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Abstract
High-refractive-index nanoparticles (NPs), such as silicon NPs, were considered as effective carriers in their response to a magnetic field at optical frequencies. Such NPs play an important role in many state-of-the-art technologies in nano-optics. Although the resonance properties of these NPs when varying their structural parameters have been studied intensely in the past few years, their interaction with the underlying substrate has seldom been discussed, in particular, when the substrate is a waveguide structure that significantly modulates the optical responses of the NPs. We proposed and studied a selective magnetic coupling system comprising a Si–NP on a metal-dielectric waveguide (MDW). The MDW structure supports either a transverse electric (TE) or a transverse magnetic (TM) mode that induces a large polarization dependence in the magnetic resonance. A new manifestation of the optical spin Hall effect was demonstrated in which a vertical rotating magnetic dipole excites a TE-type waveguide mode with a specific unidirectional emission. Making use of this polarization response, we developed a scanning imaging system that can selectively map the transverse or longitudinal magnetic field component of a focused beam depending on the type of MDW used in the system. This selective magnetic resonance coupling system is expected to be valuable for studying the fundamental interactions between the magnetic field and matter and for developing related nano-applications.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Light, as an electromagnetic wave, has both electric and magnetic field components [1]. In studying light–matter interactions, nanoparticles (NPs) are important tools because of their sub-wavelength size and abundant resonance characteristics [2–4]. At optical frequencies, noble metal NPs are commonly used to explore the physical properties associated with the electric field component such as intensity, phase, polarization, and angular momentum [5–10]. However, because the response of these metallic materials to the magnetic field is weak [11], studying the magnetic field–matter interactions and their potential applications has been challenging [12,13]. Recent work has reported dielectric NPs of high refractive index can elicit large resonance enhancements in both the electric and magnetic fields [14–16], providing thereby an opportunity to expand our understanding of light–matter interactions.
Silicon NPs, commonly used semiconductor NPs, have very rich Mie resonances [17]. Over the spectral range for magnetic resonances, the magnetic modes of Si–NP can provide a dominant contribution to the total scattering. Making use of these magnetic modes, many interesting optical phenomena have been demonstrated, such as backward scattering and unidirectional scattering [18], and a variety of applications were developed including metasurfaces and metamaterials [14], ultra-sensitive displacement sensors [18,19], near-field imaging [20,21] and devices to measure transverse spin angular momentum [22].
The magnetic dipole resonances of a silicon NP arise from the circular currents formed inside the NP when the wavelength of the excitation is comparable to the size of the NP (d≈λ/n, d being the diameter of the NP, λ the incident wavelength, and n the refractive index of the NP) [14]. Therefore, in most instances, the structural parameters of the NP are the main features considered in tuning the resonance to meet the requirements of a certain application. However, with various substrates in use, the resonance responses of the NP are quite divergent depending on the optical properties of the substrate [23–25]. Below, we report on our investigation into a magnetic resonance system for which a silicon NP is immobilized on a waveguide structure [26–28]. The waveguide can support either TE or TM modes, which modulate the magnetic responses of the above-lying NP. Exploiting these unique polarization responses, a novel scanning imaging system was developed that maps selectively the transverse and longitudinal magnetic field components of a focused beam depending on the type of waveguide used in the system. This selective magnetic resonance coupling system provides an alternative method to reveal physical properties of the magnetic field for optical frequencies and opens up new perspectives in developing nano-photonic devices.
2. Theoretical analysis
To understand the resonance properties of silicon NPs, the scattering efficiency of a silicon NP in air was calculated using the Mie theory. With the size of NPs varying from 100 nm to 200 nm, the results for the visible spectra range 0.4 µm–0.8 µm (Fig. 1) show the spectra for the total scattering of the NPs, revealing resonances corresponding to a magnetic dipole (labeled MD), an electric dipole (ED), a magnetic quadrupole (MQ), and an electric quadrupole (EQ). For clarity, the contributions from the electric and magnetic components were extracted [Figs. 1(b) and (c)]. The magnitudes of the magnetic resonances are greater than those of the electric resonances, the magnetic dipole mode being strongly dominant. Therefore, the magnetic dipole resonance of a silicon NP is an effective near-field bridge between nano-structures.
Fig. 1. (a) Scattering spectra calculated using Mie theory of an isolated Si nano-sphere of diameter (d) ranging from 100 nm to 200 nm in a medium of air. The marked resonances correspond to the magnetic dipole (MD), electric dipole (ED), magnetic quadrupole (MQ), and electric quadrupole (EQ) mode. (b, c) Contributions of the resonances from the respective electric and magnetic field components.
