Unidirectional emission of phase-controlled second harmonic generation from a plasmonic nanoantenna

2.1 Characteristics of nanoantena elements

From the selection rules for SH generation of isolated single metal nanoparticles, which are derived from parity conservation laws [33, 34], the general SH-emission patterns are based on quadrupoles and clearly differ from the dipolar scattering pattern in linear response [19, 22, 35, 36]. Meanwhile, the near-fields of multiple elements with different dipole resonances at their fundamental and SH wavelengths can spatially overlap at the fundamental and SH wavelengths, allowing dipolar SH emission [13, 14, 16, 37]. To obtain a compact and simple configuration, we overlap the spatial modes within a single element featuring two orthogonal plasmonic dipole modes. Figure 1B shows scanning electron microscope (SEM) images of the V- and Y-shaped nanoparticles studied in this work. These particles were fabricated on a glass coverslip by electron-beam lithography combined with a lift-off process. They were composed of evaporated gold with a thickness of 30 nm. Their geometries are defined by their arm length L, opening angle of the arms θ, and tail length L _Y (L _Y = 0 for the V-particle). The extinction spectra of both particle shapes exhibit two main resonance bands at visible and near-infrared wavelengths under y- and x-polarized illuminations, respectively (see Figure 1C and D). Their corresponding phase distributions (insets of Figure 1C and D) show orthogonal plasmonic dipole modes D _x and D _y along the incident x- and y-polarizations, respectively. The D _x band of the V-particle almost coincides with that of the Y-particle because it is determined by the length and opening angle of the arms (i.e., L and θ, respectively). Increasing the tail length L _Y shifts the D _y resonance wavelength to the red side (see also Figure S1) [38]. The near-field intensity distribution of the D _x mode overlaps with that of D _y at the end of each arm (Figure 1E and F). Moreover, the SH polarization in Figure 1G, induced by the D _x near field, should allow phase matching with the D _y mode. These results indicate that the SH polarization can be coupled to the D _y mode, where D _x and D _y are associated with active and passive modes, respectively.

2.2 Dipolar SH emission from a single element

To demonstrate this near-field coupling, we analyzed the angular distributions of SH-emission intensity from the V-shaped nanoparticle (Figure 2). The SH wavelength was matched to the D _y resonance peak at 750 nm in Figure 1C. Although the excitation (fundamental) wavelength at 1500 nm was far from the D _x resonance peak, the D _x mode was excited as confirmed in the near-field and charge distributions (see Figure S2). The magnitude of the SH emission is typically proportional to both of not only the square of the near-field of the fundamental mode, i.e., the D _x field in this study, but also the mode field at the SH wavelength, i.e., the D _y field [39]. Indeed, a strong enhancement of the SH emission for the V-shaped nanoparticle under the similar excitation condition has been demonstrated, even though the fundamental-mode field is not resonantly enhanced [40]. The distributions of azimuthal angle φ and polar angle θ in Figure 2A were measured using back focal plane (BFP) imaging [41]. When nanoparticles are placed on the high-refractive-index substrate, the maximum radiation to the substrate is observed at angles equal to or greater than the critical angle of the substrate interface [42]. Under x-polarized illumination, the V-particle exhibited y-polarized dipole-like SH emission which were maximized near the critical angle of ∼41.14° for an air-glass interface (Figure 2B and D). The SH emission pattern and its polarization distribution well agreed with those of light scattering in the linear response to y-polarized light at 750 nm, which directly excites the D _y mode (Figure 2C and E). This result shows that the induced SH polarization was efficiently coupled to the D _y mode orthogonal to the incident polarization. It should be noted that coupling via the spatial overlap and phase matching between orthogonal dipole modes circumvents the selection rule even for an isolated nanoparticle.

Figure 2:

(A) Illustration of the coordinate system. The incident light is polarized along the x-direction to excite the D _x mode for the SH generation. (B) Measured angular distributions of the SH-emission intensity from the V-shaped element on the substrate in Figure 1. The azimuthal angle φ and polar angle θ in (A) were obtained using back focal plane imaging (41). The SH wavelength matches the D _y resonance peak at 750 nm. (C) Measured light scattering pattern in the linear response to y-polarized light illumination at 750 nm, which directly excites the D _y mode. (D and E) Polarization analysis of the SH-emission intensity in (B) and the linear scattering intensity in (C), respectively, obtained through an analyzer. The results are in good agreement with each other. The color scale indicates the normalized scattered light intensity.

