1. Introduction

Surface plasmon polaritons (SPPs) are the collective oscillation of free electrons propagating at metal-dielectric interface [1]. Benefitting from the localized enhancement of SPPs, plasmonic imaging shows high sensitivity to single label-free nanoparticles by enhancing the weak scattering. After interacting with single nanoparticles at metal-dielectric interface, the launched SPPs induce localized enhancement around the nanoparticles, and SPP scattering reradiates. Then, the SPP scattering interferes with the launched SPPs and generate interference fringes. As a result, the plasmonic imaging of single nanoparticles contains the localized enhancement and interference fringes, simultaneously. Further, the near-field SPP field distribution transforms to far field via leakage radiation for fast imaging [2]. Owing to high sensitivity and fast speed, plasmonic imaging has been utilized in label-free and fast detection to single viruses [3,4], nanoparticles [5–8], exosomes [9], DNA molecules [10], cells [11], and graphene sheets [12], which plays an important role in environmental monitoring and biomedical research.

As optical and chemical properties of nanoparticles highly depend on their sizes and compositions, the increasing applications of nanoparticles call for the simple and fast identification methods for figuring particle sizes, shapes, and materials out. Presently, electron microscope achieves the single nanoparticle imaging, while it does not obtain the features of nanoparticles. Raman spectroscope determines the particle composition by using Raman vibration, while single nanoparticle recognition is still a challenge to Raman detection [13]. Mass spectrometry presents the particle size and composition recognition. Yet, it is high cost and needs time-consuming sample preparation [14]. Besides the superiority of plasmonic imaging in label-free and fast detection to single nanoparticles, plasmonic imaging also indicates its potential candidates in fast single nanoparticle identification, as it comprises plenty of information associated with the nanoparticle sizes, shapes, and permittivity. Sun et al. had investigated the localized enhancement tailored by nanoparticle sizes and permittivity. The plasmonic imaging of polystyrene (PS) and silicon (Si) nanospheres was compared, and the dependence of localized enhancement on particle sizes and permittivity was revealed [5]. Qian et al. built the relationship between interference fringes with particle sizes and refractive indexes. Owing to the phase shift induced by particle size and refractive index, particles were identified from fringe patterns [6]. People also investigated the plasmonic imaging to single nanorods. Jiang et al. illustrated the plasmonic imaging to single CdS nanorods and revealed the dependence of interference patterns on nanorod orientations, which shows the capability for determining the nanorod orientations [7]. Yu et al. demonstrated the plasmonic imaging to single DNA molecules and illustrated the variation of imaging contrast induced by DNA orientation, which also shows the orientation-related imaging [10]. Besides the nano-objects, plasmonic imaging is also used for detecting the micron-objects. Wei et al. reconstructed the boundary of single graphene sheets whose size is several microns [12], and Peterson et al. detected the single cells with size being several-tens microns [11]. As mentioned above, although the plasmonic imaging had been used for identifying the particle sizes, shapes, and permittivity, the in-depth and thorough investigation on influence of nanoparticle features to plasmonic imaging is still in lack, which hinders the further application to single nanoparticle identification.

In this letter, we illustrated the influence of particle sizes, shapes, and permittivity to spatial resolution, imaging contrast, and interference fringes of plasmonic imaging. Via both simulation and experiment, we found that Au nanospheres showed improved spatial resolution compared with PS nanospheres. We also found metallic and semiconductor nanospheres illustrated higher imaging contrast compared with dielectric nanospheres under same diameters, and larger particles showed higher contrast. Moreover, we retrieved size parameters from plasmonic imaging to manifest the fringe characteristics, and nanowires manifests very different decay rate of size parameters compared to nanospheres, which indicates that particle shapes take effect on interference patterns. This work demonstrated an in-depth understanding to plasmonic imaging and provided the guidance for fast identification to single nanoparticles.

