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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.