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Abstract
Imaging and characterization of surface plasmon polaritons (SPPs) are crucial for the research and development of the plasmonic devices and circuits. Here, we report on direct imaging of SPPs propagation on SiO2/metal interface with subwavelength spatial resolution using up-conversion fluorescence microscopy, that exploits rare-earth ions, such as Er3+, Yb3+, and Nd3+, doped nanoparticles as the fluorophores. We demonstrated that by further taking the intensity ratio of the image obtained with fluorescent emission at different wavelengths, we are able to substantially enhance the features associated to the SPP wavefronts in the image for quantitative analysis, such as the wavevector and propagation direction of the SPPs. Our results agree with the theoretic prediction of the SPP wavelengths quantitatively. We further demonstrate the evolution of the SPP wavefronts due to refraction SPPs, and reproduced the experiment with finite difference time domain (FDTD) method simulations. The relative refractive index of SPP estimated from the experiment also agrees quantitatively with those extracted from the theory and the simulation.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Surface plasmon polaritons (SPPs) are electromagnetic waves that propagate along the interface between a metal and a dielectric medium with the electric field strength decaying exponentially in the directions perpendicular to the interface [1]. Thus, SPPs are highly confined to the interface, leading to an enhancement of the electromagnetic field which provides an opportunity for applications in integrated optical circuits for communication and bio-chemical sensors in subwavelength dimensions [2]. There have been enormous interests in the imaging of SPP propagation on the metal surfaces since it is important for the design and construction of the circuits with plasmonic or photonic devices [3,4]. Due to the evanescent nature of the electric field associated with the SPPs, it is impossible to observe the SPP propagation with conventional optical microscopies, and there is a continuous interest in developing techniques for imaging the propagation of SPPs and their interaction with surface structure. Thus, being able to directly image wave fronts of SPP propagation is a further step forward to the pathway of the investigation and development for plasmonic circuits research.
There have been two types of methods developed for imaging the propagation and properties of SPPs: the scanning probe microscopy and direct imaging microscopy. For the scanning probe microscopy methods, the near-field scanning optical microscope (NSOM) [5–7] directly probes the near field of SPPs with a physical tip to scan across the region of interest. NSOM is able to potentially produce SPPs images with spatial resolution beyond the diffraction limit. However, the fact that the NSOM imaging is time consuming and the tip used to collect the near field signal may interfere with SPPs under investigation limit the effectiveness of this approach. In transient absorption microscopy (TAM) [8], a focused probing laser pulses are used to replace the NSOM tip, and ultrafast laser pulses are employed to excite SPPs on the metallic structures. The probe beam pulses at shorter wavelength was scanned across the sample to detect the transient absorption variation induced by the SPPs, thus produces the images of the SPPs. This technique requires delicate optical pump–probe instrumentation, which are not quite accessible to general researchers of the SPP community. For direct imaging microscopy, two-photon photo-emission electron microscopy (PEEM) [9–12] adapted the optical pump-probe approach to excite the SPPs on metal surface but uses the probes beam pulses to illuminate the entire field of view to extract the electrons participating the SPP propagation on the sample surface to form a direct image of the SPPs. Although the two-photon PEEM images revealed detailed and insightful images of the SPP wave front, the ultrahigh vacuum instrumentation of PEEM with its interfacing with the pump-probe optics poses a great technical challenge for most researchers, and in fact only a handful of research groups have access to such systems. For the purpose of simply imaging the distribution of the SPP field, on the other hand, the leakage radiation microscopy (LRM) [13–14] and the fluorescent optical microscopy [15–18] have substantially lowered the technical barrier of instrumentation at the expense of subwavelength resolution. For a thin enough metallic film supported by a dielectric substrate, such as glass slides, the electromagnetic boundary conditions dictate the “leaking” of the SPP propagation on the metal and air interface in terms of a propagating light from the metal and glass interface, which can be collected by an optical microscope to form a time-averaged image of the SPP intensity distribution. The resolution of the