nano-optics with single quantum systems

10.1098/rsta.2003.1352

Nano-optics with single quantum systems

By Bert Hecht

NCCR Nanoscience, Nano-Optics Group, Institute of Physics,University of Basel, Klingelbergstrasse 82,

4056 Basel, Switzerland

Published online 13 February 2004

This paper reviews the recent progress in using single quantum systems, here mainlysingle fluorescent molecules, as local probes for nano-optical field distributions. Westart by discussing the role of the absorption cross-section for the spatial resolu-tion attainable in such experiments and its behaviour for different environmen-tal conditions. It is shown that the spatial distribution of field components in ahigh-numerical aperture laser focus can be mapped with high precision using singlefluorescent molecules embedded in a thin polymer film on glass. With this proof-of-principle experiment as a starting point, the possibility of mapping strongly confinedand enhanced nano-optical fields close to material structures, e.g. sharp metal tips,is discussed. The mapping of the spatial distribution of the enhanced field at anetched gold tip using a single molecule is presented as an example. Energy transfereffects and quenching are identified as possible artefacts in this context. Finally, it isdemonstrated that the local quenching at a sharp metal structure nevertheless can beexploited as a novel contrast mechanism for ultrahigh-resolution optical microscopywith single-molecule sensitivity.

Keywords: nano-optics; single molecules; two-level systems;absorption cross-section; field enhancement; quenching

1. Introduction

Nano-optics is a branch of optics that describes the phenomena that occur when lightinteracts with pieces of nano-matter. That is, pieces of matter that are either verysmall in themselves or exhibit features of sub-wavelength dimensions down to a fewnanometres. Small particles, sharp tips, single molecules or atoms, and semiconductorquantum dots are just a few examples that fall into this category. A major findingof nano-optics is that strongly enhanced and spatially confined optical fields canexist under certain conditions in the vicinity of nano-matter. The understanding andexploitation of such effects will have a major impact on future optical technologybecause it will strongly influence such important fields as high-resolution opticalmicroscopy, optical data storage, nonlinear optics and optical communication.

The recent progress in nano-optics and nano-photonics is based strongly on theever-improving understanding of how to tune the properties of nano-matter, i.e. itsgeometrical shape and material composition, and how to manipulate the incident

One contribution of 13 to a Theme ‘Nano-optics and near-field microscopy’.

Phil. Trans. R. Soc. Lond. A (2004) 362, 881–899881

c© 2004 The Royal Society

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light in the right way to achieve desired effects, such as extreme local-field enhance-ment (Hartschuh et al. 2003; Martin & Girard 1997; Sanchez et al. 1999; Stockle etal. 2000) or control of the flux of light at sub-wavelength dimensions (Bouhelier etal. 2001; Ebbesen et al. 1998; Hecht et al. 1996; Krenn et al. 1999a,b; Novotny et al.1995). Concomitantly, modern techniques for material processing on the nanometrescale, such as high-resolution focused-ion-beam milling (Krogmeier & Dunn 2001;Lacoste et al. 1989; Muranishi et al. 1997; Vasile et al. 1991; Veerman et al. 1999),become more widely available, and novel, more complex (prototype) material struc-tures can be created. A number of papers in this Theme issue deal with this task ofgetting better control over nano-optical fields.

In this paper we discuss the interaction of single quantum systems, such as singlefluorescent molecules, with confined light fields. This is important for several rea-sons: the interaction of light with single quantum systems, which can be modelledas quantum-mechanical few-level systems, can be described very accurately theoret-ically. With respect to optics, single quantum systems, because they usually react asindividual dipoles, represent the fundamental building blocks of nano-matter. Thus,a single quantum system represents a precisely defined nano-optical model systemwhose behaviour can be easily predicted and compared with experiments. By know-ing the properties of a given quantum system, detailed knowledge of the excitingoptical field can be obtained, since it behaves like a nano-antenna: its fluorescenceintensity depends on the modulus squared of the electrical-field strength along thedirection of its absorption dipole moment. This allows us to measure the spatialdistribution of specific field components in confined optical fields with very high pre-cision. It is obvious that the possibility of characterizing nano-optical fields is a keyrequirement for further progress in the field of nano-optics.

Here, we will elaborate on the conditions under which single quantum systemscan be used to probe confined fields. We show that single fluorescent moleculescan be exploited to perform precise metrology of confined fields, which is hardlypossible otherwise. Operational conditions for optimal performance, as well as limitsand pitfalls when mapping confined nano-optical fields bound to nano-matter usingsingle quantum systems, are discussed.

2. Interaction of light with single two-level quantum systems

We are interested in the amount of scattered light that is emitted by a single two-level quantum system as a function of the excitation intensity and the excitationfrequency. The absorption cross-section describes the geometrical area from whichlight is collected by the quantum system before it is re-emitted in new directions ordissipated as heat.

