Nonlinear optics in all-dielectric nanoantennas and metasurfaces: a review Download: 1044次
1 Introduction
Nonlinear effects in electricity and magnetism have been recognized since Maxwell’s time. However, much progress has been made in the field of nonlinear optics since the discovery of the laser,1 which made high-intensity optical fields easily feasible. The field started to grow with the first experimental work of Franken et al.2 on optical second-harmonic generation (SHG) in 1961 and the theoretical work of Bloembergen et al.3,4 on optical wave mixing in 1962. Over the following decades, the field of nonlinear optics witnessed enormous growth, leading to the observation of new physical phenomena and giving rise to novel concepts and applications including high-harmonics generation and frequency mixing that can act as new light sources or as amplification schemes, light modulators for controlling the phase or amplitude of a light beam, optical switches, optical logic, optical limiters, and numerous ways of processing the information content of data images, which created revolutionary change in photonics technology in the 20th century.5,6 Almost all those achievements were made on conventional bulk crystals where cumbersome phase-matching conditions limit the efficiency of the nonlinear processes.
The current research trend in nonlinear optics has moved toward miniaturized optical materials in truly compact setups. In recent years, significant advancements in nanofabrication techniques have considerably broadened the experimental and theoretical framework in which nonlinear optical processes are explored. Major work over the past decade has been done in design and fabrication to simultaneously address the efficiency and phase matching in nonlinear generation within the subwavelength regime. Metamaterials and their two-dimensional counterparts, metasurfaces,7
Free from phase-matching limitations and featuring a unique control over nonlinear fields, plasmonic metasurfaces have been employed to the fullest extent for the generation of high-harmonics, frequency mixing, and other nonlinear effects.10,11,16
Metasurface can locally control the phase, amplitude, or the polarization state of light waves that propagate through or reflect from them. The concept of phase tailoring plasmonic metasurfaces at a nonlinear regime enables both the coherent generation and the manipulation, such as beam steering and lensing of light beams. Nonlinear phase control has been demonstrated for SHG, THG, and FWM in metallic thin films.24,25,85 Recently, a plasmonic metasurface hologram has been realized at the THG frequency.31 In addition, nonlinear holography has been demonstrated to be operated at both fundamental and second-harmonic frequencies using a Pancharatnam–Berry (PB) phase change, which operates in both the linear and the nonlinear optical regimes simultaneously.27
So far, we have seen that surface plasmon polaritons are capable of enhancing and spatially confining optical fields beyond the diffraction limit. Plasmonic effects in metallic nanostructures have been extensively used to enhance and control nonlinear optical processes at the nanoscale, such as harmonic generation, wave mixing, supercontinuum generation, nonlinear imaging, and holography. However, several disadvantages limit their applicability in nonlinear nanophotonic applications, including high dissipative losses and inevitable thermal heating, leading to low optical damage thresholds. Thus, the use of all-dielectric metasurfaces supporting magnetic resonances, and the ability to withstand much higher pump field intensities, would be a promising route to obtaining higher nonlinear conversion efficiencies.86 Furthermore, it has been discovered that highly efficient and flexible light manipulation can be achieved at the nanoscale by tuning the electric and magnetic responses of all-dielectric nanostructures.16,87
In this review, we highlight recent progress in the field of nonlinear optical processes with all-dielectric nanosystems, from nonlinear frequency generation and phase control to applications. The review is organized as follows. In Sec.
There are many publications available on nonlinear optical effects in artificial materials including epsilon-near-zero materials, perovskites, two-dimensional materials, and multiple quantum wells. A detailed overview of these topics is well beyond the scope of this review. For a detailed and complete survey, we refer readers to a well-known review paper on these topics.16
2 Multipolar Resonances in All-Dielectric Systems
In this section, we discuss the different modes that are available in all-dielectric nanostructures and their dependence on geometry, which is responsible for nonlinear field enhancement. The optical response of spherically symmetric scatterers, irrespective of their size and constituting medium, can be analytically predicted by expanding the electromagnetic fields in the multipolar basis. This is commonly known as the Lorenz–Mie theory.90 For lossless and nonmagnetic materials, their scattering properties can be fully determined when two parameters are specified: the permittivity
Fig. 1. Mie resonances in dielectric nanostructures. (a) Schematic illustration of the charge–current distributions that give rise to the electric dipole ( ), magnetic dipole ( ), electric quadrupole , and magnetic quadrupole (Ref. 98). (b) The simulated multipolar decomposition of the scattering cross section of an individual silicon nanodisk with height and diameter in air (Ref. 99). (c) SEM image of one of the fabricated silicon disk arrays (Ref. 99). (d)–(f) Dark-field optical microscope images (top left), SEM images (top right), and dark-field scattering spectra (bottom) of spherical silicon (Si) nanoparticles with approximate diameters of (d) 100 nm, (e) 140 nm, and (f) 180 nm (Ref. 87). Figure reprinted with permission: (a) Ref. 98, © 2014 by the American Physical Society (APS); (b) and (c) Ref. 99, © 2016 by the Nature Publishing Group (NPG); (d)–(f) Ref. 87, © 2012 by NPG.