images is limited by the optical diffraction at the free space wavelength of the corresponding SPP. Therefore, subwavelength information about the SPPs is unattainable for LRM. The fluorescent microscopy replaced the physical tip in the scanning microscopy with fluorophores to extract the near field information of the SPPs. The fluorophores are placed at the metal surface with a spacer layer in between, and the near field of the SPP excites the fluorophores. The objective lens of an optical microscope collects the fluorescent signals and produces a time-averaged image of the SPP field distribution. For down-conversion fluorescence, the emission wavelength is larger than that of the free-space wavelength corresponding to the SPPs, therefore it is quite difficult to access subwavelength information from the fluorescent image. However, for up-conversion fluorescence [19–24], where the emission wavelengths can be significantly shorter than the excitation wavelength, obtaining detailed information about the SPPs wave front structures is feasible in principle. Recently, Yin et al. has reported on imaging SPPs excited on Au pads with up-conversion fluorescence microscopy [17]. Their fluorescent images demonstrated clear beat envelope patterns resulted from the interference between the incident light and the SPPs excited on the Au pads. Although the quality of the images well surpasses that of the down-conversion fluorescent images of SPPs reported previously in the literature [15–16,25], the detailed information about the SPP wavefronts has not yet been demonstrated. It is of essential importance and a great progress for the development for plasmonic research that the up-conversion fluorescent microscopy demonstrates sub-wavelength resolution imaging of the SPPs. This implies that with relatively fewer instrumental challenges, the interaction of SPPs with micro- or nanoscopic metal structures can be investigated under more versatile settings other than the ultrahigh vacuum environment of the two-photon PEEM experiment.
In this report, we demonstrate subwavelength resolution of SPP images with up-conversion fluorescent microscopy. By spin-coating rare-earth ion doped up-conversion nanoparticles on a silver film with SiO2 spacer layer in between, we were able to show the fluorescent images that resolved the wave fronts of SPPs propagation on the sample. By further image processing of taking the intensity ratio of the fluorescent images obtained at different emission wavelengths, which we refer to as the fluorescent intensity ratio (FIR) image, we removed the smooth varying components of the SPP intensities to enhance the high spatial frequency component of the SPP field signal, and made the SPP wave fronts as the main features in the images. We further apply this technique to investigate the simple refraction of SPP propagation across a boundary, which separates regions of different effective refractive index for SPP propagation. We extracted from the FIR images the wavelengths and the propagation directions of the SPPs and estimated the relative refractive indices. We also carried out numerical simulations and theoretical analysis for the relative refractive index for SPP propagation. The results agree with the experiment quantitatively. Our results present a new approach for direct imaging of SPPs with subwavelength spatial resolution for plasmonic research.
2. Method
2.1 UCNPs fluorescence microscopy
Figure S1 shows the optical setup of our up-conversion fluorescent microscope system. For the excitation light we used a 793 nm wavelength laser to emit a collimated laser beam. The half-wavelength waveplate in front of the laser was to adjust the orientation of the laser beam polarization to pass the polarizing beam splitter (PBS) before the spatial light modulator system (SLM, Twist Nematic, TN type). The two mirrors after the half-wave plate guided the laser beam toward a beam expander equipped with a spatial filter (SF) to further increase the beam diameter and to refine the wave vector components of the laser beam. The SLM was used to modulate the intensity of the laser beam illuminating the sample. Due to the nematic liquid crystal used in the SLM, the polarization of the reflected beam was rotate by 90° relative to the incident beam. The 793-nm laser beam reflected from SLM was further reflected by PBS and a mirror subsequently to enter a 4-f system, that consists of the identical lenses L2 and a 40x objective lens (OL) with the numerical aperture (NA) of 0.75, and became again a collimated beam when reaching the sample. An iris was placed on the optical path in between the first two L2 lens for refining the collimation of the incident beam. The polarization of the incident laser beam was adjusted to be normal to the grooves of the SiO2 grating. The incident direction of the excitation beam was fine-tuned near normal incidence to optimize the brightness and the contrast of the fringes in the fluorescent images.
