• Photonics Research
  • Vol. 9, Issue 6, 950 (2021)
Bin Wang1、2、†, Ying Che2、†, Xiangchao Zhong2, Wen Yan2, Tianyue Zhang2、4、*, Kai Chen2, Yi Xu3, Xiaoxuan Xu1, and Xiangping Li2、5、*
Author Affiliations
  • 1The Key Laboratory of Weak-Light Nonlinear Photonics, Ministry of Education, School of Physics, Nankai University, Tianjin 300071, China
  • 2Guangdong Provincial Key Laboratory of Optical Fiber Sensing and Communications, Institute of Photonics Technology, Jinan University, Guangzhou 510632, China
  • 3Department of Electronic Engineering, College of Information Science and Technology, Jinan University, Guangzhou 510632, China
  • 4e-mail: tyzhang@jnu.edu.cn
  • 5e-mail: xiangpingli@jnu.edu.cn
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    DOI: 10.1364/PRJ.419300 Cite this Article Set citation alerts
    Bin Wang, Ying Che, Xiangchao Zhong, Wen Yan, Tianyue Zhang, Kai Chen, Yi Xu, Xiaoxuan Xu, Xiangping Li. Cylindrical vector beam revealing multipolar nonlinear scattering for superlocalization of silicon nanostructures[J]. Photonics Research, 2021, 9(6): 950 Copy Citation Text show less

    Abstract

    The resonant optical excitation of dielectric nanostructures offers unique opportunities for developing remarkable nanophotonic devices. Light that is structured by tailoring the vectorial characteristics of the light beam provides an additional degree of freedom in achieving flexible control of multipolar resonances at the nanoscale. Here, we investigate the nonlinear scattering of subwavelength silicon (Si) nanostructures with radially and azimuthally polarized cylindrical vector beams to show a strong dependence of the photothermal nonlinearity on the polarization state of the applied light. The resonant magnetic dipole, selectively excited by an azimuthally polarized beam, enables enhanced photothermal nonlinearity, thereby inducing large scattering saturation. In contrast, radially polarized beam illumination shows no observable nonlinearity owing to off-resonance excitation. Numerical analysis reveals a difference of more than 2 orders of magnitude in photothermal nonlinearity under two types of polarization excitations. Nonlinear scattering and the unique doughnut-shaped focal spot generated by the azimuthally polarized beam are demonstrated as enabling far-field high-resolution localization of nanostructured Si with an accuracy approaching 50 nm. Our study extends the horizons of active Si photonics and holds great potential for label-free superresolution imaging of Si nanostructures.

    1. INTRODUCTION

    Dielectric nanomaterials with high refractive indices have been widely studied in recent years owing to their low optical loss, unique optical responses, and compatibility with the manufacturing process of complementary metal-oxide semiconductor technology [13]. Strong electric and magnetic Mie resonances in high-index dielectric nanostructures play a crucial role in the nanoscale confinement of electromagnetic near fields for the enhancement of many optical nonlinear effects [47]. In addition, they engender various interference phenomena in the far field by engineering the interplay of optical-induced multipoles [8,9]. New developments further reveal that, even though the ohmic losses are inherently low for dielectrics, Mie resonances provide strong local heat on account of the absorption of incident light and the transduction into thermal energy. These attributes substantially increase the temperature of nanostructures, paving the way for all-dielectric thermophotonics [1012]. Isolated resonant dielectric nanoparticles have been identified as highly effective optical heaters [10,1315]. Moreover, functional all-dielectric metasurfaces can be actively tuned simply through thermal actuations based on the large thermo-optical coefficient of the materials [1621]. Giant photothermal nonlinearity mediated by resonant modes has been recently revealed in a single silicon (Si) nanostructure, which can be 3 to 4 orders of magnitude greater than unstructured bulk Si [22,23]. Such a unique photothermal mechanism provides a novel scenario of dynamical reversible tuning of optical responses in all-dielectric nanostructures through an optical stimulus.