Mie resonators featuring both electric and magnetic responses are seen as a promising platform capable of leading to a practical realization of the Kerker conditions103,104 (suppression of the back-scattered field under given conditions) with nonmagnetic materials.105,106 An experimental verification of this effect in high-refractive-index particles was carried out in the microwave range107 and subsequently observed in the visible range with silicon93 and gallium arsenide (GaAs) nanoparticles,108 where the Kerker effect was due to the interference between the fields radiated by the induced electric and magnetic dipoles. It has been shown that a generalization of this effect to higher-order multipoles is also possible.109,110
For metallic nanoantennas, the electric dipole modes usually dominate the Mie scattering. In contrast to plasmonics, strong localization of electric and magnetic fields at the nanoscale due to Mie resonances inside dielectric nanoparticles enhances nonlinear effects. It has been acknowledged that the intrinsic microscopic nonlinear electric polarizability of resonant nanoparticles may induce magnetic nonlinear effects.111 The presence of both electric and magnetic nonlinearities enhances the interference effects, which in turn increase the efficiency and control the polarization of the nonlinear processes, as well.89,112
Another important resonance mode that can be achieved in dielectric nanostructures possessing more complex design is the Fano resonance.113,114 The Fano resonance is considered as an asymmetric lineshape of resonances, which arises from an interference of discrete (resonance) states with broadband (continuum) states.113 To observe Fano resonance from all-dielectric nanoparticles/metasurfaces, one of the important concepts is to include interaction between resonant (bright) and nonresonant (dark) scattering modes [
Fig. 2. Fano resonances and AMs in dielectric nanostructures. (a) Schematic illustration of the interference between the bright- and the dark-mode resonators, (b) corresponding SEM image of a single-unit cell of the fabricated metasurface, and (c) corresponding experimental transmittance ( ), reflectance ( ), and absorption ( ) spectra, showing a Fano-type resonance (Ref. 114). (d) Schematic illustration of an anapole excitation: the toroidal dipole moment is associated with the circulating magnetic field accompanied by electric poloidal current distribution. As the symmetries of the radiation patterns of the electric P and toroidal T dipole modes are similar, they can destructively interfere, leading to total scattering cancelation in the far-field with nonzero near-field excitation (Ref. 115). (e) Calculated spherical electric dipole (black), Cartesian electric (red) and toroidal (green) dipole moments contribution to the scattering by a dielectric spherical particle of refractive index and wavelength 550 nm, as a function of the diameter. The anapole excitation is associated with the vanishing of the spherical electric dipole when the Cartesian electric and toroidal dipoles cancel each other (Ref. 115). Figure reprinted with permission: (a)–(c) Ref. 114, © 2014 by NPG; (d) and (e) Ref. 115, © 2015 by NPG.
High-index dielectric nanoparticles also support other unusual electromagnetic scattering modes such as anapole modes (AMs).115
3 Third-Order Nonlinear All-Dielectric Nanostructures and Metasurfaces
A wide range of theoretical and experimental studies of nonlinear plasmonics have already laid the foundation of modern nonlinear optics with nanostructures. However, all-dielectric arrangements can support even stronger nonlinear optical responses as well as novel functionalities enabled by signified magnetic dipole and higher-order Mie-type resonances, compared to their plasmonic counterparts. In this section, we present an overview of the state-of-the-art progress in the area of nonlinear interactions of high-index dielectric nanostructures and metasurfaces, supporting additional magnetic resonances. In addition, dielectric nanostructures are able to withstand much higher pump fields, making them a promising way to obtain higher nonlinear conversion efficiencies.89,91,120 The electric field enhancement in dielectric nanostructures is typically smaller than in the plasmonic ones; however, additional volume resonance can be added to make the overall enhancement larger, as the field confinement in dielectric nanostructures is not restricted to the surface only, as in their metallic counterparts.
