The exact nature of the signal in scanning apertureless microscopy techniques is the subject of much debate. We have sought to resolve this controversy by carrying out simulations and experiments on the same structures. Simulations of a model of tip–sample coupling are shown to exhibit features that are in agreement with experimental observations at dimensions below the diffraction limit. The simulation of the optical imaging process is carried out using atomic force microscope data as a topographical template and a tip–sample dipole coupling model as the source of optical signal. The simulations show a number of key fingerprints including a dependence on the polarization of the external laser source, the size of the tip, and index of refraction of the sample being imaged. The experimental results are found to be in agreement with many of the features of the simulations. We conclude that the results of the dipole coupling theory agree qualitatively with experimental data and that apertureless microscopy measures optical properties, not just topography

Bridger, P. M.

Hill, C. J.

McGill, T. C.

Picus, G. S.

English

Caltech Authors - Main

APPLIED PHYSICS LETTERS VOLUME 75, NUMBER 25 20 DECEMBER 1999Scanning apertureless microscopy below the diffraction limit:
Comparisons between theory and experiment
C. J. Hill, P. M. Bridger, G. S. Picus, and T. C. McGilla)
Thomas J. Watson, Sr. Laboratory of Applied Physics, 128-95, California Institute of Technology,
Pasadena, California 91125
~Received 23 April 1999; accepted for publication 27 October 1999!
The exact nature of the signal in scanning apertureless microscopy techniques is the subject of much
debate. We have sought to resolve this controversy by carrying out simulations and experiments on
the same structures. Simulations of a model of tip–sample coupling are shown to exhibit features
that are in agreement with experimental observations at dimensions below the diffraction limit. The
simulation of the optical imaging process is carried out using atomic force microscope data as a
topographical template and a tip–sample dipole coupling model as the source of optical signal. The
simulations show a number of key fingerprints including a dependence on the polarization of the
external laser source, the size of the tip, and index of refraction of the sample being imaged. The
experimental results are found to be in agreement with many of the features of the simulations. We
conclude that the results of the dipole coupling theory agree qualitatively with experimental data and
that apertureless microscopy measures optical properties, not just topography. © 1999 American
Institute of Physics. @S0003-6951~99!02451-1#The attainment of the goal of imaging structures on the
near-atomic scale could revolutionize chemistry, biology,
and condensed matter physics. To this end, many imaging
techniques have been developed which claim to measure op-
tical properties at resolutions well below the classical diffrac-
tion limit for the illuminating wavelength. One of the most
promising of these is the scanning apertureless microscope
~SAM! technique pioneered by Wickramasinghe.1,2 Yet, as is
often true with the proximal probe techniques, there have
been a number of questions about what exactly is measured.
Some of the controversy centers around whether or not one
can separate information that is topographical in nature from
that which is optical in any near-field imaging technique.3 In
this letter, we present both simulations and experiment which
show that the technique measures optical properties of the
sample not accessible by a straightforward atomic force mi-
croscope ~AFM! measurement.
The experimental setup upon which the analysis is based
consists of a Digital Instruments Bioscope AFM operating in
tapping mode, with the AFM tip illuminated by an external
HeNe laser source through the camera port of a Nikon Dia-
phot 200 which forms the base of the bioscope. The signal
scattered off of the tip is collected and then filtered by a
lock-in amplifier with the tip oscillation frequency as a ref-
erence. This technique allows the simultaneous measurement
of sample topography with the AFM as well as information
that is ostensibly optical in nature with the SAM. A simpli-
fied schematic of the experimental setup is shown in Fig. 1.
An in-depth discussion of the experimental technique can be
found in the paper by Bridger.4
The optical image is the direct measurement of the in-
tensity of the radiation scattered by the AFM tip at the os-
cillation frequency. In our simulations we model the AFM
tip as a radiating dipole, where the expression for the far-
a!Electronic mail: tcm@ssdp.caltech.edu4020003-6951/99/75(25)/4022/3/$15.00
Downloaded 03 Apr 2006 to 131.215.225.171. Redistribution subject tfield intensity pattern produced by such a dipole is
I t5
ce0k4
~4pe0!2d2
^uptu2&sin2 f , ~1!
where I t is the intensity, pt is the dipole moment of the tip, d
is the distance to the detector, k is the wave number of the
radiation, c is the speed of light, e0 is the permittivity of free
space, and f is the angle between the vector from the tip to
the detector and the dipole moment of the tip.5 The term in
the above equation that contains optical information about
the sample is pt , the dipole moment of the tip, which is
