Letter pubs.acs.org/NanoLett
Nonlinear Optical Magnetism Revealed by Second-Harmonic Generation in Nanoantennas Sergey S. Kruk,*,† Rocio Camacho-Morales,† Lei Xu,† Mohsen Rahmani,† Daria A. Smirnova,†,§ Lei Wang,† Hark Hoe Tan,‡ Chennupati Jagadish,‡ Dragomir N. Neshev,† and Yuri S. Kivshar† †
Nonlinear Physics Centre, Research School of Physics and Engineering and ‡Department of Electronic Materials Engineering, Research School of Physics and Engineering, The Australian National University, Canberra ACT 2601, Australia § Institute of Applied Physics RAS, Nizhny Novgorod 603950, Russia S Supporting Information *
ABSTRACT: Nonlinear effects at the nanoscale are usually associated with the enhancement of electric fields in plasmonic structures. Recently emerged new platform for nanophotonics based on high-index dielectric nanoparticles utilizes optically induced magnetic response via multipolar Mie resonances and provides novel opportunities for nanoscale nonlinear optics. Here, we observe strong second-harmonic generation from AlGaAs nanoantennas driven by both electric and magnetic resonances. We distinguish experimentally the contribution of electric and magnetic nonlinear response by analyzing the structure of polarization states of vector beams in the secondharmonic radiation. We control continuously the transition between electric and magnetic nonlinearities by tuning polarization of the optical pump. Our results provide a direct observation of nonlinear optical magnetism through selective excitation of multipolar nonlinear modes in nanoantennas. KEYWORDS: Nonlinear nanophotonics, optical magnetism, second-harmonic generation, dielectric nanoantennas, semiconductors, nanofabrication generation (SHG) can contain multipolar field contributions with varied strengths and phases enriching the spectrum of constructive and destructive interference effects that can be analyzed by the methods of multipolar nonlinear nanophotonics.9 Magnetic nonlinear effects were searched in the past in metallic nanostructures.4,10 However, intensity of SHG observed there is very weak, and it was not sufficient enough to compete with traditionally stronger nonlinear effects produced by electric response.11 The limitations for the efficiency and functionalities of metal structures at optical frequencies are imposed by Ohmic losses, small mode volumes, and low laser damage thresholds. This situation changed recently with the development of a new branch of all-dielectric resonant nanophotonics.3 High-permittivity all-dielectric nanoparticles are emerging as a promising platform for a wide range of nanophotonic applications that utilize localized magnetic resonant modes, recently observed experimentally in entire optical spectral range.3 Such nanoparticles offer unique opportunities for the study of nonlinear effects as they enhance the frequency
N
onlinear optics describes intensity-dependent optical phenomena facilitated by strong light-matter interaction. The commonly known nonlinear process is doubling the input frequency of light when a nonlinear crystal is illuminated by an intense light field.1 The optical properties of nanoscale structures differ substantially from bulk materials because they are affected by strong confinement effects and resonances. In particular, an important consequence of localized resonances is a strong enhancement of the local electric fields with the formation of hot spots that are known to boost dramatically nonlinear optical effects in nanostructures.2 For many years, the study of nonlinear effects at the nanoscale has been dominated by the enhancement of electric fields and second-harmonic effects of the electric origin.2 This comes from negligible optical magnetism of materials at a microscopic level. However, recently it became evident that an intrinsic microscopic electric response of materials structured at the nanoscale may lead to an optically induced resonant magnetic response.3 Unlike unstructured natural materials, magnetic response at optical frequencies appears naturally in different types of metamaterials and individual nanoparticles. Nonlinear effects driven by magnetic resonances4−8 can have very different properties compared to nonlinear effects that occur due to the electric resonances. When both electric and magnetic nonlinearities are present, the second-harmonic © 2017 American Chemical Society
Received: April 10, 2017 Revised: May 13, 2017 Published: May 16, 2017 3914
DOI: 10.1021/acs.nanolett.7b01488 Nano Lett. 2017, 17, 3914−3918
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Nano Letters
Figure 1. Electric versus magnetic second-harmonic generation in AlGaAs nanoantennas. (a) Schematic structure and SEM image of fabricated individual AlGaAs nanoantenna. (b) Crystalline structure of AlGaAs and relative directions of optical pump propagation k and electric field E. (c,d) Concept images of distinct polarization patterns of (c) electric and (d) magnetic second harmonics for the simplest cases of dipolar radiation. Blue arrows show the electric field vectors for the SH radiation patterns. (e) Far-field polarization distributions of the electric and magnetic multipoles in the plane ⊥ to the z-axis [see Figures S2 and S3 in Supporting Information for details].