For the imaging system the fluorescent light emitted from the sample and the reflected incident light were collected by the same OL toward the dichroic mirror DM1, which separates the incident light from the fluorescent light, and the second dichroic mirror DM2 further separates fluorescent light of different wavelengths. The fluorescent light with wavelength shorter than 537nm was reflected by DM2 toward lens L3, passing through a band pass filter (525 nm ± 8 nm) and form an image of the sample on the CCD1 camera. The fluorescent light with wavelength longer than 537 nm passes DM2, another lens identical to L3 (also labelled as L3), and a band pass filter (549 nm ± 10 nm), forming another image of the sample on CCD2 camera. CCD1 and CCD2 cameras are identical, whose position and orientations were adjusted with to produce images of the same magnifications and the field of the views as much as possible. A MATLAB program was developed to calculate the pixel-by-pixel intensity ratio of the fluorescent images obtained by the CCD cameras.
2.2 Sample fabrication
For the sample design shown in Fig. 1(a), a 100-nm-thick Ag layer was first deposited on an ITO coated glass substrate with a thermal evaporator. Then a 20-nm-thick SiO2 layer was deposited on top of the Ag layer with an electron beam evaporator. We fabricated the SiO2 grating and rectangular SiO2 pads for SPPs refraction experiment with electron beam lithography (EBL). We first spin-coated a layer of PMMA film on top of the SiO2 layer. Before the electron beam exposure, the PMMA film was soft-baked at 180 °C for 5 min. We patterned the PMMA film with array of grooves and rectangles, and deposited a 40-nm-thick layer of SiO2 film on the sample. The lift-off process removed the PMMA film and the SiO2 on top of it, leaving the final SiO2 grating structures and the rectangular pads on the sample. The sample structures were characterized with scanning electron microscopy (SEM) and atomic force microscopy (AFM). Finally, the UCNPs solution in cyclohexane solvent with concentration of 8 mg/ml was spin-coated on the sample to form a monolayer coverage of the UCNPs as the fluorophores for up-conversion fluorescent microscopy. Fig. S2 shows a cross-sectional view of the layer-by-layer thin film coatings of the sample.
Fig. 1. (a) Schematics of a cross-sectional view of the sample design. The main structure consists of the SiO2 grating and the SiO2 pad. The red line profiles represent the SPPs wave coupled by the grating and propagating at the interface between the SiO2 layer and the Ag film. The angle θ indicates the incident orientation of the wave vector k0 of the collimated 793 nm wavelength laser beam. The filled green circles at the top represent the UCNPs spin-coated on the sample. (b) SEM image of the top view of the sample structure in panel (a) prior to the spin-coating of the UCNPs. The azimuthal orientation of the SiO2 pad is 45° relative to the grating structure. (c) and (d) the AFM images of the SiO2 grating and the SiO2 pad of the sample in panel (b), respectively, and the height line profiles extracted from the position indicated by the red dash lines in the images. The period of the grating is 675 nm. The height of SiO2 grating and SiO2 pad is ∼40 nm above the 20-nm-thick SiO2 layer, therefore the total thickness of the SiO2 pad is ∼60 nm.
2.3 Synthesis of NaYF4:Yb3+, Er3+@NaYF4:Yb3+, Nd3+ @ NaYF4 core@shell@shell UCNPs
Monodisperse core-shell-shell hexagonal-phase (β-phase) NaYF4:Yb3+, Er3+@ NaYF4:Yb3+, Nd3+ @ NaYF4 nanocrystals were synthesized with a thermal decomposition process [19,26–27]. A brief description of the procedure follows.