We start by considering the most fundamental system for studying the interactionof light with a single quantum system, i.e. the interaction of a single-frequency-laser field with a single, two-level quantum system. If the spatial extension of thequantum system (ca. 1 nm) is small compared with the length-scale of the spatialintensity variations in the excitation laser field, the interaction of the laser field withthe quantum system can be treated in the dipole approximation. A fully quantummechanical solution of the problem then yields, for the total scattering cross-section σ

Phil. Trans. R. Soc. Lond. A (2004)

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Nano-optics with single quantum systems 883

(Mandel & Wolf 1995),

σ =3λ2

2π

[12

(Ω

β

)2

+ 1 +(

ω − ω0

β

)2 ]−1

, (2.1)

where Ω is the Rabi frequency. Ω describes the coupling strength of the two-levelsystem with the laser field and is defined as Ω = −d12 · E0/ with d12 = 〈1|d|2〉,where d is the dipole operator of the system and |1〉 and |2〉 are the ground and theexcited state of the two-level system, respectively. E0 is the exciting electric fieldvector. The other quantities appearing in equation (2.1) are 2β, the decay rate ofthe excited state, and ω − ω0, the detuning of the frequency of the excitation laserω with respect to the resonance frequency of the two-level system ω0.

For zero detuning and weak excitation, the scattering cross-section of the two-levelsystem approaches the limiting value of 3λ2/2π. This is a value that is of the orderof (λ/2)2, which is much larger than any physical realization of a two-level system,like a molecule or an atom. The physical reason for this counterintuitive behaviouris the following: for an ideal two-level system that is pumped resonantly by a single-frequency laser, the scattered light has a fixed phase relation to the excitation fieldand both can interfere in the vicinity of the two-level system. If both the incomingand the scattered fields are of comparable strength, the field distribution that wouldbe present without the absorber is significantly altered in the vicinity of the two-level system. The interference results in a redirection of the energy flow towardsthe absorber, which can be studied by plotting the field lines of the Poynting vectoraround the absorber. This effect is well known and documented e.g. in fig. 1 of Bohren(1983) and fig. 7 of Paul (1995).

A molecule or atom excited as described above would clearly not be suitable as alocal probe for nano-optical fields. However, the very large absorption cross-sectioncould still have very interesting physical consequences, such as a possible direct detec-tion of single molecules or atoms by their absorption (Plakhotnik 2002). Experimentalexamples for two-level systems in this regime are single ions in traps (Guthohrlein etal. 2001) and molecules embedded in a matrix at cryogenic temperatures where allexcitations, such as phonons, are frozen out (Michaelis et al. 2000; Moerner & Orrit1999).

Looking at equation (2.1), there are two ways of decreasing σ such that it becomesmuch smaller than the wavelength. The first possibility is to increase the excitationintensity. As is evident from equation (2.1) and figure 1a, the absorption cross-sectionfalls off as 1/ω2 because of saturation of the transition. Here the scattered light nolonger increases linearly with the excitation, but increases more slowly. The secondpossibility is to increase the detuning of the excitation laser. This also has the effectof increasing the relative magnitude of incident and scattered light, since a higherexcitation intensity has to be employed in order to achieve the same scattering. For alarge detuning far out to the blue, when dealing with molecules, eventually one endsup pumping vibrational levels of the excited state, e.g. the first vibrational level ofthe molecule. This is sketched in figure 2.

The vibrational levels dissipate the vibrational energy into the environment andtherefore decay very rapidly (of the order of 1 ps) to the vibrational ground state ofthe first excited state. The fluorescence that is now emitted, due to the interactionwith the environment has lost all memory about the excitation and can no longerinterfere. This dephasing process reduces the size of the absorption cross-section to


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10 20

0.1

0.2

0.3

0.4

Rabi frequency

abso

rptio

n cr

oss-

sect

ion

10 20detuning ( − 0) /

0

0.5 (a) (b)

σ/λ

2

Ω /β βω ω0

Figure 1. Absorption cross-section of a two-level system as a function of (a) the Rabi frequencyand (b) the detuning of the single-frequency excitation field. The peak absorption cross-sectionof 3λ2/2π is reached at very weak excitation and zero detuning.

k12 = I

k23

k31

fluorescence

2

1

3k21 = kr + knrσ

Figure 2. Jablonski diagram of the energy levels in a typical fluorescent molecule. Straightlines denote optical transitions, wavy lines denote non-radiative decay and the dashed linedenotes intersystem crossing. The excitation can either be resonant, pumping a zero-phonontransition, or non-resonant, pumping higher vibrational states of the excited state. Redshiftedfluorescence occurs from the vibrational ground state of the excited state into vibrational levelsof the ground state. A transition to a long-lived dark (triplet) state is also possible. Its presencestrongly influences the photophysical parameters of the emission process. Labels: 1, groundstate of the molecule; 2, singlet first excited sate; 3, triplet first excited state; k12, excitationrate; σ, absorption cross-section; I, excitation intensity; k21, total decay rate of the first excitedsinglet state; kr, radiative decay rate; knr, non-radiative decay rate; k23, intersystem crossingrate; k31, triplet decay rate.