Subsequently, we investigated the optical responses of silicon NPs on a substrate. The presence of the substrate affects the scattering properties of NPs [29], particularly so if the substrate is a waveguide that supports either a TE mode or a TM mode. Here, a type of metal-dielectric waveguide (MDW) was employed that supports both TE and TM modes. The MDW is a thin gold film deposited on a glass substrate, covered with an alumina (Al2O3) layer [Fig. 2(c), inset]. We first simulated the resonance properties of the MDW without Si–NP. In the simulation, the wavelength of incident light was set at 633 nm, the light being incident on the waveguide structure from the glass side. The thickness of the gold film was set at 40 nm. Contour maps of the reflectivity of the MDW with the thickness of the alumina layer (denoted as “t”) varying from 0 to 0.5 µm were generated for the TE [Fig. 2(a)] and TM [Fig. 2(b)] modes. One finds only the TM mode being supported for thickness of the alumina layer varying from 0–80 nm, the TE mode for thickness from 80–200 nm, and both modes for larger thickness. Therefore, we can select an appropriate thickness of alumina layer as needed. In subsequent analyses, a 115-nm-thick alumina layer was adopted in forming the TE-type substrate, whereas a 50-nm-thick gold film with no alumina layer (i.e., a surface plasmon polariton (SPP) waveguide) was adopted in forming a TM-type substrate. Their corresponding reflectivity curves were developed [Figs. 2(c) and (d)]. The results above were calculated through transfer matrix theory, in which the main parameters were set as follows: the refractive index of gold ngold = 0.18344 + 3.4332i and the refractive index of alumina nalumina = 1.67.
Fig. 2. (a, b) Contour maps of the reflectivity of a metal-dielectric waveguide for the TE and TM modes. The inset to (c) shows a schematic of the MDW, which is a 3-layer structure comprising an alumina layer, a thin gold film, and a glass substrate. The thickness of the gold film was set at 40 nm. (c) Reflectivity curves of an MDW with an alumina layer that is 115-nm thick, for which only a TE mode is supported. (d) Reflectivity curves of a 50-nm gold-film waveguide with no alumina layer (i.e., a SPP waveguide), for which only a TM mode is supported.
A silicon NP on different waveguide structures was investigated in regard to its resonance response when illuminated by light [Fig. 3(a)]. The incident light is partly scattered by the silicon NP. The wave-vector matching criterion determines the coupling of that part of the light to the waveguide. This waveguide mode propagates through the waveguide and is re-radiated into the glass substrate at a specific angle of resonance [Figs. 2(c) and (d)]. This is a phenomenon similar to surface-plasmon coupled emission occurring on a SPP waveguide, and therefore is referred to as the waveguide-mode-coupled emission (WMCE). Because the wave-vector of each waveguide mode is larger, the re-emission angle of the WMCE is larger than the angle of total internal reflection, and hence it is naturally separated from the direct transmission light in the Fourier domain.
Fig. 3. (a) Schematic illustrating the interaction of the NP with light and its re-emission as scattering radiation via the WMCE at a resonance angle. (b)–(e) Contour maps of the WMCE efficiency spectra for the TE-type (top panels) and TM-type (bottom panels) waveguide structure when the silicon NP was illuminated with a horizontal (left panels) and vertical (right panels) magnetic field component. (f)–(k) Simulation results of the far-field Fourier-domain patterns of the WMCE with TE-type (left column) and TM-type (right column) waveguides for x-polarized (top row) and z-polarized (middle row) magnetic dipoles and circularly-polarized magnetic dipoles in the x-z plane (bottom row).
As the presence of the substrate breaks the symmetry of the system, the resonance of the silicon NP becomes polarization dependent. The WMCE spectra were calculated using a finite-difference time-domain (FDTD) method (FDTD solutions, Lumerical Inc.), with different incident polarizations [Figs. 3(b)–(e)]; panels (b) and (c) are results corresponding to a transverse magnetic field, and panels (c) and (e) are results corresponding to a longitudinal field component. In the simulation, the different magnetic field components were achieved by exciting two counter-propagating waveguide modes using two total-field scattering-field (TFSF) sources. An evanescent standing wave is formed above the interface, where the longitudinal and transverse field components are alternately distributed. By changing the phase difference between the two TFSF sources (0 or π), the dominant field component can be tuned to the geometric center of the system where the NP with a diameter of 170 nm is located and interacts with the field. The wavelengths of the resonance modes and their relative magnitudes in the presence of the MDW change considerably when compared with those given in Fig. 1(c). For a TE-type waveguide, the WMCE caused by a longitudinal magnetic field is stronger than that with a transverse magnetic field [Figs. 3(b) and (c)], whereas the opposite occurs for a TM-type waveguide [Figs. 3(d) and (e)].