    The significant advantage of all-optical tuning is that unprecedented flexibility in manipulating multipolar light–matter interactions can be facilitated by means of smart engineering of the illumination beam [2426]. By harnessing spatially variant electric polarizations mediated by tightly focused cylindrical vector beams (CVBs), different multipolar resonances can be selectively excited, resulting in separate control over the induced electric and magnetic multipoles [2729]. Fully exploiting these benefits enables the extreme tailoring of both linear and nonlinear emission properties. The excitation of dark modes [30,31], angular tuning of directional scattering [3234], and enhanced nonlinear light generation [3538] in all-dielectric nanostructures have been increasingly observed. In particular, the unique focusing properties drive the recently developed concepts of vector-field nonlinear microscopy by utilizing CVBs for the characterization of nanostructures [36,39], thereby expanding the capabilities of nonlinear microscopes. Owing to these developments, exciting advances are expected to reveal new applications that leverage innovative combinations of high-index metaoptics and vector-field nonlinear microscopy.

    In this report, we show the photothermal nonlinearity of Si nanoresonators that are strongly influenced by excitation polarization states. Resonance-enhanced photothermal nonlinearity governed by an out-of-plane magnetic dipole (MD) is achieved via azimuthally polarized (AP) beam illumination with the desired excitation wavelength, which is 80% reversible, as well as by repeatable all-optical modulation of the scattering signal. In contrast, a significantly low photothermal nonlinearity is observed in Si nanodisks pumped with a radially polarized (RP) beam, which results from differently induced multipolar modes. Remarkable scattering saturation, which is a consequence of the intense AP beam, efficiently suppresses the scattering intensity of the overlapping excitation of the probe beam. This naturally constitutes a configuration similar to the stimulated emission depletion (STED) microscope [40,41]. In our technique, the AP beam generates a doughnut focal spot and is used as a robust saturation beam. The beam is scattered from Si nanodisks under the Gaussian probe beam to engender an imaging contrast. We therefore demonstrate the realization of far-field high-resolution localization of densely spaced Si nanodisk arrays with exceptional localization accuracy up to 50 nm (λ/11). Our results provide a new means of controlling and modulating the nonlinear scattering response induced by the photothermal mechanism. Moreover, our proposed technique offers important potential in applications in label-free high-resolution imaging for all-dielectric metasurfaces and Si photonics.

    2. RESULTS AND DISCUSSION

    Schematic illustration of the superlocalization imaging and experimental setup. (a) The principle of superlocalization imaging is based on scattering suppression of Si nanodisks at the peripherals of the doughnut-shaped AP saturation beam. (b) Diagram of the reflectance laser scanning confocal system. M1, M2, silver mirrors; DM, dichroic mirror; BS, beam splitter; OL, objective lens; PC, polarization converter.

    Figure 1.Schematic illustration of the superlocalization imaging and experimental setup. (a) The principle of superlocalization imaging is based on scattering suppression of Si nanodisks at the peripherals of the doughnut-shaped AP saturation beam. (b) Diagram of the reflectance laser scanning confocal system. M1, M2, silver mirrors; DM, dichroic mirror; BS, beam splitter; OL, objective lens; PC, polarization converter.

    A schematic of the experimental setup for measuring nonlinear scattering signals from Si nanodisks and realization of superlocalization imaging is shown in Fig. 1(b). A commercial polarization converter (ARCoptix, S.A.) was used to convert a linearly polarized (LP) continuous wave laser beam of 639 nm collimated by a 4f system into an AP beam. The verification of the polarization state of AP is shown by Fig. 7 in Appendix A. It was then collinearly aligned with the LP Gaussian mode probe beam (561 nm). The two laser beams were simultaneously scanned through the Si nanodisks, and the backward scattering of the sample was collected using an oil-immersed objective lens (100×, NA=1.4, Olympus). The microscope scattering images were obtained by synchronizing a photomultiplier tube (PMT) and a galvo mirror scanner. They were recorded with a step size of 7 nm and a dwell time of 10 μs.