2.3 SHG phase control

Our directional SH nanoantenna requires precise phase control of the dipolar SH emissions from individual elements. The surface SH polarization at a certain position r can be written as P _nnn(r, 2ω) = ε ₀ χ ⁽²⁾ _nnn E _n(r, ω)E _n(r, ω), where χ ⁽²⁾ _nnn and E _n(r, ω) are the components of the surface susceptibility tensor and electric field, respectively, normal to the surface of the nanoparticle at the fundamental (excitation) wavelength (a detailed explanation is provided in Section S1). These components are known to dominate the surface SH response of metal nanoparticles [24, 25]. From the above equation, the phase of the SH polarization can be determined from the phase of E _n(r, ω). When the excitation wavelength is much longer than the resonant wavelength, both the electric near-field and plasmon of the dipole mode oscillates in-phase with the excitation. As the excitation wavelength approaches the resonance peak, their relative phases shift by π around the resonance spectral position (Figure S3). However, in our case, the SH wavelength must remain near the D _y resonance peak to obtain the stable dipolar SH emission (a detailed explanation is provided in Section S2). Because the excitation wavelength remains far from the D _x resonance peak, the phase control of the SH polarization is restricted. To control the phase of the dipolar SH emission, we instead focus for the first time on the phase shift in the coupling of the SH polarization to the D _y mode. The D _y resonance wavelength can be controlled through the tail length L _Y of the Y-shaped nanoparticle (Figure S1) without changing the D _x band, i.e., the phase of the induced SH polarization (see Figure 1). Under this control method, the effect of the D _y resonance on the phase of the SH emission can be simply analyzed.

The D _y resonance effect was revealed by observing the interference between the dipolar SH emissions from the V- and Y-shaped nanoparticles (Figure 3A). When two coherent dipoles with separation distance d oscillate with a phase difference ΔΦ, the retardation phase kd due to propagation of their radiation with wavenumber k can compensate ΔΦ in one direction along the line connecting the dipoles, and add in the opposite direction. When two dipoles have equal magnitude, their radiation power is proportional to cos((ΔΦ + kd)/2) in one direction and cos((ΔΦ − kd)/2) in the other. In the present study, the SH wavelength λ _SH and distance d between the nanoparticles were fixed at 725 and 180 nm (∼λ _SH/4), respectively, giving k _SH d ∼ π/2 (Figure 3B and C). Therefore, depending on ΔΦ, the dipolar SH emissions constructively interfere in one direction along the x-axis and destructively interfere in the opposite direction. The pairs of V- and Y-nanoparticles were periodically arranged with a pitch of 650 nm in the x-direction to increase the signal-to-noise ratio of the SH interference signals due to the diffraction grating effect [43]. In this configuration, the ΔΦ-dependent interference can be seen as light diffraction in the +1st and −1st orders along the x-axis. The intensity ratio of the ±1st order diffracted SH emissions as well as the D _y resonance clearly depended on the tail length L _Y of the Y-particle (see Figure 3C and D). When a pair of V-particles was used, i.e., L _Y = 0, the SH-emission pattern should be symmetric, with the same SH intensity of the +1st and −1st diffraction orders. In addition, ΔΦ should be π because the intensity of the 0th order diffracted SH emission was attenuated by destructive interference. As the D _y resonance redshifts with increasing L _Y, the SH intensity ratio in the ±1st diffraction orders increased in Figure 3(D and E), meaning that ΔΦ approaches 3π/2 of the optimal conditions of radiation asymmetry. As the D _x band that determines the phase of the SH polarization is independent of L _Y (Figure S4), the asymmetry of the ±1st diffraction orders arises from the redshifted D _y resonance of the Y-particle at the SH wavelength. In other words, the phase of the dipolar SH emission can be controlled simply by changing L _Y (which alters the D _y resonance). By this method, we can precisely design the SH phase differences between the elements in the nanoantenna. Moreover, these results strongly support that the SH signal was emitted by the induced SH polarization coupled to the D _y mode rather than directly from the SH polarization.

