Finite-Difference Time-Domain (FDTD) calculations are used to characterize the electric field in the vicinity of a sharp silver or gold cone with an apex diameter of 10 nm. The simulations are utilized to predict the intensity and the distribution of the locally enhanced electric field in tip-enhanced Raman spectroscopy (TERS). A side-by-side comparison of the enhanced electric field induced by a radially and a linearly polarized light in both gap-mode and conventional TERS setup is performed. For this purpose, a radially polarized source is introduced and integrated into the FDTD modeling. Additionally, the optical effect of a thin protective layer of alumina on the enhancement of the electric field is investigated.
© 2013 Optical Society of America
The development of tip-enhanced Raman spectroscopy (TERS) is a revolutionary advancement in vibrational spectroscopy of materials and biomaterials, providing a spatial resolution and sensitivity on the scale of a few nanometers [1–3]. For example, TERS has been successfully employed to study a large variety of samples such as isolated carbon nanotubes [2,4], individual RNA strands , isolated mitochondria of cells , or interactions of proteins with biocrystals . The principle of TERS is based on the excitation of the localized surface plasmon resonance (LSPR) at the extremity of a sharp metallic tip with a typical radius of 20-40 nm. The optimal excitation of the LSPR is thus critical to provide maximum enhancement from the tip apex which acts as a nanoantenna for both excitation and emission processes . In the best conditions, Raman intensity maps with lateral resolution of less than 15 nm can be obtained , in contrast to the resolution limit of conventional optical microscopy limited by the the Abbe’ criterion (~250 nm) . The enhancement of the electric field in TERS depends critically on various parameters such as the polarization of the excitation beam, the metallic nature and the geometry of the metallic tip, as well as the sample substrate . So far, finite-difference time-domain modeling (FDTD) of the electromagnetic field has been applied successfully to optimize TERS parameters such as the length and the radius of the tip, the material of the tip and the tip-sample distance [12–14]. In this work, we use FDTD to precisely estimate the impact of both radially and linearly polarized sources on the enhancement of the electric field. While a linearly polarized source is commonly used for TERS, radially polarized modes are of great interest to conduct TERS experiments in axial illumination geometry [15–17]. Laser beams with radial polarization provide unique focusing properties including a strong longitudinal electric field component generated at the focal point . In TERS, a polarization component of the incident light along the tip axis induces a strong surface charge density at the sharp apex of the metallic tip which is a prerequisite for local enhancements . To conduct the presented calculation, a radially polarized source is designed and integrated into the FDTD modeling. The choice of the material for simulated tip and substrate is limited to silver and gold as they are the two most popular metals that are successfully tested for TERS measurements in UV-Vis range [9,19]. The presented simulations are performed at two distinct wavelengths of 532 and 632.8 nm, in order to excite the LSPR of silver and gold tips, respectively. These parameters also match our practical TERS experimental conditions [7,20]. Furthermore, we analyze how a thin protective layer of alumina alters the confinement of the enhanced electric field. Although such protective layer does extend the lifetime of the metallic tip by preventing the rapid oxidation and mechanical wear under ambient conditions, it also interferes with the local enhancement [21–23].
