1. Introduction

Polarization, as an intrinsic nature of light, is of great importance to serve as a degree of freedom for optical application. In nano-optics, highly confined electromagnetic (EM) fields with inhomogeneous polarization distribution have been widely applied in many areas, such as surface-enhanced Raman spectroscopy (SERS) [1–3], super-resolved imaging [4–6], optical trapping [7–9], bio-sensing [10,11], etc. Such confined EM fields can be generated in a tight-focusing configuration [12–14] or by exciting the surface plasmon polaritons (SPPs) [15,16], with the latter been extensively studied due to their subwavelength and enhancement nature [17,18]. In order to verify that a designed optical field meets the requirements in applications, it is crucial to acquire the knowledge of the generated field with high precision. However, compared to the traditional scalar fields, these confined EM fields are more difficult to be measured due to their vectorial features as well as their fine spatial distributions.

Near-field scanning optical microscopy (NSOM) is a common tool for imaging these complicated optical fields, which employs a nano-probe to couple the confined EM fields to far field for characterization. The scattering-type NSOM probes, normally solid metallic or silicon tips, are more sensitive to the longitudinal component of the EM fields due to the vertical alignment of the tips [19,20]; while the sensitivity of fiber-tips remains controversial between the transverse field sensitivity [21,22] and the sensitivity to the gradient of longitudinal field [23]. As an alternative option, the nanoparticle-on-film structures aroused great interest in recent years for NSOM. Nanoparticle-on-film structures are commonly used configurations for studying the light-matter interaction in nano-optics owing to their flexible parameters and the ease for manufacturing. Metal nanoparticle-on-film structures, which compose of metallic nanoparticles on a metal film, are able to support plasmonic gap modes between the nanoparticle and metal film [24–26]. These gap modes were employed to map the longitudinal field component of both SPPs and tightly-focused EM fields because of the high coupling efficiency of the vertical gap mode induced by the longitudinal field [27,28]. Dielectric nanoparticle-on-film structures, which compose of non-metallic materials such as silicon and silica, possess many interesting electromagnetic response [29–32]. By studying the structure composed of silicon nanoparticle and glass substrate with Mie theory, the reconstruction of tightly focused EM fields has been reported, which is a kind of post-processing imaging method [33]. As we can find, although many state-of-the-art methods have been proposed to uncover the near field distribution, there still lacks a reliable technique, which aims to map the weak transverse field distribution of SPPs with high contrast and precision. This hinders our understanding on the vectorial features of SPPs such as the spin angular momentum, a rapidly developing area in recent years [34–37].

In this paper, we propose a direct imaging technique for mapping the near-field distributions of the transverse field of SPPs, which employs a dielectric-nanoparticle-on-metal-film (DNP-MF) configuration as a near-field probe. The angular distribution of the scattering radiation from a dielectric nanoparticle is strongly polarization dependent, which provides us a strategy to extract the signals that are induced by the desired field component. The nanoparticle size effect on the collection efficiency of the scattering radiation was analyzed numerically and verified in experiment. Transverse components of SPPs excited by various vector beams were mapped, which accord excellent with the theoretical ones. This technique provides a new tool for studying the near-field features of SPPs, and together with other NSOM techniques, are valuable for exploring the vectorial features of the EM fields such as transverse spin, spin-orbit interactions, etc.

2. Theoretical design and analysis

The schematic of the proposed DNP-MF configuration is illustrated in Fig. 1(a). A Polystyrene (PS) nanoparticle is immobilized on a thin metal film as a near-field probe to scatter the SPP fields to the far field to be collected. The radiation direction of the scattered light is affected by the polarization of the near-field components, which results in a spatial separation in the back focal plane of the collection objective. This provides us a path to extract different field components of SPPs. To get a comprehensive understanding of the influence of the field polarization on the radiation direction, numerical simulations were performed with the finite difference time-domain (FDTD) method. In the simulation, the refractive index of the PS particle was set to be 1.58. The thickness of silver film was fixed at 50 nm. The gap between the particle and the film was set to be 2 nm. For simplicity, an x-polarized and a z-polarized plane wave is employed as the light source respectively, to mimic the interaction of the DNP-MF structure with the transverse and longitudinal field. Figs. 1(b) and 1(c) are the simulated far-field projections when the particle with a diameter of 300 nm was illuminated respectively by the two plane waves. It was seen that the scattering light excited by the in-plane polarization concentrates in the central region [Fig. 1(b)], while that excited by the out-of-plane one radiates to the large angles [Fig. 1(c)]. Therefore, by limiting the collection angle (θ_max) which refers to the numerical aperture (NA) of collection objective in experiment, the mapping of SPPs transverse electric fields can be achieved, as illustrated in Fig. 1(a).