Preparation of NaYF4:Yb3+, Er3+ core solution:
We first prepared the core solution by mixing 0.78 mmol of YCl3 (yttrium (III) chloride, anhydrous powder, 99.99%), 0.2 mmol of YbCl3 (ytterbium (III) chloride, anhydrous powder, 99.99%), 0.02 mmol of ErCl3 (erbium (III) chloride, anhydrous powder, 99.99%) with 15 ml ODE (1-octadecence, technical grade, 90%) and 6 ml OA (oleic acid, technical grade, 90%) into a round-bottom flask. The solution was heated to 180 °C with vigorous magnetic stirring under nitrogen atmosphere until the solution became transparent. The solution was then heated to 110 °C for 1 h under vacuum, and slowly cooled down to ∼ 50 °C afterwards. In the meantime, we prepared a second solution with following procedures: 0.1 g of NaOH (sodium hydroxide, pellet, 98%) was dispersed into 10 ml methanol, then 0.148 g NH4F (ammonium fluoride, anhydrous powder, 99.99%). This solution was then slowly added to the core solution at ∼ 55 °C – 60 °C. The final core solution was heated to 120 °C for 20 mins to remove the methanol, and subsequently heated to 110 °C for 1 h under vacuum, then cooled to room temperature for storage.
Preparation of NaYF4:Yb3+, Nd3+ inner shell solution:
We followed the procedure similar to what described above to prepare the inner shell solution: 1 mmol of YCl3, 0.2 mmol YbCl3, and 0.8 mmol NdCl3 (Neodymium (III) chloride, anhydrous powder, 99.99%) were mixed with 15 ml ODE (1-octadecence, technical grade, 90%) and then 6 ml OA (oleic acid, technical grade, 90%) into a round-bottom flask. The solution was heated to 180 °C with vigorous magnetic stirring under nitrogen atmosphere until the solution became transparent. The solution was then heated to 110 °C for 1 h under vacuum, and slowly cooled down to ∼50 °C. The methanol solution of 0.2 g of NaOH and 0.296 g of NH4F was added to the shell solution slowly. The final inner shell solution was heated to 120 °C for 20 mins to remove the methanol, and subsequently heated to 110 °C for 1 h under vacuum, then slowly cooled to room temperature for storage.
Preparation of NaYF4 outer shell solution:
We again followed the similar procedure described above to prepare the “outer shell solution”: 1 mmol of YCl3 were mixed with 15 ml ODE (1-octadecence, technical grade, 90%) and then 6 ml OA (oleic acid, technical grade, 90%) into a round-bottom flask. The solution was heated to 180 °C with vigorous magnetic stirring under nitrogen atmosphere until the solution became transparent. The solution was then heated to 110 °C for 1 h under vacuum, and slowly cooled down to ∼50 °C. The methanol solution of 0.2 g of NaOH and 0.296 g of NH4F was added to the shell solution slowly. The final inner shell solution was heated to 120 °C for 20 mins to remove the methanol, and subsequently heated to 110 °C for 1 h under vacuum, then slowly cooled to room temperature for storage.
Synthesis of Core@Shell@Shell UCNPs
Under a nitrogen atmosphere, the core solution was first heated to 300 °C for 45 min to synthesize the core crystals (molar ratio [Y]:[Yb]:[Er] = 78:20:2) of the UNCPs. Then the temperature of the solution is lowered to 280 °C, and 8 ml of the inner shell solution was slowly added to the core solution at the rate of 0.05 ml/min to coat the core particles with the inner shell (NaYF4: Yb3+, Nd3+). Subsequently, another 8 ml of the outer shell solution was added to the solution under the same condition and rate to further coat the core@shell particles with the outer shell (NaYF4). The final solution was then slowly cooled to room temperature, and then centrifuged at 6000 rpm for 10 min to precipitate the UCNPs from the solution. To remove the remaining surfactant and the NaF impurities from the chemical process described above, we used a mixture of cyclohexane and ethanol to perform the washing procedure at least 3 times, and the resultant nanocrystals were re-dispersed into cyclohexane for future use. The TEM image of the final UCNPs are show in Figure S3(b).