2. Simulation

We simulated the electric field intensity ${|E |^2}$ of PS, Au, and Si nanospheres with different diameters using commercial Finite Difference Time Domain (FDTD) software from Lumerical Solutions, Inc. [15]. A three-layer structure is used to simulate the Krechtsmann configuration for SPP excitation, including the glass substrate, gold film, and air medium. The permittivities of glass, gold, and air are ${\varepsilon _{glass}} = 3.1684$, ${\varepsilon _{Au}} = \textrm{ - }11.8351 + 1.2410i$ [16], and ${\varepsilon _{air}} = 1$, respectively. The Au-air interface is set as $z$ = 0, and a nanosphere is positioned at the interface with center coordinate being (0, 0, $r$), in which r is the radius of nanospheres. The FDTD simulation area is 10 µm × 10 µm × 1 µm. The mesh area is 5 µm × 5 µm × 0.18 µm, and the size of each mesh is 6 nm × 5 nm × 5 nm. The Total Field Scattered Field (TFSF) plane wave is used as excitation source with 633 nm wavelength and an incident angle of $36.05^\circ $ for SPP excitation. We set electric field monitor at $z$ = 5 nm and perfectly matched layer (PML) as boundary condition. The simulated electric field intensity ${|E |^2}$ of PS (${\varepsilon _{PS}} = 2.528$), Au (${\varepsilon _{Au}} = \textrm{ - }11.8351 + 1.2410i$), and Si (${\varepsilon _{Si}} = 11.56$) nanospheres with diameters being 60 nm, 100 nm, 200 nm, 300 nm, 400 nm, 500 nm, and 1000 nm are presented in Figs. 1 (a), (b), and (c), respectively. With diameter increasing, all the PS, Au, and Si nanospheres show stronger localized enhancement and fringe intensity. For the same diameters, Au and Si nanospheres show stronger electric field intensity compared with that of PS nanospheres, which is originated from the stronger localized enhancement and scattering intensity induced by metallic and semiconductor nanoparticles.

 

Fig. 1. Simulated electric field intensity of (a) PS, (b) Au, and (c) Si nanospheres with diameters being 60 nm, 100 nm, 200 nm, 300 nm, 400 nm, 500 nm, and 1000 nm from left to right. (d) The imaging contrasts and (e) size parameters of PS, Au, and Si nanospheres retrieved from (a), (b), and (c). The critical size ${l_0}$ of PS, Au, and Si nanospheres are labeled.

Download Full Size | PDF

We retrieved the imaging contrast from the simulated imaging according to Michelson's contrast formula $C = \frac{{{I_{max}} - {I_{min}}}}{{{I_{max}} + {I_{min}}}}$, where ${I_{max}}$ and ${I_{min}}$ represent the intensity of brightest and darkest region [17]. As shown in Fig. 1 (d), simulation of the above three nanospheres shows higher imaging contrast with bigger particle diameter. Also, Au and Si nanospheres whose permittivity are higher than PS nanospheres have higher contrast than PS nanospheres with the same diameter. To quantitatively describe the effect of particle size along y axis on interference fringes, we introduced a size parameter $\varphi = \frac{L}{l}$, where L is the distance between maxima counterparts of first order interference fringes along $x$ = 1.5 µm [6,18] (the white dashed lines shown in Fig. 1), and l is the particle size along y axis. As shown in Fig. 1 (e), with l increasing from 60 nm to 1000 nm, L decreases and the size parameter approaches to a constant. We fitted the l dependent $\varphi $ using exponential function $\varphi = b + {e^{R(l - {l_0})}}$. The fitting formula of PS, Au, and Si nanospheres are ${\varphi _{PS}} = 4.46241 + {e^{ - 0.01282(l - 337.14)}}$, ${\varphi _{Au}} = 4.26243 + {e^{ - 0.01348(l - 315.21)}}$, and ${\varphi _{Si}} = 5.56211 + {\textrm{e}^{\textrm{ - }0.0157(l\textrm{ - }294.51)}}$, respectively, With $l = {l_0}$, $\varphi = b + 1$, where ${l_0}$ is the critical size indicating the decay rate of $\varphi $. With $l < {l_0}$, the decay rate of $\varphi $ reduces sharply. With $l > {l_0}$, the decay rate of $\varphi $ becomes slow and approaches to constant b. For PS, Au, and Si nanospheres, the critical sizes are ${l_0}$ = 337.14 nm, 315.21 nm, and 294.51 nm, respectively.