roughly the physical size of the molecule and is present even at cryogenic tempera-tures. At room temperature, collisions of a molecule with matrix phonons dominateall other dephasing processes. They destroy any coherence between excitation andemission, instantaneously reducing the absorption cross-section again to roughly thephysical size of the absorber. In conclusion, single quantum systems can be employedas probes for nano-optical fields with spatial variations on length-scales well belowthe wavelength if, under the experimental conditions chosen, their absorption cross-section is reduced well below its maximum value of 3λ2/2π. This is always the case ifthe coherence between excitation and scattered light is disturbed or their respectivestrengths become unfavourable by any of the effects described above. In particular,


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2 4 6 8 10 12 14

0.2

0.4

0.6

0.8

1.0

0|Ed|2 / IS

R/R

∞Figure 3. Saturation behaviour of the emission rate of

a single molecule as a function of the excitation intensity |Ed|2.

for single fluorescent molecules on surfaces or embedded in solid matrices at ambientconditions this condition is always fulfilled. For typical fluorescent dyes the absorp-tion cross-section is of the order of 10−16 cm2, which corresponds to (0.1 nm)2.

3. Using fluorescent molecules at ambient conditionsas local-field probes

Because of the strong dephasing, single fluorescent molecules at ambient conditionscan be described very well by a system of rate equations (see, for example, Loudon1983) that relate the probabilities of finding the molecule in any of the states ‘1’, ‘2’or ‘3’, as defined in figure 2. Here states ‘1’ and ‘2’ are the singlet ground and firstexcited states, respectively, and ‘3’ is the triplet state with population probabilitiesp1, p2 and p3. The populations change with rates specified in figure 2. In particulark21 = kr + knr is the sum of the radiative and the non-radiative decay rate. Solvingthe system of rate equations for the three-level system under steady-state conditionsleads to the following relations between the emission rate R = krp2 and the excitationintensity that enters the equations via the relation k12 = σ|Ed|2. Here Ed = d · E0/|d|is the field component along the direction of the absorption dipole moment of themolecule. Finally,

R(Ed) = R∞|Ed|2IS

[1 +

|Ed|2IS

]−1

, (3.1)

where R∞ and IS are defined by the photophysical parameters of the molecule as

IS =(kr + knr + k23)k31

σ(k23 + k31), (3.2)

R∞ =k31(kr + knr)

k23 + k31. (3.3)

Equation (3.1) describes a saturation behaviour plotted in figure 3. The satura-tion behaviour is characterized by the two parameters R∞ and IS, where the formerdescribes the emission rate at infinitely strong excitation and the latter is the inten-sity at which the emission rate equals R∞/2. Typical values for R∞ and IS for asingle dye molecule at room temperature are 106 s−1 and 1 kW cm−2, respectively.


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For small excitation intensities, i.e. |Ed|2 IS, a linear relation between the emis-sion rate R and the absolute square of the excitation field component |Ed|2 can beestablished as

R =R∞IS

|Ed|2 = σk21

k21 + k23∼ σ|Ed|2. (3.4)

The last term in equation (3.4) is correct because the intersystem crossing rate k23is small compared with the decay rate k21. This equation relates the rate of emittedphotons to the absolute square of the field component along the absorption dipolemoment of the fluorescent molecule and is at the core of field mapping with singlequantum systems.

4. Mapping the field distribution in a focused laser beam

Mapping confined optical fields is a rather difficult task. Ideally, for a full characteri-zation, one would like to measure direction, amplitude and phase of a given confinedfield distribution in three dimensions. Field amplitudes can be accessed by measuringthe local intensity in a confined field. Usually small scattering centres or fluorescentbeads are employed for this purpose, since their scattering is proportional to thelocal-field intensity (see, for example, Bouhelier et al. 2003). Using two foci of thesame kind that are slightly offset, phase information can also be retrieved based oninterferometric spatial autocorrelation (Muller et al. 1997). Near-field optical micro-scopes can also be used to map confined fields, but have limited precision, sincethe size of the optical probe disturbs the field to be measured (Rhodes et al. 2002).Although they are useful, all these methods are unable to measure the local electricfield direction.

Building on what was discussed in the previous sections, here we show that singlefluorescent molecules immobilized in a polymer matrix at ambient conditions canmap not only the local intensity of a focal field but also its direction. The possibilityof mapping confined fields was first noted when distinct patterns appeared in imagesof single fluorescent molecules using aperture scanning near-field optical microscopy(Betzig & Chichester 1993; Veerman et al. 1999) and confocal microscopy (Xie &Trautman 1998).

In order to demonstrate the power of this approach fully we apply it to a confinedfield that, unlike the fields in a sub-wavelength aperture, has field components ofcomparable magnitude in all three directions of a Cartesian coordinate system. Thiscan be achieved by focusing a linearly polarized annular laser beam using a high-numerical-aperture (high-NA) microscope objective (Sick et al. 2000, 2001).

