ARTICLE IN PRESS

Journal of Luminescence 107 (2004) 176–181

In situ characterization of optical tips using single fluorescent nanobeads . C. Woehl* Aure! lien Drezet, Serge Huant, Jorg Laboratoire de Spectrom!etrie Physique, Universit!e Joseph Fourier Grenoble et CNRS, BP 87, 38402 Saint Martin d’H"eres Cedex, France

Abstract Aperture-type near-field scanning optical microscopy (NSOM) can be used to image single dipolar emitters at a spatial resolution beyond the diffraction limit. In addition, such imaging provides the intrinsic possibility to determine the three-dimensional orientation of the emitter due to the complexity of the tip’s electromagnetic field. However, this determination necessitates the use of an appropriate analytical model for the tip field and a knowledge of crucial experimental parameters like aperture diameter, feedback distance, and the polarization direction of the incident light. A frequently cited model is the Bethe–Bouwkamp solution for a circular, sub-wavelength hole in a metallic screen illuminated by a plane wave. However, this model is unable to even qualitatively explain the experimental images of fluorescent nanobeads obtained with an aperture-type NSOM. We therefore present a simple, analytical model that fits all experimental data quantitatively and provides a realistic representation of the tip’s electric field. We also propose the use of small fluorescent nanobeads in an experimental scheme for the in situ characterization of aperture diameter, feedback distance, and polarization direction of the incident light. r 2004 Elsevier B.V. All rights reserved. PACS: 07.79.Fc; 33.50.
j; 42.25.Fx; 41.20.Jb Keywords: Near-field scanning optical microscopy; Analytical model; Tip aperture; Feedback distance; Fluorescent bead; Fluorescence imaging

1. Introduction Image interpretation for aperture-type near-field scanning optical microscopy (NSOM) in illumination mode [1–3] not only requires a precise knowledge of experimental parameters like aperture diameter and feedback distance but also a good model for the electromagnetic field surrounding the optical probe. The first two parameters are *Corresponding author. Tel.: +33-476514810; fax: +33476635495. E-mail address: [email protected] (J.C Woehl).

crucial in that they determine the instrument’s optical resolution, but they are often not precisely known under the actual experimental conditions. The aperture diameter is usually determined from optical throughput measurements, the angle dependence of the optical tip’s far-field transmission [4], or, less frequently, from electron microscopy. The tip-sample distance is evaluated using external calibration curves based on a reference point for zero distance (like a tunneling current between the tip’s metal coating and a specially prepared sample surface) and the known behavior of the piezo scanner. However, it is unclear how a

0022-2313/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jlumin.2003.12.053

ARTICLE IN PRESS A. Drezet et al. / Journal of Luminescence 107 (2004) 176–181

calibration curve obtained under such specific conditions changes for near-field imaging of other surfaces. Even with a satisfactory knowledge of these parameters, it is necessary to rely on theoretical models for the electromagnetic field near the optical probe in order to analyze experimental images. This is especially important for the observation of objects much smaller than the aperture diameter, like single fluorescent molecules or fluorescent nanobeads. A frequently cited model for interpreting such images is the Bethe– Bouwkamp solution for a small hole in a conducting screen illuminated by an incident plane wave [5, 6], which seems to be a rather questionable model for an optical probe. Often, elaborate numerical calculations for specific tip–sample configurations are carried out which, however, rest approximative in nature because they depend on the choice of boundary conditions, discretization and iteration procedures used [7–9]. It seems therefore desirable to find a simple but realistic, analytical description of the probe’s electromagnetic field. The electric field component is of particular interest since it dominates the interaction with fluorescent nano-objects. In previous work, we have proposed a far-field description of the electromagnetic field due to a fiber tip [10, 11], and we now present a simple model for the electric field component close to the tip. Our model accurately reproduces the experimental results and contributes to an understanding of the physics of the optical probe. In this context, we propose fluorescent nanospheres as valuable objects for an in situ determination of both tip aperture and feedback distance under the actual experimental conditions. Further experiments are in progress to validate this proposition and to obtain a three-dimensional intensity map for the electric field surrounding an optical tip. In contrast to the other models commonly employed, we find that the Ex component of the electric field near the tip aperture is very weak which is of fundamental importance for image interpretation. We plan to address this distinctive feature by NSOM imaging of molecular fluorescence with polarization detection.