We also simulated the electric field intensity ${|E |^2}$ of PS and Ag (${\varepsilon _{Ag}} = \textrm{ - }18.3596 + 0.4786i$) nanowires with different diameters and lengths, as shown in Fig. 2. The FDTD simulation area is 10 µm × 10 µm × 1 µm. The mesh area is 9 µm × 9 µm × 0.18 µm, and the size of each mesh is 6.5 nm × 6.5 nm × 6.5 nm. In Figs. 2 (a) and (b), the diameter of PS and Ag nanowire is fixed to 200 nm, and the lengths are 126 nm, 633 nm, 1500 nm, and 3000 nm, respectively. With the length increasing, the parabolic-shaped interference fringes change to line-shaped fringes that reflect the shape of the nanowires. In Fig. 2 (c), we fixed the length of Ag nanowires to 3000 nm and changed the diameters as 50 nm, 100 nm, 150 nm, and 200 nm, respectively. With diameter increasing, the intensity of interference fringes strengthens. Meanwhile, owing to the evanescence of SPPs, less SPPs transmit through the nanowires, if the nanowire diameter is comparable with the skin depth of SPPs, which shows better imaging contrast. Thus, the larger nanowire diameter is, the better imaging contrast is.

 

Fig. 2. Simulated electric field intensity of (a) PS and (b) Ag nanowires with fixed diameter as 200 nm and changed lengths as 126 nm, 633 nm, 1500 nm, and 3000 nm (from left to right), respectively. (c) Simulated electric field intensity of Ag nanowires with fixed length as 3000 nm and changed diameters as 50 nm, 100 nm, 150 nm, and 200 nm (from left to right), respectively. (d) The imaging contrasts of simulated results of PS and Ag nanowires with different lengths retrieved from (a) and (b). (e) The imaging contrasts of simulated results of Ag nanowires with different diameters retrieved from (c). (f) The size parameters of PS and Ag nanowire retrieved from (a) and (b). The critical size ${l_0}$ of PS and Ag nanowires are labeled.

Download Full Size | PDF

We also extracted the imaging contrast and size parameters $\varphi $ from simulated images. In Fig. 2 (d), we compared the imaging contrast of PS and Ag nanowires. As described previously, Ag nanowires have higher contrast than PS nanowires with the same size. For both PS and Ag nanowire, the imaging contrast increases slightly with the increasing nanowires lengths. Moreover, we compared the plasmonic imaging with different diameters, and the retrieved imaging contrast increases with diameter changing from 50 nm to 200 nm, as shown in Fig. 2 (e). The diameter indicates more influence on imaging contrast than nanowire length, which shows consistence with simulations in Figs. 2 (b) and (c). We also extracted the size parameters $\varphi $ from Figs. 2 (a) and (b), which are illustrated in Fig. 2 (f). Different with nanospheres shown in Fig. 1, L increases with l increasing from 126 nm to 3000 nm. Although the size parameter $\varphi $ of nanowires decreases with the increasing nanowire length, the reduction rate of nanowires’ $\varphi $ is slower than that of nanospheres. Also, the fitting formula of Ag and PS nanowires are ${\varphi _{Ag}} = 1.79345 + {e^{ - 0.00421(l - 767.32)}}$ and ${\varphi _{PS}} = 1.91546 + {\textrm{e}^{ - 0.0043(l - 797.02)}}$, respectively, which indicates the critical sizes of Ag and PS nanowires are ${l_0}$ = 767.32 nm and 797.02 nm, respectively. Compared with nanospheres, critical sizes of nanowires ${l_0}$ indicates a larger value, which confirms the less reduction rate of size parameter $\varphi $ of nanowires.

