We study spatially isolated, individual gold nanorods placed at a planar interface between two dielectric media using confocal interference scattering microscopy in combination with higher order laser modes. Approaching refractive index matching conditions, we observe that the elastic scattering patterns of individual nanorods exhibit an exponential increase of both the scattering intensity and the signal-to-background ratio. In case refractive index matching conditions are fullfilled, the data acquisition rates are maximized and suitable for in-vivo biological measurements. In all cases, the characteristic two-lobe shape of the scattering patterns of single nanorods remains unchanged while the sign of the image contrast is a direct consequence of the refractive index variation occurring at the interface.
© 2008 Optical Society of America
Metallic nanoparticles have a promising future in nano-science and -technology due to their favorable and tunable optical properties originating from particle plasmons (PPs), i.e. collective oscillations of free electrons in the conduction band. PPs are determined by material, size and shape of the nanoparticles [1–8] as well as by their aggregation . Moreover, PPs have been recognized to be strongly influenced by extrinsic parameters like the dielectric properties of the local surrounding medium [10, 11]. Novel applications comprise utilization of metal nanoparticles as non-toxic and non-bleaching labels in biology and biomedicine, e.g. [12–15] and references therein, as well as highly sensitive biochemical nano-sensors [10, 11, 16–19].
Metallic nanoparticles have been studied extensively in combination with optical microscopy [1, 20–22] and considerable effort has been spent on detection and visualization of individual metallic nanoparticles with diameters down to 1.4 nm [23–27]. In this context, confocal interference scattering microscopy (CISM) in combination with tightly focused fundamental as well as higher order laser beams has been used for imaging elastic scattering pattern of individual, spatially isolated metallic nanoparticles . In CISM, see for example [29,30], the image contrast results from the interference between the light scattered by an object and the light reflected from the interface where the object is located. This method allows topological measurements with nanometer-precision as well as the determination of the shape and the orientation of single nanoparticles having dimensions much smaller than the wavelength of the excitation laser lig! ht [28, 31, 32]. The possibility of combining fast imaging and high topological sensitivity recommends implementation of CISM on the single nanoparticle level for applications like chemical sensing or time lapse imaging of biological processes occurring at the cell membrane. In a preliminary step, however, the influence of changes in the local environment, either liquid or solid, on the elastic scattering properties of individual metal nanoparticles acting as optical nanosprobes has to be investigated.
In this article, we study experimentally and theoretically the scattering patterns of the same group of spatially isolated, individual gold nanorods placed at a planar interface between two transparent dielectric media under controlled variation of their refractive indices. The intensities of both the excitation light elastically scattered by individual nanorods and the excitation light locally reflected at the nearby interface were found to vary by up to three orders of magnitude while the ratio between them is enhanced by up to five orders of magnitude if refractive index matching conditions are fulfilled. In this case, the signal-to-background ratios of measured single nanorod scattering patterns reach a level sufficient for in-vivo biological measurements. Our simulations reproduce the experimental results by accounting for both the aspect ratio and the volume of individual gold nanorods and the changes of the reflection coefficients occurring at the local interfa! ce. Changing the transition direction of the interface (high n/low n to low n/high n) results in a sign inversion of the image contrast; an effect that could be utilized for detecting even weak dielectric interfaces.
2. Materials and methods
2.1. Sample preparation
Gold nanorods were synthesized utilizing a seed-mediated approach , subsequently purified from excess surfactant and characterized both individually on a glass surface using atomic force microscopy (AFM) and in aqueous solution using extinction spectroscopy (see Fig. 1). Throughout this work we will neglect the effect of the surfactant belayer capping the gold nanorods . The AFM image Fig. 1(a) shows a spatially isolated, individual gold nanorod having a height of 15 nm on a glass cover slip spin coated from a high diluted aqueous solution (0.5 rods per µm 2) for optical measurements (for details, see ). The extinction spectrum of the nanorod solution (see Fig. 1(c)) exhibits two maxima reflecting their plasmon resonances along the short axis b and the long axis a. The measured spectrum was fitted with an analytical expression based on Mie theory [33,36]. From the fit results, we estimate that the particles have an average aspect ratio R=a/b of 2.6. By combining the results obtained from both AFM and spectroscopic measurements, we estimate the average dimensions of gold nanorods to be 15 nm x 38 nm in good agreement with the values given in .