For simplicity, a magnetic dipole model was employed to simulate the polarization effect on the coupling efficiency. The far-field Fourier-domain radiation patterns of the WMCE were generated for a magnetic dipole oscillating horizontally, vertically, and rotating in the plane normal to the interface [Figs. 3(f)–(k)]. The amplitudes of the dipoles used in the simulation are set to be 1. The WMCE induced by an in-plane dipole is suppressed strongly by the TE-type waveguide [Figs. 3(f) and (g)], whereas it couples effectively to the TM-type waveguide. The situation is reversed for an out-of-plane dipole [Figs. 3(h) and (i)]. A more interesting phenomenon occurs with a TE-type waveguide when the WMCE induced by a vertical rotating dipole exhibits a specific unidirectionality [Fig. 3(j)]. The extinction ratio can be optimized by changing the amplitude ratio of the two dipoles. This is another manifestation of the optical spin Hall effect in terms of the magnetic dipole coupled to a TE-type waveguide, as compared with the previously reported effect where the electric dipole was coupled with a TM-type waveguide (SPPs) [30]. This phenomenon however was not observed for a rotating magnetic dipole on a TM-type waveguide [Fig. 3(k)] as the waveguide couples to a vertical magnetic dipole with a very low efficiency [Fig. 3(i)]. In summary, the coupling efficiency of the magnetic dipole with the TE-type and TM-type waveguides varies widely and shows a strong polarization dependence. This enables us to develop many novel applications in optics associated with the magnetic field component.
3. Experimental results
To verify the above prediction in an experiment, we built a WMCE microscopy system [Fig. 4(a)], comprising a He–Ne laser operating at 633-nm wavelength to produce a light-beam source. After passing through a half wave-plate (HWP) and a vortex wave-plate (VWP) to modulate its polarization, the light beam was focused by an objective lens (Olympus, NA=0.8, 100×) onto a silicon NP immobilized on a waveguide structure. The WMCE caused by the NP was collected by another oil-immersion objective lens (Olympus, NA=1.49, 100×). The signal was then split into two paths. One was directed to a charge coupled device (CCD) camera mounted at the back focal plane (BFP) of the collection objective to capture the Fourier-domain image of the WMCE; the other was directed to a photo-multiplier tube (PMT, R12829, Hamamatsu Photonics) at the back image plane using a fiber coupler to obtain the intensity of the WMCE signal. The sample was fixed on a piezo-electric scanning stage (P-545, Physik Instrumente) to scan the NP over the focal region.
Fig. 4. (a) Experimental setup for investigating the WMCE of the scattering radiation from a silicon NP under the illumination with a focused azimuthally polarized beam. HWP: half-wave plate, VWP: vortex wave plate, BS: beam splitter, PMT: photo-multiplier tube. (b) The SEM image of a single silicon nanoparticle with size of 170 nm.
The sample was prepared as follows. The layers of gold film and alumina were deposited in sequence onto a coverslip using electron beam deposition to form the desired waveguide structure. It was then floated upside-down onto a 4-mercaptobenzoic acid (4-MBA) molecule ethanol solution for 20 minutes to form a self-assembled monolayer of 4-MBA molecules. This increases the hydrophilicity of the sample surface considerably. After water-rinsing and nitrogen-drying, a droplet of diluted silicon NP (diameter ∼170 nm) suspension was dropped onto the prepared substrate and allowed to evaporate naturally. The sample was ready to use after another round of water-rinsing and nitrogen-drying.
In the experiment, an azimuthally polarized beam (APB) was generated as the incident beam by rotating the HWP and WVP to a certain angle. A tightly focused APB generates a strong magnetic field component at the central area of the focal plane, for investigating the magnetic response of the silicon NP modulated by the waveguide. When a silicon NP was scanned from the center of the focal plane to one side with a 100-nm step size, the first five WMCE radiation patterns were captured by the CCD camera at the BFP of the collection objective [Figs. 5(a)–(j)]; the top (bottom) panels are the results for TE-type (TM-type) waveguide structures. For each image, the inner donut-shaped beam profile is the light transmitted directly through the waveguide structure, whereas the outer ring/arc-shaped signal is the WMCE. For a clear interpretation, the intensity and phase distributions of the longitudinal and transverse magnetic field components of a focused APB at the focal plane were calculated using the Richards–Wolf diffraction theory [31] [Figs. 5(k) and (l)].