2.4 Numerical simulation
3D finite difference time domain method (FDTD) calculations was performed with the Lumerical software. The refractive index of Ag, SiO2 was based on the material data of Lumerical FDTD, UCNPs refractive index was set to be 1.57 [28]. For the simulation results shown in this paper, we applied normal incidence condition for the excitation light. The number of the SiO2 grating period was reduced to 4, which is numerically sufficient to demonstrate the coupling of the SPP at the SiO2/Ag interface. The average spacing and orientation of the fringes in the E-field intensity images was used to derive the SPPs wavelengths at the region outside and inside of the SiO2 pad for the estimation of the relative refractive index of SPP propagation.
3. Results
Figure 1(a) shows the schematics of the sample design. The main structure consists of pairs of the SiO2 waveguide gratings and the rectangular pads on the SiO2 spacer layer covered Ag film. Each SiO2 grating contains 40 grooves with the spatial period of 675nm and 45% slot-tooth duty cycle (defined as the ratio of the tooth width to grating period). The structure of the grating is designed to optimize the coupling between the 793 nm wavelength incident light and the SPP propagating at the 20-nm-thick SiO2 spacer layer /Ag interface. For each SiO2 grating-pad pair, one SiO2 rectangular pad was fabricated next to each waveguide grating. The thickness of the SiO2 in the pad is 60 nm, which is 40 nm thicker than the spacer layer. The change of SiO2 thickness results in the change of the SPP wavelength at the Ag/SiO2 interface. Figure 1(b) shows a top view SEM image of the sample. Below we refer to the mutual angle between the pad and the grating as the azimuth angle of the pad, which is 45° in Fig. 1(b). For fluorescent imaging, a layer of UCNP was spin-coated on top of the sample surface. In this work, we present results obtained from the grating and SiO2 pad with different azimuth angle (i.e. 30°, 45°, 60°). Figure 1(c) and 1(d) show AFM images of the SiO2 grating and the SiO2 pad in Fig. 1(b), respectively, and the height line profiles extracted from the images. The line profiles confirm that the height of grating and pad is ∼40 nm thicker than the SiO2 spacer film. In the results reported below, we first present the results of the up-conversion fluorescent microscopy obtained from the “free surface area”, which is the surface area next to the gratings but on the opposite side of the SiO2 pad. We demonstrate with these results the subwavelength resolution of the upconversion fluorescent images of SPP propagation and the image processing technique to enhance the SPP features for quantitative analysis. We then present the results of SPPs refraction across the boundary of the SiO2 pad, with quantitative analysis of the characteristics of the incident light and the SPP propagating on the SiO2 layer covered Ag film.
Figure 2 shows the up-conversion fluorescent microscope images of the grating structure and the free surface areas next to the grating. Figure 2(a) and 2(b) show the fluorescent images obtained with fluorescent emission at wavelengths of 525 nm and 549 nm, respectively. The vertical fringes in both images appeared only when the SiO2 grating structure was illuminated by the incident light. Therefore, the fringes are clearly associated to the SPP propagated at the SiO2/Ag interface. The average spacing between the fringes is 718 nm for both Fig. 2(a) and 2(b). The fact that we can resolve these fine features mainly results from the shorter-wavelength signals generated by the up-conversion fluorescence, which were collected by the objective lens for imaging. The intensity of the fringe decays with the distance from the grating structure and become almost invisible at about 30 µm and beyond. Figure 2(c) shows the average intensity line profiles extracted from the images in Fig. 2(a) and 2(b). Both intensity line profiles show clearly that the overall intensities decay with the distance. Note that the fringes in the fluorescent images correspond to the fine ripples in the intensity line profiles, which persists throughout the intensity plot even at regions where the fringes are nearly invisible.
