pubs.acs.org/NanoLett
Three-Dimensional Orientation of Single Molecules in a Tunable Optical λ/2 Microresonator Raphael Gutbrod,† Dmitry Khoptyar,‡ Mathias Steiner,§ Anna M. Chizhik,† Alexey I. Chizhik,† Sebastian Ba¨r,† and Alfred J. Meixner†,* †
Institute of Physical and Theoretical Chemistry, Eberhard-Karls-University Tuebingen, 72076 Tuebingen, Germany, Department of Physics, Lund University, S-221 00 Lund, Sweden, and § IBM Research Division, T J Watson Research Center, Yorktown Heights, New York 10598 ‡
ABSTRACT A tightly focused radially polarized laser beam forms an unusual bimodal field distribution in an optical λ/2-microresonator. We use a single-molecule dipole to probe the vector properties of this field distribution by tuning the resonator length with nanometer precision. Comparing calculated and experimental excitation patterns provides the three-dimensional orientation of the single-molecule dipole in the microresonator. KEYWORDS Microcavity, single molecule detection, nanoscopy, optical vector field, nanooptics
A
molecular dipole in an optical microresonator1 represents a model system in cavity quantum electrodynamics, single-molecule optics, and nanophotonics and finds potential application as a single-photon source2 or as an integrated nanoemitter.3 The optical confinement in the microresonator allows enhancement4 or inhibition5 of the spontaneous emission rate of embedded molecules and results in strong modifications of their fluorescence line shape.6–8 Moreover, the efficiency of the Fo¨rster resonance energy transfer (FRET) between adjacent dye molecules depends on the local photonic mode density and can be modified in the microresonator.9 However, the microresonator-controlled emission depends critically on the position and orientation of the molecular transition dipole moment with respect to the mirrors,6,7 and for FRET experiments it is important to know the relative orientation of the donor and the acceptor.10 Hence, it is crucial to determine the intracavity orientation of a molecular transition dipole moment in situ. Several techniques have been used to detect single-molecule orientations in free space, i.e., in the absence of the optical confinement induced by the cavity mirrors. This includes near-field optical imaging,11,12 far-field polarization microscopy,13 defocused optical imaging,14 and the use of a radially polarized laser beam (RPDB).15,16 In this Letter, we report a method to measure the orientation of single dye molecules in an optical λ/2-microresonator. The introduced method relies on the inhomogeneous distribution of in-plane and longitudinal field components in the focal volume of a RPDB inside the microresonator.
The tunable optical microresonator is sketched in Figure 1. The cavity is formed by two silver mirrors (thickness of the upper mirror, 60 nm; lower mirror, 30 nm) that have been evaporated onto a standard glass cover slide and the curved surface of a plano-convex lens (f ) 150 mm). Efficient laser excitation and detection of single molecule fluorescence are accomplished through the lower cavity mirror. A SiO2 layer defines the spacing between the molecules and the lower mirror and, hence, the z-position of the molecules with respect to the optical resonator. Spatially isolated species of a fluorescent perylene derivative (ab-
FIGURE 1. Scheme of the tunable microresonator with (1) glass coverslip, (2) silver mirrors, (3) silica spacer layer, (4) active layer with immobilized single molecules, (5) refractive index matching liquid, (6) lens, and (7) piezoelectric elements. A sketch of the confocal microscope with the beam conversion optics for producing a radially polarized laser beam (RPDB) is also shown. The coordinate system defines the orientation of the molecular transition dipole b µ with respect to the cavity mirrors (inset).