 

Fig. 1. (a) Scheme of a nanoparticle-on-film structure as a near-field probe for mapping the transverse field component of SPPs. A PS nanoparticle is immobilized on a metal film to scatter the SPPs to the far field. θ_max represents the largest collection angle, which is determined by the NA of objective. (b) and (c) Far-field projections of the scattered light from the nanoparticle that are excited by the in-plane and out-of-plane polarization, respectively. The white dashed circles refer to the collection region (NA = 0.7). (d) The calculated intensity ratio of the scattering lights excited by the two polarizations that are collected by the objective, plotting against the size of the nanoparticles. The curves with different colors represent different NAs of the collection objective ranging from 0.1 to 1. (e) Details of the dashed curve in (d) when NA = 0.7.

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The choice of the PS-particle size is important to guarantee an effective imaging of the SPPs transverse field. In the following simulation, the diameter of PS particle was varied from 90 nm to 400 nm and the collected intensity ratio σ_t/σ_l of the scattered light excited by the transverse and longitudinal field with same amplitude was calculated when the collection NA increased from 0.1 to 1, with the results shown in Fig. 1(d). Overall, both the NA and the size of the particle influence dramatically the intensity ratio σ_t/σ_l. To fit the case in experiment, the curve for NA = 0.7 [dashed line in Fig. 1(d)] is picked out and is replotted in Fig. 1(e). As we can see, the collected intensity ratio σ_t/σ_l can be more than 2 orders of magnitude at an optimized particle diameter ∼ 300 nm. This enables us to extract the weak transverse field of SPPs that is embedded in the strongly dominant longitudinal field.

3. Experiment setup

The experiments were performed subsequently to investigate the effect of PS particle size on the mapping results. The diagram of setup was illustrated in Fig. 2. A He-Ne laser with wavelength of 633 nm was utilized as a light source. A combination of half-wave plate and vortex wave plate (VWP) was employed to modulate the polarization of the laser beam. It was then tightly focused by an oil-immersion (Olympus, 100×, NA = 1.49) objective onto the DNP-MF sample, to excite the SPPs on the surface of the silver film. An opaque disk was inserted at the center of the beam right below the objective, to reduce the background noise introduced by the transmitted light. A CCD (charge-coupled device) camera was placed at the back focal plane (BFP) of the excitation objective to capture the reflected beam from the sample, which is able to verify the excitation of SPPs [Fig. 2(c)]. The scattering signals from the dielectric nanoparticle were collected by another objective (Olympus, 60×, NA = 0.7), which were finally coupled into a photomultiplier (PMT, Hamamatsu, R12829) by an optical fiber for further processing. The sample was fixed on a piezo-stage (Physik Instrumente, P-545) for performing the two-dimensional scanning over the near-field region of the excited SPPs.

 

Fig. 2. (a) Experimental setup for mapping the intensity distribution of SPPs. (b) The SEM image of a single PS nanoparticle with size of 320 nm. (c) The image of the reflected beam captured at the back focal plane of the excitation objective lens. The sharp dark arcs indicate the excitation of SPP. VWP: vortex wave plate, HWP: half-wave plate, QWP: quarter-wave plate.

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The DNP-MF sample was prepared as follows. A thin silver film with thickness of 50 nm was firstly formed on a cleaned glass coverslip by electron beam deposition. It was then immersed into a 4-mercaptobenzoic acid (4-MBA) molecule ethanol solution for about 15 minutes to form a self-assembled monolayer of 4-MBA molecules. The coated substrate was then rinsed with deionized (DI) water and dried by a nitrogen stream. A droplet of diluted PS nanoparticle suspension was dropped onto the prepared substrate and evaporated naturally. The sample was ready for use in the experiment after the DI water rinsing and nitrogen-drying.

