NSOM the Fourth Dimension: Integrating Nanometric Spatial and FemtosecondTime Resolution

AARON LEWIS, UDI BEN-AMI, NILY KUCK, GALINA FISH, DORA DIAMANT, LEV LUBOVSKY, KLONY LIEBERMAN, SHARON KATZ, AMIR

SAAR, MICHAEL ROTH

Division of Applied Physics, The Hebrew University of Jerusalem, Jerusalem, Israel

SCANNING Vol. 17, 3–13 (1995) Received April 18, 1994© FAMS, Inc.

Summary: Photonic devices are becoming the cornerstone ofnext generation systems for computing and information pro-cessing. This paper reports on the first steps in the developmentof methods to understand these devices with nanometric (10−7

cm) spatial and femtosecond (10−15 s) time resolution. Thebasis of this achievement is the dramatic developments thathave occurred in the past few years in a new area of opticscalled near-field optics. Near-field optics is a form of lenslessoptics with a resolution that is subwavelength and which isindependent of the wavelength of the light being employed. Wereport in this paper the transmission of pulses with tens of fem-tosecond duration through subwavelength, near-field opticalelements. We also report on a femtosecond near-field opticallight source with cross-correlating capabilities and on thegrowth of GaAs in the tip of micropipettes for use as an ultra-fast electro-optical switch which can cross-correlate optical,electrical, and electro-optical effects. These developments areespecially relevant in the investigation of photonic devicessince such devices can alter their characteristics as a functionof size in the mesoscopic regime from just below lens-basedoptical resolutions to dimensions that approach atomic scalesof ~1 nm (10−7 cm). In view of the fact that these devices andthe processes that govern them also exhibit ultrafast speeds, thecombination of state of the art femtosecond laser spectroscopywith the unique features of near-field optics is a critical step inadvancing our next generation understandings of such materi-als and structures so that their full potential in information pro-cessing can be achieved.

Key words: near-field optics, nonlinear optics, scanned probemicroscopy, beta-barium borate, gallium arsenide

Introduction

Near-Field Optics

Over the last several years, an exciting field of optics hasbeen emerging that portends a new era in optical resolutionbeyond the diffraction limit of conventional far-field opticalinstruments. This field, near-field optics, is now the focus ofthis special issue of Scanning.

The simplest emulation of near-field optics replaces the tra-ditional optical element of geometric optics, the lens, with anaperture of subwavelength dimension that is used to limit theextent of a larger light beam. This subwavelength aperture isbrought close, within the near-field, to a surface that is to beimaged or illuminated. As a rule of thumb, the near-field dis-tance can be considered to be less than the dimension that is thediameter of the subwavelength aperture. The radiation as itpropagates from the subwavelength aperture through the near-field regime exponentially decreases in intensity. Concomi-tantly, the dimension of the spot of light spreads out due to theeffects of diffraction, as the radiation propagates into the far-field which is generally considered to lie at a distance of manywavelengths from the subwavelength aperture.

The first reported investigations in the optical near-field wereby Lewis et al. (1983). This report was followed by publica-tions by Lewis et al. (1984) and by Pohl and co-workers (1984)who reported an independent activity in this area at IBMZurich. All optical instruments in operation before 1983worked in the far-field with a resolution limit that is approxi-mately λ/2 of the wavelength of light, λ, that is employed in theimaging. Such conventional instruments work with an opticalelement, a lens, that is held many wavelengths away from theobject that is the focus of attention. The dominance of the far-field in electrodynamics is best highlighted by the treatmentgiven to the subject of the near-field in a standard textbook onelectrodynamics such as Jackson’s Classical Electrodynamics.In this book (Jackson 1975) of several hundred pages there isonly one paragraph that explicitly refers to the near-field. Theexperiments of the past decade in near-field optics are nowslowly altering this imbalance and there is increasing evidencethat the exponential growth of near-field optics will alter thelandscape in optical imaging, measuring, and writing beyondthe restrictions of the far-field diffraction limit.

Address for reprints:

Aaron LewisDivision of Applied PhysicsThe Hebrew University of JerusalemJerusalem, 91904, Israel

Original Papers

The origins of near-field optics in our laboratory arose byposing a very simple question to which we have accumulateda surprising number of interesting answers over the years. Thequestion we asked was whether there were specific areas inoptics where lenses fail to perform adequately. In our searchfor answers we have discovered at least four diverse areas inwhich lenses cannot achieve the required tasks at hand. In eachcase the techniques of lensless optics provide a critical solutionin an area of optics in which no definitive solution has existed.