3. Experiment and results

We prepared three types of nanoparticles dispersing on Au film, i. e. PS and Au nanospheres, as well as Ag nanowires. The diameters of PS nanospheres are 60 nm (10 mg/ml), 100 nm (0.025 mg/ml), 200 nm (0.025 mg/ml), 500 nm (10 mg/ml), and 1000 nm (0.025 mg/ml). The diameters of Au nanospheres are 60 nm, 100 nm, and 200 nm (Optical density being 5 cm^-1). The diameters of Ag nanowires are 50 nm (10 mg/ml) and 200 nm (10 mg/ml) with average length being 5 µm. The concentrations of PS, Au, and Ag nanoparticle solutions are diluted to 1.79 × 10⁻³ mg/ml, 2.9 × 10⁻³ mg/ml, and 1.25 × 10⁻⁴ mg/ml with alcohol for suitable dispersity. After preheating the cover glass with Au film to 160 °C for 10 minutes, the diluted solutions are dripped on Au film and the nanoparticles adsorbed on Au surface rapidly before clustering. The SEM imaging of dispersed nanoparticles on Au film is shown in Fig. 3.

 

Fig. 3. The SEM imaging of single (a) PS nanosphere with diameter being 200 nm, (b) Au nanosphere with diameter being 200 nm, (c) Ag nanowire with diameter being 200 nm and length being 4.48 µm, and (d) Ag nanowire with diameter being 50 nm and length being 1.42 µm.

Download Full Size | PDF

The experimental setup based on a home-built objective-coupled Kretschmann configuration is shown in Fig. 4 (a). In this experiment, a p-polarized laser with 633 nm wavelength is used for SPP excitation and focused on the back focal plane of the objective (Olympus APON100×HOTIRF). A 50 nm thickness Au film evaporated on cover glass and the incident angle adjusted to around $37^\circ $ for SPP excitation on Au-air interface. After interacting with single nanoparticles, the near-field SPP intensity distribution is transformed to far field via radiation leakage (LR) [2] and captured by a CCD camera (AVT Guppy F146B, Allied Vision Technologies Inc.) for plasmonic imaging. In order to decrease the experimental errors, we take the average of twenty images with nanoparticles as sample and averaged images without nanoparticles as reference. Then, the plasmonic imaging of single nanoparticles is obtained after subtracting the reference from sample, which is processed by Image J software.

Firstly, we analyzed the spatial resolution of plasmonic imaging by using single PS and Au nanospheres with diameter being 60 nm [19]. The point spread function (PSF) of plasmonic imaging to single PS nanospheres is shown in Fig. 4 (b), which shows tails along SPP propagation direction. By retrieving the vertical (x axis) and horizontal (y axis) line profiles of SPP intensity, the vertical and horizontal spatial resolutions relative to the full width at half maximum (FWHM) of line profiles are obtained in Figs. 4 (c) and (d), which is 678 nm and 447 nm, respectively. The larger vertical spatial resolution is originated to the tails induced by propagation length of SPPs. For Au nanospheres, the plasmonic imaging shows donut-shaped PSF, with the vertical and horizontal spatial resolution being 508 nm and 428 nm, respectively. Ten measurements are taken to average the FWHM for diminishing the experimental error. It shows that the nanoparticle permittivity affects the spatial resolution of plasmonic imaging. With the high absorption of metal, the SPP transmission through the particle decreases that eliminates the tails, the metallic nanoparticles brought smaller and more symmetric spatial resolution, consequently.

 

Fig. 4. (a) The schematic of plasmonic imaging setup. The PSFs of plasmonic imaging to single (b) PS and (e) Au nanoparticles with diameter being 60 nm. The plasmonic intensity profiles of single PS nanoparticles along (c) vertical and (d) horizontal dashed lines, and the plasmonic intensity profiles of single Au nanoparticles along (f) vertical and (g) horizontal dashed lines.

