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© 2023 Optica Publishing Group. Users may use, reuse, and build upon the article, or use the article for text or data mining, so long as such uses are for non-commercial purposes and appropriate attribution is maintained. All other rights are reserved. 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 ¿(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. The authors thank Zack Coppens and Dana Dement for useful discussions and help with the sample. LRS, JT, and CC acknowledge to US Army Research Laboratory Cooperative Agreement N° W911NF1920279 issued by US ARMY ACC-APG-RTP and Spanish Agencia Estatal de Investigación (project no. PID2019-105089GBI00/AEI/10.130397501100011033). MAV was partially sponsored by the Army Research Laboratory under Cooperative Agreement N° W911NF2020078.

The predominant methods currently used to determine nonlinear optical constants like the nonlinear refractive index n2 or the third order susceptibility χ(3) 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 picosecond or femtosecond laser pulsed regimes demands the development of new theoretical tools, and diverse 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 the 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, for example, silicon, gold, and indium tin oxide (ITO), 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 of nonlinear dispersion based on the nonlinear oscillator model. Based on our assessment of third harmonic generation conversion efficiencies in silicon, we predict χω(3) and χ3ω(3) are of order 10−17 (m/V)2 in the visible and near IR ranges, with respective peaks of 10−14 (m/V)2 and 10−16 (m/V)2 in the UV range. Similarly, gold’s χω(3) and χ3ω(3) are of order 10−17–10−16 (m/V)2, and predict χω(3)∼10−17(m/V)2 and χ3ω(3)∼10−18(m/V)2 for ITO. These results clearly suggest that judicious exploitation of the nonlinear dispersion of ordinary semiconductors has the potential to transform device physics in spectral regions that extend well into the UV range.

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 ∣ χ 1064 n m ( 3 ) ∣≈ 10 − 18 ( m/V ) 2 , triggered mostly by hot electrons.

The use of semiconductors, metals and conductive oxides in the process of fabrication of actual nano devices is at the front edge of nowadays technology, exploiting the properties of light propagation and localization at nanometric scale in new and surprising ways. At these scales the usual theory describing the nonlinear (NL) effects of electromagnetic fields should be revisited and analyzed. We report a collection of experimental results of nonlinear harmonic generation in different nanolayers: semiconductors, conductive oxides and metals. The comparison of these experimental results with numerical predictions of our theoretical model identifies, distinguishes and explains the different nonlinear contributions to the harmonics generated by these materials at nanoscale. Our model accounts for surface, magnetic and bulk nonlinearities arising from free and bound charges, preserving linear and nonlinear dispersion, nonlocal effects due to pressure and viscosity.

We present an experimental study of second harmonic generation from a 20nm-thick indium tin oxide layer in the proximity of its epsilon-near-zero condition. We report measurements of second harmonic efficiencies as a function of the input wavelength and angle of incidence close to the epsilon-near-zero crossing point. We perform theoretical simulations using a hydrodynamical model that is able to capture all major physical mechanisms driving the nonlinear electrodynamic behaviour of conductive oxides. The experimental and theoretical results are compared and a very good quantitative and qualitative agreement is found.

We report a comparative experimental and theoretical study of second harmonic generation from a 20nm-thick indium tin oxide nanolayer in the proximity of the epsilon-near-zero condition. We record the efficiency of the second harmonic signal both as a function of wavelength as well as of the angle of incidence around the epsilon-near-zero crossing point. We compare our experimental results with numerical simulations based on a hydrodynamical model able to capture all major physical mechanisms driving the electrodynamic behavior of conductive oxide layers, with unique aspects of the different nonlinear sources. We found a very good quantitative and qualitative agreement between experiment and theory.