The first area where lenses fail to perform adequately is, ofcourse, as noted above, in the area of the resolution that can beachieved by far-field optics. This has led to extensive efforts innear-field optics in our laboratory (Betzig et al. 1987;Harootunian et al. 1986; Kuck et al. 1992; Lewis 1985; Lewisand Lieberman 1991a, b; Lewis et al. 1983, 1984, 1988;Lieberman and Lewis 1991a, b, 1993; Lieberman et al. 1990,Palanker and Lewis 1991; Rudman et al. 1992; Shalom et al.1992; Shchemelinin et al. 1993; Turovets et al. 1993) and in theexponentially growing number of laboratories throughout theworld. The present universally accepted method for producingthe lensless element for near-field optics that was introducedby our laboratory in 1986 (Harootunian et al. 1986) is the appli-cation of a method of pulling glass with microprocessor-coor-dinated heat, tension, and cooling to generate appropriatelytapered glass tubes with highly reproducible subwavelengthapertures at the tip.

A second area where lenses fail to perform adequately is inthe area of concentrating deep ultraviolet radiation. Such radi-ation is readily produced by argon fluoride excimer lasers at193 nm which is a wavelength that is somewhat longer than thevacuum ultraviolet region and thus, unlike wavelengths in thevacuum ultraviolet, can propagate in air. An important charac-teristic of 193 nm radiation is that it can remove material withultralow ablation thresholds and with minimal heat deposition.In addition, because of strong absorption in most materials,each pulse of this laser can be controlled to remove much lessthan 0.1 µof the surface being irradiated. Furthermore, in termsof biological applications, numerous studies have shown thatwith 193 nm radiation no mutagenic effects have beenobserved. Thus, such a laser should be ideal for cellular and tis-sue ultramicrosurgical applications.

Nonetheless, the argon fluoride excimer laser had neverbeen used for ultramicrosurgical applications for a variety ofreasons. First, diffraction-limited optics are impossible toobtain in this region; second, even if such optics existed, thelarge divergence in the beam of this laser makes it impossibleto obtain diffraction-limited resolution; third, there are no effec-tive fibers for this wavelength; and fourth, the large absorptioncross section of most materials at this wavelength extend to bio-logical fluid and make a lens-based delivery system, which hasto be placed at some focal distance from the surface to beablated, impractical. Once again the methodologies we havedeveloped for producing lensless optical elements for near-fieldmicroscopy, which involve the tapering of glass tubes withmicroprocessor control, work very successfully in developinga means to deliver with microspot dimensions this laser towithin a few microns of the tissue that is to be removed. Thus

we have been able to overcome any interference from the sur-rounding biological medium that is critical in the delivery ofthe 193 nm laser wavelength in an organ such as an eye. Thishas permitted the ultimate in laser ultamicrosurgery availabletoday (Laufer et al. 1993, Lewis et al. 1992, Palanker et al.1991, Palanker et al. 1994).

A third area where there are no effective, wavelength-inde-pendent optical elements for concentration of electromagneticradiation is the hard and soft x-ray regime. We discovered thatthe lensless optical solutions developed for near-field opticsonce again prove to be a unique advance in this important areaof x-ray optics. Specifically, we have shown that accuratelytapered hollow glass pipettes are ideal devices for concentrat-ing, directing, and aperturing x-ray beams (Livins et al. 1990;Stern et al. 1988; Thiel et al. 1989, 1992, 1993).

Finally, a fourth area in which lenses fail to perform ade-quately is in the manipulation of ultrashort pulses of laser light.The present article focuses on this significant problem andreports on experiments that highlight the singular capabilitiesof the lensless optical solution we suggested and have devel-oped over the past decade in this important area of photonics.

Near-Field Optics and Femtosecond Lasers: A Synergistic Combination

Ultrashort, femtosecond (fsec) laser pulses have made majorcontributions to our understanding of a variety of important andfundamental problems in photonics. This is especially the casein the field of photonic devices based on semiconductor physicsand technology. A few examples of such problems are carrierdynamics in semiconductor devices, resonant tunneling diodes,emission in quantum-confined structures, and other significantfields. In most of these areas the answers to the fundamentalquestions depend on the dimensionality of the structure in ques-tion. Specifically, the observations associated with many of thephysical phenomena dealing with advances in photonics per-tain to a function of the size of the device in the “mesoscopic”regime, which is the intermediate distance scale, filling the gapbetween the atomic (1 nm) and the micrometer scale (1000nm). As a consequence, quantum mechanical effects willstrongly affect the working principles of these devices. Forexample, some striking differences between mesoscopic struc-tures and conventional integrated circuits may be observed fora wide variety of structures and some of these differences aresummarized in Table I (PHANTOMS, IMEC).

Numerous investigations in the past few years have shownthe utility of ultrafast lasers in the investigations of the manyfundamental and applied questions in mesoscopic physics.Specifically, these lasers together with cross correlation tech-niques have been able to answer many questions of fundamen-tal importance in the design of ultrafast photonic devices.