stipulated by a specific tensorial form of the quadratic optical nonlinearity dictated by the crystalline structure of AlGaAs, and resonant excitation of dipolar modes in the nanodisk. The tensor of the second-order nonlinear susceptibility of the [100] grown sample of AlGaAs possesses a zinc blende crystalline structure, and it contains only off-diagonal elements (2) χ(2) with i ≠ j ≠ k. In the principal-axis system of the ijk = χ crystal, the ith component of the nonlinear electric polarization vector (defined as the electric dipole density in the material at (ω) (ω) SH frequency) is given by P(2ω) = ε0χ(2) i ijk Ej Ek . When FW wave-vector is parallel to [001] axis aligned with the out-ofplane z axis, and the angle between the FW electric field and [100] crystalline axis in-plane is φ, the P is recast to
conversion efficiency beyond what is possible with plasmonics.12,13 Negligible resistive losses of dielectric nanoparticles avoid heating problems and allow excitation at much higher light intensities, which is of paramount importance for the efficiency of nonlinear optical phenomena. Nonlinear response can be further enhanced and altered substantially by nonlinear interference and wave mixing effects.6,7,14,15 The key question is how to differentiate experimentally the optically induced electric and magnetic nonlinear contributions and how to control the process of emission of the secondharmonic radiation from nanoparticles. In this Letter, we present a direct experimental demonstration of nonlinear optical magnetism in AlGaAs nanoantennas. As electric and magnetic nonlinear processes generate light with orthogonal polarizations to distinguish these two types of nonlinear response, we measure the polarization states over the directionality diagrams of the nanoantennas’ emission. The continuous transition between electric and magnetic nonlinearities is achieved by tuning the polarization of the incident fundamental beam. For our experiments, we choose AlGaAs as material with the second-order nonlinearity for optical nanoantennas, as it allows record-high nonlinear conversion efficiencies.14,16−18 To make nanoantennas, we employ an AlGaAs-in-insulator fabrication procedure,14 containing epitaxial growth of 300 nm AlGaAs film in conjunction with electron-beam lithography and a sequential bonding procedure to a glass substrate. Our final sample contains high-quality Al0.2Ga0.8As nanodisks embedded in a transparent benzocyclobutene (BCB) layer with the refractive index similar to that of glass placed on a glass substrate [see Figure 1a for a schematics and an example of the fabricated AlGaAs optical antenna]. We proceed with analytical considerations of the second harmonic (SH) in AlGaAs nanoantennas. We show that a multipolar composition of the SH light can be controlled by a polarization of the fundamental wave (FW). This effect is
P(2ω)
⎛ ⎞ Ez(ω)(E(yω) cos 2φ − Ex(ω) sin 2φ) ⎜ ⎟ ⎜ ⎟ (ω) (ω) (ω) (2) ⎜ φ + φ E ( E cos 2 E sin 2 ) ⎟ z x y ∝χ ⎜ ⎟ ⎜(Ex(ω) cos φ + E(yω) sin φ)(E(yω) cos φ − Ex(ω) sin φ)⎟ ⎜ ⎟ ⎝ ⎠
(1)
We next analyze the induced nonlinear multipolar sources utilizing Mie modes of a spherical dielectric particle. We consider the FW field distribution inside the nanoparticle in the form of a linear superposition of electric dipole and magnetic dipole modes (ED+μMD) with μ being the ratio of their amplitudes. The FW electric field inside the nanoantenna we write as a superposition of corresponding vector spherical harmonics X1,±1 [see Materials and Methods in the Supporting Information for details]. We then employ general expressions for the electric and magnetic multipolar coefficients at the SH wavelength aE,M (l,m)19 as defined by the overlap integrals of the electric current and charge sources with spherical harmonics, j = 2iωP(2ω) and ρ = ∇·P(2ω) [see details in the Supporting Information]. As a result, we obtain two distinct multipolar structures of the SH field for two principal cases of the fundamental wave 3915
DOI: 10.1021/acs.nanolett.7b01488 Nano Lett. 2017, 17, 3914−3918