Figure 4 illustrates how such a depolarization effect comes about by focusing with ahigh-NA microscope objective. It further shows how the specific spatial field patternsof the focal fields are produced by interference of the converging beams in the focalregion. Figure 4a shows a side view of the focusing geometry. Beams at the outer rimof the lens become strongly deviated by refraction. This leads to a strong tilting ofthe electric fields for some of the incoming beams, which introduces longitudinal-fieldcomponents. The latter are of opposite sign for the upper and the lower half of thelens and thus in the focal plane, on the y-axis, they cancel each other. Away fromthe y-axis, around the geometrical focus, however, significant z-oriented fields exist.Finally, this leads to the appearance of a double-lobed pattern (see figure 4c, bottom).Figure 4b illustrates how y-oriented fields are generated by high-NA focusing. It shows


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z

x

y

y

x

x

(a) (b) (c)

500 nm

y|2

|Ez|2

x|2

Figure 4. Focusing with high NA. (a) Side view of the focusing geometry for linear (x-)polarizedincoming light. Rays at the outer rim are strongly deviated due to refraction. As a result, theelectric field vector acquires a strong longitudinal-field component. Longitudinal componentsfrom the upper and lower half-space cancel exactly in the geometrical focus and on the linex = 0, but not otherwise. This leads to a double-lobed spatial distribution of longitudinal fieldsaround the focus as depicted in (c), bottom image. (b) Front view of the focusing geometry forlinear (x-)polarized incoming light showing that y-components are introduced by rays gettingrefracted at the diagonal positions. The y-components cancel on the lines x = 0 and y = 0. Thisresults in a cloverleaf spatial pattern. (c) Spatial distributions of the field components presentin a high-NA focus.

a view of the focusing geometry along the optical axis. Beams that start off the mainaxes at the outer rim of the lens contribute most strongly to such components, due tothe specific tilting of the electric field vectors upon refraction. Here it is also evidentthat these field components must vanish on the x- and y-axes in the focal planebecause of destructive interference. Finally, due to the non-zero y-oriented fields awayfrom the geometrical focus, a four-lobed cloverleaf pattern appears. Usually, the y-patterns are weak compared with the x- and z-components, which are of comparablemagnitude. However, if a plane interface between two dielectrics perpendicular to theoptical axis, which coincides with the focal plane, is introduced, then the y-patternsbecome much more intense and are now comparable in strength to the x- and z-fields(Sick et al. 2001). This is the field distribution of interest.

The experimental set-up necessary to perform the field mapping is shown in fig-ure 5. It is essentially a scanning confocal optical microscope with a ring-shaped(annular) illumination beam (Sick et al. 2000, 2001). The diameter of the centralbeam block is chosen so that it is just below the critical angle of total internal reflec-tion. Therefore, most of the beams converging towards the focus will become totallyinternally reflected at the interface. The annular excitation beam is reflected intoa high-NA microscope objective, which focuses the beam to a diffraction-limitedspot on the sample. The sample is a 20 nm poly(methyl methacrylate) polymerfilm (PMMA) on glass that contains single fluorescent molecules (1, 1′-dioctadecyl-3, 3, 3′, 3′-tetramethylindocarbocyanine, DiI) in a low concentration such that sin-gle fluorescent molecules are spaced more than 1 µm apart from each other. Therefractive index of the film equals that of glass, so all the molecules can be consid-


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xyzscanner

Ar+

lase

r

O

DM

M

F L2

SPAD

SL1 P

F

(a) (b)

Figure 5. Scanning confocal optical microscopy with annular illumination focused to the poly-mer–air interface. (a) Detail of the sample showing randomly oriented molecules (double arrows)mapping the field distribution in the focus. (b) Overview of the set-up. For details see the textand Sick et al. (2000, 2001). Labels: SPAD, single photon counting detector; DM, dichroic mir-ror; O, microscope objective; L1 and L2, lenses; S, beam block; M, mirror; F, filter; P, fibrepolarizer (Polarite, General Photonics).

ered to sit very near to the dielectric–air interface. The orientation of absorptiondipole moments in such a sample is random, so all possible field components canbe probed. The excitation intensity is kept well below the saturation intensity ofDiI. The fluorescence intensity is then proportional to the absolute square of thelocal-field component along the absorption dipole of DiI. It is important to note thatin the set-up of figure 5b the confocal geometry is somewhat relaxed, so an area ofca. 1000 nm in diameter in the sample plane has a uniform collection efficiency or,in other words, the active area of the detector demagnified back into the sampleplane by geometrical optics is ca. 1000 nm. This ensures that larger patterns can bemapped quantitatively. The spatial mapping of the focused field is done by rasterscanning the sample through the fixed focus and recording the fluorescence intensityat each pixel.

The result of such an experiment is shown in figure 6. The left panel shows a typicalsingle-molecule image. Each molecule exhibits a specific pattern corresponding tothe specific orientation of its absorption dipole. For better visibility of the patterns,the image has been median filtered to suppress dark pixels due to triplet blinking.The right panel shows a set of calculated field patterns that should be observed fordifferent discrete orientations of the molecular absorption dipole moment (Sick et al.2000). The strong resemblance between the calculated patterns and the measureddata first of all shows that the concept of a linear absorption dipole moment mappingthe focal field is valid. It also shows that if the field distribution is well known, thenit is possible to obtain detailed insight into the orientation of individual molecules.We will, however, not elaborate further on this issue, but rather refer the interestedreader to the literature (Sick et al. 2001).