Fig. 5. (a)–(e) WMCE images of scattering radiation from a 170-nm-sized silicon NP via a TE-type waveguide, obtained by stepwise scanning the NP from the center of the focal plane to one side at 100-nm step intervals. (f)–(j) Corresponding images for a TM-type waveguide. (k, l) The calculated intensity and phase distributions of the longitudinal (H⊥) and transverse (H//) magnetic field components of a focused APB at the focal plane.
At the center of the focal spot (x = 0 µm), the signal of the WMCE for a TE-type substrate exhibits a complete bright ring [Fig. 5(a)], yet no WMCE signal was observed for a TM-type substrate [Fig. 5(f)]. This is because the transverse magnetic field component is absent at this point [Fig. 5(k)], which are in accord with the results in Figs. 3(h) and (i). As the NP moves away from the center along the x-axis, a transverse magnetic field component appears that has a π/2 phase difference with the longitudinal field component [Fig. 5(l)]. This indicates an elliptical polarization (being circular polarization at the intersection points) of the magnetic field that interacts with the NP. Therefore, a specific unidirectionality is induced in the WMCE for a TE-type waveguide [Figs. 5(c)–(e)] because of the optical spin Hall effect, as predicted in the earlier theory [Fig. 3(j)]. For the TM-type structure, the appearance of a transverse magnetic field causes the WMCE patterns [Fig. 3(g)–(j)] with two bright arcs oriented symmetrically about the direction perpendicular to the polarization of the transverse magnetic field [Fig. 3(k)]. Meanwhile, the magnitude of the WMCE becomes stronger with increasing transverse magnetic field.
Furthermore, taking advantage of the different responses of the two waveguide structures to the magnetic field polarization, selective characterization of the magnetic field components by choosing an appropriate silicon NP size is possible. In the experiment, an opaque circular disk was inserted into the PMT-path to block the transmitted light, with only the WMCE signal being collected by the PMT [Fig. 4(a)]. Silicon NPs with a 170-nm diameter were immobilized on TE-type and TM-type substrates and were employed to map the intensity distribution of a tightly focused AP beam. The WMCE efficiencies for the two different substrates and both the transverse and longitudinal magnetic field components were calculated [Figs. 6(a) and (b)]. For a light wavelength of 633 nm, as employed in the experiment, the TE-type structure is evidently more sensitive to the longitudinal magnetic field [Fig. 6(a)], whereas the TM-type structure is more sensitive to the transverse field [Fig. 6(b)]. The mapped intensity distributions of the focused APB using the two different waveguide structures [Figs. 6(c) and (d)] were obtained by scanning the silicon NP over the focal region. For comparison, the distributions obtained using the Richards–Wolf theory were produced for the longitudinal and transverse magnetic field components [Figs. 6(e) and (f)]. As predicted above, the mapped distributions with a NP on a TE-type or TM-type substrate agree well with corresponding longitudinal and transverse magnetic field components.
Fig. 6. (a) and (b) Calculated WMCE efficiency spectra for a 170-nm-sized silicon NP residing on a TE-type and a TM-type waveguide structure, respectively. (c) and (d) Experimental mapping results of a tightly focused AP beam using the TE-type and TM-type structures. (e) and (f) Calculated intensity distributions of the longitudinal and transverse magnetic field components of a tightly focused AP beam generated for comparison.
4. Conclusion
We proposed and investigated a selective magnetic resonance system for which a silicon NP resides on an MDW substrate. This MDW supports either a TE-type or a TM-type waveguide mode that modulates the magnetic response of the system significantly and induces strong polarization dependence. A new manifestation of the optical spin Hall effect was demonstrated in which a vertical rotating magnetic dipole coupled to a TE-type waveguide mode with a specific unidirectionality. We further developed a scanning imaging system, making use of the unique magnetic polarization response of the structure that maps the transverse or longitudinal magnetic field component of a focused beam selectively depending on the type of the MDW used in the system. This kind of selective magnetic resonance coupling system may open up new perspectives for understanding light–matter interactions and for developing nanophotonic technologies, such as near-field magnetic field imaging, polarization component separation for magnetic field and designing of optical device with magnetic response.
Funding
National Key Research and Development Program of China (2015CB352004); Science, Technology and Innovation Commission of Shenzhen Municipality (KQTD2015071016560101, KQTD2017033011044403, ZDSYS201703031605029); National Natural Science Foundation of China (61427819, 61490712, 61622504, 61905163); Leading Talents Program of Guangdong Province (00201505); Natural Science Foundation of Guangdong Province (2016A030312010); China Postdoctoral Science Foundation (2018M643161, 2019M663048).
Acknowledgments
L. Du acknowledges the support given by Guangdong Special Support Program.
Disclosures
The authors declare no conflicts of interest.
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