177

2. Experimental Fluorescent molecules, when in resonance with the excitation light, can be used as selective detectors for the incident light polarization since the fluorescence intensity is proportional to ðl  EÞ2 where l is the molecular transition dipole moment and E the electric component of the excitation field. Fluorescent nanobeads contain an ensemble of N arbitrarily oriented and incoherently emitting molecules. Their fluorescence intensity is proportional to Ip

N X i¼1

N ðli  Ei Þ2 E m2 /E 2 Ssphere 3

volume

;

where m is the typical value for the molecular transition moment. Strictly speaking, the electric field E denotes not only the incident excitation field but also the perturbation and reaction of the bead, a second-order effect that can be neglected in this analysis. Fluorescence labeled nanospheres act therefore as isotropic volume detectors of the average electric field intensity and can be used to produce an intensity map of the electric excitation field without any further knowledge of orientational parameters. In contrast to single molecules which are vector detectors, fluorescent nanospheres, in the limit of very small sizes, act as scalar detectors of the electric field. In order to map the electric field distribution of light exiting from a NSOM tip, we imaged fluorescent nanobeads with a diameter much smaller than the optical aperture size. Carboxylate-modified, yellow–green fluorescent nanospheres (Molecular Probes) with diameters of 220 nm 7 5% are deposited from basic solution (pH 10–11) on a PMMA layer spin-coated onto a clean lass cover slide. A few hundred mW of the 514.5 nm line of an Argon ion laser are coupled into a single mode optical fiber with a tapered, metal coated end presenting an optical aperture (typical transmission of 10
3–10
2) which excites the sample, held at nanometer distance using a feedback loop with tuning fork detection [12]. The emission is collected in the far field above the sample surface using an Al mirror and, after removal of residual excitation light using color

ARTICLE IN PRESS 178

A. Drezet et al. / Journal of Luminescence 107 (2004) 176–181

glass filters (Schott) and interference filters, detected by a channel photomultiplier (PerkinElmer) in photon counting mode. The integration time for each point in the image is 50 ms. As can be seen in Fig. 1, all recorded fluorescence images present two fluorescence lobes with the same orientation and shape, indicating that the nanospheres act as probes for the optical tip and not vice versa, a property that has been used to characterize the quality of NSOM aperture tips [13]. 3. Results and discussion To explain the observed intensity distribution, we have developed a simple model for the electric field around the metal coated aperture tip. Our model is based on the assumption that the electric field E expð
iotÞ produced by the tip is essentially static (satisfying the potential condition r  E ¼ 0) and is completely characterized by the electric charge distribution located on the metal coating of the tip apex. Let us call (x,y) the aperture plane and z the tip axis, with the incident light polarized along x and propagating in the z direction. The linearly polarized, optical LP0,1 mode in the single mode fiber is mainly coupled to the fundamental,

Fig. 1. NSOM images of fluorescent nanobeads whose diameter is much smaller than the size of the tip’s optical aperture. The fluorescent beads act as scalar, isotropic volume detectors for the electric field component and give rise to the same intensity patterns for all observed nanobeads.

transverse electric mode of the conical wave guide preceding the aperture zone [14, 15]. The cos f dependence of this guided mode (f being the angle with respect to the polarization plane) will therefore appear in the induced polarization charges in the surrounding metal coating at the tip apex. We can therefore assume a surface charge density s of the form sðr; f; zÞ ¼ f ðr; zÞ cos f for any point ½x; y; z ¼ ½r; f; z on the metal coating. In the simplest case, we can assume a linear, ring-like charge density cðfÞ ¼ c0 cos f concentrated at the rim of the tip aperture of radius a (see Fig. 2A). A map of E2 and the squared electric field components is presented in Fig. 3A for the (x,y) plane at z ¼ 0:3a from the aperture plane. This ring charge model produces two intensity lobes for the electric field intensity and is therefore able to qualitatively explain the experimentally observed emission lobes. Nevertheless, it is an oversimplification because (i) it

Fig. 2. Cross-section of an optical fiber tip with the associated electric field lines and a logarithmic intensity map. The polarization of the incident light propagating in the fiber core (z direction) is oriented along the x-axis. The electric field is generated by polarization charges in a perfect metal coating modeled by (A) a linear charge distribution around the aperture rim, and (B) a surface charge distribution on the lateral and inner surface of the metal coating surrounding the tapered fiber (aperture diameter 2a). The parameters r (distance from the aperture rim) and the cone angle b are indicated in the figure. The electric field lines in the immediate vicinity of the metal surface show artefacts mainly due to the numerical discretization procedure, which become, however, insignificant at larger distances.

