chi3(3w) are of order 10^(-17)(m/V)^2, in the visible and IR ranges, with respective peaks of 10^(-14) and 10^(-16)(m/V)^2 in the UV range. Similarly, gold's chi3(w) and chi3(3w) are of order 10^(-17) and 10^(-16)(m/V)^2, and predict chi3(w)~10^(-17)(m/V)^2 and chi3(3w)~10^(-18)(m/V)^2 for ITO. These results suggest that judicious exploitation of the nonlinear dispersion of ordinary semiconductors can transform device physics in spectral regions that extend well into the UV range.

Understanding how light interacts at the nanoscale with metals, semiconductors, or ordinary dielectrics is pivotal if one is to properly engineer nano-antennas, filters and, more generally, devices that aim to harness the effects of new physical phenomena that manifest themselves at the nanoscale. We presently report experimental results on second and third harmonic generation from 20nm- and 70nm-thick gold layers, for TE- and TM-polarized incident light pulses. We highlight and discuss for the first time the relative roles bound electrons and an intensity dependent free electron density (hot electrons) play in third harmonic generation. While planar structures are generally the simplest to fabricate, metal layers that are only a few nanometers thick and partially transparent are almost never studied. Yet, transmission offers an additional reference point for comparison, which through relatively simple experimental measurements affords the opportunity to test the accuracy of available theoretical models. Our experimental results are explained well within the context of the microscopic hydrodynamic model that we employ to simulate second and third harmonic conversion efficiencies, and to simultaneously and uniquely predict the nonlinear dispersive properties of a gold nanolayer under pulsed illumination. Using our experimental observations and our model, based solely on the measured third harmonic power conversion efficiencies we predict |chi3|~10^(-18)-10^(-17)(m/V)^2, triggered mostly by hot electrons, without resorting to the implementation of a z-scan set-up.

Using a hydrodynamic approach we examine bulk- and surface-induced second and third harmonic generation from semiconductor nanowire gratings having a resonant nonlinearity in the absorption region. We demonstrate resonant, broadband and highly efficient optical frequency conversion: contrary to conventional wisdom, we show that harmonic generation can take full advantage of resonant nonlinearities in a spectral range where nonlinear optical coefficients are boosted well beyond what is achievable in the transparent, long-wavelength, non-resonant regime. Using femtosecond pulses with approximately 500 MW/cm2 peak power density, we predict third harmonic conversion efficiencies of approximately 1% in a silicon nanowire array, at nearly any desired UV or visible wavelength, including the range of negative dielectric constant. We also predict surface second harmonic conversion efficiencies of order 0.01%, depending on the electronic effective mass, bistable behavior of the signals as a result of a reshaped resonance, and the onset fifth order nonlinear effects. These remarkable findings, arising from the combined effects of nonlinear resonance dispersion, field localization, and phase-locking, could significantly extend the operational spectral bandwidth of silicon photonics, and strongly suggest that neither linear absorption nor skin depth should be motivating factors to exclude either semiconductors or metals from the list of useful or practical nonlinear materials in any spectral range., Comment: 12 pages, 4 figures

Second and third harmonic generation in the opaque region of a GaAs wafer is experimentally observed both in transmission and reflection. These harmonic components can propagate through an opaque material as long as the pump is tuned to a region of transparency or semi-transparency, and correspond to the inhomogeneous solutions of Maxwell's equations with nonlinear polarization sources. We show that measurement of the angular and polarization dependence of the observed harmonic components allows one to infer the different nonlinear mechanisms that trigger these processes, including bulk nonlinearity, magnetic Lorentz and surface contributions. Experimental results are compared with a detailed numerical model that takes into account these different effects., Comment: 13 pages 7 figures

We explore the outcomes of detailed microscopic models by calculating second- and third-harmonic generation from thin film surfaces with discontinuous free-electron densities. These circumstances can occur in structures consisting of a simple metal mirror, or arrangements composed of either different metals or a metal and a free electron system like a conducting oxide. Using a hydrodynamic approach we highlight the case of a gold mirror, and that of a two-layer system containing indium tin oxide (ITO) and gold. We assume the gold mirror surface is characterized by a free-electron cloud of varying density that spills into the vacuum, which as a result of material dispersion exhibits epsilon-near-zero conditions and local field enhancement at the surface. For a bylayer consisting of a thin ITO and gold films, if the wave is incident from the ITO side the electromagnetic field is presented with a free-electron discontinuity at the ITO/gold interface, and wavelength-dependent, epsilon-near-zero conditions that enhance local fields and conversion efficiencies, and determine the surface's emission properties. We evaluate the relative significance of additional nonlinear sources that arise when a free-electron discontinuity is present, and show that harmonic generation can be sensitive to the density of the screening free-electron cloud, and not its thickness. Our findings also suggest the possibility to control surface harmonic generation through surface charge engineering., Comment: 19 pages, 6 figures, 49 references

