Letter Cite This: Nano Lett. XXXX, XXX, XXX−XXX
pubs.acs.org/NanoLett
Micro-Refractometry and Local-Field Mapping with Single Molecules A. V. Naumov,*,†,‡ A. A. Gorshelev,† M. G. Gladush,†,‡ T. A. Anikushina,†,‡ A. V. Golovanova,†,‡ J. Köhler,§,∥,⊥ and L. Kador*,§ †
Institute for Spectroscopy, Russian Academy of Sciences, Moscow 108840, Russia Moscow State Pedagogical University, Moscow, 108840, Russia § University of Bayreuth, Institute of Physics, D-95440 Bayreuth, Germany ∥ University of Bayreuth, Spectroscopy of Soft Matter, D-95440 Bayreuth, Germany ⊥ Bavarian Polymer Institute, D-95440 Bayreuth, Germany Nano Lett. Downloaded from pubs.acs.org by UNIV OF SOUTH DAKOTA on 09/06/18. For personal use only.
‡
S Supporting Information *
ABSTRACT: The refractive index n is one of the most important materials parameters of solids and, in recent years, has become the subject of significant interdisciplinary interest, especially in nanostructures and meta-materials. It is, in principle, a macroscopic quantity, so its meaning on a length scale of a few nanometers, i.e., well below the wavelength of light, is not clear a priori and is related to methods of its measurement on this length scale. Here we introduce a novel experimental approach for ∼ mapping the effective local value n of the refractive index in solid films and the analysis of related local-field enhancement effects. The approach is based on the imaging and spectroscopy of single chromophore molecules at cryogenic temperatures. Since the fluorescence lifetime T1 of dye molecules in a transparent matrix depends on the refractive index due to the local density of the electromagnetic field (i.e., of the photon states), one can obtain ∼ the local n values in the surroundings of individual chromophores simply by measuring their T1 times. Spatial mapping of the ∼ local n values is accomplished by localizing the corresponding chromophores with nanometer accuracy. We demonstrate this approach for a polycrystalline n-hexadecane film doped with terrylene. Unexpectedly large fluctuations of local-field effects and ∼ effective n values (the latter between 1.1 and 1.9) were found. KEYWORDS: Refractive index, single-molecule spectroscopy, low temperature, zero-phonon line, point-spread function
S
luminescence kinetics of single QDs has been introduced in ref 17. ∼ Measuring local refractive-index values, n , is extremely important due to the fast development of quantum- and nanotechnologies, as well as materials and life sciences. If the sample or its characteristic structures have sizes below the wavelength of light, the usual, and some advanced (e.g., refs 18 and 19), refractometry techniques are not applicable. Certain progress has recently been reported in ref 20, where computer simulations demonstrated that n fluctuations on subdiffraction length scales can be extracted from the analysis of scattered light. This method does not allow for actual mapping of the local index of refraction, however. Recently, the idea has been formulated that microspectroscopy of SMs based on their zero-phonon lines (ZPLs) can be applied to mapping local fields and fluctuations of the local
uper-resolution microscopy based on the precise localization of single fluorescent chromophore molecules (SMs) has opened the nanometer world to light microscopy1,2 and has found numerous and multidisciplinary applications.3−7 The underlying concept is that dye molecules are effective point light sources, the positions of which can be determined with a much higher accuracy than the Abbe diffraction limit, provided that the Airy disks of their fluorescence emission do not overlap at each instant of time.8,9 Super-resolution microscopy is evolving quickly, as more fluorescent dyes and imaging techniques become available.10−12 It has also been demonstrated that single quantum emitters (organic dye molecules, semiconductor quantum dots (QDs), molecular complexes, and dielectric and hybrid nanoparticles) can be used as nanometer-sized probes for well-defined quantities in physics. Examples are nanothermometry,13 nanomagnetometry,14 the detection of local acoustic strain,15 and tracing single charges.16 The possibility to probe local ∼ values, n , of the refractive index, n, by the detection of the © XXXX American Chemical Society
Received: April 30, 2018 Revised: July 27, 2018
A
DOI: 10.1021/acs.nanolett.8b01753 Nano Lett. XXXX, XXX, XXX−XXX