ARTICLE IN PRESS A. Drezet et al. / Journal of Luminescence 107 (2004) 176–181

179

Fig. 3. Intensity maps for the electric field (E2, E2x, E2y, and E2z ) at a distance of z ¼ 0:3a from the tip aperture of radius a (the images in each column share the same colorbar). Electric field created by (A) a ring-like charge distribution on the rim of the optical aperture as illustrated in Fig. 2A, (B) a surface charge distribution as illustrated in Fig. 2B, and (C) a planar Bethe aperture (Bouwkamp solution). The images on the first line correspond to those that would be obtained using a pointlike, scalar detector for the electric field (e.g. an idealized, infinitely small fluorescent nanosphere). As can be seen, only the first two models are able to produce two lobes for the E2 distribution. The last three lines correspond to fluorescence images predicted for pointlike vector detectors for the electric field (e.g. single fluorescent molecules) oriented along the x, y, and z direction, respectively.

does not obey Maxwell’s boundary conditions on the metal, and (ii) it implies a logarithmic energy divergence at the aperture rim. This latter point is forbidden by the classical analysis of light diffraction by an edge or a corner [16]. In our problem, the edge-corner condition naturally leads to the requirement that the electric surface charge density increases not faster than

ð1=rÞn where r is the distance from the rim (see Fig. 2B) and where n ¼ 1
p=ð2p
bÞ is a function of the corner angle b [17]. We must therefore impose s ¼ gðr; zÞ=rn cos f (g has no singularity at the rim), and we suppose g ¼ s0 ¼ const: since the variation of g is negligible for objects like the tip apex which have a size

ARTICLE IN PRESS A. Drezet et al. / Journal of Luminescence 107 (2004) 176–181

180

Imax/Icenter 100 nm

10 20

Axial distance (nm)

30 40 50 60

Imax

70 80 Icenter

90 100

(A)

(B)

Fig. 4. Theoretical evolution of characteristic parameters for fluorescence imaging of nanospheres with increasing axial distance Dz. (A) Cartography of the fluorescence intensity in the ðx; zÞ plane and lobe separation distance as a function of Dz. The solid and dotted lines mark the intensity maxima with increasing axial distance for the surface and ring charge model, respectively. (B) Variation of the contrast ratio between maximum intensity on top of the lobes (Imax) versus the center intensity (Icenter, see insert) as a function of Dz (same scale as in A).

on the order of or smaller than one wavelength. The angle b and the tip angle a are related by a ¼ p
2b: The divergence of s at the aperture rim r ¼ 0 is artificial since the total integrated energy in its vicinity remains finite [18]. The electric field produced by such a surface charge distribution is represented in Fig. 3B and shows the same intensity lobes as the simpler ring model. It is interesting to note that the image representing E2 is entirely dominated by the x- and z-components of the electric field, and carries direct information on their squared maximum values in the image plane: the x component is highest in the image center (where the z-component is negligible) while the z-component is highest in the lobe centers (where the x component is very weak). The Bouwkamp solution for a planar Bethe aperture, presented in Fig. 3C, shows strong, qualitative differences with respect to the presented models, most importantly the much weaker z-component and a dominant Ex term. This is also true for the complete solution to the Bethe problem as given by Meixner–Andrejewski [19].

This model is unable to even qualitatively account for the experimentally observed fluorescence images as can be seen from its E2 distribution. In order to obtain valid simulations for the nanobead fluorescence images, the calculated electric field intensities need to be averaged over the bead volume for each scan position. It is interesting to see how these images change with increasing tip–sample distance. Fig. 4A presents simulated line scans along the symmetry axis of fluorescence images with increasing axial distance Dz (i.e. the distance between the aperture plane and the closest point on the bead surface) for fluorescence imaging of the smallest commercially available fluorescent nanospheres (diameter of 20 nm) by a typical NSOM tip (optical aperture of 100 nm in diameter, cone angle a of 30 , 100 nm Al coating). As can be seen, the separation between the two lobes decreases with increasing axial distance. This can be explained by the fact that the two lobes are essentially due to the Ez component which decays rapidly with increasing distance from the aperture rim. It can be noted