For the optical experiments, droplets of water (n 2=1.34) and immersion oil (n 2=1.518) were successively deposited on the surface of a microscope glass cover slip (n 1=1.518) bearing spatially isolated, individual gold nanorods for studying the influence of the changing interface as well as the modified local dielectric environment on the scattering patterns of the same nanorods. In a second step, we prepared samples by sealing a diluted nanoparticle solution between two glass cover slips to investigate the influence of the change of the transition direction of the interface (high n/low n and low n/high n, respectively) on the scattering patterns of individual nanorods. Here, the distance of the cover slips was determined by confocal microscopy to be approximately 2 µm.
2.2. Optical setup and signal detection
All scattering images were acquired with a home-built inverted confocal microscope as sketched in Fig. 2 that was equipped with a HeNe-Laser operated at 633 nm. A higher order laser mode, i.e. an azimuthally polarized doughnut mode (APDM), having a diameter of 4 mm, was tightly focussed on individual gold nanorods and the elastically scattered light was collected on a point-like detector. Details regarding the experimental arrangement can be found in [28,31]. The detected signal IAPD consists of the coherent interference between the excitation light reflected at the interface where the nanorod is located and the light elastically scattered by the particle:
Here, |E r|2 represents the intensity of the excitation light reflected at the interface, i.e. the image background intensity IBKG. |E s|2 represents the pure scattering signal of the particle and is proportional to its squared volume . The interference term 2|E s||E r |cosϕ depends critically on the phase ϕ between the reflected and the scattered field. The sum of the second and third term on the right hand side of Eq. 1 describes the image contrast in the scattering pattern of a single particle. The phase of the scattered field is determined by the spectral properties of the PPs, the material and the dimensions of the nanoparticle as well as the refractive index of the surrounding media whereas the phase of the reflected field is affected by the numerical aperture of the microscope objective. Importantly, the refractive index mismatch, i.e., the difference between the refractive indices of the two dielectrics forming the interface, is critical for the phases of both fields so that small variations can switch the sign of the image contrast.
Starting from Eq. 1 the scattering pattern of an individual gold nanorod (I Nano) can be described in the following way:
Equation 2 is valid if the reflected field at the interface is comparable to or smaller than the transmitted field. Eq. 3 can only be used if the dielectric interface fulfills index matching conditions, i.e. E r=0, while Eq. 4 also holds close to the index matching regime. Depending on the actual size and shape of a specific nanoparticle as well as the excitation wavelength used, more complex approaches might be required.
An individual gold nanorod renders a characteristic two-lobe scattering pattern that reveals the particle’s position and orientation with nanometer-accuracy [28, 31]. In Fig. 2 Inset (I, a), a typical scattering pattern imaged for a spatially isolated gold nanorod deposited on glass, covered by water and excited using an APDM is shown. In order to estimate the orientation and the position of single gold nanorods , we used a two dimensional fit algorithm running on Matlab® that produces a virtual scattering pattern (see Fig. 2, Inset (I, b) by fitting the experimental data with a model function (Eq. 8 of ). The corresponding theoretical scattering pattern is shown in Fig. 2, Inset (I, c). It was simulated based on Mie theory and analytical calculations of the optical field distribution of an APDM in the focal regime of a high NA objective lens ! accounting for Eq. 1. The simulation does not require free parameters and constitutes a physical interpretation of the imaging process. A detailed discussion of the underlying model is subject of a parallel publication.
3. Results and discussion
3.1. The refractive index mismatch at the interface
To investigate the effect of the interface and the local dielectric environment, we recorded successively scattering patterns of the same set of spatially isolated, individual gold nanorods in three different configurations: First, deposited on a microscope glass cover slip exposed to air (glass-air interface; see Fig. 3, left schematic), second, covered with a droplet of water (glass-water interface; see Fig. 3, middle schematic) and, third, after evaporation of the water, covered with a droplet of immersion oil (glass-oil interface; see Fig. 3, right schematic) effectively achieving refractive index matching conditions. A detailed description of the sample and the confocal microscopy setup can be found in the Materials and Methods section. There, we also outline the analytical description of the detectable scattering signal.