    Simulated total scattering spectra and the Cartesian multipolar decomposition of single Si nanodisks (diameter D=200 nm, height h=50 nm) under (a) linear and (b),(c) CVB illumination. Black dashed lines indicate the position of excitation wavelength.

    Figure 2.Simulated total scattering spectra and the Cartesian multipolar decomposition of single Si nanodisks (diameter D=200  nm, height h=50  nm) under (a) linear and (b),(c) CVB illumination. Black dashed lines indicate the position of excitation wavelength.

    Experimental observation of photothermal nonlinearity via backward scattering measurements using CVBs. (a)–(c) Measured PSFs of a single nanostructure under different AP beam intensities at a 639 nm wavelength. (a) At low excitation intensity, the PSF shows the doughnut-shaped focal spot generated from the conventional AP. (b),(c) When the intensity reaches a nonlinear region, scattering saturation occurs, and the corresponding PSFs show a low intensity at the doughnut crest. The intensity lateral profiles (white dashed lines) are plotted on the right. (d) The nonlinear dependency of scattering on irradiance intensities and the evolution of PSFs of the Si nanodisk array for AP excitations at a 639 nm wavelength; (e) for RP excitation, negligible nonlinearity is observed, and the scattering shows a linear response in accordance with the increasing irradiance intensities.

    Figure 3.Experimental observation of photothermal nonlinearity via backward scattering measurements using CVBs. (a)–(c) Measured PSFs of a single nanostructure under different AP beam intensities at a 639 nm wavelength. (a) At low excitation intensity, the PSF shows the doughnut-shaped focal spot generated from the conventional AP. (b),(c) When the intensity reaches a nonlinear region, scattering saturation occurs, and the corresponding PSFs show a low intensity at the doughnut crest. The intensity lateral profiles (white dashed lines) are plotted on the right. (d) The nonlinear dependency of scattering on irradiance intensities and the evolution of PSFs of the Si nanodisk array for AP excitations at a 639 nm wavelength; (e) for RP excitation, negligible nonlinearity is observed, and the scattering shows a linear response in accordance with the increasing irradiance intensities.

    Figure 3(d) shows that nonlinear scattering can empower distinctive PSFs in confocal reflectance imaging of closely packed Si nanodisk arrays. The confocal image at low excitation intensities for such nanodisk arrays is blurry, owing to the restriction of the diffraction limit. However, scattering saturation at high excitation intensities leads to a large reduction in scattering, thus producing subdiffractive features in scattering PSFs. For comparison, scattering images were also recorded under the illumination of the RP beams. An RP beam with the same wavelength turns off the MD resonance, exciting only electric modes. At a wavelength of 639 nm, the RP beam excites at the spectral position far from the ED peak, producing negligible photothermal nonlinearity. Therefore, only a linear scattering behavior is observed [Fig. 3(e)]. Numerical calculations reveal that there are more than 2 orders of magnitude difference when changing the excitation beam from AP to RP (Fig. 8 in Appendix A). It is also worth noting that strong nonlinearity is also expected in the anapole state, where a TD and an ED are coexcited. Nevertheless, anapole excitation in the Si nanodisks falls outside the experimentally accessible range.

    Superlocalization of densely spaced Si nanodisks. (a) PSFs of nonlinear scattering from periodic Si nanodisk arrays evolving with increasing excitation intensities. A correlated SEM image is also presented. (b) Localization accuracy scaling as PSFs obtained at different saturation AP beam intensities. The error bars represent the deviations of FWHM values from 28 nanodisks in the scanning frame. (c) Reversibility of nonlinear scattering is confirmed by the full recovery of measured FWHM from the same nanodisks under repetitive measurements.

    Figure 4.Superlocalization of densely spaced Si nanodisks. (a) PSFs of nonlinear scattering from periodic Si nanodisk arrays evolving with increasing excitation intensities. A correlated SEM image is also presented. (b) Localization accuracy scaling as PSFs obtained at different saturation AP beam intensities. The error bars represent the deviations of FWHM values from 28 nanodisks in the scanning frame. (c) Reversibility of nonlinear scattering is confirmed by the full recovery of measured FWHM from the same nanodisks under repetitive measurements.