Fig. 2. The up-conversion fluorescent microscopy images of the sample from the free area on the left side of the grating in Fig. 1(a). (a) and (b) are the fluorescent images obtained from the same area simultaneously with the 525 nm and 549 nm wavelength emission, respectively. The crayon dashed rectangle in panel (a) indicates the position of the SiO2 grating. (c) The fluorescent intensity line profiles extracted from the orange dashed rectangles indicated in panel (a) and (b). The intensity is averaged along the direction normal to the long axis of the rectangle. The red (blue) curve represents the 549 (525) nm wavelength emission intensity line profile. The insets show detailed structure of the fluorescent intensity line profiles associated to the vertical fringes in the fluorescent images. (d) The FIR image calculated with the image in panel (a) the image in (b). (e) The FIR line profile extracted from the dashed rectangle in (d), again averaged in the direction normal to the long axis of the rectangle. The insets show the detailed structure of the ratio line profiles at the same horizontal ranges as those of the insets in panel (c). The size of the scale bar in panel (a), (b), and (d) is 10 µm.
Given the fact that the fluorescent intensities of the 525-nm-wavelength emission and that of the 549-nm-wavelength emission have slightly different power law dependence on the excitation light intensity at the intensity used in the experiment (Fig. S3(d)), we removed the effect of the smoothly varying background intensity in the images by taking the ratio of the intensities of the two images in Fig. 2(a) and 2(b) pixel by pixel, and the resulting FIR image in Fig. 2(d) shows that the fringes are now clearly visible almost all the way to the right boundary of the image, which is about 40 µm from the grating, and interestingly the grating area is now marked with a distinctly different gray level. Figure 2(e) shows the FIR line profile extracted from the FIR image in Fig. 2(d), and it is clear that the ripples are well preserved after the removal of the smooth varying background.
Next, we present the results of the quantitative analysis of the fringes associated to the SPP propagated at the SiO2/Ag interface with the FIR images obtained from our up-conversion fluorescent microscopy. Figure 3(a) shows the FIR image of the fringes on both side of the grating, and Fig. 3(b) and 3(c) shows the line profiles extracted from the image in Fig. 3(a) at positions indicated with the dashed line segments. By fitting the line profiles to a sinusoidal function, we obtained the magnitude of the wavevectors as k1 = 9.81 ± 0.03 µm-1and k2 = 8.81 ± 0.01 µm-1 from the fringes on the left-hand side and the right-hand side of the grating, respectively. By assuming that the fringes resulted from the interference between the E-field of the incident light and that of the SPPs and that the incident light illuminated the sample with a small tilt angle θ off the surface normal as shown in Fig. 1(a), we express the k1, k2 in terms of the wavevectors of the SPPs and the incident light with the following equations.
where kSPP(20nm), and k0 are the wavevector of the SPP propagating on 20-nm-thick SiO2 covered Ag surface and that of the 793-nm wavelength incident light, respectively. By assigning k0 = 2π / 793 nm-1, we obtained kSPP(20nm) = 9.31 ± 0.03 µm-1, which corresponds to the SPP wavelength λSPP(20nm)= 674.8 ± 2.5 nm, and the incident angle θ = 3.61° ± 0.01°. To verify that the SPP wavelength obtained from the analysis described above to be the wavelength of the SPP propagating at the 20-nm-thick SiO2/Ag interface covered with a layer of UNCPs, we carried out theoretical analysis of the SPP wave propagation with the electromagnetic boundary conditions shown in