Harmonic generation from silicon membranes at visible and ultraviolet wavelengths.

Nonlinear silicon photonics offers unique abilities to generate, manipulate and detect optical signals in nano-devices, with applications based on field localization and large third order nonlinearity. However, at the nanoscale, inefficient nonlinear processes, absorption, and the lack of realistic models limit the nano-engineering of silicon. Here we report measurements of second and third harmonic generation from undoped silicon membranes. Using experimental results and simulations we identify the effective mass of valence electrons, which determines second harmonic generation efficiency, and oscillator parameters that control third order processes. We can then accurately predict the nonlinear optical properties of complex structures, without introducing and artificially separating the effective χ(2) into surface and volume contributions, and by simultaneously including effects of linear and nonlinear dispersions. Our results suggest that judicious exploitation of the nonlinear dispersion of ordinary semiconductors can provide reasonable nonlinear efficiencies and transformational device physics well into the UV range.

Harmonic generation from gold nanolayers: bound and hot electron contributions to nonlinear dispersion.

Understanding how light interacts with matter at the nanoscale is pivotal if one is to properly engineer nano-antennas, filters and other devices whose geometrical features approach atomic size. We report experimental results on second and third harmonic generation from 20 nm- and 70 nm-thick gold layers, for TE- and TM-polarized incident light pulses. We discuss the relative roles that 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 to compare experimental measurements with 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. Using our experimental observations we estimate ∣χ1064nm(3)∣≈10-18 (m/V)2, triggered mostly by hot electrons.

ENZ materials and anisotropy: enhancing nonlinear optical interactions at the nanoscale.

Epsilon-near-zero materials are exceptional candidates for studying electrodynamics and nonlinear optical processes at the nanoscale. We demonstrate that by alternating a metal and a highly doped conducting-oxide, the epsilon-near-zero regime may be accessed resulting in an anisotropic, composite nanostructure that significantly improves nonlinear interactions. The investigation of the multilayer nanostructure reveals the actual role of the anisotropy, showing that high degrees of anisotropy might be necessary to effectively boost nonlinear processes. Moreover, using a microscopic, hydrodynamic approach we shed light on the roles of two competing contributions that are for the most part overlooked but that can significantly modify linear and nonlinear responses of the structure: nonlocal effects, which blueshift the resulting resonance, and the hot electrons nonlinearity, which redshifts the plasma frequency as the effective mass of free electrons increases as a function of incident power density and enhances the nonlinear signal by several orders of magnitude. Finally, we show that, even in the absence of second order bulk nonlinearity, second order nonlinear processes are also significantly enhanced by the layered structure.

Harmonic generation in the opaque region of GaAs: the role of the surface and magnetic nonlinearities.

Phase-locked second and third harmonic generation in the opaque region of a GaAs wafer is experimentally observed and analyzed both in transmission and reflection. These harmonic components, which are generated close to the surface, can propagate through an opaque material as long as the pump is tuned to a region of transparency or semitransparency 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 not only the bulk nonlinearity but also the surface and magnetic Lorentz contributions, which usually are either hidden by the bulk contributions or assumed to be negligible. The experimental results are compared with a detailed numerical model that takes into account these different effects, including for the first time combined linear and nonlinear material dispersions in a nonlinear Lorentz oscillator model of the bulk nonlinearities. Our results suggest that the intensity of the second harmonic signal generated by the surface can be more intense than the signal generated by the bulk. These findings have significant repercussions and are consequential in nanoscale systems, which are usually investigated using only dispersionless bulk nonlinearities, with near-complete disregard of surface and magnetic contributions and their microscopic origins.

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 [Phys. Lett. A157, 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. We discuss the conditions that could modify both linear and nonlinear electromagnetic responses.

Amplitude and phase modulation in microwave ring resonators by doped CVD graphene.

In this paper, we numerically and experimentally demonstrate how to modulate the amplitude and phase of a microwave ring resonator by means of few-layers chemical vapour deposition graphene. In particular, both numerical and experimental results show a modulation of about 10 dB and a 90 degrees-shift (quadrature phase shift) when the graphene sheet-resistance is varied. These findings prove once again that graphene could be efficiently exploited for the dynamically tuning and modulation of microwave devices fostering the realization of (i) innovative beam-steering and beam-forming systems and (ii) graphene-based sensors.

Comparative analysis of ferroelectric domain statistics via nonlinear diffraction in random nonlinear materials.

We present an indirect, non-destructive optical method for domain statistic characterization in disordered nonlinear crystals having homogeneous refractive index and spatially random distribution of ferroelectric domains. This method relies on the analysis of the wave-dependent spatial distribution of the second harmonic, in the plane perpendicular to the optical axis in combination with numerical simulations. We apply this technique to the characterization of two different media, Calcium Barium Niobate and Strontium Barium Niobate, with drastically different statistical distributions of ferroelectric domains.