However, in many of these photonics problems there is anelement of spatial resolution inherent in the physical phenom-ena but missing from the experimental results. For example, inquantum well lasers there are open questions concerning theconcentration of charge in specific quantum wells of the laser

4 Scanning Vol. 17, 1 (1995)

as the laser action evolves. Theoretical suggestions and calcu-lations exist (Tessler and Eisenstein 1993), but experimentalverification of these calculations require techniques that cancombine the results of ultrafast lasers with a spatial resolutionthat is impossible to achieve with the methodologies of geo-metric optics.

Femtosecond Lasers Encounter Problems with Geometric Optical Elements

To demonstrate this lack of suitability of geometric optics tothe needs of ultrafast spectroscopy of mesoscopic systems, thereader is referred to Figure 1. This figure, prepared several yearsago by Fork et al. (1990), compares the history of the spatialresolution of microscopic measurements with light and thetemporal resolution of optical pulses that have reached theirpinnacle with the discovery of methods to generate fsec pulsesof light. In this figure it can be seen that, in 1990, the highestresolution that could be achieved by diffraction-limited opticswas 0.5 µ (0.5 × 10−4 cm) which is far from the spatial resolu-tions generally required to observe interesting mesoscopic phe-nomena.

In fact, the problem of resolution with fsec pulses of light iseven worse than what is seen in Figure 1. The difficulties thatfsec pulses encounter with geometric optical elements are two-fold. First, as an ultrashort pulse traverses, for example, a lensit experiences dispersive effects that broaden the pulse in time.Second, ultrashort pulses exhibit uncertainty broadening (∆E∆t > h) and thus their spectra are extremely broad. Therefore,

it is impossible to achieve even diffraction-limited optical res-olution.

These problems notwithstanding, ultrafast investigationson mesoscopic structures often require ultrahigh resolution.Consider, for example, the conservative notion that an alter-ation induced in a material by a fsec pulse spreads with thespeed of light. At such a speed the area over which the partic-ular phenomenon will spread in an fsec is 0.3 µ. In actuality,many phenomena in such semiconductor structures spread atconsiderably less than the speed of light. For example, the ini-tial velocity of an excited electron in GaAs is only 107 cm/swhich means that in a 6 fsec pulse (the shortest pulse that hasbeen created to date) the electron travels only 6 Å. Thus, bothin terms of the dimensionalities of the mesoscopic structuresand the speed at which the effects caused by the light matterinteraction spread, a spatial resolution is required that cannotbe achieved even in systems in which diffraction-limitedoptics are possible.

Development of Diffraction-Unlimited, Lensless, Near-Field Optics

Fortuitously, as noted in the introduction of this paper, therehave been exciting developments in diffraction-unlimited near-field optics. This is based on an approach in which a subwave-length light probe is scanned within the near-field of a surfacebefore far-field diffraction effects can occur. This type of near-field scanning optical microscopy (NSOM) brings optics to a newrealm of resolution, as shown in Figure 2. This regime of opticalresolution is precisely what is required for investigating the meso-scopic phenomena that underlie the advances taking place in pho-tonic structures. These developments in optics are displayed inFigure 3, superimposed on Figure 1 which compares temporaland spatial resolution. If the optical elements of near-field opticscan be effectively combined with ultrafast lasers, then a whole setof exciting experiments will evolve which will combine nanome-ter spatial resolution with fsec time resolution.

The Near-Field Optical Probe As a Unique,Multifunctional, Lensless, Optical, and ScannedProbe Element

Reproducible experiments in near-field optics have evolvedout of the realization in our laboratory (Harootunian et al. 1986)

A. Lewis et al.: NSOM the fourth dimension 5

TABLE I Mesoscopicª physics and technology

“Classical” device Mesoscopic structure

Ordinary conduction channels Electron waveguidesQuantized carrier motion in at most one direction Quantized carrier motion in at least one directionIncoherent propagation Coherent propagationMulticarrier transport Single electron transportLocal ohmic resistivity, scaling, and length Nonlocal quantized ohmic resistivitySteady-state limited drift velocities High overshoot drift velocities

ªThe term “mesoscopic” refers to an intermediate distance scale, filling the gap between the atomic (1 nm) and the micrometer scale (1000 nm).This summary has been taken from Phantoms, IMEC, Leuven, Belgium.

10−1

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Mode locked laserColliding pulse laser

Combined amplitude and phase shaping

Pulse compression

Res

olut

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(cm

)

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olut

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(s)

FIG. 1 The optical temporal resolution compared with the limits of spa-tial resolution based on geometrical optics. Taken from Fork RL,Avramopoulos H, Valdmanis JA, American Scientist 78, 216 (1990).