    Figure 4(a) presents a series of scattering images with significantly improved resolution under increased saturation beam intensities. These raw superresolved images, combined with the verification of the correlated SEM image, clearly demonstrate that Si nanodisks—indistinguishable in conventional confocal imaging at low excitation intensities—are distinctly resolved at high irradiance intensities (see Visualization 1 for more results). Figure 4(b) quantifies the dependence of localization accuracy on the applied saturation beam intensity, which is based on the statistics of the full width at half-maximum (FWHM) of the imaging spots. The measured FWHM can be sharply squeezed to approximately 50 nm by impinging the AP beam with an intensity of 1.1  MW/cm2 on the nanodisks to match the MD resonances. Compared to conventional STED fluorescence microscopy [46], our technique reduces the saturation intensity by approximately 2 to 3 orders of magnitude. Moreover, this localization accuracy is the highest achieved to date in accordance with the far-field fluorescence-free scheme. Furthermore, the label-free modality is extremely beneficial for contactless inspection of Si photonics. The reversibility of nonlinear scattering is proved by the complete recovery of the FWHM of the nanodisks under repeated measurements of switching the saturation beam on and off, as shown in Fig. 4(c), thus confirming the high stability of the entire process.

    It should be emphasized that we use Si nanodisks for the proof-of-concept, demonstrating the high-resolution localization based on the photothermal mechanism. The photothermal nonlinearity is associated with the size or shape of the Si nanostructure. Specifically, on one hand, the Si nanostructure illuminated by the laser beam converts incident light into heat. The particle temperature subsequently rises nonlinearly with the incoming light intensity, with the slope that depends on the particle size, shape, laser wavelength, and material properties [22,23]. One the other hand, the size and shape also determine the spectral features of the Mie resonances supported by the structure. Resonant optical excitation enables the boosted photothermal nonlinearity to induce a significant change of permittivity of the nanostructure, resulting in the nonlinear dependence of optical scattering on the illumination intensity. Particularly, the scattering signal decreases when the excitation intensity increases, referred to as scattering saturation. The large scattering saturation produced by photothermal nonlinearity can be utilized as an all-optical control over scattering efficiency of another laser beam, laying the foundation for the high-resolution localization based on STED-inspired imaging techniques. As observed in this work, a deep scattering saturation is highly desirable for higher spatial localization accuracy.

    Since the photothermal effect and temperature-dependent permittivity are clearly inherent material properties, the proposed concept is generally applicable to wide nanophotonic systems, especially for dielectric resonant nanostructures made of Si, germanium, III–V semiconductors, or other multicomponent materials demonstrating unique Mie resonances. Besides, vectorial light with unique polarization characteristics enables selective and enhanced coupling to multipolar resonances. Therefore, we envision the applicability of our method is universal for other complex vectorial beams to tailor the dominant multipolar resonances, providing flexible control of multipolar resonances at the nanoscale.

    3. CONCLUSIONS

    In summary, CVBs were implemented to investigate the photothermal nonlinearity of Si nanostructures. Efficient nonlinear scattering was observed by selectively exciting the out-of-plane magnetic Mie resonances with an AP vector beam. Switching to the RP beam resulted in negligible scattering nonlinearity owing to the off-resonance excitation of activated electric multipolar modes. The AP beam with sufficiently high intensities could induce strong scattering saturation of the Si nanodisks on account of the MD-enhanced photothermal effect. An 80% reduction in the scattering signal indicated that the AP beam acted as a saturation beam to efficiently suppress the scattering of another probe beam. In addition, the doughnut-shaped focal spot made the AP beam an ideal candidate for effective STED-like configurations. We further demonstrated the far-field superlocalization of densely packed Si nanodisk arrays with a record-high 50 nm FWHM, corresponding to λ/11 precision. Considering the compatibility of Si materials and complementary metal-oxide-semiconductor manufacturing processes, our findings open new possibilities for all-optical label-free inspection of Si-based structures, with great potential for many applications, such as nonlinear nanophotonics, wafer lithography, and Si-integrated circuits.