In Fig. 3(a)–(c), experimental scattering patterns of the same set of spatially isolated, individual gold nanorods are shown for three different interfaces, or, in other words, different local dielectric environments, that are indicated in the schematics above. As can be seen in the corresponding cross sections in Fig. 3(g)–(i), the signal-to-background ratio as well as the contrast in the scattering images for the same particle vary dramatically: Stepwise approaching the index matching regime realized by the glass-oil interface, we observe a simultaneous increase of the scattering signal and the signal-to-background ratio as well as a sign inversion of the image contrast. While the variation of the local dielectric environment results in significant changes of scattering amplitude and image contrast for the same particle, the overall shape of the scattering pattern does not change significantly. Discrepancies that can be recognized by compa! ring the scattering patterns of different nanorods result from differences in their individual geometry as will be discussed in the next paragraph.
We utilized the model function (see Eq. 8 of ) to determine the signal amplitude, position and orientation of individual nanorods as well as the relative distances between them. The orientation could be determined with a standard deviation of approximately 1 degree corresponding to a rotational arch of 0.8 nm assuming a nanorod length of 45 nm. Relative particle distances were extracted with nanometer-precision and relative errors below 1 percent. The results for scattering amplitudes, orientations and relative distances of the particles were used as parameters for simulating the corresponding theoretical scattering patterns that are shown in Fig. 3(d)–(f). For simulating the scattering patterns at the glass-air and glass-water interface, respectively, we used Eq. 2 as specified in the Materials and Methods section. In fact, in these cases, the electric field reflected at the interface E r is not negligible and strongly affects the amplitude and the phase of the overall scattering signal. For the glass-oil interface, the scattering patterns are well-described by Eq. 3 (see Materials and Methods section). In this case, the inversion of the image contrast is a direct consequence of E r⋍0 as will be discussed in the following.
The scattering patterns shown in Fig. 3 can be rationalized by decomposing the total scattering signal into contributions arising from the reflected field E r and the scattered field E s. We investigate the influence of E r by measuring the image background intensity |E r|2 as a function of the laser excitation power for the three different interfaces discussed above. As can be seen in Fig. 4, we obtain a linear dependence between |E r|2 and the laser excitation power for each of them, as expected. As an important result, for a given laser excitation power (as indicated by the dashed vertical line in Fig. 4), the measured background intensity |E r |2 reaches a minimum at the oil-glass interface and is two (three) orders of magnitude smaller as measured for the glass-water (glass-air) interface. Simultaneously, the contribution of the scattered field E s! to the overall detected intensity, i.e. (|E s|/|E r|)2, increases exponentially by five orders of magnitude towards the index matching regime, i.e. n 2=n 1=1.518, as can be seen from the calculation result shown in the inset in Fig. 4. As a result, we expect the image contrast (see Fig. 3(d)–(f)) to increase for a decreasing difference between the refractive indices n 1, n 2 of the dielectrics and to invert the sign approaching the index matching regime, i.e. n 1⋍n 2. Under this condition, the interference term in Eq. 1 becomes negligible and Eq. 3 delivers a valid approximation assuming perfect focusing conditions as well as a perfect dielectric interface. As a key result, the
index matching condition delivers optimized imaging conditions for small metallic nanoparticles, in particular for low laser excitation powers, that are suitable for 1! t in-vivo measurements in biological environments.
3.2. Particle geometry and image contrast
Small differences in the shapes of scattering patterns of different gold nanorods that can be recognized from Fig. 3(a)–(c) are induced by phase and amplitude modulations of the optical fields involved and they have been accounted in the simulations of the corresponding theoretical images shown in Fig. 3(d)–(f). In the following, we discuss how the small variations of the shape of the scattering patterns are related to the geometry of individual gold nanorods. For simplicity, we assume refractive index matching conditions at the interface where the particle is located, i.e. n 2=n 1, or, in terms of our experiment, the glass-oil interface as shown in Fig. 3(c). In this case, there is no phase term contributing to the overall image signal I Nano (see Eq. 3) and the scattering signal depends exclusively on the aspect ratio R=a/b, or, equivalently, the plasmonic properties of gold nanorods.