Nowadays, nanostructures are routinely fabricated and integrated in different photonic devices for a variety of purposes and applications. For instance, nonlinear silicon photonics is an area of interest due to its high compatibility with CMOS technology, offering structure sizes down to 10nm at low cost. When the nanoscale is reached, light-matter interactions can display new phenomena, conventional approximations may not always be applicable, and new strategies must be sought in order to study and understand light-matter interactions at the nanoscale. In this work, we report a comparative experimental and theoretical study of second and third harmonic generation from silicon with the aim of explaining the nonlinear optical properties of this material at the nanoscale. We measure second and third harmonic efficiencies as a function of angle of incidence, polarization and pump wavelength. We compare these measurements with numerical simulations based on a microscopic hydrodynamic model which accounts for different possible contributions to the nonlinear polarization. This way, we have the ability to explain properly the SH and TH signals arising from different silicon samples. Once we have this knowledge, we are able to design more complex structures, such as silicon nanowires, where higher conversion efficiencies can be achieved.

The use of semiconductors, metals, or ordinary dielectrics in the process of fabrication of nanodevices is at the front edge of nowadays technology, exploiting the properties of light propagation and localization at nanometric scale in new and surprising ways. Understanding accurately how light interacts with these materials at the nanoscale is crucial if one is to properly engineer nano-devices. When the nanoscale is reached, light-matter interactions display new phenomena where conventional approximations may not always be applicable and they should be either revised or voided. In this work, we measure the efficiency of second and third harmonic generation from gold nanolayers. The experimental results are compared with numerical simulations based on a detailed microscopic hydrodynamic model that considers different effects playing a role in the nonlinear response, not usually considered by more generic models. The agreement between experimental and theoretical results proves the importance of all these contributions.

We discuss a dynamical model of harmonic generation that arises from surfaces that demarcate two different metals or conductors, or the electron cloud that spills outside a simple metal surface and the interior bulk, having different electron densities, for example a noble metal such as gold, and indium tin oxide (ITO). While in general two adjacent materials may contain free and bound charges that determine their respective dielectric constants, the transition region may be characterized by a large discontinuity in the free electron density, , epsilon-near-zero conditions, or multiple, nested plasmonic resonances. For example, , while the free-electron cloud that spills outside a noble metal surface decreases as a function of position from the hard ionic surface. These discrepancies lead to the prediction that the angular dependence of second harmonic generation (SHG) from a simple planar structure is direction-dependent, and highlights the sensitivity of both SHG and third harmonic generation to the makeup of the surface and what surrounds it. Our calculations also suggest that the nonlinear optical analysis of more complicated, hybrid structures, such as metal/oxide nanoantennas or metasurfaces, should always be performed by including effects that are generally overlooked, such as nonlocal effects (viscosity and pressure); the presence of linear and nonlinear quantum tunneling currents in the nano- and sub nano-gaps between the nanoantenna and embedded nanoparticles; linear and nonlinear contributions of bound (inner-core) electrons to the dielectric constant.

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

The absorption of electromagnetic waves has always attracted a large interest because of its cross-the-board nature that spans from microwave to optical frequencies in both linear and nonlinear regimes. At the same time, the experimental isolation of bi-dimensional (2D) materials has recently unveiled how single layers might also be very attractive because of their unprecedented optical and absorption properties. In particular, graphene, a 2D version of graphite, exhibits a remarkably high absorption value (∼2.3%) in the visible range [1] when compared to metals or dielectric materials. In this paper, we will review and illustrate the quest for the enhanced absorption in photonic nanostructures that incorporate monolayer and multilayer graphene sheets emphasizing the difference in terms of configurations and strategies proposed in literature. Then, we will detail the optical performance of graphene-based one-dimensional (1D) gratings that support guided mode resonances showing how it is possible to tune theoretically and experimentally their total absorption ranging from 2.3% to perfect absorption by means of metallic and dielectric reflectors or engineered super cells.

We discuss the nature of leaky modes with large phase velocity and an effective refractive index and group velocity near zero in planar arrays of subwavelength dielectric or metallic spheres far from their resonances. Large field enhancements with $Q$ factors exceeding $10{}^{10}$ are theoretically predicted for these modes. Those theoretical findings may have important applications in optical switching and memories, quantum information processing, optical storage, and enhancement of optical nonlinearities. Preliminary experimental results at microwave frequencies qualitatively confirm these predictions.