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 references

We numerically and experimentally investigate graphene-based optical absorbers that exploit guided mode resonances (GMRs) achieving perfect absorption over a bandwidth of few nanometers (over the visible and near-infrared ranges) with a 40-fold increase of the monolayer graphene absorption. We analyze the influence of the geometrical parameters on the absorption rate and the angular response for oblique incidence. Finally, we experimentally verify the theoretical predictions in a one-dimensional, dielectric grating and placing it near either a metallic or a dielectric mirror.

A one-dimensional dielectric grating, based on a simple geometry, is proposed and investigated to enhance light absorption in a monolayer graphene exploiting guided mode resonances. Numerical findings reveal that the optimized configuration is able to absorb up to 60% of the impinging light at normal incidence for both TE and TM polarizations resulting in a theoretical enhancement factor of about 26 with respect to the monolayer graphene absorption (about 2.3%). Experimental results confirm this behaviour showing CVD graphene absorbance peaks up to about 40% over narrow bands of few nanometers. The simple and flexible design paves the way for the realization of innovative, scalable and easy-to-fabricate graphene-based optical absorbers.

Perfect, narrow-band absorption is achieved in an asymmetric 1D photonic crystal with a monolayer graphene defect. Thanks to the large third order nonlinearity of graphene and field localization in the defect layer we demonstrate the possibility to achieve controllable, saturable absorption for the pump frequency.

We present a theoretical analysis of the effects of short range surface plasmon polariton excitation on sub-wavelength bridges in metal gratings. We show that localized resonances in thin metal bridges placed within the slit of a free-standing silver grating dramatically modify transmission spectra and boost absorption regardless of the periodicity of the grating. Additionally, the interference of multiple localized resonances makes it possible to tailor the absorption properties of ultrathin gratings, regardless of the apertures' geometrical size. This tunable, narrow-band, enhanced-absorption mechanism triggered by resonant, short range surface plasmon polaritons may also enhance nonlinear optical processes like harmonic generation, in view of the large third-order susceptibility of metals.

We investigate second and third harmonic generation in a slab of material that displays plasma resonances at the pump and its harmonic frequencies. Near-zero refractive indices and local field enhancement can deplete the pump for kW/cm2 incident powers, without resorting to other resonant photonic mechanisms. We show that low-threshold, highly-efficient nonlinear processes are possible in the presence of losses and phase-mismatch in structures that are 104 times shorter than typical KDP or LiNbO3 crystals, for relatively low irradiance values.

The inclusion of atomic inversion in Raman scattering can significantly alter field dynamics in plasmonic settings. Our calculations show that large local fields and femtosecond pulses combine to yield: (i) population inversion within hot spots; (ii) gain saturation; and (iii) conversion efficiencies characterized by a switch-like transition to the stimulated regime that spans twelve orders of magnitude. While in Raman scattering atomic inversion is usually neglected, we demonstrate that in some circumstances full accounting of the dynamics of the Bloch vector is required.

We theoretically investigate second harmonic generation in extremely narrow, sub-wavelength semiconductor and dielectric waveguides. We discuss a novel guiding mechanism characterized by the inhibition of diffraction and the suppression of cut-off limits in the context of a light trapping phenomenon that sets in under conditions of general phase and group velocity mismatch between the fundamental and the generated harmonic., Comment: 10 pages, 5 figures

We study Raman scattering in active media placed in proximity of different types of metal nanostructures, at wavelengths that display either Fabry-Perot or plasmonic resonances, or a combination of both. We use a semi-classical approach to derive equations of motion for Stokes and anti-Stokes fields that arise from quantum fluctuations. Our calculations suggest that local field enhancement yields Stokes and anti-Stokes conversion efficiencies between five and seven orders of magnitudes larger compared to cases without the metal nanostructure. We also show that to first order in the linear susceptibility the local field correction induces a dynamic, intensity-dependent frequency detuning that at high intensities tends to quench Raman gain.

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.