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Nano Letters refractive index in thin dye-doped films.21 The ZPL, which corresponds to the transition between the electronic ground and excited state without absorption or generation of a lattice vibration (phonon) or molecular vibration, is the most sensitive component of a SM spectrum.22 At cryogenic temperatures, the ZPLs of organic chromophores can be as narrow as a few ten MHz and, thus, react upon changes in the environment with extreme sensitivity. The first studies of the detection and spectroscopy of SMs were performed at low temperatures and addressed the ZPLs due to their narrow spectral widths.23−25 Super-resolution microscopy based on the ZPLs of SMs at cryogenic temperatures can also be performed26 and has an additional advantage. At low temperatures, the inhomogeneous spectral distribution of an electronic transition is much broader than the individual molecular ZPLs, usually by several orders of magnitude, so a tiny subensemble of the molecules can be excited separately with a tunable narrow-band laser. The microscopy technique, therefore, does not depend on stochastic transitions of the molecules between an emissive and a dark state, but the molecules can be addressed in a deliberate and controlled way by tuning the laser wavelength within the inhomogeneous band. While the localization of SMs has been exploited in numerous studies, applications of the additional analysis of spectroscopic data, in particular of the sensitive ZPLs at low temperatures, are still rare. A few years ago, the possibilities of super-resolution microscopy with SMs and the extreme sensitivity of their ZPLs have been combined for spectrally selective imaging of a giant ensemble of SMs.27 The study provided structural information about the polycrystalline host matrix on the nanometer scale, well below the Abbe limit, and unraveled clear correlations between the locations of the individual chromophores and their ZPL properties.28 Here we present the results of the first experimental study aimed at mapping the fluctuations of the local index of refraction in a thin film (with thickness below 1 μm) of polycrystalline n-hexadecane (n-Hex) weakly doped with terrylene (Tr). The method is based on combined fluorescence imaging and fluorescence excitation spectroscopy of the ZPLs of a large number of single Tr molecules at cryogenic temperatures. The fluorescence lifetimes of single chromophore molecules and their temporal fluctuations in polymer films had been measured in a previous study at room temperature.29,30 The data were analyzed in terms of the polymer dynamics, but they were not combined with spatial mapping. The main motivation of the studies presented in this work is the following: if one plans to construct a nanodevice based on single quantum emitters embedded in a transparent dielectric, it is necessary to understand how large the deviations of its emitting properties from the averaged (macroscopic) values due to fluctuations of the local fields can be. Usually the spectral width of the ZPLs of SMs in a solid matrix has three main contributions: The natural line width, Γ0, which is determined by the lifetime, T1, of the excited state, additional broadening by quadratic electron−phonon coupling (dephasing), and, mainly in amorphous or disordered systems, interaction with localized tunneling excitations (spectral diffusion).31,32 The latter two contributions are strongly temperature-dependent and become negligible at sufficiently low temperatures. A fourth contribution can be power broadening caused by too high of an intensity of the probing
laser. If all additional broadening mechanisms are negligible and only the natural line width, Γ0, remains, the fluorescence lifetime, T1, can be calculated from it according to the relation T1(n) = 1/[2π Γ0(n)]
(1)
Both T1 and Γ0 are related to the local electromagnetic fields at the position of the molecule and their interaction with its electron system. More specifically, a series of theoretical and experimental studies have shown that the exact value of the excited-state lifetime, T1 (and, hence, of Γ0), depends on the refractive index n of the matrix.33−35 (See reviews in refs 36 and 37.) Different models were used to derive the functional dependence T1(n). In most of them, the host matrix was considered a continuum, and the chromophore molecule was assumed to occupy a real or virtual cavity inside it. Also some hybrid models were designed, which combine a continuous host with discrete shells of particles around a chromophore.30 In general, the dependence T1(n) can be expressed in the form τ0 T1(n) = nf (n) (2) where τ0 is the excited-state lifetime in vacuum and the factor f(n) describes the local-field enhancement in the solid. This function may be interpreted as a description of the ratio between the local and the macroscopic electric light field strength. Experiments indicate that different models (with different results for f(n)) seem to apply to different dye−matrix systems.37 Eq 2 is based on the approximation that the dielectric host material can be treated as a continuous medium. The