Year

6 Scanning Vol. 17, 1 (1995)

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Modelocked laserColliding pulse laser

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Pulse compression

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olut

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(cm

)

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olut

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FIG. 3 The NSOM contribution to nanometer optical spatial resolutioncompared with the ultimate in temporal resolution available today.Adapted from Fork RL, Avramopoulos H, Valdmanis JA, American Sci-entist 78, 216 (1990).

that highly controlled glass-pulling techniques could be appliedto the development of tapered glass structures with nanometerdimension apertures and light sources at the tip and, as notedabove, with other unique characteristics. One emulation of thistechnology for producing a near-field optical element is ametal-coated nanopipette.

Optical microscopy

Abbe

Zernicke

Electron

microscopy

SEM NSOM

TEM

STM

2000195019001850

1µ

100nm

10nm

1nm

1Å

FIG. 2 The historical development of microscopic resolution with scan-ning near-field optical microscopy highlighted in the region of the graphfilled in with “x”. Adapted from Pohl DW, in Advances in Optical andElectron Microscopy (Ed. Shepard C). Academic Press Ltd. London(1992).

Scanninglaser microscopy

These nanopipettes have been shown to be multifunctionalelements for scanned probe microscopy, and this multifunc-tional character will be crucial for the integration of fsec laserspectroscopy with near-field optics. Specifically, nanopipetteshave been shown to be able to image surfaces simultaneouslywith near-field optics and scanning tunneling microscopy(Lieberman and Lewis 1993). Nanopipettes are also superbforce sensors (Shalom et al. 1992). With bent tips (Fig. 4) theycan monitor normal and lateral forces (Shalom et al. 1992), andas straight structures they can detect lateral forces(Shchemelinin et al. 1993, Toledo-Crow et al. 1992).

Nanopipettes have also been shown to be nanometer dimen-sion vessels in which a variety of materials can be grown anddeposited in the tip. These materials have converted the pipettetip into a subwavelength light source (Lewis and Lieberman1991, Lieberman et al. 1990) (Fig. 5), and with metals drawnto the tip of the nanopipette this structure has been convertedinto a point thermocouple with which the image shown in Fig-ure 6 of the thermal characteristics of a focused laser beam wasobtained.

Near-Field Elements for Femtosecond Illuminationand Correlation

Figure 7 schematically describes several possible methodsof integrating fsec pulses with subwavelength illumination andcross-correlation methods based on our development oftapered near-field optical probes with controlled glass-pullingtechniques. This integration of near-field optics and fsec spec-troscopy uses the known multifunctional characteristics of thenear-field optical elements emphasized in the previous section.

The simplest concept of integrating fsec spectroscopy withnear-field optics is schematically depicted in Figure 7a in whicha fsec pulse is transmitted through a subwavelength aperture.In this paper we report on experiments that are applicable toillumination, collection, and cross correlation with nanometricspatial resolution. Another approach to forming a fsec pulse oflight at the tip of a lensless optical element is to deposit a non-linear optical material, such as beta-barium borate, in the sub-wavelength tip of the micropipette. This type of tip has thepotential of also acting as a method of cross correlating pulseswith high spatial resolution (Fig. 7a). As described below,experiments have achieved such nonlinear effects in the tip ofthe micropipette. This is a first step in the production of a fseclight source of nanometer dimensions.

Alternately, hybrid techniques of scanned probe micro-scopies that are integrated together with the ultrafast switch-ing of semiconductor materials with fsec pulses of light can beused to cross correlate the time dependence of ultrafast phe-nomena in materials, and this is schematically represented inFigure 7b. In this diagrammatic representation, a semicon-ductor material such as GaAs is grown in the tip of amicropipette and such a material can be switched with fsecpulses of light so that the conductivity of the semiconductorcan be altered with appropriate time delays. This would allow

A. Lewis et al.: NSOM the fourth dimension 7

FIG. 4 (a) A nanopipette to sense surface forces bent at the tip with a focused carbon dioxide laser. (b) Methods have been developed to polish the surfaceof the pipette at the bend to produce an integral mirror. A laser beam is reflected off this mirror onto a position sensitive detector so that small movementsof the cantilever, due to the effect of surface forces at the tip, are sensitively monitored. This is a standard method that is used in atomic force microcopy.

FIG. 5 Light emission from a nanopipette with a 100 nm tip, emitting anintensity of 3 µW.

FIG. 6 The thermal image of a laser beam focused to a diameter of 0.5microns obtained with a nanopipette. Platinum was drawn through thenanopipette to the tip using techniques developed in Jerusalem. The pipettewas also coated on the outside by aluminum making a point contact withthe metal in the tip which creates a point thermocouple.

GaAsGaAs

a) b)

8 Scanning Vol. 17, 1 (1995)

FIG. 8 The energy spread of a 62 fsec pulse before (thick solid line) andafter it traverses through pipettes with a variety of tip dimensions.