Optically transparent microwave screens based on engineered graphene layers.

We propose an innovative approach for the realization of a microwave absorber fully transparent in the optical regime. This device is based on the Salisbury screen configuration, which consists of a lossless spacer, sandwiched between two graphene sheets whose sheet resistances are different and properly engineered. Experimental results show that it is possible to achieve near-perfect electromagnetic absorption in the microwave X-band. These findings are fully supported by an analytical approach based on an equivalent circuital model. Engineering and integration of graphene sheets could facilitate the realization of innovative microwave absorbers with additional electromagnetic and optical functionalities that could circumvent some of the major limitations of opaque microwave absorbers.

Graphene-based perfect optical absorbers harnessing guided mode resonances.

We investigate graphene-based optical absorbers that exploit guided mode resonances (GMRs) attaining theoretically 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 by placing it near either a metallic or a dielectric mirror, thus achieving very good agreement between numerical predictions and experimental results.

Graphene-based absorber exploiting guided mode resonances in one-dimensional gratings.

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 (≈2.3%). Experimental results confirm this behavior showing CVD graphene absorbance peaks up to about 40% over narrow bands of a few nanometers. The simple and flexible design points to a way to realize innovative, scalable and easy-to-fabricate graphene-based optical absorbers.

Nonlinear control of absorption in one-dimensional photonic crystal with graphene-based defect.

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.

Nonlinear dynamics in low permittivity media: the impact of losses.

Slabs of materials with near-zero permittivity display enhanced nonlinear processes. We show that field enhancement due to the continuity of the longitudinal component of the displacement field drastically enhances harmonic generation. We investigate the impact of losses with and without bulk nonlinearities and demonstrate that in the latter scenario surface, magnetic and quadrupolar nonlinear sources cannot always be ignored.

Enhanced efficiency of the second harmonic inhomogeneous component in an opaque cavity.

In this Letter, we experimentally demonstrate the enhancement of the inhomogeneous second harmonic conversion in the opaque region of a GaAs cavity with efficiencies of the order of 0.1% at 612 nm, using 3 ps pump pulses having peak intensities of the order of 10 MW/cm(2). We show that the conversion efficiency of the inhomogeneous, phase-locked second harmonic component is a quadratic function of the cavity factor Q.

Enhanced second-harmonic generation from resonant GaAs gratings.

We theoretically 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 1064 nm, we predict second-harmonic conversion efficiencies approximately 5 orders of magnitude larger than conversion rates achievable in either bulk or etalon structures of the same material.

Harmonic generation in metallic, GaAs-filled nanocavities in the enhanced transmission regime at visible and UV wavelengths.

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 χ(3) contributions. For GaAs we use nonlinear Lorentz oscillators, with characteristic χ(2) and χ(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) TE- and TM-polarized harmonics can be generated efficiently; (iii) the χ(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 2 GW/cm2.

The role of ferroelectric domain structure in second harmonic generation in random quadratic media.

We study theoretically and numerically the second harmonic generation in a nonlinear crystal with random distribution of ferroelectric domains. We show that the specific features of disordered domain structure greatly affect the emission pattern of the generated harmonics. This phenomena can be used to characterize the degree of disorder in nonlinear photonic structures.

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.

Cross-phase-modulation-induced instability in photonic-crystal fibers.

Cross-phase-modulation-induced instability is identified as a significant mechanism for efficient parametric four-wave-mixing frequency conversion in photonic-crystal fibers. Fundamental-wavelength femtosecond pulses of a Cr, forsterite laser are used in our experiments to transform the spectrum of copropagating second-harmonic pulses of the same laser in a photonic-crystal fiber. Efficient generation of sidebands shifted by more than 80 THz with respect to the central frequency of the second harmonic is observed in the output spectrum of the probe field.

Tuning the frequency of ultrashort laser pulses by a cross-phase-modulation-induced shift in a photonic crystal fiber.

Femtosecond pulses of fundamental Cr:forsterite laser radiation are used as a pump field to tune the frequency of copropagating second-harmonic pulses of the same laser through cross-phase modulation in a photonic crystal fiber. Sub-100-kW femtosecond pump pulses coupled into a photonic crystal fiber with an appropriate dispersion profile can shift the central frequency of the probe field by more than 100 nm, suggesting a convenient way to control propagation and spectral transformations of ultrashort laser pulses.

TE and TM guided modes in an air waveguide with negative-index-material cladding.

We numerically demonstrate that a planar waveguide in which the inner layer is a gas with refractive index n0 = 1, sandwiched between two identical semi-infinite layers of a negative index material, can support both transverse electric and transverse magnetic guided modes with low losses. Recent developments in the design of metamaterials with an effective negative index suggest that this waveguide could operate in the infrared region of the spectrum.