Figure 3:

Phase control of the dipolar SH emission.(A) Interference between two coherent dipoles separated by distance d, oscillating with phase difference ΔΦ. When the SH wavelength λ _SH and d are fixed, the ΔΦ between the dipolar SH emissions from the V- and Y-elements causes constructive and destructive interferences in opposite directions along the x-axis. (B, C, and D) SEM images, extinction spectra of D _y modes and measured diffraction patterns of SH emissions, respectively, of pairs of V- and Y-elements (L = 120 nm and θ = 110°) with different tail lengths L _Y. The scale bar in (B) is 100 nm. λ _SH and d are 725 nm (blue stripe in (C)) and 180 nm (∼λ _SH/4), respectively, giving k _SH d ∼ π/2. In (D), the individual pairs are arranged in a two-dimensional array (Λ _x  = 650 nm and Λ _y  = 800 nm) to increase the signal-to-noise ratio of the SH interference signals along the x-axis due to the diffraction grating effect. (E) Correlation between the SH intensity ratio of the ±1st diffraction orders [labeled −1st and +1st in (D)] and the peak shift of the D _y resonance of the Y-element in (C).

2.4 Directional SH emission from a nanoantenna

To further understand the behavior of the directional SH nanoantenna, we measured the wavelength dependence of the SH-emission patterns from a single pair of V- and Y-shaped nanoparticles with a tail length of 25 nm for the Y-particle (see Figure 3B). The maximum directivity of the SH emission, i.e., perfect constrictive and destructive interference in Figure 3A, can be achieved for k _SH d ∼ π/2 + mπ (m = 0, ±1, ±2…) and ΔΦ = π/2 + nπ (n = 0, ±1, ±2…). The distance d between the nanoparticles was set to obtain the maximum directivity for the SH wavelength λ _SH = 725 nm, i.e., k _SH d ∼ π/2. The phase difference ΔΦ can be also optimized by controlling the excitation wavelength because ΔΦ depends on the SH wavelength around the D _y resonance. Figure 4A displays the BFP images under x-polarized illumination at different wavelengths. The antenna exhibited strong lateral directionality at the SH wavelength λ _SH between the D _y resonance peaks of the V- and Y-elements. The intensity was maximized near the (φ, θ) = (180°, 45°) direction exceeding the critical angle. In general, nanoparticles emit light into a substrate with higher refractive index, and index-matching shifts the emission direction to θ = 90°. It should be noted that linear scattering at the fundamental wavelength λ _ex is omnidirectional, i.e., dipole radiation (Figure S5). In other words, the omnidirectional excitation of the antenna permits directional SH emission. To realize directional SH emission, we exploited the different plasmon modes of antenna excitation and SH emission. When the D _y modes of the antenna were directly excited by y-polarized light, the linear response was also unidirectional side scattering, similarly to that of SH emission (Figure 4B). Interestingly, the linear scattering and SH emission appeared in opposite directions, although the radiation patterns from the individual antenna elements were almost identical (Figure 2). These results are supported by numerical simulations (see Figure 4C and D). In the SH generation process, the D _y modes were excited by the SH polarization normal to the surface localized at the arm ends of the V- and Y-nanoparticles (Figure 1G). Therefore, the phase of the SH emission was flipped by inverting the Y-element in the antenna, as shown in Figure 4E. This explains the phase difference ΔΦ = π between the SH emissions of a V-particle pair in Figure 3. Conversely, in the linear process, the incident y-polarized light excited the D _y modes of the V- and Y-elements in the antenna in-phase (Figure 4F). Thus, ΔΦ of the SH emission from the directional antenna differed by π from that of linear light scattering, resulting in opposite propagation directions of the two emissions.