Shcherbakov et al.121 demonstrated a strong nonlinear response from dielectric nanostructures made of silicon nanodisks. They exhibited enhanced THG, which was observed by the naked eye using both an isolated nanodisk and an array of nanodisks, which were optically pumped in the vicinity of the magnetic dipole resonance, as shown in
Fig. 3. Third-order nonlinear effects. (a) THG spectroscopy of Si nanodisk arrays. The negative logarithm of the normalized transmission spectrum of the sample with period , height , and diameter is shown by the gray area, indicating a resonance at . The THG spectrum of the sample (purple dots) shows a strong enhancement within the spectral band of the resonance. The inset shows the SEM image of the sample (Ref. 121). (b) Power dependence and conversion efficiency of the resonant THG process in Si nanodisks. Blue circles denote the THG power dependence obtained at fundamental wavelength. Left inset: photographic image of the sample irradiated with the invisible IR beam. The blue point is the scattered THG signal. Right inset: conversion efficiency of the nanodisk sample as a function of the pump power (Ref. 121). (c) THG power as a function of the pump power for the Fano-resonance metasurface. The red circles indicate the measured data, and the blue line is a numerical fit to the data with a third-order power function. Left inset: SEM image of the sample; right inset: extracted absolute THG efficiency (Ref. 122). (d) Measured THG power versus the excitation of the AM in silicon nanodisks. Left inset: THG intensity image taken at ; scale bar is and top view of the simulated distribution of the electric field intensity for a disk diameter of 875 nm. Right inset: conversion efficiency as a function of pump power (Ref. 127). (e) Measured nonlinear response of a Ge disk when exciting at HOM1 and HOM2 modes simultaneously. Inset: extinction spectrum of a Ge disk of 200-nm height and 625-nm radius (Ref. 129). (f) Measured nonlinear response of the Ge disk when exciting at two different wavelengths comprising HOM1 (Ref. 129). Figure reprinted with permission: (a) and (b) Ref. 121, © 2014 by the American Chemical Society (ACS); (c) Ref. 122, © 2015 by ACS; (d) Ref. 127, © 2016 by ACS; (e) and (f) Ref. 129, © 2017 by ACS.
THG from a Fano nonlinear metasurface consisting of resonant Si nanodisks and nanoslits, supporting resonant dark (magnetic dipole) and bright (electric dipole) modes, respectively, was demonstrated by Yang et al.122 The nanostructures were fabricated by electron beam lithography followed by reactive-ion etching after depositing a 120-nm-thick poly-Si layer on a quartz substrate. The measured conversion efficiency was
Benefiting from the high damage threshold of all-dielectric nanostructures, a silicon metasurface created by means of laser-induced self-organized nanostructuring of thin Si films was employed to generate a 30-fold enhanced third-order nonlinear response, demonstrating UV femtosecond laser pulses at a wavelength of 270 nm with a high peak and average power (
Germanium (Ge) is another excellent material for nonlinear metasurfaces, because of its high refractive index in the visible range and large third-order susceptibility. THG in thin Ge nanodisks under normally incident laser excitation can be boosted via a nonradiative AM. Grinblat et al.127 demonstrated strong THG by exciting a Ge nanodisk near the AM [
Very recently, Wang et al.130 demonstrated a new concept for embedding any functionality into a nonlinear all-dielectric metasurface made of silicon, producing phase gradients over a full 0- to
Fig. 4. Nonlinear phase control with silicon metasurfaces. (a) Geometries and nonlinear phases of Si nanopillar metaatoms. Shown are the sizes of the nanopillars and corresponding analytical and numerical results for the phase of the third-harmonic field for a pump wavelength of 1615 nm and linear polarization of the pump along the a -axis. (b) SEM image of the silicon metasurface. (c) Phase profile of the THG field encoded into the metasurface. (d) -space image of the forward THG signal. A total of 92% of THG is directed into the designed diffraction angle , where . (e) Cross section of a generated donut-shaped vortex beam at the THG taken along the propagation direction behind the metasurface. Inset: cross-section perpendicular to the optical axis at distance (Ref. 130). Figure reprinted with permission: (a)–(e) Ref. 130, © 2018 by ACS.
So far, we have seen that the choice of the appropriate confined optical mode and mode overlap (in the case of wave mixing) are the two utmost important factors to get maximum conversion efficiency. These investigations reveal useful pathways for the further optimization of third-order optical processes in all-dielectric nanostructures.
4 Second-Order Nonlinear All-Dielectric Nanostructures and Metasurfaces
In Sec.