In the following we concentrate on the metrology issue. Figure 7 shows a directcomparison between measured and calculated fundamental field patterns without


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2 µm0

200

counts ms−1

0

1

x

yz

1 µm

90º 67.5º 45º 22.5º 0º

90º

67.5º

45º

22.5º

0ºβ

φ

βφ

Figure 6. Experimental and theoretical field maps of an annular laser focus. Left, scan imageshowing a variety of different patterns corresponding to dipoles of different orientations mappingdifferent components of the same field distribution. Cut-off patterns appear due to photobleach-ing. Right, simulation of patterns for the geometry of the experiment. (Adapted from Sick et al.(2000).)

any fit parameters in a 1 µm× 1 µm square. Only a normalization factor was used tomatch the maximum fluorescence intensities in both theory and experiment. What isimmediately evident is the exact fit of the positions of the respective maxima in eachof the patterns. The widths of the various peaks are also extremely well matched.This demonstrates that, for the given conditions, the fields have been mapped bya single dipole that does not influence the field to be measured, as was discussedabove. Unfortunately, the field distributions analysed here, because they are of far-field nature, have no features that would allow us to test the maximum resolutionpossible in this configuration. However, from the discussion above we can infer thatthe spatial resolution for field mapping should only be limited by the absorptioncross-section of the molecules used under the specific conditions of the experiment.As mentioned above, for ambient conditions and molecules embedded in a polymer,the absorption cross-section becomes considerably smaller than 1 nm2.

5. Mapping the field distribution at a sharp tip

It is also obvious that the probing of optical near-field distributions would be adesirable extension of the methodology discussed above. While mapping of the opticalfields close to a sub-wavelength aperture has been done before (Betzig & Chichester1993; Veerman et al. 1999), the highly confined fields at a sharp metal tip haverarely been investigated in the context of single-molecule imaging, although othertechniques have been applied to investigate the confinement of light at sharp tips(Ashino & Ohtsu 1998; Azoulay et al. 1999; Hamann et al. 2000; Hartschuh et al.2003; Hayazawa et al. 2000, 2001; Hillebrand et al. 2002; Sanchez et al. 1999; Stockleet al. 2000; Zenhausern et al. 1995). Figure 8 shows a possible experimental set-up


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Pol.

distance (µm)

normalized intensity

100 nm 100 nm 100 nm

|Ex|2 |Ey|2 |Ez|2

dist

ance

(µm

)

norm

aliz

ed in

tens

ity

1.0 0.5 0

0.4

0.2

0

−0.2

−0.4

1.0 0.5 0 1.0 0.5 0 1.0 0.5 0

0.4

0.2

0

−0.2

−0.4

0.4

0

−0.4

0.4

0

−0.4

1.0

0.5

00.40.2−0.2−0.4 0 0.40.2−0.2−0.4 0 0.40.2−0.2−0.4 0

distance (µm) distance (µm)

normalized intensity

(a)

(b)

(c)

Figure 7. Metrology of confined fields. (a) Direct comparison of measured and calculated fieldpatterns for the three fundamental absorption dipole orientations with respect to the interfaceand the incoming linear polarization. No fit parameters are used besides a normalization factor.Line cuts through both (b) the measured and (c) the calculated patterns, respectively. The cutsare along the full and the dashed lines superimposed on the images. (Adapted from Sick et al.(2001).)

for mapping the confined field at a tip with a single fluorescent molecule. It is verysimilar to the set-up used for mapping the field distribution in the focused annularbeam. Here a tip is illuminated by a focused laser beam of suitable mode profilethrough a glass slide that is coated with a 20 nm thick layer of PMMA. The PMMAagain contains single fluorescent molecules in a suitable concentration, as described


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Ar+

lase

r

O

DM

M

F L2

SPAD

SL1 P

F

(a) (b)

xyzscanner

xyzscanner

Figure 8. Mapping of nano-optical fields at a sharp tip. (a) Detailed view of the sample area. Aprobe molecule is illuminated continuously at a very low excitation rate such that its emissionrate is just above the background. The tip is then scanned over the molecule and its fluorescenceis recorded as a function of the tip position. (b) Overall set-up similar to the one in figure 5b.

84 cts

500 nm

(b) (c)

(d) (e)60

40

20

03.02.01.00

x (µm)

FWHM305 nm

31cts

7

86420x (µm)

cts / 1.8 ms

480 nmFWHM

0

(a)

40

20

0

cts / 1.8 ms

Figure 9. Mapping the field at a sharp gold tip. (a) Scanning confocal optical microscopy ofthe polymer film on glass containing the probe molecules (terylene). Inset, line cut throughthe probe molecule along the dotted line. (b) Fluorescence intensity of the probe molecule as afunction of the tip position. Part (c) shows the intensity same as (b), but the molecule bleaches.The remaining signal is subtracted from (a) to generate the image in (d), which shows the truespatial distribution of the field component mapped by the probe molecule. (e) Gaussian fit to theline cut through (d), yielding the width and the height of the peak over background. (Adaptedfrom Kramer et al. (2002).)