We show a new path to {\epsilon}~0 materials without resorting to metal-based metamaterial composites. A medium that can be modeled using Lorentz oscillators usually displays {\epsilon}=0 crossing points, e.g. {\epsilon}=0 at {\lambda}~7{\mu}m and 20{\mu}m for SiO2 and CaF2, respectively. We show that a Lorentz medium yields a singularity-driven enhancement of the electric field followed by dramatic lowering of thresholds for a plethora of nonlinear optical phenomena. We illustrate the remarkable enhancement of second and third harmonic generation in a layer of {\epsilon}~0 material 20nm thick, and discuss the role of nonlinear surface sources.

We study second harmonic generation in nonlinear, GaAs gratings. We find large enhancement of conversion efficiency when the pump field excites the guided mode resonances of the grating. Under these circumstances the spectrum near the pump wavelength displays sharp resonances characterized by dramatic enhancements of local fields and favorable conditions for second harmonic generation, even in regimes of strong linear absorption at the harmonic wavelength. In particular, in a GaAs grating pumped at 1064nm, we predict second harmonic conversion efficiencies approximately five orders of magnitude larger than conversion rates achievable in either bulk or etalon structures of the same material., Comment: 8 pages

We have conducted a theoretical study of harmonic generation from a silver grating having slits filled with GaAs. By working in the enhanced transmission regime, and by exploiting phase-locking between the pump and its harmonics, we guarantee strong field localization and enhanced harmonic generation under conditions of high absorption at visible and UV wavelengths. Silver is treated using the hydrodynamic model, which includes Coulomb and Lorentz forces, convection, electron gas pressure, plus bulk X(3) contributions. For GaAs we use nonlinear Lorentz oscillators, with characteristic X(2) and X(3) and nonlinear sources that arise from symmetry breaking and Lorentz forces. We find that: (i) electron pressure in the metal contributes to linear and nonlinear processes by shifting/reshaping the band structure; (ii) TEand TM-polarized harmonics can be generated efficiently; (iii) the X(2) tensor of GaAs couples TE- and TM-polarized harmonics that create phase-locked pump photons having polarization orthogonal compared to incident pump photons; (iv) Fabry-Perot resonances yield more efficient harmonic generation compared to plasmonic transmission peaks, where most of the light propagates along external metal surfaces with little penetration inside its volume. We predict conversion efficiencies that range from 10-6 for second harmonic generation to 10-3 for the third harmonic signal, when pump power is 2GW/cm2.

We demonstrate second and third harmonic generation from a GaP substrate 500{\mu}m thick. The second harmonic field is tuned at the absorption resonance at 335nm, and the third harmonic signal is tuned at 223nm, in a range where the dielectric function is negative. These results show that a phase locking mechanism that triggers transparency at the harmonic wavelengths persists regardless of the dispersive properties of the medium, and that the fields propagate hundreds of microns without being absorbed even when the harmonics are tuned to portions of the spectrum that display metallic behavior.

In this letter we experimentally demonstrate second harmonic conversion in the opaque region of a GaAs cavity with efficiencies of the order of 0.1% at 612nm, using 3ps pump pulses having peak intensities of order of 10MW/cm2. We show that the conversion efficiency of the inhomogeneous, phase-locked second harmonic component is a quadratic function of the cavity factor Q.

We present a systematic analysis of the optical properties of slit arrays in metal films. An exhaustive investigation of geometrical and dispersive properties reveals the resonance features of these structures, including the role of surface waves and their relationship with features in the transmission spectrum. Although enhanced transmission windows are significantly dominated by the longitudinal resonances localized inside the slits, the periodicity introduces transverse resonances that can either enhance or inhibit light transmission. We thus illustrate the intriguing interaction regime between longitudinal and transverse resonances, where the two modes hybridize leading to the formation of a photonic band gap spectrum.

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 typos

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.

We predict and experimentally observe the enhancement by three orders of magnitude of phase mismatched second and third harmonic generation in a GaAs cavity at 650nm and 433nm, respectively, well above the absorption edge. Phase locking between the pump and the harmonics changes the effective dispersion of the medium and inhibits absorption. Despite hostile conditions the harmonics become localized inside the cavity leading to relatively large conversion efficiencies. Field localization plays a pivotal role and ushers in a new class of semiconductor-based devices in the visible and UV ranges.

We numerically demonstrate inhibition of absorption, optical transparency, and anomalous momentum states of phase locked harmonic pulses in semiconductors, at UV and extreme UV frequencies, in spectral regions where the dielectric constant of typical semiconductors is negative. We show that a generated harmonic signal can propagate through a bulk metallic medium without being absorbed as a result of a phase locking mechanism between the pump and its harmonics. These findings may open new regimes in nonlinear optics and are particularly relevant to the emerging fields of nonlinear negative index meta-materials and nano-plasmonics, especially in the ultrafast pulse regime.