Resonantly enhanced SHG using GaAs-based dielectric metasurfaces, made of arrays of cylindrical resonators, has demonstrated SHG enhancement factors as large as
Fig. 5. Second-order nonlinear effects at GaAs metasurfaces. (a) SHG power dependence at low pump intensities, and the deviation from the quadratic relationship at higher pump intensities due to the damage of GaAs resonators. Left inset: SEM image of the fabricated GaAs resonator array. Right inset: SHG conversion efficiency as a function of pump power (Ref. 132). (b) Schematic illustration of an optical metamixer consisting of a square array of subwavelength GaAs dielectric resonators. Two femtosecond near-IR pulses pump the metamixer and a variety of new frequencies are simultaneously generated. Top inset: SEM image of the GaAs metamixer (scale bar ). Bottom inset: energy diagrams of the seven nonlinear optical processes that occur simultaneously at the metasurface: SHG, THG, FHG, SFG, TPA-PL, FWM, and SWM (Ref. 133). (c) Measured nonlinear spectrum exhibiting 11 generated peaks originating from seven different nonlinear processes when two optical beams at and are used to simultaneously pump the GaAs metasurface. Blue labels indicate harmonic-generation processes and photoluminescence arising from two-photon absorption that each requires only one pump beam. Red labels indicate frequency mixing that involves both pump beams (Ref. 133). Figure reprinted with permission: (a) Ref. 132, © 2016 by ACS; (b) and (c) Ref. 133, © 2018 by NPG.
Recently, the same group demonstrated a GaAs metasurface-based optical frequency mixer [
By shaping the unidirectional SHG radiation pattern from aluminum gallium arsenide (AlGaAs) nanodisk antennas as well as its polarization state, generation of cylindrical vector beams of complex polarization has been experimentally demonstrated.112 In these experiments, nonlinear conversion efficiencies exceeding
In an unconventional way, Bar-David and Levy135 recently reported the generation of second-harmonic signal from an amorphous silicon metasurface. The second-harmonic signal was generated mostly from the surface, following selection rules that rely on the asymmetry of the meta-atoms.
The superiority of the fabricated materials is utmost important to get efficient nonlinear phenomena. Fabrication of the dielectric metasurfaces of nonzero second-order bulk susceptibility requires special attention to maintaining their high quality, as they are made of III–V semiconductor nanostructures. In this context, widegap materials, such as ZnO, GaN, or
The high-index dielectric metasurfaces provide strong nonlinear response, low dissipative losses, and high damage threshold. These advantages make them a powerful platform for modern nonlinear nanophotonics. The presence of both the electric and the magnetic responses makes it possible to tune the scattering patterns and design switchable flat optical devices engaging these nonlinearities.
5 All-Dielectric Ultrafast Optical Switching
One of the biggest advantages of metasurfaces is their ability to spatially vary and tune the optical parameters of the surface. Such spatial variations enable new opportunities for the observed ultrafast optical switching, namely to construct ultrafast displays that can switch between two or more different images at the femtosecond timescale. Ultrafast optical switching that is based on the free-carrier nonlinearity in semiconductors suffers from long switching time (limited to tens of picoseconds) due to two-photon absorption and comparatively large free-carrier lifetime.137
Fig. 6. Ultrafast optical switching with silicon metasurfaces. (a) Experimental (dots) and theoretical (solid lines) dependencies of the normalized reflectance change on the laser fluence (F ) for three cases: (i) a 220-nm-thick silicon film (marked by black color), (ii) the “near-resonance nanoparticle” (marked by red color) and (iii) the “off-resonance nanoparticle” (marked by green color). Inset: schematic illustration of the scattering manipulation by an intense femtosecond laser pulse. The intense laser pulse switches the scattering of the particle to a Huygens source regime when the incident light is scattered in the forward direction (Ref. 154). (b) Left: illustration of the ultrafast all-optical switching in resonant silicon nanodisks based on two-photon absorption. Right: tailoring the all-optical switching in silicon nanodisks. Shown are the relative transmission changes for different samples (Ref. 155). Figure reprinted with permission: (a) Ref. 154, © 2015 by ACS; (b) Ref. 155, © 2015 by ACS.