Fig. S6, and numerically solved the resulting equations for the SPP wave vector kx in Eq. (S1)-(S5) [29]. By varying the thickness of the SiO2 spacer layer we obtained from the solution the SPP wavelength as a function of the SiO2 layer thickness. The results are shown in Fig. 3(e). The SPP wavelength decreases with the thickness of the SiO2 layer. The quantitatively agreement between the SPP wavelengths obtained from the experiment and the theory validates our assumption of the physical origin of the fringes in the image and confirms that our up-conversion fluorescent microscopy has achieved resolving the wave front structures associated to the SPPs, which would otherwise require delicate pump-probe imaging techniques to achieve such resolution [8–11].Fig. 3. (a) The fluorescent intensity ratio image of the sample area with the SiO2 grating and the SiO2 pad. The scale bar in the image is 5 µm. (b), (c), and (d) are the line profiles extracted from the image at the position indicated with the orange dash line segments labelled “1”, “2”, and “3”, respectively. Each line segment is locally normal to the fringes in the image. The red curves represent the line profile, and the blue dashed curves represent the results of the curve fitting with a sinusoidal function. (e) The SPP wavelength plotted as a function of SiO2 layer thickness. The solid curve is the theoretical prediction for the system with the boundary conditions shown in Fig. S6. The filled circles are the wavelengths obtained from the analysis of experimental results shown in panel (b), (c), and (d). The open circles are the results from the analysis of results of the FDTD simulation. (f) The relative refractive index for SPP propagation between 60-nm-thick SiO2/Ag interface and 20-nm-thick SiO2/Ag interface plotted as a function of the incident angle of the SPPs. The horizontal solid line indicates the value of theoretical prediction. The filled and the open symbols represent the experimental and simulation results, respectively. The circles represent the relative refractive indices obtained with the SPP wavelengths, and the squares for the results from the analysis of the incident and the refraction angles of the SPPs.
We performed the same curve fitting to the FIR line profile extracted from the SiO2 pad region along the third dashed line segment marked in Fig. 3(a), and the results are shown in Fig. 3(d). The wavevector obtained from the fitting is k3 = 9.75 ± 0.02 µm-1, which is the resultant wavevector from the interference between the incident light and the refracted SPP in the 60-nm-thick SiO2 pad region. Due to the refraction of the SPP at the left boundary of the SiO2, the propagation of the SPP deviates from horizonal direction as indicated by the dashed line segment. We thus calculate the SPP wavevector in the pad region with the following equation
where angle ϕ is the angle between horizontal direction and the SPP propagation direction in the SiO2 pad, and $\phi=7.0^{\circ}\pm0.7^{\circ}$ according to the analysis of the orientation of the fringes in the SiO2 pad area. The value of k0·sinθ is same as that in Eq. (1) and Eq. (2). From Eq. (3) we obtained kSPP(60nm) = 10.25 ± 0.06 µm-1, which corresponds to the wavelength λSPP(60nm)= 612.9 ± 3.8 nm for the SPP propagating at the SiO2 pad region. As shown in Fig. 3(e), the experiment again agrees with the theory quantitatively.The fact that the SPP wavelength changes with the SiO2 spacer layer thickness indicates that refraction of SPP should occur at the boundary of the SiO2 pad in Fig. 3(a). According to the Snell’s law of refraction, the relative refractive index of the 60-nm-thick SiO2 pad /Ag interface with respect to the 20-nm-thick SiO2/Ag interface for SPP propagation can be calculated with the following equations.