final equations describing the local-field effects within microscopic models (which consider the atomistic structure of the material) usually reduce to this form as well. Since the microscopic structure and dynamics of the material can be subject to strong local variations, a correct description requires that the concept of an “effective local refractive index n” be introduced, as is demonstrated below. Eq 2 is valid if the excited singlet state |S1> of a dye molecule relaxes solely via photon emission, i.e., if its fluorescence quantum yield, ΦF, is 100%. The ΦF value of Tr was reported to be 0.69 (ensemble value).38 The intersystem crossing yield is only between 10−5 and 10−6.39,40 Since the lifetime of the triplet state is longer than the fluorescence lifetime by several orders of magnitude, transitions to the triplet state do not contribute to the ZPL widths but appear only as blinking of the SM fluorescence. Possible variations of the nonradiative singlet−singlet relaxation rate will be discussed later. Recently, we have analyzed the data of the natural fluorescence lifetime, T1, of individual Tr molecules in a set of five different matrices, both molecular crystals and polymers, in terms of their n dependence (room-temperature data).21 The T1 data had been measured in ref 41. The experimental relation T1(n) was shown to be best represented by the socalled virtual-cavity model, which yields the function34 f (n) = [(n2 + 2)/3]2
(3)
Hence, we use this model in the present paper as well. When we selected the model that describes the dependence T1(n) best, the vacuum fluorescence lifetime, τ0, was treated as an unknown adjustable parameter (Figure 2 of ref 21). Independent knowledge of τ0 would be optimal for a precise description of T1(n). A possible error of this parameter does B
DOI: 10.1021/acs.nanolett.8b01753 Nano Lett. XXXX, XXX, XXX−XXX
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Figure 1. Mapping of SM distribution, local-field enhancement, and microrefractometry in n-Hex/Tr at T = 1.5 K. (a) White-light photograph of the sample film with thickness of approximately 1 μm. (b, c) Overlay of the white-light image and the lateral positions of SMs, the coordinates of which were found from an analysis of the fluorescence images as described in the text. Each detected Tr molecule is depicted by a yellow dot. In two separate experimental runs, 5729 (b) and 2933 (c) single molecules were recorded with laser intensities of 3 W/cm2 and 20 mW/cm2, ∼ respectively. (d) Spatial variation of the effective local index of refraction n in the sample plane. Each dot corresponds to a single Tr molecule, for ∼ which the saturation behavior was measured and analyzed (1950 SMs in total). The color of the dots encodes the n value calculated from the lifetime-limited ZPL widths according to the virtual-cavity model (eqs 1 − 3). (e) Topogram showing the distribution of the averaged local index of ≃ ≃ refraction, n , in the sample plane. For each elemental area of the topogram (square with a size of 0.5 μm on both axes), the n value was obtained by ∼ averaging the local nj of all SMs j located within a circle with a diameter of 10 μm around this area.
high enough for achieving an accuracy of a few nanometers for the lateral coordinates. From the lifetime-limited ZPL width, Γ0, of each SM, the ∼ local effective refractive index n in its environment was calculated by numerically inverting eqs 1−3. Combining these values with the spatial coordinates of the respective SMs enabled us to map the refractive-index distribution in the sample film with nanometer accuracy. The results are plotted in Figure 1. Panel a shows a white-light transmission photograph of an area 50 μm × 50 μm in size on the polycrystalline sample film, and panels b and c the inhomogeneous spatial distribution of individual Tr molecules (yellow dots) in this area. In two separate experimental runs, 5729 (b) and 2933 (c) SMs were recorded with excitation intensities of 3 W/cm2 and 20 mW/cm2, respectively. The accumulation of the dopant molecules in certain areas between cracks is obvious. For refractive-index determination, a smaller set of SMs (1950) was studied in a third experimental run with a series of different excitation intensities to ensure that the data are not affected by power broadening. The natural line width, Γ0, of each SM was obtained by extrapolating its measured line width to zero excitation intensity. Details are given in the ∼ Supporting Information. The resulting spatial distribution of n is shown by the color-coded dots in Figure 1d. A surprisingly ∼ large variation with n ranging from 1.1 to 1.9 within very short ∼ distances was found. Averaging these n values over circular areas of 10 μm diameter yields the smoothed topogram of Figure 1e.