To visualize the influence of R on the shape of the scattering pattern, we calculated the integrated scattering intensity as a function of the aspect ratio for a single gold nanorod and the result is shown in Fig. 5. The curve suggests that, despite the sharp maximum occurring at R⋍2.1 due to the plasmon resonance of gold nanorods embedded in oil, the total scattering intensity of the nanorod increases moderately, proportional to the volume of the particle. Three representative simulated scattering patterns for R=2.5, 4 and 7, respectively, are also shown in Fig. 5. Apparently, the nanorod with R=2.5 appears as the strongest scatterer offering the brightest signal and represents the average aspect ratio of gold nanorods observed in our experiments. For an increasing R, the overall scattering intensity as well as the shape of the scattering patterns are modified. Hence, we conclude that variations of the aspect ratio are ma! inly responsible for the differences of the scattering patterns observed for different nanorods in our experiments (compare, for example, the scattering patterns in Fig. 3(c)).
3.3. Direction of refractive index transition and contrast inversion
In the following, we demonstrate that CISM allows to localize even weak dielectric interfaces and to distinguish the direction of the refractive index transition (high n to low n or low n to high n) by analyzing the contrast of the scattering pattern of an individual gold nanorods. As sketched in Fig. 6, spatially isolated, individual gold nanorods were located at either a glass-water (high n to low n) or water-glass (low n to high n) interface with respect to the microscope objective focused on the sample from below (see also Fig. 2). All scattering patterns acquired from nanorods located at the lower interface (transition high n to low n) exhibit negative image contrast as can be seen in Fig. 6, Inset(I). In contrary, all the scattering images measured from nanorods located at the upper interface (transition low n to high n) show inverted, i.e. positive, image contrast (see Fig. ! 6, Inset (II)). The explanation of this phenomenon is that the reflection coefficients of the two interfaces differ by a phase factor of π effectively switching the overall phase of the reflected field E r .
Measuring the sign or varitions of the image contrast could represent a promising experimental approach to determine the position of a particle within an interface between two dielectric media or to detect small local changes in the dielectric properties of the interface itself. Monitoring dielectric modifications in active interfaces like, for example, a cell membrane with high spatial resolution could allow for tracking the flow of single proteins into and out of a cell or to determine the amount of particles passing through a membrane.
We have investigated the scattering patterns of individual, spatially isolated gold nanorods placed at a planar interface between two transparent media. We measured the effect of the refractive index mismatch on the scattering intensity, the signal-to-background ratio as well as the image contrast and its sign. We found that the scattering properties of each single particle could be modified by varying in-situ the dielectric properties of the surrounding media. As a major result, the signal-to-background ratio was found to be maximized in the index matching regime, i.e. for diminishing reflection of excitation light at the interface. Under this condition, the scattering patterns are determined exclusively by the geometrical and, hence, plasmonic properties of the particles. Moreover, we demonstrated that scattering patterns of individual gold nanorods reveal the nature of closely spaced dielectric interfaces due to a sign inversion of the image contrast.
The combination of CISM and higher order laser modes provides simultaneously accurate topological information like the position, the shape and the orientation of metallic nanoparticles [28,31,32] and allows for monitoring small variations in their local dielectric environment. Our results demonstrate the potential of advanced confocal microscopy techniques, see also e.g. [39, 40], for the in-vivo detection of metallic sensors attached to or incorporated in biological systems.
We acknowledge stimulating discussions with Achim Hartschuh (LMU, Munich, Germany) and Stefanie Reichelt (Cancer Research UK, Cambridge, UK) as well as experimental assistance by Frank Wackenhut. Financial support was provided by the Deutsche Forschungsgemeinschaft DFG (Me 1600/6-1/2) and the Landesstiftung Baden-Württemberg. Scan images were in part processed using WSxM software from nanotec .
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