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above. Mapping is performed by choosing a molecule as a probe by moving it to thefocus and then scanning the tip with respect to this fixed molecule. While the tip isscanned, the fluorescence intensity of the molecule is recorded as a function of thetip position. By doing this, the field component along the absorption dipole of themolecule is mapped.

In an ideal experiment the orientation of the absorption dipole moment is char-acterized independently beforehand, e.g. by illuminating it with a focused annularbeam. This would allow us to determine the orientation by fitting theoretical pat-terns to measured ones (see, for example, Kreiter et al. 2002). This in turn wouldallow us to map specific field components of a strongly confined field. The latterexperiment has not yet been performed; however, in a proof-of-principle study it wasshown that such experiments are feasible (Kramer et al. 2002). Figure 9 shows therespective results. Figure 9a shows a 10 × 10 µm2 confocal image of a thin PMMAfilm on a glass slide containing terylene molecules. A bright molecule is chosen asthe probe by moving it permanently into the far-field illumination focus by means ofthe sample scan stage. The line cut in the inset of figure 9a shows that the full widthat half-maximum (FWHM) of the fluorescence peak due to the molecule is about480 nm. This relatively large size is due to the fact that a microscope objective withan NA of 0.9 was used.

The tip used in the present experiment is an etched gold tip made from a gold wire.After the molecule is found and positioned into the focus, the excitation intensityis lowered such that the fluorescence of the molecule is just barely visible. This hasto be done, since the local field at the tip is expected to be much enhanced withrespect to the excitation field, and the molecule would run into saturation otherwise.Figure 9b shows the fluorescence of the molecule chosen in figure 9a as a function ofthe tip position. The tip scan starts at the top left corner. The fluorescence stays ata very low level until the tip comes closes in to the molecule. A strong increase in thefluorescence of the molecule is observed as the tip is scanned over it. After the tippasses the molecule, the fluorescence decreases again and goes back to the originalvalue. Figure 9c shows the image obtained in the subsequent tip scan. The moleculephotobleaches after a few lines, which is evident from the initial flickering and thefinal termination of the fluorescence. The remainder of the image consequently showsthe effect of the tip alone. A faint background, presumably due to surface enhancedRaman scattering from contaminants on the tips surface, is visible. The differencebetween figure 9b and figure 9c is displayed in figure 9d. It represents the background-corrected spatial distribution of the enhanced field at the tip. Unfortunately, theorientation of the absorption dipole moment of the molecule is unknown in thisexperiment and consequently the mapped field component is also unknown. However,what is evident is that there is a strong enhancement of the field beneath a gold tip.Figure 9e shows a line cut through figure 9d, which was fitted by a Gaussian. The fitparameters yield the field enhancement factor and the width of the enhanced region.The fluorescence increase amounts to 5.7 ± 0.3 and the width is ca. 305 nm.

The intensity enhancement factor of 5.7 is clearly larger than 4. An intensityenhancement factor of 4 can be achieved at a planar perfect mirror simply by con-structive interference. The width of the enhancement area is clearly smaller than thediffraction-limited spot size (see figure 9a). This indicates the near-field character ofthe observed phenomenon.


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We will not go into detail about the reason for the enhancement observed. This isdiscussed at length in Kramer et al. (2002). Briefly, it is believed that the enhancedfluorescence is due to localized plasmon fields and not to a non-resonant enhancement(lightning-rod effect) at the tip apex. This is supported by observations. For gold-coated glass tips a resonance at hν = 2.11 eV (λ = 588 nm), close to our wavelength,was reported (Ashino & Ohtsu 1998). When performing similar experiments withgold-coated atomic-force-microscope tips at an excitation wavelength of λ = 532 nm,we observe no significant field enhancement. When using Pt/Ir (90:10) tips insteadof gold tips, no significant enhancement was observed. Considerable non-resonantenhancement only occurs at very sharp tips in the presence of excitation-field com-ponents along the tip axis, which is not the case in the experiment described.

6. Energy transfer and quenching

In the following we would like to discuss important effects that always have to betaken into account when optical fields are bound to material structures, i.e. energytransfer and quenching effects.

It is a fundamental notion that nano-optical fields are bound to a material struc-ture. The evanescent fields that are responsible for the spatial confinement can onlyexist in a close symbiosis with collective electron excitations in metals or with drivingpropagating fields in a second half-space in the case of total internal reflection. Thepresence of matter inevitably has an influence on the possibility of probing thesenano-optical fields quantitatively, since not only is the field to be probed interactingwith and sustained by the nano-matter, but also the probe (and the field it emitsinto the far-field towards a detector) feels the presence of matter nearby. The effect ofnearby material structures on molecular fluorescence was studied both theoreticallyand experimentally for stratified systems (Chance et al. 1978; Lukosz 1981; Lukosz& Kunz 1977b) and spherical systems (Dulkeith et al. 2002; Leung 1990; Leung &George 1987; Ruppin 1982). Phenomenologically, what happens is the following.