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Nano Letters polarization [see Tables S1 and S2 in the Supporting Information for details]. With the polarization at 0° (FW Efield ∥ to [100] axis), SH is dominated by a magnetic dipole aM(1,0), a magnetic quadruple [aM(2,0) and aM(2, ± 2)], and a magnetic octupole [aM(3,0) and aM(3, ± 2)] followed by higher order multipoles. With the pump at 45° (FW E-field diagonal to [100] axis), SH is dominated by an electric quadruple [aE(2,0) and aE(2, ±2)], and an electric octupole [aE(3,0) and aE(3, ±2)] followed by higher order multipoles. Generated electric multipoles can be distinguished from the magnetic multipoles in the far-field by their polarization distributions. For example, an electric dipole polarization follows the polar angle unit vector in the same way that in a magnetic dipole it follows the azimuthal angle unit vector. This results in “radial” polarization distribution from an electric dipole in the projection plane perpendicular to the dipole moment, and correspondingly, “azimuthal” polarization distribution from a magnetic dipole [see Figure 1c,d]. Higherorder magnetic multipoles can be clearly distinguished from electric multipoles by their polarization distributions as well [see Figure 1e and more details in Figures S2 and S3 in Supporting Information]. We emphasize that at the microscopic level the second-order optical nonlinearity in a noncentrosymmetric nonmagnetic material is driven by the electric-dipole light-matter interaction, but high-index dielectric nanoparticles with this nonlinearity can generate effectively magnetic multipoles at the harmonics. Importantly, the tensorial form of the nonlinearity along with the dipolar field excitations at the fundamental wavelength allow one to tune induced nonlinear multipoles in nanoantennas. Despite its geometrical simplicity, a nanoantenna is a resonant element that supports both electric and magnetic multipolar modes that can be generated efficiently with the nonlinear source polarization.20 The ratios of multipoles’ amplitudes depend on the ratio of antenna size and pump wavelength, being tailored by a hierarchy of the Mie resonances. Exact values of amplitude coefficients dependent on the geometry and a refractive-index contrast are further found in full-wave numerical modeling. We use the finite-element-method solver in COMSOL Multiphysics in the frequency domain. To closely resemble the experimental conditions of AlGaAs-in-insulator fabrication, we consider disk nanoantennas with 300 nm height and various diameters. The disks are embedded into a homogeneous medium with a refractive index of 1.44, matching those of both the glass substrate and the BCB layer. The material dispersion of AlGaAs is taken from the COMSOL tabulated data. We perform the calculations for 1550 nm fundamental wavelength and assume an undepleted pump approximation. We then perform a multipolar decomposition of the fields for both the fundamental wavelength and the SH as functions of disk diameters in the range of 300−500 nm. We find that at the fundamental wavelength the optical response is defined by resonant electric and magnetic dipoles [see details in Figure S1 in Supporting Information]. The SH multipolar expansion is calculated for two pump polarization angles φ = 45° and φ = 0° [see Figure 2a,b]. In accord with our analytical considerations, the numerical results suggest that the SH radiation is electric for φ = 45°, while it is predominantly characterized by magnetic multipoles for φ = 0°. For example, for a nanodisk size of 360 nm we see a clear distinction between the SH multipolar structures: for φ = 0° the SH is dominated by the magnetic octupole and magnetic dipole, and for φ = 45° the SH radiation
Figure 2. Multipolar decomposition of second-harmonic radiation as a function of the disk diameter for the orientation angles (a) φ = 0°, and (b) φ = 45°. Panel a is dominated by electric multipoles, whereas panel b is dominated by magnetic multipoles.