* Corresponding author,
[email protected]. Received for review: 10/5/2009 Published on Web: 01/11/2010 © 2010 American Chemical Society
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DOI: 10.1021/nl903318p | Nano Lett. 2010, 10, 504-508
breviated PI) serve as single dipole emitters in our experiments. Details regarding their absorption and fluorescence properties can be found in the Supporting Information. The PI molecules were deposited on the cover slide via spincoating 10 µL of a dichlormethane solution with 0.1% PMMA and a PI concentration of cPI ) 10-9 mol/L at a rotational speed of 8200 rpm. This results in a thin PMMA film with a thickness of around 8 nm that is doped with spatially isolated PI molecules. The PMMA film provides a matrix to suppress translational and rotational motion of the molecules and to maintain well-defined coupling conditions to the optical resonator during the measurements. A refractive-index matching liquid is injected between the dye-doped polymer layer and the upper cavity mirror and serves as an optically transparent, tunable intracavity medium. The microresonator assembly is placed in a mount that enables controllable tuning of the upper cavity mirror with suitable piezoelectric elements. As a result, for each embedded PI molecule the local photonic mode density can be reversibly tuned with nanometer precision without modifying the molecule’s local environment. Due to the small curvature of the upper mirror, the microresonator acts as a planar resonator for lateral dimensions in the submicrometer range. For the (x,y)position of every molecule, the mirror spacing L(x,y) and the corresponding cavity Q (∼50) can be measured from the local white light transmission spectrum with high accuracy and reproducibility.6,7 With this information, the threedimensional (3D) orientation of each molecule can be determined by fitting theoretical excitation patterns to the respective experimental excitation pattern. For single molecule excitation and imaging, we use an inverted scanning confocal optical microscope (see Figure 1) equipped with an immersion oil objective lens (100×, NA ) 1.25). A radially polarized doughnut-mode laser beam (RPDB, λlaser ) 488 nm) is created by using a polarization converter.17 A pinhole blocks the unwanted higher spatial frequencies before the RPDB is expanded to match the back aperture of the microscope objective. The collimated RPDB is then reflected by a nonpolarizing beam splitter cube into the back aperture of the microscope objective and focused into the microresonator. Different (x,y) sample positions are spatially addressed by horizontally moving the microresonator with respect to the axis of the fixed microscope objective. The single-molecule fluorescence is collected with the same objective and, after suppressing the excitation light, focused onto an avalanche photodiode. In order to prevent clipping of the fluorescence pattern of a dipole excited in the vicinity of the excitation focus, we have chosen an aperture diameter in front of the detector about three times larger than the respective airy disk diameter. Fluorescence intensity images showing single molecule excitation patterns are recorded by laterally (x,y) raster scanning the cavity with nanometer precision. By variation of the mirror spacing between successive raster scans, a series of images © 2010 American Chemical Society
can be acquired for the same molecule as a function of the mirror spacing. In the following, we develop a theoretical model which describes the shape of the fluorescence excitation patterns for a single molecular dipole as a function of the mirror spacing. Assuming a constant transition dipole orientation as well as constant mirror spacing throughout an image scan, the shape of the fluorescence excitation pattern reflects the cavity-modified excitation field distribution probed by the absorbing molecular dipole. Starting from the general theory of focusing a laser beam with a high numerical aperture optical system,18,19 the field distribution of a RPDB inside a microresonator has recently been calculated and experimentally verified.20,21 In short, the focused field intensity distribution of the RPDB is characterized by the in-plane components Ex and Ey and the longitudinal component Ez of the incident laser beam and can be expressed as
E)
(
4iL1,1,1(F, z) cos (φ) ikf2e-ikf 4iL (F, z) sin (φ) 1,1,1 2w0 -4L (F, z) 0,0,2
)
(1)
Here, (F, z, φ) are the cylindrical coordinates with z ) 0 corresponding to the focal point of a lens with focal length f, k ) 2π/λ is the wave vector of the field with the wavelength λ, and w0 is the beam waist of the laser beam. The functions L n,m,l characterize the in-plane and longitudinal components of the intracavity field.20 On the basis of eq 1 and taking the actual optical parameters of the resonator and the microscope objective into account, we can visualize the intensity distribution between the cavity mirrors which is shown in Figure 2 for three representative L values. The in-plane field components have maximum intensity in the cavity center and vanish toward the metal mirrors. In contrast, the longitudinal field component vanishes at the cavity center and has maximum values close to the silver mirrors. The optical field distribution associated with the two field components strongly varies within the microresonator and can be modified by tuning the distance between the two cavity mirrors. The excitation rate Rexc for the single molecule inside the microresonator is given by
Rexc ∝ |µb· b E |2
(2)
Here, b µ denotes the transition dipole moment of the molecule and b E the intracavity excitation field given by eq 1. We now define the orientation of the single molecule with respect to the coordinate system of the excitation field and the microresonator. The angle Ψ denotes the in-plane orientation of the molecular dipole whereas θ describes the orientation toward the optical axis (see Figure 1). In order to model the excitation pattern for a single molecule we 505
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FIGURE 2. (a-c) Calculated (x,z) intensity distribution of a radially polarized laser beam (RPDB) focused into an optical microresonator consisting of two parallel silver mirrors. The associated mirror spacing L is indicated below. The white line 30 nm above the lower cavity mirror indicates the position of the dipole emitter visualized in Figure 3. (d-f) Corresponding (x,y) intensity distribution resulting from the RPDB calculated for the position indicated by the white line.