(i) If a dissipative structure, i.e. an extended piece of metal with free electronsand associated ohmic losses, is brought within the near-field range of a probemolecule, the near field of the probe molecule induces motion of the electrons,which quickly dissipate their gained energy, e.g. into heat. This opens up anew decay channel for the excited molecular state with a non-radiative decayrate, knr (see figure 2), that allows de-excitation of the probe molecule withoutemission of a photon. For short distances this non-radiative decay rate dependson the distance between the molecule and the extended metallic body as 1/r3,where r is the distance, reflecting the decay of the dipolar near field. It followsthat, for short distances, the rate knr will dominate the radiative decay rate krand hardly any photons are subsequently emitted by the probe molecule, whilethe excited state lifetime decreases dramatically. This effect is usually calledquenching.

(ii) If a dielectric structure, e.g. a glass half-space (Kreiter et al. 2002; Lukosz &Kunz 1977a; Macklin et al. 1996) or a suitable nanostructure, e.g. a metallicnanoparticle with a plasmon resonance, a dielectric sphere with a Mie resonance(whispering-gallery mode) (Fan et al. 2000; Gotzinger et al. 2001), or a metal-coated tip (Gersen et al. 2000), is brought into close proximity with the probe


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Si3N4

glassairgold

3

2

1

5004003002001000

exci

ted

stat

e lif

etim

e (a

rb. u

nits

)

air gap (nm)

500 nm

zy

x

(a)

(b)

Figure 10. Experimental set-up and theory for local quenching. Left panel: contact-mode AFMin combination with a fixed pulsed laser beam. The inset shows scanning electron micrographsof the tips used. Clearly, the tip terminates in a wedge and not in a sharp tip as expected.Right panel: theoretical prediction of the excited state lifetime of a molecule sitting right belowthe polymer–air interface as a function of the air gap width. (Adapted from Trabesinger et al.(2002).)

molecule, the density of electromagnetic modes that is available for accepting afluorescence photon from the probe molecule is changed. In the case of strongcoupling to one or a few modes of a resonant nano- or microstructure thisleads to an enhanced emission of the coupled system with a probably stronglymodified far-field emission pattern.

In other cases the overall density of states is modulated, which leads to anenhanced or decreased lifetime of the excited state often coupled with a redi-rection of the emission (Trabsinger et al. 2003). Such effects can be observed forprobe molecules on either side of a planar dielectric interface (Drexhage 1970;Kreiter et al. 2002; Novotny 1997). Since the fluorescence is collected over aconstant solid angle, the collected fluorescence can either increase or decreasein this case.

In the experiment described earlier we saw no direct evidence of quenching ofthe fluorescence by the metal tip; however, quenching may well be present. On theone hand this could explain the small enhancement factor observed. On the other,the distance between the tip and an average molecule in the described experimentis rather large: it is the sum of the typical shear-force gap width of ca. 10 nm andthe typical depth of a molecule in the polymer film of another ca. 10 nm. This isa rather large distance over which the quenching is less effective. In view of thisargument, the enhancement factor measured must be viewed as a lower limit for thetrue value. In an ideal experiment both the fluorescence intensity in the full solidangle and the lifetime of the excited state should be measured for different distancesfrom the material structure. Changes in the lifetime in this case could be translatedinto changes in knr, which can be correlated to the emission rate.

We can conclude that the stronger the field confinement, the more difficult it is toprobe the field quantitatively by means of a small dipolar emitter, due to the emitter’scoupling to the nano-matter. The reason for this difficulty might be more complicated


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200 nm

lifet

ime

(nm

)

01

2

3

400 800 1200scan coordinate (nm)

coun

ts m

s−1

1

1

2

2

4

(a) (b)

(c) (d )

0 400 800 1200scan coordinate (nm)

5

15

25

35

Figure 11. Local quenching of a single molecule by a metallized AFM tip. (a) Fluorescenceintensity as a function of the tip position. Bottom left inset, topography at the position of thefluorescence dip. Bottom right inset, close-up of the region of the fluorescence dip marked by thewhite square. (b) Excited-state lifetime as a function of the tip position. Inset, close-up at theposition of the lifetime dip marked by the white square. (c) Cut through (a) along the white line.(d) Cut through (b) along the white line. All scale bars are 200 nm. (Adapted from Trabesingeret al. (2002).)

than one would expect from the discussion so far, which was built on a specificexample of a probing scheme. In a famous paper by Carniglia & Mandel (1971) onthe quantization of evanescent modes, commutation relations for the fields at differentspace-time points are derived which seem to exclude the sharp measurement of fieldamplitudes of evanescent fields at points with space-like distances. This might beworth further investigation but we cannot go into more detail here.