Download Full Size | PDF

We also analyzed the effects of particle permittivity and sizes on plasmonic imaging by using PS and Au nanospheres, as shown in Fig. 5. The diameters of PS nanoparticles are 60 nm, 100 nm, 200 nm, 500 nm, and 1000 nm, and diameters of Au nanoparticles are 60 nm, 100 nm, and 200 nm, respectively. In Fig. 5 (i), we retrieved the imaging contrast from simulated and experimental imaging. Both simulated and experimental results indicate that plasmonic imaging shows higher imaging contrast with bigger particle diameter. Also, the imaging contrast of Au nanospheres is higher than that of PS nanospheres with the same diameter. The saturation of the maximum intensity ${I_{max}}$ induced by CCD camera induces the discrepancy between simulated and experimental contrast of Au nanoparticles. The simulated and experimental $\varphi $ of PS and Au nanospheres are shown in Fig. 5 (j), which show good consistency.

 

Fig. 5. Plasmonic imaging of single PS nanosphere with a diameter of (a) 60 nm, (b) 100 nm, (c) 200 nm, (d) 500 nm, and (e) 1000 nm, and Au particle with a diameter of (f) 60 nm, (g) 100 nm, and (h) 200 nm. The white dashed-lines indicate the position of $x$ = 1.5 µm. The diameter-dependent (i) imaging contrast and (j) size parameters of PS and Au nanospheres retrieved from simulated and experimental imaging.

Download Full Size | PDF

Figures 6 (a) - (c) show the plasmonic imaging of single Ag nanowires to illustrate the influence of particle shapes on plasmonic imaging. The diameter of Ag nanowires is 200 nm and the lengths are larger than 3000 nm. The line-shaped interference fringes of the nanowires show agreement with the simulation in Fig. 2, which emerges with particle length being larger than 1500 nm. We calculated the contrast of Ag nanowires imaging in Figs. 6 (e) and (f). The diameter indicates more influence on imaging contrast than nanowire length, which shows consistence with simulations in Fig. 2. We also extracted the size parameters $\varphi $ from simulated and experimental images, respectively, which are illustrated in Fig. 6 (g). It indicates that the size parameter $\varphi $ decreases with the increasing nanowire length, which is also consistent with the simulated results.

We found that the orientation of nanowires also affects the imaging contrast and interference fringes. In Fig. 7 (a), we simulated the electric field intensity ${|E |^2}$ of Ag nanowires with diameter of 200 nm and length of 3000 nm. The white arrows in figures indicate the SPP propagation direction, and the orientation angle between long axis of nanowire and SPP propagation direction is 0°, 30°, and 90°, respectively. The orientation of nanowires introduces alteration of interference fringes. With orientation angles being 0°, the diameter of nanowires interacts with launched SPPs, the parabolic-shape interference fringes emerge. With the orientation angle increasing to 30°, asymmetric line-shaped interference fringes induce. When the orientation angle increases to 90°, the nanowire length interacts with launched SPPs and symmetric line-shaped interference fringes show up. The alteration of fringes can be used to identify the orientation of nanowires, as mentioned in Ref. [7]. The experimental results in Fig. 7 (b) demonstrate good consistency with simulation. In Fig. 7 (c), the retrieved imaging contrasts of Ag nanowires with different orientation angles are indicated. With the orientation angles increasing, the contrast decreases, which shows agreement with the results in Ref. [10].

Finally, we presented a comprehensive understanding to the imaging contrast and size parameter influenced by nanoparticle sizes, shapes, and permittivity. Figure 8 (a) indicates the imaging contrast of PS and Au nanospheres with diameters being 60 nm, 100 nm, and 200 nm, and Ag nanowires with diameters being 50 nm, 100 nm, and 200 nm. As previously mentioned, nanoparticles with larger permittivity possess stronger imaging contrast. For Au nanospheres and Ag nanowires, the saturation of the maximum intensity ${I_{max}}$ in experiment leads to the discrepancy between experimental and simulated results. As a result, the particle sizes and permittivity influence the contrast of plasmonic imaging.