12010080604020

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nsity

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the modulation of the flow of current between two elec-trodes—one inside the pipette and the other represented by thecoating on the pipette exterior. This approach of altering thetip characteristics with appropriate time delays in pairs of fsecpulses has considerable potential for integrating both the tun-neling and force characteristics of micropipettes with surfacephenomena that have been altered optically with fsec timeduration. As the experiments described below will indicate,significant achievements have been made in this interestingapproach to fsec scanned probe microscopy.

In summary, the experiments highlighted in the sectionsbelow are based on the structure and the unique multifunctionalcharacteristics of micropipettes that should be of significancein the goal of monitoring fsec spectral phenomena with nano-metric spatial resolution.

Nanopipette Transmitting a Femtosecond Pulse ofLight without Significant Pulse Broadening

Experimental Results

Using such pipettes we have completed preliminary inves-tigations on the simplest scheme of all that could integrate near-field optics with fsec pulses and, that is, to pass a fsec laser pulsethrough the empty void of a glass micropipette coated withmetal. From the point of view of illuminating or collecting fsec

pulses of light in highly localized regions in space, the questionis whether the subwavelength, conducting aperture at the tip ofthe micropipette would alter the characteristics of such lightpulses. The question is significant not only in terms of the prac-tical applications of fsec near-field optics, but also in terms ofdeveloping a fundamental understanding of how light is trans-mitted in spaces which have dimensions below the cutoff fre-quency beyond which light can only be transmitted with largeevanescent losses.

The initial results obtained are displayed in Figure 8. Theseresults relate the observed energy spread of a pulse of 60 fsec(estimated for a sech2 pulse shape) from a colliding pulse modedye laser emitting radiation at 610 nm as a function of thepipette diameter. In each experiment shown in this figure thereare two curves: a heavy solid curve which is the energy spreadof the pulse without the presence of the pipette, and a curvereproduced with a lighter line that corresponds to the energyspread of the pulse after it passes through the opening at thepipette tip. These results indicate that transmission through sub-wavelength apertures of the dimensions indicated in Figure 8

FIG. 7 (a) Tips for space and time cross correlations with near-field scan-ning optical microscopy. (b) A structure for correlating fsec optical phe-nomena with scanning tunneling and force microscopy measurements.

Optical elements

Hybrid elements

TunnelingTip excitation with

subsequent sample excitation

ForceSample excitation with

subsequent tip excitation

Cross correlation

In sample

Intip

SampleSample

Laser Laser

Metalcoating

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SampleSample

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(b)

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A. Lewis et al.: NSOM the fourth dimension 9

does not reduce the energy spread. It follows that for such aper-tures, even if further experimentation indicates that the pulse isindeed longer after it traverses the subwavelength pipette tip,we will be able to apply a reverse chirp to the pulse in order toobtain the desired time resolution. This methodology can onlybe applied when the chirp affected by the subwavelength opti-cal element is linear.

Theoretical Understandings

To understand these results within a theoretical frameworkwe performed calculations that employed a model of a seriesof slits with increasingly small diameters (Fig. 9). The modespropagating in this structure that were investigated had an elec-tric field vector that was parallel to the walls of the slit whichwas approximated as an ideal conductor. Thus, the electric fieldwas assumed to be zero at the walls. The modes in the slit wererepresented as sine waves, and a linear combination of modeswas employed initially. The calculated propagation of thosemodes at each step was accomplished by ensuring that thefunction and the first derivative were continuous in the trans-mission across a step in the decrease of the dimension of theslit. In this fashion the wave was propagated through the modelstructure of slits with decreasing diameters and the result wasevaluated at the end of the sequence of slits.

Each mode, n, was described according to the equation forthe electric field

(1)

with ω the frequency, L the width of the slit, and t the time. Ateach point in the step there were propagating and reflectingmodes the coefficients of which were calculated from the con-tinuity conditions of the function and its first derivative.

We started with several modes with n = 1 and the same kx =πnx/L, but with different ω and therefore a different kz, sincekx

2 + kz2 = ω2/c2. The sum of these modes resulted in a sharp

electric field in the z direction. The transmission of each ofthese modes was calculated separately, and at the end of thesimulated pipette they were combined to give the spread of theelectric field distribution.

rEn = y sin(πnx / L)e i[(ω 2 /c2 −(πn/L)2 ]1/2 z e iω t

n∑

FIG. 9 The model of a pipette used in the calculating fsec pulsetransmission.

Conductor

Transmittedwave

Conductor

Incidentwave

Reflectedwave

z

FIG. 10 A comparison of the results obtained from a model calculationof fsec pulse transmission in which the alteration in the pulse is followedthrough progressively decreasing dimensionalities. The results show max-ima of the magnetic plus electric fields as a function of time [starting at t=0in (a)]. Each maximum is in a different cross-section of our model pipettewith increasingly smaller diameters.