In what follows we show that the localized quenching process at a sharp metal-lized tip (Yang et al. 2000) can possibly be used as a novel contrast mechanism tospatially resolve individual molecules by selective quenching (Novotny 1996; Traut-man & Ambrose 1997). In order to observe and prove the presence of quenching, theaverage distance between the tip and the molecules must be reduced. This is doneby applying contact mode atomic force microscopy. Pulsed excitation (532 nm wave-length, 150 ps pulse width, 76 MHz repetition rate) is used to continuously probe the


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excited state lifetime of the molecules under investigation via time-correlated single-photon counting. These two ingredients are the main new features of the experimentalset-up sketched in figure 10a. Again the fluorescent molecules are embedded in a thinpolymer film on glass. The tip is now an Si3N4 pyramid at the end of an atomic forcemicroscope (AFM) cantilever coated with a 20 nm layer of gold and operating in con-tact mode. Scanning electron microscopy images of the tip are displayed as insetsin figure 10a. A wedge-like shape of the tip is clearly visible and is a well-knownproperty of this type of probe. The length of the wedge at the apex is a little lessthan 200 nm. It is expected that the shape of the tip will somehow be reflected inthe quenching patterns to be observed.

Figure 10b shows the result of a calculation which assumes that a system of strati-fied layers can locally approximate well the system under investigation. The lifetimeof the excited state of a molecule just below the interface between air and polymer(glass) is plotted as a function of the width of the air gap between the polymer andthe gold layer. For the two fundamental orientations of the molecular emission dipolemoment, parallel and perpendicular to the interface, a distinct behaviour is observed:while for both orientations a decay of the excited-state lifetime with decreasing gapwidth is observed, this decay is much more short-ranged for the molecule with theemission dipole parallel to the interface. Here a decay constant of less than 20 nmis observed, which clearly highlights the potential for ultrahigh-resolution opticalmicroscopy of single molecules by selective quenching. It seems to be possible toresolve two molecules that are as close as ca. 20 nm by switching them off selectivelyby means of a sharp metallic tip. The power of this approach lies in the possibilityof continuing to obtain the full spectral information, e.g. the emission spectrum, ofthe unperturbed molecule.

In order to provide a proof of principle, a quenching experiment was performedwith samples that contained an isolated single molecule. Once a molecule is found ina confocal scan it is kept fixed in the focus and the AFM tip scan starts. Both thefluorescence intensity and the excited state lifetime of the molecule are recorded as afunction of the tip position. The results shown in figure 11 were obtained with the tipshown in figure 10. Figure 11a shows the behaviour of the fluorescence intensity, whilefigure 11b shows the excited state lifetime as a function of the tip position. Whilein the fluorescence intensity image the molecule starts to feel the presence of the tipat larger distances, which results in interference-like fringes, in the lifetime image nosuch fringes are present. When the tip is in close proximity to the molecule, a stronglocal decrease in the fluorescence intensity is observed. Its shape resembles that ofthe wedge at the AFM tip apex; however, it is divided in two lobes. The separationcan be explained by examination of the topographic image acquired simultaneously.It shows a contaminant particle just at the position of the separation. Its height isca. 10 nm, which causes the tip to retract by this amount while scanning over theparticle. According to the graph in figure 10b, this should be enough to completelyremove the molecule from the quenching condition. We therefore conclude that theseparation of the two lobes provides evidence of the strong distance dependence ofthe quenching effect predicted in figure 10b. At the same time, the lifetime of themolecular excited state shows a clear reduction where the decreased fluorescenceoccurs. The respective line cuts show that the lifetime image has a similar edgeresolution than the fluorescence-intensity image.


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7. Conclusion

After all we have discussed, it is clear that there is a strong potential of a singlequantum system, such as single fluorescent molecules, to be used to study the prop-erties of nano-optical fields. The theoretical resolution limit was found to be of theorder of the physical size of the molecules under conditions where the absorptioncross-section is far from its peak value. We have also seen that it might not be soeasy to really exploit the potentially ultrahigh spatial resolution. This is becauseoptical fields with spatial variations on the nanometre scale can only exist in closeproximity to some nanometre-scale material structure that will strongly influencethe emission of the probe molecule. This might be a more complex problem than itlooks at first glance. It questions the principal possibility of measuring field strengthin nano-optical fields. It is possible that non-zero field commutators at different spa-tial positions play a role in this context. Finally, we have also shown that quenchingeffects, if they occur, are not at all detrimental, but can be exploited as a contrastmechanism for high-resolution optical microscopy with single-molecule sensitivity byexploiting tip-induced local quenching effects.

The author sincerely thanks all the people that contributed to the work described in this paper:(in alphabetical order) A. Kramer, M. Kreiter, M. Prummer, B. Sick, W. Trabesinger andU. P. Wild. Stimulating discussion with H.-J. Eisler, T. Latychevskaia, Y. Lill and D. W. Pohlare acknowledged. Financial support via a professorship of the Swiss National Science Foun-dation (SNSF) and funding received within the National Center of Competence in Research‘Nanoscale Science’ and projects within the SNSF and the KTI/CTI of the Swiss Federal Officefor Professional Education and Technology are gratefully acknowledged.

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