Unity transmittance at an interface between bulk media is quite common for polarized electromagnetic waves incident at the Brewster angle, but it is rarely observed for sound waves at any angle of incidence. In the following, we theoretically and experimentally demonstrate an acoustic metamaterial possessing a Brewster-like angle that is completely transparent to sound waves over an ultra-broadband frequency range with >100% bandwidth. The metamaterial, consisting of a hard metal with subwavelength apertures, provides a surface impedance matching mechanism that can be arbitrarily tailored to specific media. The nonresonant nature of the impedance matching effectively decouples the front and back surfaces of the metamaterial allowing one to independently tailor the acoustic impedance at each interface. On the contrary, traditional methods for acoustic impedance matching, for example in medical imaging, rely on resonant tunneling through a thin antireflection layer, which is inherently narrowband and angle specific.

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 spatial symmetry breaking, the magnetic portion of the Lorentz force, and quadrupolar contributions from inner core electrons. The material is assumed to have a nonzero, third-order nonlinearity that gives rise to most of the third harmonic signal. Using the parameters of bulk silicon we predict that cavity environments modify the dependence ofsecondharmonicgenerationonincidentangle,whileimprovingthirdharmonicconversionefficiencybyseveral orders of magnitude relative to bulk silicon. This occurs despite the fact that the harmonic signals may be tuned to a wavelength range where the dielectric function of the material is negative: A phase-locking mechanism binds the generated signals to the pump and inhibits their absorption. These results point the way to alternative uses and flexibility of materials such as silicon as nonlinear media in the visible and UV ranges.

We experimentally demonstrate the existence of a Brewster-like broadband extraordinary optical transmission band, in a very thick metal plate with an array of slits as narrow as $\ensuremath{\lambda}$/750 in the 8- to 40-GHz regime, by measuring the transmission from normal incidence to near grazing angles and mapping out the entire angular transmission spectrum. In the case of very narrow slits, an order of magnitude larger transmission is obtained at the Brewster angle when compared to the normal-incidence Fabry-P\'erot resonance transmission peaks. Full-wave numerical simulations are in excellent agreement with the measurements, paving the way for the observation of this phenomenon in the optical regime.

We study inhibition of absorption, transparency, energy and momentum transport of the inhomogeneous component of harmonic pulses in dielectrics and semiconductors, at visible and UV wavelengths, focusing on materials like GaP. In these spectral regions GaP is characterized by large absorption, metallic behavior or a combination of both. We show that phase locking causes the generated inhomogeneous signals to propagate through a bulk metallic medium without being absorbed, that is occurs even in centrosymmetric materials via the magnetic Lorentz force, and that the transport of energy and momentum is quite peculiar and seemingly anomalous. These results make it clear that there are new opportunities in ultrafast nonlinear optics and nano-plasmonics in new wavelength ranges., 16 pages, 5 figures, 1 video

We present a detailed analysis of the optical properties of one-dimensional arrays of slits in metal films. Although enhanced transmission windows are dominated by Fabry-Perot cavity modes localized inside the slits, the periodicity introduces surface modes that can either enhance or inhibit light transmission. We thus illustrate the interaction between cavity modes and surface modes in both finite and infinite arrays of slits. In particular we study a grating that clearly separates surface plasmon effects from Wood-Rayleigh anomalies. The periodicity of the grating induces a strong plasmonic band gap that inhibits coupling to the cavity modes for frequencies near the center of the band gap, thereby reducing the transmission of the grating. Strong field localization at the high energy plasmonic band edge enhances coupling to the cavity modes while field localization at the low energy band edge leads to weak cavity coupling and reduced transmission.

Extraordinary transmission through thick gratings results from resonances inside the apertures and is narrowband. We report observation of extremely broadband transmission through thick gratings at angles of incidence related to a Brewster angle.

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., Keywords: Enhanced Transmission, Second Harmonic Generation, Surface Plasmon, Sub-wavelength Slit

We are designing and fabricating arrays of subwavelength SP structures in metal films and combining these structures with EO polymers to understand the interaction of the EO polymer with the enhanced electric fields of the plasmons. We have designed and modeled resonance structures to maximize extraordinary transmittance. We are making a systematic study of SP structure shapes by studying circular holes, elliptical holes and slits. Initially we have fabricated and begun optical evaluation of subwavelength slits in gold films. Slits with 32 nm width and 120 nm width have been fabricated by a focused ion beam system. Preliminary optical transmittance measurements in the visible and NIR are underway and will be compared to theoretical modeling.