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The results obtained in this simulation are shown in Figure10. This simulation used 50 steps to approximate the pipette. Acomparison of the nature of the pulses after 0 steps and after 40steps is shown in this figure. The pulses used were 3 fsec andafter passing through such steps they increase in width due tothe fact that higher order modes become evanescent as thedimension of the slit is reduced to a dimension that is less thanthe dimension through which such pulses can propagate. The

t

t

H2+E2

H2+E2> >

> >

usually is achieved with bulk crystals using the proper choiceof polarization of the two waves as well as the direction of theirpropagation. Yet, for crystallites much smaller than the coher-ence length, Lc= π/∆k, appreciable conversion efficiency canbe obtained for arbitrary orientation of the crystallites, espe-cially when considering the very high average power of inci-dent fsec pulses from a laser such as a Coherent Radiation Mirafsec Titanium-Sapphire laser. Thus, powdered single crystalsof beta-barium borate placed in the pipette tip are expected toyield a nonlinear response when illuminated with pulses fromthe Titanium-Sapphire laser.

To test this hypothesis, a crushed powder of beta-bariumborate was introduced into the tip of a micropipette which wascoated with metal for near-field optical applications. This pow-der was illuminated with a 120 fsec pulse from a CoherentRadiation Mira Titanium-Sapphire laser. Each pulse of the laserhad an energy of picojoules. The resulting second harmonicemission at 400 nm was photographed through suitable filterswith a Zeiss inverted microscope at a magnification of 500times. The far-field detection of this second harmonic genera-tion from the beta-barium borate tip of the micropipette is seenin Figure 11. Based on the dimensionality of the tip shown inFigure 11, it is estimated that, if an unamplified titanium sap-phire laser emitting 200 mW at a repetition rate of 108 Hz is

10 Scanning Vol. 17, 1 (1995)

FIG. 11 Frequency doubling in the tip of a micropipette with beta-bar-ium borate microcrystals.

theoretical simulation indicates that the alteration in a 3 fsecpulse as it goes through an aperture that is one-tenth the wave-length of the light should spread the radiation in time by morethan double the initial 3 fsec pulse width. Thus, our experi-mental observation of minimal effects on the 65 fsec pulses wehave transmitted through apertures of at most 1/6 of the laserwavelength is understandable.

A caveat on these deductions is the fact that modes that arereflected back from the direction of the taper should once againbe reflected into the propagating direction by the next largerstep, but our theoretical model did not consider the back reflec-tion of these modes. Initial investigations on the effect of thesereflected modes indicated that they should make a noticeablecontribution on the final solution, and our continuing studiesare aimed at refining the model in this direction. In addition, itshould be noted that dispersion effects due to the penetration ofthe pulse into the walls were not taken into account.

Future directions in this sequence of experiments are toemploy the sensitivity of the character of these pulses to exter-nal influences in order to understand—using the synergisticinterplay between the theory and the experiments in this area—the mechanism by which light is transmitted through structureswith subwavelength dimensions in the mesoscopic domain inwhich there is an interesting mix of classical and quantumeffects.

Nonlinear Optical Tips as Femtosecond LightSources and Cross Correlators

In previous studies (Lieberman et al. 1990, Lewis andLieberman 1991) we have shown that the tip of a micropipettecan be converted into a subwavelength light source. An exam-ple of this was shown previously in Figure 5. An importantquestion was whether a nonlinear material such as beta-bariumborate could be introduced into the tip of a micropipette and,using fsec illumination, whether nonlinear optical processescould be used to generate a fsec light source of nanometerdimensionality. Beta-barium borate is an exemplary materialfor such tests since it has very large effective nonlinear suscep-tibilities that are six times those of KDP. It has high opticalhomogeneity and a wide transparency range (0.19–3.3mm).Thus, this crystal is an ideal choice for second harmonic gen-eration (SHG) and for optical parametric oscillation of, forexample, the tunable near-infrared light from a Titanium-S sap-phire fsec laser.

SHG is the second-order nonlinear optical process when twofields of frequency ω are mixed (added up) to produce a thirdfield of frequency 2ω. The elementary theory of the processshows that the relative efficiency of the SHG is dependent onthe phase mismatch (∆k) between the primary (ω) and sec-ondary (2ω) waves and on the crystal length, L:

I(2ω) ~ L2 . [sin(∆kL/2) / (∆kL/2)]2. (2)

It is clear from this equation that the maximum efficiency of theSHG requires perfect phase matching, namely ∆k=0, which

(Pohl 1992) that is a liquid at room temperature and can read-ily be used to fill the inner cavity of such pipettes. The semi-conductor material in the tip is chosen for its photoconductiveproperties so that it can be turned on at some point in time by afsec pulse of light to allow current to flow from the outer to theinner electrode or the reverse.