not affect the main conclusion of our work regarding the strong spatial fluctuations of local fields in n-hexadecane, however (see below). Fluorescence excitation spectra of SMs were measured by scanning a tunable stabilized single-mode cw dye laser across the inhomogeneous absorption band, while images of the Stokes-shifted fluorescence were being recorded with a highly sensitive EMCCD camera. All measurements were performed in superfluid helium at 1.5 K where all thermal broadening effects are definitely frozen out. For all of the SMs included in the data evaluation (1950 in total), the dependence of the ZPL width on the laser excitation intensity, Γ(PLAS), was measured and the natural line width, Γ0, was obtained as the low-power limit. Details are given in the Supporting Information. The fluorescence image of each SM was analyzed at the spectral maximum of its ZPL. Fluorescent SMs are point-like light sources considerably smaller than the wavelength of the emitted light. Hence, if the point-spread function (PSF) of the optics collecting the fluorescence photons is known, one can pinpoint the coordinates of the emitter with an accuracy that is not determined by the diffraction limit of far-field optics but only limited by the stability of the experimental setup and the signal-to-noise ratio of the detected fluorescence. We simply considered each individual fluorophore as a point light source emitting its photons isotropically into the full solid angle of 4π. Then the far-field image of the luminescence is an Airy disc, and the lateral coordinates of its center can be determined by fitting a two-dimensional Gaussian function to the luminescence image on the camera chip. The signal-to-noise ratio was C
DOI: 10.1021/acs.nanolett.8b01753 Nano Lett. XXXX, XXX, XXX−XXX
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∼
Figure 2. Distributions of the effective local refractive index, n , of different materials. (a) n-Hex/Tr as measured in this work at T = 1.5 K (1950 SMs); (b) amorphous polyethylene (circles; 380 SMs) and single-crystalline naphthalene (triangles; 54 SMs) doped with Tr as published in ref 21. ∼ In all cases, n was calculated from Γ0 according to the virtual-cavity model for the local-field enhancement factor, f(n). Solid lines correspond to Gaussian fit functions. Arrows indicate the macroscopic n values of the corresponding undoped bulk materials as measured with a standard Abbe ∼ refractometer. For details regarding the n-Hex data, see the text and the Supporting Information. (c) Absolute difference Δn i,j of the local values of ∼ n calculated for any two SMs (with indices i and j) as a function of their spatial (lateral) distance Δri,j in the n-Hex/Tr film. The red line represents ≃ ∼ an average of Δn i,j(Δri,j) over 100 data points. The data are plotted in double-logarithmic representation. (d) Averaged values n of the local ∼ refractive index, n , as obtained by averaging over area elements with an increasing size d on the n-Hex/Tr film.