from the same disk is dominated by the electric quadrupole. Thus, the disk shows magnetic or electric SHG depending on the angle φ of the pump polarization. We further take a closer look at this specific nanodisk size. We calculate numerically the far-field radiation patterns of the SH from the nanoantenna for the two cases of pump polarizations (see Figure 3a,c). Figure 3b,d shows the projection of the 3D patterns onto 2D planes in forward and backward directions. We notice that polarization patterns are similar to radial for φ = 45° with a small degree of ellipticity, and they are similar azimuthal for φ = 0°. We then proceed with experimental study of the SH in AlGaAs nanodisk antennas. We fabricate the nanodisks with an optimized diameter of 360 nm and optically pump them with a femtosecond laser beam at a central wavelength of 1550 nm and an average beam power of 1 mW at a repetition rate of 5 MHz. The beam is focused by an infrared objective (NA = 0.85) to a diffraction limited spot of 2.2 μm, resulting in a peak intensity of 7 GW/cm2. A visible objective (NA = 0.9) collects the SH signal from the disk in the forward direction, while the focusing objective collects SH radiation in the backward direction. The SH signal is detected by two cooled CCD cameras, calibrated with a power meter. On the CCD cameras, we measure the polarization-resolved radiation diagrams (backfocal plane images) of SH radiation using the method described earlier in ref 21. We experimentally observe distributions of the electric field vectors for 45° and 0 °FW polarization [see Figure 3b,d]. We next study a multipolar structure of the SH as a function of pump polarization angle φ. As the angle φ is tuned, we observe a smooth transition from magnetic to electric SHG [see Figure 4a]. We note that polarization of the SH electric 3916
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Figure 3. Directionality and polarization diagrams of the SH signal. (a,c) Calculated radiation patterns of SH for the pump polarization at 45° and 0° angles, respectively. (b,d) Polarization inclinations of SH in the forward and backward directions both experimentally measured and numerically calculated at 45° and 0° angles correspondingly. Numerical aperture of experimental forward and backward directionality is 0.9 and 0.85. Calculations in (b,d) show full numerical apertures of 1.44 (inner circles show experimentally captured portion).
The results are shown in Figure 4b. We observe a transition from electric to magnetic second-harmonic generation. In conclusion, we have observed directly the nonlinear optical magnetism in AlGaAs nanoantennas by analyzing the polarization states of the nonlinear emission. Our experiments are supported by the multipolar field decomposition. We have demonstrated a control over a continuous transition between electric and magnetic nonlinear responses by tuning polarization of the optical pump.
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ASSOCIATED CONTENT
* Supporting Information S
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.7b01488. Details on theoretical calculations, and optical diagnostics (PDF)
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Figure 4. Transition between electric and magnetic second-harmonic generation. (a) Total efficiency of the SH radiation and sums of electric and magnetic multipolar contributions as functions of the angle φ between the pump electric field E and [100] crystalline axis. (b) Calculated and experimentally retrieved portion of magnetic contribution for the SH radiation.
*E-mail:
[email protected]. ORCID
Sergey S. Kruk: 0000-0003-0624-4033 Mohsen Rahmani: 0000-0001-9268-4793 Dragomir N. Neshev: 0000-0002-4508-8646
multipoles in the far-field along the pump polarization axis E(ω) is ∥ to E(ω) [see Figure 1e], and polarization of the SH magnetic multipoles is ⊥ to E(ω). This allows us to quantify both numerically and experimentally the relative contributions of electric and magnetic multipoles into SHG as
∫ |E⊥(ρ , θ)|2 dρ M= ∫ |Etot(ρ , θ)|2 dρ
AUTHOR INFORMATION
Corresponding Author
Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors acknowledge a support of the Australian Research Council and thank R.W. Boyd, N. Engheta, S. Larouche, A. Miroshnichenko, and L. Novotny for stimulating discussions. They acknowledge the use of the Australian National Fabrication Facility (ANFF) at the ACT Node. The theoretical model was developed with the support of the Russian Science Foundation (Grant No. 17-12-01574). Rocio CamachoMorales acknowledges a grant from Consejo Nacional de Ciencia y Tecnologı ́a (CONACYT), México.
(2)
where ρ and θ are polar coordinates of the far-field directionality diagrams, θ equals to the angle of the FW polarization, ρ is limited by the numerical aperture of the experimental system. Etot is amplitude of the SH field and E⊥ is a portion of the field ⊥ to the pump polarization axis. Here the integration is performed over the range of ρ captured experimentally. M = 1 corresponds to purely magnetic multipolar radiation, M = 0 corresponds to purely electric multipolar radiation. We retrieve the portion of magnetic contribution from both numerical simulations and experiments. In experiments, we measure the polarization resolved radiation diagrams for pump polarizations between 0° and 45° with 5° step [see the diagrams in Figure S4 of Supporting Information].
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REFERENCES
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