Summary form only given. Negative refraction and sub-wavelength imaging in the visible part of the spectrum are numericlly investigated using a multilayer, metal-dielectric photonic band gap structure. Results show that the main underlying physical mechanism for sub-wavelength focusing comes as a result of resonance tunneling, field localization and propagation effects, and that surface plasmons do not play a significant role. The advantage of these structures is that both tunability and high transmission are achievable across the visible wavelength regime as well as into the infrared regime.

We proposed a coherent source based on parametric down-conversion in a photonic crystal. Our design is based on the band edge or defect-mode field enhancement phenomena near a photonic band gap. The numerical results show that a range of bandwidths, intensities, and frequencies up to 12 THz can be obtained.

International Quantum Electronics Conference 2004, San Francisco, California United States, 16–21 May 2004, We propose a device based on a one-dimensional photonic band gap structure that is optimized for the generation of coherent, THz radiation tunable up to 10 THz.

We report theoretical predictions and experimental results on the formation of pass bands and stop bands of extraordinary acoustic transmission in multilayer structures based on alternating layers of acoustic metamaterial and air. The metamaterial layers can be made of any acoustically hard material perforated with a two-dimensional array of subwavelength apertures. In this way, it is possible to tailor the density and speed of sound of an otherwise acoustically bulk hard material with fixed properties. The sonic band structure allows transmission passband and stop bandgaps that depend on the layer thicknesses and effective properties of the metamaterials. In addition, we show the existence of resonant tunneling due to the formation of an acoustic passband in a spectral region of low transmission for a single layer. This opens the possibility to engineer different types of phononic materials to manipulate and control acoustic waves.

We experimentally and theoretically investigate electromagnetic funneling in thick plasmonic gratings as the aperture size approaches zero. Both resonant and nonresonant funneling mechanisms were observed to provide near unity transmission for aperture widths of ∼λ/100. As the apertures become smaller, the resonant funneling process enters into a region of strong absorption followed by complete reflection. In sharp contrast, the broadband, nonresonant funneling mechanism continues to transmit energy at high levels for screens of

We exploit the metamaterial properties of a thick metallic grating with extreme sub-wavelength slits on a metallic slab to achieve complete absorption of transverse magnetic polarized microwaves. We measure narrow bands of total absorption (up to 99.9999%) from normal to grazing incidence that can be tuned by varying an air gap between the grating and the slab. Unlike typical absorbers, the structure is mostly metallic with a 97% filling factor, and no absorptive material beside the metal itself is employed. We access the absorption properties of metals in the microwave where they are commonly believed to be perfect reflectors.

We demonstrate experimentally the existence of an omnidirectional reflection band of a two-dimensional metamaterial structure consisting of split ring resonators and thin conducting wires. Experimental angular reflectance data agree reasonably well with simulations using model dispersion relations for the effective dielectric permittivity and magnetic permeability that were fitted to the experimentally retrieved material parameters. The tunability of the reflection bandwidth is demonstrated by changing the effective electric plasma frequency. These findings are also relevant to optical frequencies where similar metamaterial composites have been fabricated.

The authors present a theoretical analysis of a super-resolving lens based on one-dimensional metal-dielectric photonic band gap composed of Ag∕GaP multilayers. The lens contains a total of ten optical skin depths of Ag, yet maintains a normal incidence transmittance of ∼50% for propagating waves over the super-resolving wavelength range of 500–650nm. The individual Ag layers are 22nm thick and can be readily fabricated in conventional deposition systems. The importance of antireflection coatings for the transmission of evanescent and propagating waves is illustrated by comparison to periodic and symmetric structures without the coatings.

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

We proposed a coherent source based on parametric down-conversion in a photonic crystal. Our design is based on the band edge or defect-mode field enhancement phenomena near a photonic band gap. The numerical results show that a range of bandwidths, intensities, and frequencies up to 12 THz can be obtained.

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