In Fig. 8 (b), we compared the relationship of $\varphi - {l_0}$ curves of nanospheres (Au, Si, and PS) and nanowires (Ag and PS). We extracted $\varphi $ and ${l_0}$ from simulation with $x$ = 1 µm, 1.5 µm, 2 µm, and 2.5 µm, respectively. The linear fitting to $\varphi - {l_0}$ curves of nanospheres are ${\varphi _{PS}} = \textrm{ - }14.568 + 0.05617{l_0}$, ${\varphi _{Au}} = \textrm{ - }11.693 + 0.05235{l_0}$, and ${\varphi _{Si}} = \textrm{ - }11.252 + 0.0568{l_0}$, respectively. We also extracted the $\varphi - {l_0}$ curve of experimental results to PS nanospheres as shown in Fig. 8 (b), with linear fitting ${\varphi _{PS}} = \textrm{ - }3.6932 + 0.02726{l_0}$. The linear fitting to simulated $\varphi - {l_0}$ curves of nanowires are ${\varphi _{PS}} = 1.399 + 0.00196{l_0}$ and ${\varphi _{Ag}} = 1.497 + 0.00171{l_0}$. It indicates that nanospheres and nanowires show different $\varphi - {l_0}$ slopes. The distinct slope discrepancies between nanospheres and nanowires manifest the different decay rates of $\varphi $, which builds the connection between particle shapes and interference patterns.

 

Fig. 6. (a) - (c) Plasmonic imaging of single Ag nanowires with lengths being 2730 nm, 3340 nm, and 5160 nm, the diameters are fixed as 200 nm, (d) plasmonic imaging of Ag nanowires with length of 2290 nm and a diameter of 50 nm. The white dashed-lines manifest the position of $x$ = 1.5 µm. The contrast of Ag nanowires extracted from simulated and experimental plasmonic imaging with (e) different lengths and (f) different diameters. (g) The size parameters of Ag nanowires retrieved from simulated and experimental imaging.

Download Full Size | PDF

 

Fig. 7. (a) Simulated electric field intensity and (b) experimental plasmonic imaging of Ag nanowires with orientation angles being 0°, 30°, 90° (from left to right), respectively. The white arrow manifests the SPP propagation direction. (c) The contrast of simulated and experimental imaging to single Ag nanowires.

Download Full Size | PDF

 

Fig. 8. The imaging contrasts of simulated and experimental results of Au and PS nanospheres with diameter being 60 nm, 100 nm, and 200 nm, and Ag nanowires with diameter being 50 nm, 100 nm, 200 nm. (b) Comparison of $\varphi - {l_0}$ slopes between simulation of PS, Au, Si nanospheres, Ag and PS nanowires, as well as the experimental results of PS nanospheres.

Download Full Size | PDF

4. Conclusion

In summary, we illustrated the effects of particle shapes, sizes, and permittivity on plasmonic imaging. We found that the Au nanospheres brought smaller and more symmetric spatial resolution compared with PS nanospheres. It also indicated that the imaging contrast is affected by both particle sizes and permittivity. Particles with larger diameters introduce higher contrast and metallic as well as semiconductor nanoparticles bring higher contrast compared with dielectric nanoparticles. Furthermore, a size parameter $\varphi $ is introduced to quantitatively describe the change of interference fringes induced by particles sizes, shapes, and permittivity. By analyzing the reduction rate of size parameter dominantly influenced by particle shapes, the connection between particle shape and interference patterns is built. We also demonstrated that the orientation of Ag nanowires influences the interference fringes and the contrast, which indicates the capability for determining the nanowire orientation. Our study paves the way for understanding the effects of particle features on plasmonic imaging, and provides the guidance for identifying single nanoparticles quickly.