FIGURE 3. The calculated (x,y) excitation patterns show the normalized intensity distributions of a single molecule embedded in a planar microresonator excited with a radially polarized laser beam for different mirror spacings L and dipole orientations θ. The patterns obtained without cavity mirrors are shown as a reference. The dipole emitter is located 30 nm above the lower cavity mirror (see white dashed line in Figure 2) and Ψ is set to 0° for all images. The size of each image is 1.5 × 1.5 µm2.
calculate the projection of the intracavity field distribution on the molecular dipole moment, which results in
ESM )
(
ikf2e-ikf 4iL1,1,1(F, z) cos(φ + ψ) sin(θ) 2w0 -4L0,0,2(F, z) cos(θ)
)
depends only on the dipole orientation (θ, Ψ). Hence, by comparing experimental and calculated single molecule excitation patterns, we can determine the orientation of a single molecule in the optical microresonator. The molecule dipole orientation Ψ in the (x,y) plane lies between the projection of the transition dipole moment on the (x,y) plane and the x-axis of the scanning setup. This can be determined with high accuracy using a fit algorithm described in ref 22. In short, the fit algorithm performs a coordinate transformation between the coordinate system of the scanning setup (see Figure 1) and the molecule’s coordinate system where the orientation of the transition dipole moment defines the x-axis. The orientation θ in the (x,z) plane is determined in a second step by fitting a theoretical curve for a fixed value of Ψ to an experimental line section. The error is determined based on the deviation between calculated and experimental data points and details regarding both data and error analysis can be found in the Supporting Information. In Figure 4, we show a series of experimental excitation patterns acquired from the same single PI molecule immobilized in the tunable microresonator. The SiO2 spacer layer (see Figure 1) with a thickness of 50 nm defines the z-position of the molecule and the mirror spacing L remains the only adjustable parameter. As we tune the mirror spacing of the cavity from L ) 127 nm to L ) 172 nm and backward to L ) 133 nm, we observe that the initial double lobe excitation pattern is reversibly transformed into a single spot pattern, as expected for molecular dipole orientations between 0° < θ < 90°. In Figure 4c where the longitudinal field
(3)
Representative patterns calculated according to eq 3 for seven different dipole orientations and three L values are shown in Figure 3. As a reference, we also show the calculated patterns for a molecular dipole without cavity mirrors. The modification of the shapes of the excitation patterns for different L values is a direct consequence of the modified (x,z) intensity distribution inside the microresonator as shown in Figure 2. The in-plane field components are characterized by two off-axis lobes whereas the longitudinal field component has a distinct peak on the optical z-axis. A molecule with its transition dipole moment oriented perpendicular to the optical axis (θ ) 90° in the inset of Figure 1) can be excited only by the in-plane field components. As a result, the excitation pattern consists of two symmetric lobes. A molecule having its dipole oriented along the optical axis (θ ) 0°) is probed exclusively by the longitudinal field component which results in a single spot pattern at the (x,y) position of the molecule. Molecules with intermediate dipole orientations 0° < θ < 90° are simultaneously excited by inplane and longitudinal field components and exhibit two lobes with varying intensities. If the actual mirror spacing L and the z-position of a single molecule are known, the intensity distribution in the fluorescence excitation pattern © 2010 American Chemical Society
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FIGURE 4. A series of experimental (upper row) and calculated (lower row) fluorescence excitation patterns for one single PI molecule in a tunable microresonator excited with a radially polarized laser beam for different mirror spacings L. The PI molecule is located 50 nm above the lower cavity mirror. The patterns are calculated for a transition dipole moment orientation of θ ) 35°, Ψ ) 165°, and the in-plane orientation is indicated by the white dashed arrow in (d). The size of each image is 1.5 × 1.5 µm2.
