Physical Review B

Understanding how light interacts with matter at the nanometre scale is a fundamental issue in optoelectronics and nanophotonics. In particular, many applications (such as bio-sensing, cancer therapy and all-optical signal processing) rely on surface-bound optical excitations in metallic nanoparticles. However, so far no experimental technique has been capable of imaging localized optical excitations with sufficient resolution to reveal their dramatic spatial variation over one single nanoparticle. Here, we present a novel method applied on silver nanotriangles, achieving such resolution by recording maps of plasmons in the near-infrared/visible/ultraviolet domain using electron beams instead of photons. This method relies on the detection of plasmons as resonance peaks in the energy-loss spectra of subnanometre electron beams rastered on nanoparticles of well-defined geometrical parameters. This represents a significant improvement in the spatial resolution with which plasmonic modes can be imaged, and provides a powerful tool in the development of nanometre-level optics.

Mapping surface plasmons on a single metallic nanoparticle

Plasmonics has emerged as an important research field in nanoscience and nanotechnology. Recently, significant attention has been devoted to the observation and the understanding of nonlinear optical processes in plasmonic nanostructures, giving rise to the new research field called nonlinear plasmonics. This review provides a comprehensive insight into the physical mechanisms of one of these nonlinear optical processes, namely, second harmonic generation (SHG), with an emphasis on the main differences with the linear response of plasmonic nanostructures. The main applications, ranging from the nonlinear optical characterization of nanostructure shapes to the optimization of laser beams at the nanoscale, are summarized and discussed. Future directions and developments, made possible by the unique combination of SHG surface sensitivity and field enhancements associated with surface plasmon resonances, are also addressed.

Optical Second Harmonic Generation in Plasmonic Nanostructures: From Fundamental Principles to Advanced Applications

Nonlinear nanophotonics is a rapidly developing field of research with many potential applications for the design of nonlinear nanoantennas, light sources, nanolasers, and ultrafast miniature metadevices. A tight confinement of the local electromagnetic fields in resonant photonic nanostructures can boost nonlinear optical effects, thus offering versatile opportunities for the subwavelength control of light. To achieve the desired functionalities, it is essential to gain flexible control over the near- and far-field properties of nanostructures. To engineer nonlinear scattering from resonant nanoscale elements, both modal and multipolar control of the nonlinear response are widely exploited for enhancing the near-field interaction and optimizing the radiation directionality. Motivated by the recent progress of all-dielectric nanophotonics, where the electric and magnetic multipolar contributions may become comparable, here we review the advances in the recently emerged field of multipolar nonlinear nanophotonics, starting from earlier relevant studies of metallic and metal–dielectric structures supporting localized plasmonic resonances to then discussing the latest results for all-dielectric nanostructures driven by Mie-type multipolar resonances and optically induced magnetic response. These recent developments suggest intriguing opportunities for a design of nonlinear subwavelength light sources with reconfigurable radiation characteristics and engineering large effective optical nonlinearities at the nanoscale, which could have important implications for novel nonlinear photonic devices operating beyond the diffraction limit.

Multipolar nonlinear nanophotonics

Silicon is evolving as a versatile photonic platform with multiple functionalities that can be seamlessly integrated. The tool box is rich starting from the ability to guide and amplify multiple wavelength sources at GHz bandwidths, to optomechanical MEMS. The strong confinement of light in ultra small structures also enables the generation of strong optical forces. We have recently shown that nonlinear optical forces can enable controllable manipulation of photonic structures. These advances should enable future micro-optomechanical systems (MOMS) with novel and distinct functionalities. A research area that recently has emerged is nonlinear optics using silicon photonics. Since the birth of nonlinear optics, researchers have continually focused on developing efficient nonlinear optical devices that require low optical powers. The strong light confinement in silicon waveguides results in a high effective nonlinearity ad enables fine tuning of waveguide dispersion which is essential for phase matching of parametric nonlinear optical processes such as four-wave-mixing (FWM) We demonstrated FWM-based frequency conversion in waveguides using as little as 1 mW of pump power in a ring-resonator geometry, and ∼100 mW of pump power over bandwidths exceeding 800 nm in a straight-waveguide device. In addition, by using the concept of time-space duality we have shown the temporally stretching and compressing of optical waveforms which allows for seamless transformation between the GHz and THz regimes.

Nonlinear silicon photonics

Nonlinear properties of a multi-layer stack of graphene sheets are studied. It is predicted that such a structure may support dissipative plasmon-solitons generated and supported by an external laser radiation. Novel nonlinear equations describing spatial dynamics of the nonlinear plasmons driven by a plane wave in the Otto configuration are derived and the existence of single and multi-hump dissipative solitons in the graphene structure is predicted.