ARTICLE IN PRESS A. Drezet et al. / Journal of Luminescence 107 (2004) 176–181

that this near-field effect is a general feature since both the ring charge model as well as the surface charge model give rise to a very similar behavior (see the dotted and solid lines shown in Fig. 4A). Fig. 4B presents the variation of the contrast ratio Imax/Icenter between the maximum intensity on top of the lobes versus the center intensity with increasing axial distance. The dependence is very strong for the first 20 nm but levels out at large distances from the tip aperture. (In this case, the differences between the surface model and the ring model are much more pronounced.) It should be emphasized that this ratio is a direct experimental measure for the squared ratio of the z versus xcomponents of the electric field (as discussed earlier) in the limit of small nanospheres. On the basis of the surface charge model, we propose to use the lobe separation and contrast ratio Imax/Icenter from fluorescence images of small nanospheres to determine in situ both the aperture radius a and the axial distance Dz under the actual experimental conditions. In addition, the polarization of the incident light can be deduced from the symmetry axis passing through the lobes. For the experiment presented in Fig. 1, we have determined, from simulations for 220 nm diameter beads, the aperture radius and axial distance to be a ¼ 300 and Dz ¼ 18 nm: In this case, the experimental profiles of fluorescence intensity along the symmetry axis are in perfect agreement with the simulated curve.

4. Summary and conclusions We have presented a simple, theoretical model for the electric field of light transmitted by a conical NSOM tip. Our model is able to explain, both qualitatively and quantitatively, the recorded fluorescence images of nanospheres that are small compared to the aperture diameter. The widely admitted Bouwkamp solution for the planar Bethe aperture fails to explain these images even qualitatively. Fluorescent nanospheres are valuable objects since they act as isotropic volume detectors for the squared electric field intensity. Together with the proposed model, they can be used for an in situ determination of both tip

181

aperture and axial distance under the actual experimental conditions which is significant for practical purposes. We also plan to use these objects in order to establish a detailed electric field intensity map of a NSOM tip in all three dimensions. Based on the proposed model, it is possible to determine the orientation of single molecule emitters in all three dimensions from recorded fluorescence images, which has important implications for the addressing of single molecules and optical nanomanipulations.

Acknowledgements Support through the Volkswagen Foundation, the Institut de Physique de la Matie" re Condense! e, and the CNRS is gratefully acknowledged.

References [1] D.W. Pohl, W. Denk, M. Lanz, Appl. Phys. Lett. 44 (1984) 651. [2] E. Betzig, J.K. Trautman, T.D. Harris, J.S. Weiner, R.L. Kostelak, Science 251 (1991) 1468. [3] E. Betzig, J.K. Trautman, Science 257 (1992) 189. [4] C. Obermuller, . K. Karrai, Appl. Phys. Lett. 67 (1995) 3408. [5] H.A. Bethe, Phys. Rev. 66 (1944) 163. [6] C.J. Bouwkamp, Philips Res. Rep. 5 (1950) 321. [7] L. Novotny, D.W. Pohl, P. Regli, J. Opt. Soc. Am. A 11 (1994) 1768. [8] O.J.F. Martin, C. Girard, A. Dereux, Phys. Rev. Lett. 74 (1995) 526. [9] C. Chicanne, et al., Phys. Rev. Lett. 88 (2002) 097402. [10] A. Drezet, J.C. Woehl, S. Huant, Europhys. Lett. 54 (2001) 736. [11] A. Drezet, J.C. Woehl, S. Huant, Phys. Rev. E 65 (2002) 046611. [12] K. Karrai, R.D. Grober, Appl. Phys. Lett. 66 (1995) 1842. . [13] C. Hoppener, D. Molenda, H. Fuchs, A. Naber, Appl. Phys. Lett. 80 (2002) 1331. [14] L. Novotny, Thesis, Swiss Federal Institute of Technology, Zurich, 1996. [15] B. Knoll, F. Keilmann, Opt. Commun. 162 (1999) 177. [16] J. Meixner, Ann. Phys. 6 (1949) 1. [17] J.D. Jackson, Classical Electrodynamics, 2nd Edition, Wiley, New York, 1975. [18] R.E. Collin, Field Theory of Guided Waves, 2nd Edition, IEEE Press, New Jersey, 1991. [19] J. Meixner, W. Andrejewski, Ann. Phy. 6 (1950) 157.