(with indices i and j), we calculated the lateral distance
Figure 2a shows the distribution of the 1950 effective local ∼ refractive-index values, n , of Figure 1d. For comparison, in ∼ Figure 2b, we present the n distributions as calculated in ref 21 from the Γ0 values, which had been measured for smaller numbers of single Tr molecules in amorphous polyethylene (380 SMs)42 and single-crystalline naphthalene (54 SMs).43 Figure 2 demonstrates that the macroscopic refractive indices, which were determined on bulk samples with a standard Abbe refractometer, are very close to the maxima of ∼ the n distributions for polyethylene and naphthalene. The slightly lower bulk value of n-Hex (1.434) is probably due to the fact that it was measured at room temperature in the liquid phase. In frozen n-Hex, it is expected to be larger due to the higher material density. If we use typical values of the coefficient describing the temperature dependence dn/dT of different materials, we can estimate an increase of the index of refraction by 0.05−0.15 units between 293 and 1.5 K.44,45 This yields an estimate n ∼ 1.5 for n-Hex at 1.5 K, very close to the ∼ maximum of the measured n distribution. ∼ The coincidence of the bulk refractive indices with the n maxima for all three dye−matrix systems confirms that our method of microrefractometry is applicable, i.e., that nonradiative relaxation processes of the chromophores do not play ∼ a major role. The widths of the n distributions represent the, unexpectedly large, fluctuations of the local-field enhancement factors in the samples. The important new result is that these fluctuations can be visualized with nanometer resolution by ∼ mapping the local n values onto the sample film (Figure 1d). For a more detailed analysis, we calculate spatial correlations ∼ between pairs of n . The lateral coordinates of the 1950 Tr ∼ molecules, for which n was obtained, could be determined with an accuracy better than 25 nm. For all possible pairs of them
Δrij =
(xi − xj)2 + (yi − yj )2 as well as the absolute differ-
ence between the local refractive indices in their environment, ∼ ∼ ∼ ∼ Δnij = nj − ni . The dependence Δni,j (Δri,j) has been plotted in Figure 2c (black dots) in double-logarithmic representation. ∼ The red curve represents an average of Δni,j over each 100 data points. ∼ In order to bridge the gap between the local fluctuations of n on the nanometer scale and the macroscopic refractive index, ∼ n, we averaged the n values in areas with increasing diameter, ≃ d, on the sample film and plotted the averages n as a function of d in Figure 2d. Figure 2c,d then allows us to perform a statistical data analysis and establish a hierarchy of roughly three length scales in the doped polycrystalline n-Hex film, which show different variations of the index of refraction. We can call these length scales the “near-field”, “intermediate”, and “far-field” zone. I. In the “near-field” (also local or nanoscopic) region, two nearby SMs i and j feel the same local-field enhancement factor. Hence, at these very small distances, we measure ≃ ∼ ≃ ≃ T1i ≈ T1j and, correspondingly, ni ≈ nj ≈ n . n is subject ∼
to the same variations as n and, thus, is usually different from the macroscopic refractive index n. From Figure 2c, we can estimate the size of this region at 10−20 nm. Although the number of data points is quite limited here, one can see that there are no points with large ∼ differences Δni,j (note the logarithmic ordinate scale). The consequence is that two (or several) single quantum emitters in a dielectric material, which are only separated by a small distance around 10 nm, sense the same local D
DOI: 10.1021/acs.nanolett.8b01753 Nano Lett. XXXX, XXX, XXX−XXX
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Nano Letters field. Hence, for nano-objects of this size, one can expect that the same local-field effects are present for all the emitters within. II. In the “intermediate” (or mesoscopic) region, the lifetimes for two arbitrary SMs may be different, T1i ≠ ∼ ∼ T1j, indicating different refractive-index values ni ≠ nj .
other forms48 have already been demonstrated. The doublehelix technique has also been implemented in the cryogenic microspectroscopy of SMs with detection of ZPLs.49 It is unlikely that the thickness of our sample film of roughly 1 μm affects the measured refractive-index distribution noticeably. In previous single-molecule studies in ultrathin polymer films, deviations from the bulk behavior were only found in films with thicknesses below 100 nm.50,51 In conclusion, the present work demonstrates, how nanoscopy based on the study of single fluorescent molecules can be extended to perform advanced materials characterization. To this end, SMs are not only used as point light sources, but as sensitive multiparameter local probes by virtue of their narrow ZPLs. In the present study, simultaneous imaging and measurement of the lifetime-limited ZPL width of SMs enabled us to map the index of refraction on our sample film on the length scale of nanometers. The spatial correlations of ∼ the effective local values n allowed us to define at least three ∼ zones in which the averages of T1 and n show a different behavior. (I) In the “near-field” (nanoscopic) range, we find ∼ ∼ ≃ T1i ≈ T1j, ni ≈ nj ≈ n ≠ n in general. (II) The “intermediate”