With this structure being used in a scanning tunnelingmicroscopy mode, one can envision exciting the sample andthen measuring with some time delay the tunneling of theFermi level electrons from the sample through the tip and to theinner electrode. Alternately, in an atomic force microscopymode, one could optically open the connection between theelectrodes and then measure with some time delay the magne-tostatic forces between the tip and the sample.

GaAs Has Been Grown in the Confined Space of aPipette Tip

A crucial part of this proposed structure is the growth ofmaterials such as GaAs in the tip of the pipette. Can such a crys-tal be grown in such a confined space?

Figure 12 shows the procedure that has been developed togrow such materials in the highly confined space at the tip of aquartz pipette. It is filled with crushed GaAs, and a carbon diox-ide laser is scanned over the crystals. The carbon dioxide laserin this arrangement is colinear with a HeNe laser beam that iscolinear with the carbon dioxide laser. A ramp voltage wasimpressed on a scanning mirror assembly that translated thelaser beams along the axis of the micropipette while it wasrotated. Actually the carbon dioxide laser was split into twobeams, with one of them used to heat the whole region of thepipette tip and the other passed through a lens and focused to asmall spot. This allowed the focused laser beam to be scannedthroughout along the region of the pipette tip while the wholeend of the pipette was kept somewhat below the melting tem-perature of the semiconductor. As the semiconductor materialwas repeatedly melted by the focused laser beam in the pipettetip, it was drawn by capillary action into the very tip of themicropipette. This could be considered as a laser-based modi-fied Czochralski approach for crystal growth in confinedmedia.

Material grown by this unique method was initially charac-terized using an elemental analysis with the scanning electronmicroscope and with laser-excited photoluminescence spec-troscopy. From the chemical analysis we were able to deter-mine that the gallium and arsenide stochiolmetry was appro-priate, although there was aluminum and silicon contaminationwhich probably arose from quartz residues and our use of analuminum bowl to contain the material before crystal growth.

To obtain the photoluminescence spectra, an argon ion laserwith an emission wavelength of 514 nm was used. The tip ofthe pipette was illuminated with this laser after being filteredfor any nonlasing emission lines. The emission excited at roomtemperature was collected with appropriate lenses and trans-mitted through the entrance slit of a Spex Triplemate mono-chromator system. The emission was dispersed in terms of itswavelength by the monochromator onto a Photometrics 512

A. Lewis et al.: NSOM the fourth dimension 11

used, a least a million photons a second should be obtainedfrom a dimension of 100 nm. These types of intensities couldbe readily increased through amplification of the input energy,and such intensities are more than sufficient to produce usablefsec pulses in the blue region of the spectrum. The tip could alsoact as a subwavelength, spatially resolved cross correlator offsec duration spectral phenomena.

It should also be noted that the excitation of such nonlinearmaterials in these ultrasmall dimensions with the fsec laser sys-tem should give rise to a variety of interesting nonlinear effects.For example, consider a 1W, 100 fsec laser with a repetition rateof 108 Hz. The peak power of the pulse is given by

Ppeak ~ 1W/(1 × 10−13)(108) ~ 100 kW. (3)

If such intensities are captured within the crystal in the tip ofpipette and a conservative dimension for the crystal of 1 µ isconsidered, then

I ~ 100 kW/(π × 10−4cm)2 ~ 3 × 1012W/cm2. (4)

This is a staggering intensity for all kinds of nonlinearprocesses. For example, for optical parametric oscillation,intensities of 1010 W/cm2 are required and this can presentlyonly be obtained within the cavities of certain lasers.

The Nanopipette as an Ultrafast, Cross-Correlating, Photoconductive Switch

As diagrammatically illustrated in Figure 7b, the micro-pipette can be an effective ultrafast, subwavelength, photocon-ductive switch with tunneling and force-sensing capabilities if,for example, GaAs or InP could be deposited in themicropipette tip. This type of highly localized switch could actas a super-resolution probe for correlating phenomena inducedin photonic materials by the pulses of light emanating from anfsec laser. A pipette generated for this purpose (Fig. 7b) wouldbe coated on the outside with metal by our standard technolo-gies while leaving the top surface of the structure uncoated. Theinner electrode is achieved using an indium/gallium eutectic

FIG. 12 One of the methods we have devised for growing GaAs in the tipof quartz micropipettes.

Mirror

Beam splitter

MirrorLaser HeNe

Laser CO2

Samplepipette

Rotor

Lens

Mirror

12 Scanning Vol. 17, 1 (1995)

explained by the small size of such systems containing what iscommonly referred to as “less than a statistical number ofatoms,” indicating that thermodynamics which deal with theaverage properties of large systems are not applicable in suchcases. What is really needed is a methodical treatment of theproblem including the effect of curvature, and this is indeedpossible.