Figure 4:

(A and B) Measured angular distributions of SH emission and linearly scattered light, respectively, from a pair of V- and Y-elements with a tail length of 25 nm (see Figure 3B) at different wavelengths of incident light. λ _ex and λ _SH denote the excitation and SH wavelengths, respectively. In (B), the D _y mode of the antenna was directly excited by y-polarized light illumination. The antenna directivities of both radiations were maximized in the wavelength range between the D _y resonances of the V- and Y-elements. The SH emission in (A) and linear scattering in (B) occurred in opposite directions. (C and D) Corresponding theoretical angular distributions of the SH emission at λ _ex = 1450 nm and the linearly scattered light at λ _ex = 740 nm, respectively. (E and F) Charge and SH polarization distributions in the processes leading to unidirectional radiation of (C) and (D), respectively.

4.1 Nanoantenna fabrication

Nanoantennas were fabricated on a glass substrate using simple electron-beam lithography (EBL) and lift-off techniques. After washing a glass substrate, a film of the positive resist (ZEP520a, Zeon Chemicals Co.) was formed by spin-coating to a thickness of 200 nm. The film was exposed to a given pattern using an EBL system with a high accelerating voltage (125 kV) and was then sequentially developed in developer solution (ZED-N50, Zeon Chemicals Co.) and a rinsing agent (ZMD-B, Zeon Chemicals Co.). A 30-nm gold layer was deposited by electron-beam evaporation. The resist pattern was subsequently removed from the substrate using a resist remover (ZDMAC, Zeon Chemicals Co.), forming nanoantennas on the glass substrate.

4.2 Experimental characterization

To characterize the nonlinear and linear optical responses of the nanoantennas, we recorded the angular distributions of their SH-emission and linear-light-scattering intensities, respectively, using the BFP imaging setup depicted in Figure S6. The antennas were periodically arranged with a pitch of 2 μm. Their nonlinear and linear responses were obtained under a femtosecond pulsed laser (generated by an optical parametric amplifier) and a continuous-wave Ti:sapphire laser, respectively, with tunable wavelength ranges of 1300–1600 and 700–1000 nm, respectively. The linear polarization of the laser beams was changed to the desired direction by a half-wave plate. These laser beams were weakly focused on the antennas by a 4× objective lens with a numerical aperture (NA) of 0.13. The SH emission and linear scattering in the forward direction were collected through another 60× oil-immersion objective lens (NA = 1.49). The SHG excitation and stray light were removed by a 1150-nm cutoff short-pass filter and a 650-nm cutoff long-pass filter. To block the transmitted light while measuring the linear scattering pattern, an opaque stopper with a diameter corresponding to NA < 0.3 was installed in a secondary BFP. The BFP images were projected on a sCMOS camera and processed by a previously described method [47]. The polarizations of the SH signal and scattered light were selected by an absorptive sheet polarizer. Linear spectroscopic characterizations of the antennas were carried out using white light in the same illumination system as the laser beams. The extinction spectra of the antennas were obtained as (I _b(λ) − I _m(λ))/I _b(λ), where I _m(λ) and I _b(λ) are the spectra of the transmitted white light through the substrates with and without antennas, respectively. The polarization dependences of the extinction spectra were analyzed by placing an absorptive sheet polarizer in front of the illumination objective. The spectra were measured in the wavelength ranges 600–950 and 1050–1600 nm using silicon and InGaAs detectors, respectively.

4.3 Theoretical characterization

The linear and nonlinear responses of the nanoantennas were numerically simulated with a full three-dimensional Maxwell calculation based on a finite element method solver (COMSOL). The nanoantennas were placed on a substrate with a refractive index n of 1.52. The radius of curvature at the corners of the nanoparticle was 10 nm. The wavelength dispersion of the complex permittivity of gold was measured by Johnson and Christy [48]. The simulation method of the nonlinear response is detailed in Section S1 of the Supplementary materials. The spatial distributions of the surface SH polarizations were obtained from the square of the fundamental electric field normal to the surface. The SH electric field radiated from the nanoantennas was computed as the excitation source of the surface polarizations oscillating at the SH frequency. The angular distributions of the SH emission were calculated from the pointing vectors on a 2-μm-diameter sphere surrounding the structure.