4. Experimental results and analysis

The experimental mapping results are shown in Figs. 3(a)-(d), corresponding to the PS nanoparticles with diameter of 97 nm, 201 nm, 320 nm, 397 nm, respectively. It can be clearly seen that the remarkable difference between the mapping results with different sized nanoparticles. For the purpose of comparison, the calculated distributions of the transverse and longitudinal field components of SPPs are shown in Figs. 3(e)-(f), by using the Richard-Wolf diffraction theory. The scanned image with the 97 nm diameter PS nanoparticle [ Fig. 3(a)] was found to be more consistent with the distribution of longitudinal field component [Fig. 3(e)]. This is because of that, when the collection NA is 0.7 and the diameter of the particle is 97 nm, the calculated collection efficiency ratio σ_t/σ_l is 2.3. This efficiency ratio is not larger enough to compensate for the magnitude disparity between the transverse and longitudinal field components, as illustrated in Figs. 3(e)-(f). When the particle size is enlarged, the collection efficiency ratio σ_t/σ_l increases greatly before reaching a peak value, as shown in Fig. 2(e). In particular, when the size of particle is ∼300 nm, their efficiency ratio is optimized and is more than 2 orders of magnitude, which is larger enough to depress the effect from the longitudinal field. As the result, the scanned image with the 320 nm diameter PS nanoparticle [Fig. 3(c)] accords excellent with the calculated distribution of the transverse field component [Fig. 3(f)].

 

Fig. 3. The mapped intensity distributions of SPPs excited by a tightly-focused radially polarized beam by using a (a) 97 nm (b) 201 nm (c) 320 nm (d) 397 nm diameter PS nanoparticle, respectively. (e)-(f) the calculated distributions of the longitudinal and transverse field components, for comparison.

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We further performed additional experiments to demonstrate the reliability of the proposed technique. The PS-nanoparticles with diameter of 320 nm were employed for mapping the transverse field distributions of SPPs excited by various incident beams, including the radially polarized optical vortex beam (RPOV, topological charge l = 1), the linearly polarized Gaussian beam (LPGB), and the circularly polarized beam (CPB). The experimental mapping results are shown in Figs. 4(a)-(c), together with the corresponding calculated distributions for both the transverse [Figs. 4(d)-(f)] and longitudinal field components [Figs. 4(g)-(i)]. For comparison, the cross-section distributions of the experimental results, the theoretical transverse components and the predicted results after taking into account of the field sensitivities of the system, are shown in Figs. 4(j)-(l). It can be seen that the experimental results are in good agreement with the predicted ones, and are also close to the theoretical distributions of the transverse field despite their weak intensities compared to the longitudinal ones. This validates the reliability of the mapping method. Moreover, by comparing the scanning results in Fig. 4(a) and Fig. 4(c), it was found that the SPPs field distributions excited by the RPOV and by the CPB are same. This consistency illustrates that the spin angular momentum (SAM, s = 1) carried in a CPB is converted to the orbital angular momentum (OAM, l = 1) of the SPPs through the tight-focusing configuration [38], thus rending a same distribution with the case of RPOV. The results validate the interaction between SAM and OAM and verify that the proposed mapping technique is valuable for investigating some intricate physical processes.

 

Fig. 4. The scanned images of the transverse field component of SPPs excited by various vector beams, including: (a) radially polarized optical vortex (RPOV) beam, (b) linearly polarized Gaussian beam (LPGB) and (c) circularly polarized beam (CPB). All of the mapping results are obtained by using the optimized particle size of 320 nm in the experiment. The corresponding calculated transverse and longitudinal field distributions are shown in (d)-(f) and (g)-(i), respectively, for comparison. (j-l) The normalized cross-section distributions along x-axis of the experimental results (blue dots), the theoretical transverse components (red curves) and the weighted summation (I_w) of the theoretical transverse (I_t) and longitudinal (I_l) components (green curves) after taking into account of the field sensitivities of the system, i.e., I_w =σ_tI_t +σ_lI_l .

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5. Conclusion

To summarize, we have proposed an effective near-field scanning technique for mapping the weak plasmonic transverse field with high contrast and reliability. The method utilizes the dielectric-nanoparticle -on-film structure as a near-field probe. The distinct emission directions of the scattered radiations excited by the vertical and horizontal polarizations provide us a way to extract the signals that are induced by the transverse field of SPPs. The effect of particle size on the collection efficiency ratio of the signals were analyzed theoretically and demonstrated experimentally. Transverse components of SPPs excited by several commonly used vector beams were mapped by using the PS particles with diameter of 320 nm and objective with NA = 0.7. The mapping results accord excellent with the theoretical ones. The proposed technique significantly improves the precision for imaging the weak transverse field of SPPs and is expected to be a reliable technique for studying the vectorial features of confined optical fields.