or where θi and θr are the incident and refraction angles of SPP, respectively, at the SiO2 pad boundary. With the SPP wavevectors from the results in Fig. 3, we obtained the relative refractive index nrel = 1.10 ± 0.01 according to Eq. (4). Following the scheme shown in Fig. S4, we also estimated the incident angle θi and the refraction angle θr of SPP based on the orientations of the fringes relative to the boundary of the SiO2 pad in Fig. 3(a), and we obtained nrel = 1.11 ± 0.1 according to Eq. (5). Similar analysis for the relative refractive index was also carried out for data obtained from sample structures with SiO2 pad of different azimuthal orientations (Fig. S5). We also calculate the theoretical value of relative refractive index with the predicted wavelengths. The comparison between the theoretical values and the experimental values of the relative refractive index is shown in Fig. 3(f). The experiment agrees well with the theory.We also carried out three-dimensional numerical simulations to reproduce the experiment with a commercially available software package. Fig. S7 shows a cross-sectional view of the model for FDTD simulation. We reduced the number of the periods of the grating to make the simulation feasible with our computing facility. Figure 4 shows the results of the simulation for the case of the results shown in Fig. 3(a)–3(d). Figure 4(a) shows a two-dimensional distribution of the E-field intensity extracted from the plane at a height 10 nm above the grating structure. The fringes in the image signatures the SPP propagation at the SiO2/Ag interface. The change of the fringe configuration across the left SiO2 pad boundary indicates the refraction of the SPP. Figure 4(b) and 4(c) shows the intensity line profiles extracted from the dashed line segments indicated on Fig. 4(a) at region outside and inside the SiO2 pad, respective. By fitting the line profiles with a sinusoidal function, we obtained from the fitted wavevectors the SPP wavelengths to be 672.4 ± 0.6 nm and 612.9 ± 0.3 nm for the 20-nm-thick SiO2/Ag interface and 60-nm-thick SiO2/Ag interface, respectively. As shown in Fig. 3(e), it is clear that the simulation agrees quantitatively with the theoretical prediction. We further carried out the analysis for the relative refractive index of SPP with Eq. (4) and Eq. (5), and we obtained nrel = 1.097 ± 0.001with the SPP wavelengths, and nrel = 1.097 ± 0.066 from the incident angle and refraction angle analysis. The same analysis was also carried out for the simulations for the case of the SiO2 pad with different azimuthal orientations. The results are shown in Fig. S7, and the relative reflective index of SPP was plotted as a function of the incident angle of the SPP in Fig. 3(f). Again, we see quantitative agreement between the simulation, experiment, and the theory.
Fig. 4. The 3D-FDTD simulation of the SPP refraction. (a) The E-field intensity at the plane at the height of 10 nm above the top of the SiO2 structures plotted as the function of the lateral position. The azimuthal orientation of the SiO2 pad is 45°. The location of the SiO2 grating is indicated by the white arrow. (b)and (c) show the intensity line profiles extracted from image in panel (a) at the position indicated with the dashed line segments labelled “1” and “2”, respectively. The dash line segments are locally perpendicular to the fringes in the image. The red solid curves are the intensity line profiles, and the blue dashed curves are the results from fitting the line profiles with a sinusoidal function.
4. Conclusion
We demonstrated subwavelength resolution for imaging of the SPP propagation at SiO2/Ag interfaces with our up-conversion fluorescent microscopy using the NaYF4:Yb3+, Er3+ @ NaYF4:Yb3+, Nd3+ @ NaYF4 core@shell@shell UCNPs as fluorophores. The up-conversion fluorescent emission at wavelengths shorter than the incident light that excited the SPPs plays the key role in resolving the SPP wavefront structures in the fluorescent images. By further taking the intensity ratio of the fluorescent images obtained with the 525-nm-wavelength emission and that of 549-nm-wavelength emission, we further enhanced the SPP wave front features in the FIR images, that allow quantitative analysis for the characteristic quantities of the SPP propagation, such as the wavelengths, directions of propagation, relative refractive indices. We demonstrated such capability by investigating the refraction of SPP propagation with the grating structure and the SiO2 pad structure we fabricated on our SiO2 spacer layer covered Ag film samples. By design, the SiO2 grating structure coupled the incident light to the SPP propagating toward the SiO2 pads. Our analysis of SPP propagation with the FIR images shows good agreement between the experiment, the theory, and the numerical simulations on the SPP wavelengths and the relative refractive index of the SPP propagation at SiO2/Ag interfaces with different SiO2 film thickness. Compared to other experimental techniques that requires delicate optical pump and probe approach or even ultrahigh vacuum technology to acquire SPP images with the subwavelength resolution. We demonstrated that the up-conversion fluorescent microscopy provides a much easier approach to achieve SPP imaging with subwavelength resolution on more versatile sample structures for further development of the plasmonic research.
Funding
Ministry of Science and Technology, Taiwan (107-2112-M-194-011-MY3, 110-2112-M-194-004).
Disclosures
The authors declare no conflicts of interest.
Data availability
The data that support the finding of this study are available from the corresponding author upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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