≃
The average n in the mesoscopic zone is still subject to variations; i.e., in general it also differs from the macroscopic value. Figure 2d shows that the intermediate region roughly extends up to ∼10 μm. Quantum emitters separated by distances larger than approximately 10−20 nm are influenced by increasingly different local fields and, thus, exhibit different emitting properties. The luminescence of a group of emitters averaged over this length scale can still be different from macroscopic ensemble data. III. Finally, the “far-field” zone is of macroscopic size, so the ∼ averages of T1 and n are constant throughout the sample and correspond to the bulk values. According to Figure 2d, the far-field region begins beyond a typical size of 10 μm in our sample. Here the experiments yield macroscopic ensemble data. In our analysis, we have assumed that the fluorescence quantum yield of terrylene is unity. Ensemble measurements have shown that it is only 0.69.38 This quantity may also be subject to variations from molecule to molecule and may contribute to the measured variation of fluorescence lifetimes. An indication that the lifetime variation is still mainly due to the variation of the radiative relaxation rate, i.e., to fluctuations of the local refractive index, is its distance dependence. Nonradiative relaxation processes are expected to depend mainly on the chromophore itself and possible strain and distortion effects (which are determined by its cavity in the solid). The fact that two chromophores in the near-field zone (up to 10 nm distance) exhibit the same lifetime suggests that the different lifetimes are mainly due to fluctuations of the radiative, rather than the nonradiative, relaxation rate. ∼ The width of the n distribution in thin films of polycrystalline n-Hex (a typical Shpol’skii matrix featuring narrow inhomogeneous optical lines) is surprisingly large, ranging from about 1.1 to 1.9 refractive-index units. It is almost as broad as in the amorphous polymer polyethylene and distinctly broader than in naphthalene single crystals (cf. Figure 2a,b). Although more detailed measurements are needed for a clear ∼ statement, Figure 2a seems to indicate that the n distribution has fat tails; i.e., extreme deviations from the mean value occur more frequently than in a Gaussian. This would corroborate ∼ the importance of local effects for n .46 The meso- and macroscopic origin of the fluctuations becomes evident when ∼ we map the n values onto the sample film. There is a pronounced network of cracks and defects on the length scales of μm and below. Their presence and location is correlated ∼ with the fluctuations of n (Figure 1b−d). In the present study, we did not consider the axial (i.e., depth) coordinate, which is required for a complete characterization of the material. The extension of our technique to this coordinate, i.e., full 3D microrefractometry and mapping of local fields, is readily possible. Methods of 3D nanoscopy with SM localization based on an instrumental modification of the SM point-spread function in the form of a double helix47 or
∼
∼
(mesoscopic) zone is characterized by T1i ≠ T1j, ni ≠ nj , but ≃
also n ≠ n in general. (III) In the “far-field” (macroscopic) zone, the averages are equal to the macroscopic n value. The transitions between these regions are not well-defined and depend strongly on the local structure of the sample. We can roughly indicate them at length scales of 10−20 nm and ≃10 μm for the investigated film of n-Hex/Tr. The different ≃ variations of the average n in the three zones make microrefractometry important for such interesting phenomena as the Purcell effect52,53 or negative indices of refraction.54
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.8b01753. Sample preparation, experimental setups, experimental procedure, and extrapolation of the zero-phonon line widths of single chromophore molecules to zero temperature and zero excitation intensity to exclude thermal broadening and power broadening with example data (PDF)
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AUTHOR INFORMATION
Corresponding Authors
*E-mail:
[email protected]. *E-mail:
[email protected]. ORCID
J. Köhler: 0000-0002-4214-4008 L. Kador: 0000-0001-8084-7559 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS Financial support from the Deutsche Forschungsgemeinschaft (DFG), in particular, the Research Training Group (RTG) 1640 (“Photophysics of Synthetic and Biological Multichromophoric Systems”), is gratefully acknowledged. A.N. E
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and A.G. acknowledge support from the Deutscher Akademischer Austauschdienst (DAAD). The Russian team also acknowledges financial support from the Russian Science Foundation (14-12-01415, development of methods for statistical processing of SMSM data) and the Russian Foundation of Basic Research (17-02-00652, microrefractometry with single probe molecules).
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DOI: 10.1021/acs.nanolett.8b01753 Nano Lett. XXXX, XXX, XXX−XXX
