Efficient Forward Second-Harmonic Generation from Planar Archimedean Nanospirals

The enhanced electric field at plasmonic resonances in nanoscale antennas can lead to efficient harmonic generation, especially when the plasmonic geometry is asymmetric on either inter-particle or intra-particle levels. The planar Archimedean nanospiral offers a unique geometrical asymmetry for second-harmonic generation (SHG) because the SHG results neither from arranging centrosymmetric nanoparticles in asymmetric groupings, nor from non-centrosymmetric nanoparticles that retain a local axis of symmetry. Here we report forward SHG from planar arrays of Archimedean nanospirals using 15 fs pulse from a Ti:sapphire oscillator tuned to 800 nm wavelength. The measured harmonic-generation efficiencies are 2.6*10-9, 8*10-9 and 1.3*10-8 for left-handed circular, linear, and right-handed circular polarizations, respectively. The uncoated nanospirals are stable under average power loading of as much as 300 uW per nanoparticle. The nanospirals also exhibit a selective conversion between polarization states. These experiments show that the intrinsic asymmetry of the nanospirals results in a highly efficient, two-dimensional harmonic generator that can be incorporated into metasurface optics.

The uncoated nanospirals are stable under average power loading of as much as 300 µW per nanoparticle. The nanospirals also exhibit a selective conversion between polarization states.
These experiments show that the intrinsic asymmetry of the nanospirals results in a highly efficient, two-dimensional harmonic generator that can be incorporated into metasurface optics.
The second-order susceptibility governs a host of important nonlinear optical phenomena, including frequency mixing, sum-frequency and harmonic generation, and optical rectification.
In crystalline and molecular materials, second-order nonlinearities are non-vanishing only at surfaces or in materials with a non-centrosymmetric crystal structure; moreover, the efficient generation of a second-order nonlinear effect requires that the fundamental incident and the nonlinear outgoing waves be phase matched through a macroscopic volume of material, typically on the order of cubic millimeters. 1 Plasmonic nanostructures and nanostructure arrays also exhibit second-order nonlinearities, and can generate forward second harmonics if their geometries are not centrosymmetric. Such structures are inherently planar, and therefore compatible with thin-film optical and optoelectronic technologies and with metasurface optics. With advances in nanofabrication, the symmetry of the structures can be exquisitely controlled at the level of a few nanometers. 2 Combining these effects with ultrafast, high-intensity laser pulses yields massive electric-field enhancements and correspondingly greater second-harmonic yield. The localized surface plasmon resonance enhances efficiency, and can be designed by selecting the nanoparticle shape for a given wavelength; selective polarization response can also be designed into the nanoparticle. A number of asymmetric plasmonic geometries have been used for harmonic generation, including L-and V-shaped nanoparticles, nanocups and asymmetric trimers. [3][4][5][6][7] Larger plasmonic structures -such as the ratchet wheel -have also been shown to affect the polarization of harmonic emission. [8][9][10][11][12] However, even though metallic nanostructures can generate significant second-order nonlinear responses per volume, the nanostructure volume is incredibly small. 13 High efficiency is therefore also crucial in order to generate reasonable numbers of photons in nonlinear processes without melting or damaging the nanostructures. Aperiodic arrangements of centrosymmetric nanoparticles offers one route to enhanced nonlinear signals. 14 Creating non-centrosymmetric systems of particles with a center of inversion symmetry yields even greater harmonic conversion efficiencies. 15 The need for efficient nanostructured harmonic generators then drives the search for new plasmonic geometries with higher harmonic generation efficiencies in spite of low material volumes.
In this paper, we describe the second-order nonlinear response from arrays of planar 4π Archimedean nanospirals with sub-wavelength dimensions. The Archimedean nanospiral commends itself as a frequency-conversion architecture due to its unique asymmetry and twodimensional chiral response. Previous experiments and simulations have shown that this geometry has a spectrally complex response in the visible to the near-infrared region and spatially differentiated, near-field configurations, as well as selectively enhanced optical response to the polarization states of incident light. [16][17] These characteristics make the nanospiral a strong candidate for nonlinear optical applications where a broadband plasmonic element is necessary. Unlike plasmonic structures with globally broken symmetry created by modifying or arranging nanoparticles with some inherent local symmetry, 3-4, 7, 14 the nanospiral has no local axes of symmetry at all so that the nanospiral can generate second-harmonic light from any polarization state. This inherent lack of symmetry therefore makes the nanospiral an attractive candidate for nonlinear metasurface elements.
Figure 1(a) shows the experimental arrangement in which SHG signals from nanospiral arrays were measured. The illumination source for these experiments was a Ti:sapphire oscillator (KM Labs Cascade) with an output spectrum centered at 800 nm. The oscillator beam was directed through a 128-pixel, double-mask, spatial light modulator (SLM, Biophotonics Solutions) that uses multiphoton intrapulse interference phase scanning (MIIPS) to compress the 50 fs oscillator pulse to a transform-limited duration of 15 fs. [18][19] The laser pulse was focused on to the nanospiral array using a lens with a numerical aperture of 0.35 to create a focal spot size of 10μm. The maximum energy per pulse was 0.33 pJ at a repetition rate of 82 MHz and was varied using a half-wave plate and linear polarizer combination. After passing through the nanospiral array, the fundamental (800nm) was filtered out of the signal using a short-pass filter centered at 625 nm and a band-pass filter centered at 400 nm. The SHG signal produced by the nanospirals was detected using a solid-state photomultiplier tube (Hamamatsu, RU-9880U-110) in connection with a photon-counting system (Stanford Research Systems).