FIGURE 6. Line section along the transition dipole moment axis of molecule A (black dots) and calculated line section for a dipole orientation of θ ) 58° (red line). The dotted line is calculated for θ ) 53° and the dashed line is calculated for θ ) 66°. TABLE 1. Mirror Spacing L and Dipole Orientation (θ,Ψ) for the PI Molecules Imaged in Figure 5
FIGURE 5. Experimental excitation patterns of spatially isolated and randomly oriented PI molecules in an optical microresonator excited with a radially polarized laser beam. The molecules are located on a 30 nm SiO2 spacer layer above the lower cavity mirror. The respective mirror spacings L and orientations (θ,Ψ) are listed in Table 1.
L, nm
θ, deg
A B C D E F G
118 119 121 123 124 122 123
58 61 47 5
∆θ 53°< θ < 66° 59°< θ < 67° 44°< θ < 51° blinking 0°e θ < 10° bleached bleached
Ψ 165.8° ( 1.0° 20.0° ( 0.7° 250.7° ( 0.9° 332.7° ( 2.5° 274.5° ( 1.2°
6), we determine the orientation for the molecules with the results listed in Table 1. Molecule D exhibits strong fluorescence intensity blinking which prevents the determination of its out-of-plane dipole orientation. For molecules F and G, it is not possible to determine their orientation as they bleached irreversibly during the measurement. In summary, we presented a new method to determine the three-dimensional orientation of spatially isolated and immobilized single molecules in an optical microresonator by comparing experimental and calculated fluorescence excitation patterns. We verified the method by observing reproducible changes in the excitation pattern of the same single molecule when tuning the mirror spacing of the microresonator. This method has the potential to determine the transition dipole moment orientation in arbitrarily oriented multichromophoric molecular systems.
component Ez dominates, only the longitudinal component of the molecular transition dipole can be excited which results in a single central spot. Comparing the measured excitation patterns with the simulated patterns for different (θ,Ψ) orientations of the molecular transition dipole, we find the best agreement between experiment and calculation for θ ) 35° ( 10° and Ψ ) 165° ( 2°. The in-plane orientation of the dipole moment is indicated by the white arrow in Figure 4d. The only free parameter which has been changed for calculating the simulated patterns in Figure 4 is the mirror spacing L that has been determined by measuring the local white-light transmission spectrum.6,7 The black stripe in the experimental scan image Figure 4b originates from fluorescence intensity blinking, a phenomenon assuring the observation of a single molecule.23 In Figure 5, we show that it is possible to determine the orientation of different, spatially isolated single PI molecules labeled A, B, C, and E for a given L value. The molecules are placed on top of a 30 nm SiO2 spacer layer, and the mirror spacing L(x,y) associated with each molecule has been measured independently and is used for the calculation of the respective excitation pattern. By comparing experimental and calculated excitation patterns as well as the corresponding line sections (as shown for molecule A in Figure © 2010 American Chemical Society
molecule
Acknowledgment. The authors thank Martin Nerurkar for valuable support. Financial support from the “Kompetenznetz funktionelle Nanostrukturen” of the Landesstiftung Baden-Wu¨rttemberg and the European Comission through the Human Potential Program (Marie-Curie Research Training Network NANOMATCH, Contract MRTN-CT-2006-035884) is acknowledged. We thank Coherent GmbH Germany for providing a Sapphire 488-20 OPS laser. The WSxM software from Nanotec24 was used for scan image processing. 507
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Supporting Information Available. Dipole orientation and error analysis. This material is available free of charge via the Internet at http://pubs.acs.org.
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