We theoretically demonstrate negative refraction and sub-wavelength resolution below the diffraction limit in the UV and extreme UV ranges using semiconductors. The metal-like re-sponse of typical semiconductors such as GaAs or GaP makes it possible to achieve negative refraction and super-guiding in resonant semiconductor/dielectric multilayer stacks, similar to what has been demonstrated in metallo-dielectric photonic band gap structures. The exploita-tion of this basic property in semiconductors raises the possibility of new, yet-untapped ap-plications in the UV and soft x-ray ranges.

We theoretically investigate second harmonic generation that originates from the nonlinear, magnetic Lorentz force term from single and multiple apertures carved on thick, opaque metal substrates. The linear transmission properties of apertures on metal substrates have been previously studied in the context of the extraordinary transmission of light. The transmission process is driven by a number of physical mechanisms, whose characteristics and relative importance depend on the thickness of the metallic substrate, slit size, and slit separation. In this work we show that a combination of cavity effects and surface plasmon generation gives rise to enhanced second harmonic generation in the regime of extraordinary transmittance of the pump field. We have studied both forward and backward second harmonic generation conversion efficiencies as functions of the geometrical parameters, and how they relate to pump transmission efficiency. The resonance phenomenon is evident in the generated second harmonic signal, as conversion efficiency depends on the duration of incident pump pulse, and hence its bandwidth. Our results show that the excitation of tightly confined modes as well as the combination of enhanced transmission and nonlinear processes can lead to several potential new applications such as photo-lithography, scanning microscopy, and high-density optical data storage devices., Comment: Keywords: Enhanced Transmission, Second Harmonic Generation, Surface Plasmon, Sub-wavelength Slit

We discuss propagation effects in realistic, transparent, metallo-dielectric photonic band gap structures in the context of negative refraction and super-resolution in the visible and near infrared ranges. In the resonance tunneling regime, we find that for transverse-magnetic incident polarization, field localization effects contribute to a waveguiding phenomenon that makes it possible for the light to remain confined within a small fraction of a wavelength, without any transverse boundaries, due to the suppression of diffraction. This effect is related to negative refraction of the Poynting vector inside each metal layer, balanced by normal refraction inside the adjacent dielectric layer: The degree of field localization and material dispersion together determine the total momentum that resides within any given layer, and thus the direction of energy flow. We find that the transport of evanescent wave vectors is mediated by the excitation of quasi-stationary, low group velocity surface waves responsible for relatively large losses. As representative examples we consider transparent metallo-dielectric stacks such as Ag/TiO2 and Ag/GaP and show in detail how to obtain the optimum conditions for high transmittance of both propagating and evanescent modes for super-guiding and super resolution applications across the visible and near IR ranges. Finally, we study the influence of gain on super-resolution. We find that the introduction of gain can compensate the losses caused by the excitation of surface plasmons, improves the resolving characteristics of the lens, and leads to gain-tunable super-resolution.

We experimentally and theoretically investigate the second order nonlinear optical response of metallo-dielectric multilayer structures composed of Ag and Ta2O5 layers, deposited by magnetron sputtering. Second harmonic generation measurements were performed in reflection mode as a function of incidence angle, using femtosecond pulses originating from a Ti:Sapphire laser system tuned at 800 nm. The dependence of the generated signal was investigated as a function of pump intensity and polarization state. Our experimental results show that the conversion efficiency from a periodic metallo-dielectric sample may be enhanced by at least a factor of 30 with respect to the conversion efficiency from a single metal layer, thanks in part to the increased number of active surfaces, pump field localization and penetration inside the metal layers. The conversion efficiency maximum shifts from 70 degrees for the single silver layer down to approximately 55 degrees for the stack. The experimental results are found to be in good agreement with calculations based on coupled Maxwell-Drude oscillators under the action of a nonlinear Lorentz force term.

A metallo-dielectric multilayer structure is proposed as a novel approach to the analysis of lactose malabsorption. When lactose intolerance occurs, the bacterial overgrowth in the intestine causes an increased spontaneous emission of H2 in the human breath. By monitoring the changes in the optical properties of a multilayer palladium-polymeric structure, one is able to detect the patient's disease and the level of lactose malabsorption with high sensitivity and rapid response.