We consider first the solidification of a one-component sys-tem describing GaAs, InGaP, or Si. The rate of crystallizationof liquids that are relatively fluid at their melting temperaturesusually is fast and limited by the rate of removal of the heat offusion. Nevertheless, liquids can often be supercooled wellbelow their melting points, showing that in these cases the rateof liquid-crystal transformation is controlled by nucleation. Thecritical size for a solid particle nucleation in the liquid is givenby the condition dG/dr=0, or the minimum of the Gibbs freeenergy of the system as a function of the radius of, say, a spher-ical particle.

For the simple case of such a spherical particle, the criticalradius is given by

r* = (2γslTm)/(Lf∆T), (5)

which can be directly obtained from the capillarity, or Gibbs-Thomson, equation. Here, γsl is the solid/liquid interfacialenergy, Tm is the material melting point, Lf is the latent heat ofsolidification, and ∆T is the undercooling. Taking, for our case,r* = 5 nm and the known GaAs physical parameters: γsl = 126erg/cm2, Lf=262 cal/cm3 and Tm = 1510K, we obtain ∆T = 70K.

The critical energy that the system must acquire for suchnucleation is given by

, (6)

and for ∆T = 70K this is equal to approximately 80 kT. This isin good agreement with the average experimental nucleationenergies of 78 kT measured for many metals. In calculating gfor our curved surface we have taken into account the resultobtained using statistical methods, namely, γr/γ∝ = 1/(1+2δ/r)−1,where δhas the value of molecular dimensions, γr is the surfacetension of a surface of radius r, and γ∝ is the surface tension ofa flat surface. This gives a small correction to the calculatedvalue above of the minimum undercooling. Also, larger nucleiat smaller undercoolings can be formed at the pipette tip. Thiswould require larger critical energies for the case of homoge-neous nucleation. However, the pipette walls serve as sites ofheterogeneous nucleation, allowing for the reduction of thepotential energy for nucleation due to partial wetting of the sil-ica by GaAs or InGaP. Success of the experimental crystalgrowth of GaAs as described above proves the feasibility of ourapproach.

Conclusion

The developments reported in this paper should open awhole new area of experimentation that will result from this

∆G* =16π γ sl

3 (Tm )2[ ]3(Lf )2 (∆T)2[ ]

charge-coupled device multichannel detector cooled to liquidnitrogen temperatures in order to eliminate dark noise. Theresulting room temperature emission spectra are shown in Fig-ure 13a and b.

The results obtained in Figure 13a for bulk GaAs and in Fig-ure 13b for laser grown GaAs in the pipette tip were obtainedwith a width of 200 µ for the entrance slit of the monochroma-tor. The integration times varied from 30 to 300 s depending onwhether the bulk GaAs or GaAs in the tip of the pipette wasbeing analyzed. The relative intensities detected for the emis-sion in these two cases reflect not only this difference in inte-gration time but also the relative illumination volumes. In thecase of bulk GaAs the laser spot size was approximately 40 µ,while in the case of the GaAs in the pipette tip the illuminatedvolume was fixed not by the size of the laser beam but rather bythe size of the pipette tip which was 0.5 µ in this case.

In summary, the above results indicate that the GaAs crystalgrown in the tip of the pipette by our newly developed laser-based growth procedure is indeed of high quality.

Theoretical Understandings

In general, crystal growth of any material in capillaries, forexample, micropipettes, sets a challenge that has rarely beentackled even in basic research. Consider, for example, thegrowth in a 100 nm or smaller tip of a pipette. In such a struc-ture we are dealing with solidification not only in an unusuallyconfined space but also one with a high degree of curvature.Systems with highly curved surfaces considered until nowinclude spherical nuclei in vapors undergoing condensation(positive curvature) and liquid condensing from the vapor (neg-ative curvature). The scarcity of research in this field is

FIG. 13 Room temperature emission spectra of a test sample of GaAs (a)and GaAs grown in the tip of a micropipette (b).

750

Photoluminescence of laser grown GaAs in pipetteWavelength (nm)

Wavelength (nm)

Photoluminescence of GaAs bulk semi-insulating

Inte

nsity

(A

.U.)

Inte

nsity

(A

.U.)

800 850 900 950 1000

830 840 850 860 870 880 890

700600500400300200100

0

3500

3000

2500

2000

1500

1000

500

0

combination of near-field optics and fsec laser spectroscopy toyield ultrahigh spatial and temporal resolution of photonicdevices. As a byproduct of this research effort we fully expectthat new understandings in linear and nonlinear optical phe-nomena in confined spaces will result and new information onthe behavior of photons in confined spaces will be obtained.

Acknowledgments

The authors would like to thank the ultrafast laser group ofCoherent Radiation, Inc. for making available a Mira Titanium-Sapphire laser system which was necessary for this demon-stration of the synergistic interaction between near-field opticsand ultrafast lasers and the phenomena that they induce. Theresults suggest many future experiments which combine ultraresolution in space and time.

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