2. Results and discussion
Finite-difference time-domain approach is a reliable method for solving Maxwell’s equations in complex geometries . FDTD provides time domain information, offering insight into electrodynamics of the system . In FDTD, the electromagnetic field and structural materials of interest are described on a discrete mesh composed of so-called Yee cells. Maxwell’s equations are solved discretely in time, where the time step used is related to the mesh size through the stability criterion. This technique is an exact representation of Maxwell’s equations in the limit that the mesh spacing goes to zero. To simulate the TERS tip, a silver or gold rounded-tip cone with the tip diameter of 10 nm, and a cone angle of 25° is utilized. These parameters are estimated based on SEM images of typical tips that are used in TERS measurements. To illustrate gap-mode geometries, a film of silver or gold with 5 nm thickness is introduced inside the simulation area and located 1 nm below the cone apex. The simulation area is set up as a three-dimensional system of 100x100x126 nm3 surrounded by the perfectly matched layer (PML) boundary, wide enough in order to limit its impact on the resonance of the system. A spatial mesh of 0.15 nm and a temporal mesh of 2.8x10−16 s are set, which guaranteed numerical convergence of the results. The optical constants of alumina is described by Palik , and the one of silver and gold are obtained from CRC . All the calculated and reported intensities are normalized with respect to the intensity of the incident light. A radially polarized light has polarization vectors oriented radially in the transverse plane with respect to the propagation direction. Under a tight focusing of a radially polarized light by a high numerical aperture (N.A.) lens, the focal longitudinal electric field and the focal transverse electric field could be expressed by the following equations :Eqs. (1) and (2) was created to describe a focused radially polarized light inside the simulation area. The script was written in Matlab programming language and integrated into FDTD. This light source has been utilized for the corresponding calculations that are reported in this article. The transverse and longitudinal electric field components of the described beam are shown in Figs. 1(a) and 1(b) in 3D and 2D presentations. Focal components of a linearly polarized light are also presented for comparison. To create Figs. 1(c)-1(f), the Gaussian light is focused by passing a 1 mm diameter beam consisting of 1500 plane waves through a thin lens of 5 mm diameter and 1.2 numerical aperture.
The transverse component of a radially polarized beam consists of several concentric rings with variable intensities and a minimum intensity at the middle [Fig. 1(a)]. The longitudinal component of this beam is another set of concentric rings with overall intensities lower than the transverse component and with a maximum intensity at the center [Fig. 1(b)]. The enhancement phenomenon that occurs in TERS originates from the interaction of the longitudinal component of the focused light with the apex of the sharp metallic tip. The top view of a focused Gaussian beam consists of several concentric rings in the xy plane with a maximum intensity in the middle [Fig. 1(c)]. From the side view, the beam would be relatively elongated in the direction of propagation along z [Fig. 1(d)]. As shown in Figs. 1(e) and 1(f), the z component of the electric field in a focused Gaussian beam has two lobes in the direction of propagation with zero intensity in the middle. This minimum intensity results in the absence of significant excitation of plasmon resonances at the tip apex if the tip is located in the center of the focal region. However, tip-enhanced Raman should be observed more significantly in the case where the tip is located inside one of the two lobes of the excitation laser. For the presented simulations where the structures of a few nanometers (less than 20 nm) are studied, focused Gaussian beam are approximated with a plane wave. Here, total field scattered field (TFSF) was used to prevent the possible couplings with the boundaries of the simulation area. TFSF is a special case of plane wave that separates the computation region into two distinct regions: one contains the total field which is the sum of the incident field and the scattered field, while the second region contains only the scattered field. As depicted in Figs. 2(a)-2(f), a comparison of the localized electric field enhancement at the tip apex is performed for linear and radial polarizations. A linearly polarized source was set to propagate along the tip axis (axial illumination) or perpendicular to it (side illumination). In side illumination, the light is linearly polarized along the tip axis, while in axial illumination, the polarization of light is perpendicular to the tip axis (linear polarization) or along the tip (radial polarization). The results of these simulations are shown in Figs. 2(a), 2(c) and 2(e) when only the tip is involved in the simulation and in Figs. 2(b), 2(d) and 2(f) for gap-mode TERS. In gap-mode TERS, thin and flat gold nanoplates are generally utilized as substrate for the sample. Since the molecules or nano-object of interest are sandwiched between the two metallic interfaces formed by the tip and the metallic nanoplate, larger local enhancement of the Raman signal can be achieved . As shown in Figs. 2(a) and 2(b), for a linearly polarized beam with axial illumination configuration, the presence of the tip results in an overall electric field intensity of zero below the apex.