The nanospirals used in these experiments were created using electron beam lithography in a Raith eLINE scanning electron microscope. All experiments demonstrated here used 4π rotation nanospirals ordered in 10µm x 10µm arrays on ITO-covered glass substrates. The Archimedean nanospiral is described by the equation = , where α is a constant that determines the rate of expansion of the spiral. These particular spirals were designed such that the spacing between each subsequent arm is equal to the others. The inter-particle spacing was 610nm with a maximum nanoparticle diameter of 395nm and a thickness of 40nm areas of emission that correspond to the electric-field intensity generated in the plasmon near field. Since PEEM is a two-photon process that depends on the electric-field of the plasmon in the same way as SHG, this verifies that most of the observed SHG signal is coming from the center of the nanospiral. This makes the focusing mode ideal for harmonic generation, since second-order nonlinear phenomena depend superlinearly on the strength of the electric field. The focusing mode of the nanospiral provides the spatial concentration of optical energy necessary for efficient conversion to the outgoing second harmonic. The structure of this near-field state also provides a polarization-sensitive template for quasi-chiral properties that are described later in this paper.
The SHG measurements were not reproducible at powers greater than 280 µW per nanoparticle because laser heating deformed the nanospirals, causing them to lose their asymmetric geometry; the shape of the deformations that occurred due to melting can be seen in the Supplemental Material, Figure S1. Up until the point of deformation, the second-harmonic beam from the nanospirals showed no sign of saturation due to nonlinear down-conversion processes. After deformation, the nanoparticles exhibit neither second-harmonic response nor the other properties of the nanospirals. If the nanospirals were coated in a protective silicon layer as shown in references 3 and 7, the power threshold could almost certainly be increased beyond an incident power of 280 µW per nanoparticle in order to create even higher harmonic-generation efficiencies. The second-harmonic response to circular polarizations, however, more clearly illustrates the effects of intra-particle resonances on the electric field strengths and consequently the SHG efficiency. The polarization dependence of the SHG intensity in Fig. 3 shows that for righthanded circular polarization -rotating from the outside of the spiral to the inside -there is a larger enhancement than that observed with linear polarization. When excited with left-handed circularly polarized light the nanospirals show a significantly reduced second-order response.
The maximum and minimum SHG signals differ by a factor four, which occurs for an eccentricity of 0.66, where eccentricity is defined as the ratio of minor to major axis of the ellipse traced out by the polarization vector. This dependence on eccentricity arises because the nanospiral is not perfectly circular. The second harmonic conversion efficiency -given by The polarization response of the second harmonic emission is consistent with FDTD simulations that have been performed with this plasmonic geometry in previous work. [16][17] Simulations using Lumerical Solutions ® software show three unique near-field structures in the plasmon resonances that occur at spectrally distinct points in the optical and near-infrared band, and have been designated as standing wave, hourglass, and focusing modes. At a wavelength of 800nm, the focusing mode is excited, concentrating the near-field intensity in the center of the spiral to create a single region of high electric field. 16  can be identified as one -albeit only one -characteristic of a chiral system.
We now show that the second harmonic generated by Archimedean nanospirals reveals the complex interplay among polarization states that is the hallmark of this quasi-chiral response.
The conversion between linear and circular polarizations was investigated by placing a second quarter-wave plate and linear polarizer in the path of the SHG emission. Figure 4  This behavior seems to be reproduced by the focusing mode simulations shown in Figure 5.
When the polarization is driving the electrons towards the center of the nanospiral as shown in Figure 5 (a), the strength of the electric field is enhanced. The surface charge density of the plasmon must be ordered if it is to maintain the constructively interfering, multipolar resonance condition that will prevent second-order light from destructively interfering with itself.
When the polarization is driving the electrons away from the center of the nanospiral, on the other hand, a disordered plasmon resonance is created that is simulated in Figure 5 (b).
Depolarization in plasmon emission has been observed in simple nanoparticle geometries having resonances that overlap spectrally and spatially; the coherent emission from sub-wavelength structures may exhibit partial depolarization in various directions depending on the relative phases of the light. [26][27] The near-field structure of the LCP excitation in the nanospiral shows regions of high-electric field enhancement that are spatially spread out over larger parts of the nanospiral than in either RCP or linear excitation. This structure contains enough smaller resonances with randomly oriented propagation directions that the resulting SHG emission is completely depolarized. While the polarization conversion observed in nanospirals differs from the polarization rotation that has been demonstrated in other plasmonic geometries [23][24][25] , the conversion between linear, circular, and depolarized light is evidence of the complex interplay between the second-order response and the near-field structure of the plasmon resonance.
In summary, the Archimedean nanospiral is shown here to produce second-harmonic emission at intensities sufficient for nanotechnology devices. The capacity to modulate the intensity of the SHG by altering the polarization state of the emission, and with efficiencies as large as 1.3·10 -8 at 280 μW incident power per nanoparticle, the nanospiral is a competitive architecture for alloptical control applications. The nonlinear response to the handedness of circular polarization also reveals the relation between the complex boundary conditions imposed by the spiral shape of the nanoparticle and the plasmon resonance.
Planar frequency-conversion structures are an essential element of plasmonic circuitry. 28 By creating more efficient SHG structures that need not satisfy any phase matching conditions, and by using localized surface plasmon (LSP) resonances to further enhance efficiency, we have shown that the nanospiral is potentially significant addition to plasmonic technology. The complex plasmonic resonance structure inherent in the nanospiral, and its complex, but selectable, polarization response, bring additional dimensions to the search for efficient nonlinear plasmonic light sources.