All-optical switching of femtosecond laser pulses passing through subwavelength silicon nanodisks at their magnetic dipolar resonance was presented.155 Pump-probe measurements revealed that the switching of the nanodisks can be governed by bandwidth-limited 65-fs long two-photon absorption. The authors observed an improvement of the switching time by a factor of 80 with respect to the unstructured silicon film [
All-dielectric metasurfaces, benefited from very low intrinsic losses and localized Mie-type modes, are promising for all-optical switching and modulation. Magnetic resonances in all-dielectric metasurfaces suppress the free-carrier effect, leading to greatly reduced all-optical switching time without suffering from a strong loss in modulation depth.
6 Summary and Outlook
We have reviewed the state of the art in the intensely developing area of all-dielectric nonlinear nanostructures and metasurfaces, as a promising alternative for nonlinear plasmonic metasurfaces. We have discussed the important role of the electric and magnetic dipoles and higher-order Mie modes, in harmonic generation, wave mixing, and ultrafast optical switching, including Fano resonances and anapole moments. Electric and magnetic resonances and their interference in high-index dielectric nanostructures strongly influence the enhancement of the nonlinear optical interactions. Although the electric field enhancement in dielectric nanostructures is smaller than in the plasmonic counterparts, the additional volume resonance, coming from the field confinement of the mode in the high-index resonators, can make the overall enhancement of the nonlinear process larger. High-index dielectric nanostructures and metasurfaces, supporting additional magnetic resonances, can induce magnetic nonlinear effects, which along with electric nonlinearities increase the nonlinear conversion efficiency.
Additionally, low dissipative losses and high damage threshold of all-dielectric nanosystems provide an added degree of freedom in operating at high pump intensities, resulting in considerable enhancement of the nonlinear processes. In comparison to plasmonic nanostructures, this is a huge advantage as the loss and the thermal-heating effects are mostly undesired, and can easily lead, for metallic structures, to the destruction of the nanostructures.
Despite the tremendous progress in the enhancement of the nonlinear efficiency, much less advancement has been achieved in realizing functional nonlinear metasurface elements. Very few examples are available in the literature about nonlinear phase and wavefront control to show novel optical functionalities. The work by Wang et al.130 shows that a wavefront control of the third-harmonic field based on the generalized Huygens’s principle (which is extended to nonlinear optics) seems feasible. Using Huygens’s principle for nonlinear processes while keeping the nonlinear conversion efficiency high seems to be an important research angle for future improvements. Furthermore, the spatial control of the nonlinear phase of the THG signals depends sensitively on the precise geometry and refractive index of the nanostructures, resulting in challenging fabrication. Here, different concepts for the control of the nonlinear phase might bring further advantages. In this context, an elegant way to arbitrarily tailor the nonlinear phase would be based on the PB phase technique, which has been demonstrated for nonlinear effects at plasmonic metasurfaces.11,24 The PB phase manifests as an accumulated phase during the change of the polarization state of light, for example, if light with a particular polarization is scattered at a nanostructure. Because the PB phase depends solely on the elements’ orientation, it can be interpreted as being of geometrical nature and is often referred to as a geometrical phase. The concept was previously applied to encode phase information into planar flat surfaces with plasmonic nanostructures, giving rise to nonlinear optical holography, image generation, and beam profile manipulation.11 We note that the same symmetry selection rules for nonlinear processes as for plasmonic nanostructures are valid, resulting in symmetry-dependent nonlinear processes. By tailoring the rotation angle of each nanostructure, the angle will determine the local phase of the nonlinear material polarization. Hence, by using the control over the nonlinear PB phase, the local phase in the generation process can be controlled. This way, one can generate different nonlinear functional elements that rely on a space-dependent phase of the generated nonlinear signal. One important application of tailoring the nonlinear phase is nonlinear holography. In this context, two or more nonlinear processes can simultaneously be overlapped to create nonlinear holographic multiplexing with different frequencies.
Apart from the conventional selection of the second-order nonlinear materials, the fabrication of metasurfaces is rather complex, and another promising direction is to use complementary metal–oxide–semiconductor-compatible materials (such as Si, SiN,
All-dielectric metasurfaces have a high potential for enabling the efficient generation of new frequencies by simultaneously using more than one nonlinear process. In such a way, one can construct holographic multiplexing elements based on frequency or polarization. Nonlinear all-dielectric nanosystems might also drive rapid progress in engineering nonlinear optical effects beyond the diffraction limit and have enormous potential to develop new concepts of miniaturized efficient nonlinear photonic metadevices in the near future.
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Article Outline
Basudeb Sain, Cedrik Meier, Thomas Zentgraf. Nonlinear optics in all-dielectric nanoantennas and metasurfaces: a review[J]. Advanced Photonics, 2019, 1(2): 024002.