Here the electric field is enhanced in two areas located on two sides of the tip with respect to the tip symmetry axis. When the tip is illuminated from the side with a linearly polarized light, the electric field is confined at the tip apex [Figs. 2(c) and 2(d)]. Side illumination is specifically useful when probing opaque samples. However, microscope objectives with long working distances, and therefore low focusing power, are generally used in side illumination setups. The creation of an intensified electric field at the tip apex can also be obtained through axial illumination with a tightly focused radially polarized light. The longitudinal component of the electric field in this case is significantly enhanced at the tip apex [Figs. 2(e) and 2(f)]. The presence of thin layer of metal gives rise to a more localized confinement area around the tip apex [Fig. 2(b), 2(d) and 2(f)] when compared to the conventional TERS setup [Figs. 2(a), 2(c) and 2(e)]. The simulations show an increase of the normalized intensity of the electric field at the junction between the tip and the metal substrate. An improvement of the enhancement factor from 8 to 10 for axial illumination, from 82 to 322 for side illumination and from 720 to 11510 for radial polarization are predicted, when comparing conventional TERS and gap-mode TERS under distinct polarization configurations. Similar calculations are performed for different combinations of silver/gold tips with gold/silver substrates upon axial and side illumination by linearly and radially polarized light. The results of the 18 possible combinations are summarized in Table1.
Noticeably, under an irradiation at 532 nm, these results predict a larger enhancement factor when using a silver tip and a gold substrate as compared to the case involving a silver tip and a silver substrate. This observation is presumably related to the extinction coefficients of silver (kag(532 nm) = 3.49) and gold (kau(532 nm) = 2.1). Silver absorbs a larger part of the incident light compared to gold, thus reducing local enhancement of the electric field. This absorption weakens the excitation beam that reaches the tip apex. The absorption of the light by the silver substrate could also be quite high, breaking the observed trend for the confinement factor of the electric field. A similar trend is observed when using gold tip at 633 nm irradiation. However, this phenomenon is not observed for axial illumination with linearly polarized light, therefore, this could also be due to the orientation of the polarization direction with respect to the tip axis. The optical effect of a dielectric protective layer is investigated by adding a 1 nm thick alumina layer over the surface of the metallic cone as shown in Figs. 3(a)-3(c). The thickness and the material of the protective layer have been chosen according to the previously published studies .
Adding 1 nm of dielectric protective layer decreases the enhancement of the enhanced electric field by 50%. The observed decrease could originate from a shift in the frequency of the surface plasmon resonance. If the apex of the metallic TERS tip is considered as a nanosphere, the quasi-static dipolar plasmon resonance condition for this tip follows where and are the permittivities of the metallic sphere and the surrounding medium, respectively . In conclusion, the addition of a dielectric layer would change the plasmon resonance of the tip/substrate junction thus reducing enhancement of the local electric field. The presence of the alumina dielectric layer could also cause destructive interference of the incident light and the scattered electric field from the different interfaces.
The present work aims at exploring the influence of the incident laser polarization, and the presence of a thin metallic substrate in distinct configurations for tip-enhanced spectroscopy. We conclude that by utilizing a thin film of transparent gold or silver as a substrate for TERS measurements, a considerable increase in the sensitivity can be achieved. With regard to the polarization of the incident light, we conclude that for a linear input polarization, a side illumination is preferable with polarization axis oriented along the tip axis. Meanwhile, axial illumination by a radial polarization promotes the strongest confinement of the electric field, which is ideal for tip-enhanced measurements. However, the excitation depends on the optical properties of the junction formed by the metallic tip and substrate. The hetero-metallic junction formed by a silver tip and a gold thin film appears to be very efficient. These investigations are in good agreement with our recent study where the impact of a thin film of gold as substrate along with radially polarized Raman laser is experimentally investigated in TERS detection of a monolayer of molecules . Additionally, we demonstrate that adding a thin protective layer to the TERS tip to reduce oxidation and mechanical wear decreases the intensity of the electric field by 50%.
This research was funded by the Natural Sciences and Engineering Research Council of Canada Discovery Grant and by the Canada Research Chairs program.
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