Dissipative plasmon-solitons in multilayer graphene

We study the second-harmonic generation by a spherical dielectric nanoparticle covered by graphene. We demonstrate that a strong nonlinear response is caused by an induced surface current in the graphene nanoparticle illuminated by an external electromagnetic wave. We obtain analytical expressions for the field multipoles characterizing the second-harmonic radiation and analyze the dependence of intensity and directivity of the nonlinear scattering on the frequency and structure of the electromagnetic field, revealing the asymmetric radiation patterns due to constructive multipole interference for the resonantly enhanced second-harmonic generation.

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Second-harmonic generation by a graphene nanoparticle

By combining analytical and numerical approaches, we study resonantly enhanced second-harmonic generation by individual high-index dielectric nanoparticles made of centrosymmetric materials Considering both bulk and surface nonlinearities, we describe second-harmonic nonlinear scattering from a silicon nanoparticle optically excited in the vicinity of the magnetic and electric dipolar resonances We discuss the contributions of different nonlinear sources and the effect of the low-order optical Mie modes on the characteristics of the generated far field We demonstrate that the multipolar expansion of the radiated field is dominated by dipolar and quadrupolar modes (two axially symmetric electric quadrupoles, an electric dipole, and a magnetic quadrupole) and the interference of these modes can ensure directivity of the nonlinear scattering The developed multipolar analysis can be instructive for interpreting the far-field measurements of the nonlinear scattering and it provides prospective insights into a design of complementary metal-oxide-semiconductor compatible nonlinear nanoantennas fully integrated with silicon-based photonic circuits, as well as methods of nonlinear diagnostics

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Multipolar second-harmonic generation by Mie-resonant dielectric nanoparticles

Multimode interference and multipolar interplay govern functionalities of optical nanoresonators and nonlinear nanoantennas. Recently, excitation of the high-quality supercavity modes (quasi-BIC states) in individual subwavelength dielectric particles has been predicted to boost the nonlinear frequency conversion at the nanoscale. Here, we put forward the multipolar model which captures the physics behind linear and nonlinear response driven by such high-$Q$ modes in nanoresonators. We show that formation of the quasi-BIC state in the AlGaAs nanodisk can be understood through multipolar transformations of coupled leaky modes. In particular, the hybridized axially symmetric TE-polarized modes can be viewed as superpositions of multipoles, with a basis of parent multipoles constituted mainly by magnetic dipoles and octupole. The quasi-BIC point in the parameter space appears where dipolar losses are totally suppressed. The efficient optical coupling to this state is implemented via azimuthally polarized beam illumination matching its multipolar origin. We establish a one-to-one correspondence between the standard non Hermitian coupled-mode theory and multipolar models that enables transparent interpretation of scattering characteristics. Using our approach, we derive the multipolar composition of the generated second-harmonic radiation from the AlGaAs nanodisk and validate it with full-wave numerical simulations. Back-action of the second-harmonic radiation onto the fundamental frequency is taken into account in the coupled nonlinear model with pump depletion. A hybrid metal-dielectric nanoantenna is proposed to augment the conversion efficiency up to tens of per cent and actualize the nonlinear parametric downconversion. Our findings delineate the in-depth conceptual framework and novel promising strategies in the design of functional elements for nonlinear nanophotonics applications.

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Multipolar second-harmonic generation from high-$Q$ quasi-BIC states in nanoresonators

We put forward the multipolar model which captures the physics behind linear and nonlinear response driven by high-quality (high-Q) supercavity modes in subwavelength particles. We show that the formation of such trapped states associated with bound states in the continuum (quasi-BIC) can be understood through multipolar transformations of coupled leaky modes. The quasi-BIC state appears with increasing the order of the dominating multipole, where dipolar losses are completely suppressed. The efficient optical coupling to this state in the AlGaAs nanodisk is implemented via azimuthally polarized beam illumination matching its multipolar origin. We establish a one-to-one correspondence between the standard phenomenological non-Hermitian coupled-mode theory and multipolar models. The derived multipolar composition of the generated second-harmonic radiation from the AlGaAs nanodisk is then validated with full-wave numerical simulations. Back-action of the second-harmonic radiation onto the fundamental frequency is taken into account in the coupled nonlinear model with pump depletion. A hybrid metal-dielectric nanoantenna is proposed to augment the conversion efficiency up to tens of per cent due to increasing quality factors of the involved resonant states. Our findings delineate novel promising strategies in the design of functional elements for nonlinear nanophotonics applications.

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Alexander I. Smirnov

Papers

Dissipative plasmon-solitons in multilayer graphene

Second-harmonic generation by a graphene nanoparticle

Multipolar second-harmonic generation by Mie-resonant dielectric nanoparticles

Multipolar second-harmonic generation from high-$Q$ quasi-BIC states in nanoresonators

Multipolar second-harmonic generation from high-Q quasi-BIC states in subwavelength resonators