    APPENDIX A

    Characterizations of Periodic Si Nanodisk Arrays

    The morphology of the dense arrays of Si nanodisks was characterized by SEM and AFM. The SEM images in Fig.?5 demonstrate that the prepared Si nanodisks have a smooth surface and large-scale uniformity. The enlarged image shows that the diameter of the Si nanodisks is predominantly 200?nm. Figure?6 shows that the heights of the Si nanodisks are 50?nm.

    SEM image and magnified image of Si nanodisk arrays with a diameter of 200 nm and height of 50 nm. Scale bar, 1 μm; 400 nm.

    Figure 5.SEM image and magnified image of Si nanodisk arrays with a diameter of 200 nm and height of 50 nm. Scale bar, 1 μm; 400 nm.

    (a) AFM characterization of the Si nanodisk array sample. Scale bar, 400 nm. (b) Cross section of the height of the nanodisk at the position of the black dotted line.

    Figure 6.(a) AFM characterization of the Si nanodisk array sample. Scale bar, 400 nm. (b) Cross section of the height of the nanodisk at the position of the black dotted line.

    Experimentally generated radial beam (upper row), azimuthal beam (lower row), and their linear orthogonal components. The black arrows indicate the position of the analyzer.

    Figure 7.Experimentally generated radial beam (upper row), azimuthal beam (lower row), and their linear orthogonal components. The black arrows indicate the position of the analyzer.

    (a) Photothermal tuning of normalized scattering spectra of Si nanodisks of different polarization states at three representative temperatures: RT, 500°C, and 850°C. The dashed line indicates the position of excitation. (b) Evolution of Csca with increasing temperatures at the excitation wavelength of 639 nm; (c) required excitation intensities for temperature increase of the Si nanodisks under AP and RP illuminations; (d) resulting simulated nonlinear scattering behaviors under AP and RP illuminations; (e) simulated scattering cross sections for total scattering, forward scattering, and backscattering illuminated by AP excitation; (f) evolution of backscattering CscaB with increasing temperatures at the excitation wavelength of 639 nm.

    Figure 8.(a) Photothermal tuning of normalized scattering spectra of Si nanodisks of different polarization states at three representative temperatures: RT, 500°C, and 850°C. The dashed line indicates the position of excitation. (b) Evolution of Csca with increasing temperatures at the excitation wavelength of 639 nm; (c) required excitation intensities for temperature increase of the Si nanodisks under AP and RP illuminations; (d) resulting simulated nonlinear scattering behaviors under AP and RP illuminations; (e) simulated scattering cross sections for total scattering, forward scattering, and backscattering illuminated by AP excitation; (f) evolution of backscattering CscaB with increasing temperatures at the excitation wavelength of 639 nm.

    Comparison of AP beam spot and doughnut-shaped circularly polarized beam spot. (a) The theoretic cross sections at the position of the white dashed lines in (b) are obtained with a laser of 639 nm. Scale bar, 400 nm. (c) The experimental cross sections at the location of the white dotted lines in (d) are obtained by scanning the Si with a diameter of 200 nm with a laser of 639 nm. Scale bar, 400 nm.

    Figure 9.Comparison of AP beam spot and doughnut-shaped circularly polarized beam spot. (a) The theoretic cross sections at the position of the white dashed lines in (b) are obtained with a laser of 639 nm. Scale bar, 400 nm. (c) The experimental cross sections at the location of the white dotted lines in (d) are obtained by scanning the Si with a diameter of 200 nm with a laser of 639 nm. Scale bar, 400 nm.

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    Bin Wang, Ying Che, Xiangchao Zhong, Wen Yan, Tianyue Zhang, Kai Chen, Yi Xu, Xiaoxuan Xu, Xiangping Li. Cylindrical vector beam revealing multipolar nonlinear scattering for superlocalization of silicon nanostructures[J]. Photonics Research, 2021, 9(6): 950
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