given by
pt54pe0a t~Elaser1Es!, ~2!
where a t is the polarizability of the tip. The total field inci-
dent on the tip is the sum of the laser field Elaser and the
sample’s field Es , therefore, it is necessary to calculate the
very near field of the sample in order to determine the far-
field radiation pattern produced by the tip.
For simplicity, we model the features being imaged as
dielectric nanospheres with an induced dipole moment
which, to first order, is ps54pe0asElaser , where all of the
symbols are the same as before except that they refer to the
FIG. 1. Schematic of experimental setup. The inset gives a simplified view
of the interaction geometry.2 © 1999 American Institute of Physics
o AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp
4023Appl. Phys. Lett., Vol. 75, No. 25, 20 December 1999 Hill et al.sample instead of the tip. The value of the polarizability as is
dependent on the structure of the sample and the wavelength
of the external laser, and for spheres is expressed as
as5
es /e021
es /e012
Rs
3
, ~3!
where Rs is the radius and es is the dielectric constant of the
sphere.5 The dependence on the index of refraction is con-
tained in es , since n5Aes. The full expression for the near
FIG. 2. ~a! AFM and ~b! SAM ~random source polarization! images of two
adjacent 50 nm polystyrene nanospheres.
FIG. 3. Simulated images reconstructed from the AFM data of Fig. 2 as-
suming R tip510 nm, index n51.6, and the external source polarization
along the direction indicated by the arrow. ~a!,~b! polarizations dependence;
~c! R tip515 nm; ~d! R tip530 nm; ~e! Left bead n51.1; and ~f! Left bead
n54.0. White indicates highest intensity.
Downloaded 03 Apr 2006 to 131.215.225.171. Redistribution subject tfield of the sample, accurate to first order in the external field
Elaser cos vt, and taking into account the finite dimensions of
the dipole, is
Es5
asuElaseru
2Rs
3 S F ~R2cos u!cos vt2d13/2
2
~R1cos u!cos vt1
d2
3/2 2
vRs sin vt2
cd1
2
vRs sin vt1
cd2 G eˆ r
1sin uFcos vt2d13/2 1 cos vt1d23/2 2 vRs sin vt2cd1
2
vRs sin vt1
cd2 G eˆuD , ~4!
where r is the distance between the center of the sample and
the observation point, u is the angle between the sample’s
dipole moment and the vector locating the observation point,
v is the angular frequency of the external laser, t is time,
d6511R262R cos u, t65t2Rsd6
1/2/c , and R5r/Rs . This
near field, Es , changes the induced dipole moment of the
AFM tip and effectively modulates the scattered intensity
measured at the detector as the AFM tip scans across the
sample. In this first-order treatment the effect of the tip on
the sample field is ignored. The near field of the sample
dipole will add destructively with the external field inducing
FIG. 4. Experimental data on 200 nm polystyrene beads. ~a! AFM image;
~b! SAM image with external laser composed of mixed polarizations; and
~c!–~f! SAM images with the external laser linearly polarized in the direc-
tion indicated by the white arrow.o AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp
4024 Appl. Phys. Lett., Vol. 75, No. 25, 20 December 1999 Hill et al.the tip dipole when the tip is directly above the sample. The
fields will add constructively when the tip is on either side of
the sample along the dipole axis, although this effect is more
localized and, therefore, presumably more difficult to ob-
serve than the effects due to destructive interference.
We have imaged polystyrene nanospheres of diameters
ranging from 30 to 200 nm. The AFM image in Fig. 2 is of
two adjacent 50 nm diam polystyrene beads on glass. Also
shown is apertureless data taken with the illuminating laser
randomly polarized. In Fig. 3 we present the results of the
simulations which show the important features of the dipole
model. The AFM image is used as a topographical template
for the simulations since the dipole field influencing the tip
will be a function of the center-to-center separation between
tip and sample. To the topography we add the locations and
other pertinent information about the sample dipoles induced
by the external laser polarization. With this information we
can determine the scattered intensity at any point to construct
the final image. Unless otherwise stated, all simulations use
the parameters R tip510 nm, nsample51.6, l laser5632.8 nm.
The scales in the simulations are normalized to unity for the
level of background scattering off of the AFM tip in the
absence of modulation due to the sample’s electric field. All
are linear plots of the normalized intensity with full scale
from 0.70 ~black! to 1.8 ~white!. Values outside this intensity
range are clipped to the minimum or maximum value accord-
ingly. Figures 3~a! and 3~b! show how the near field of the
dipole orients itself with the polarization of the external laser
source. Figures 3~a! and 3~c! suggest that an enhancement in
resolution could be obtained with the proper orientation of
the source polarization. Our initial experiments have shown a
definite dependence on the polarization of the external laser
source. Figures 3~c! and 3~d! show how edge sensitivity de-
creases with increasing tip size. Although a larger tip radius
means a larger scattering cross section, and hence, more sig-
nal, the change in signal intensity with respect to the back-
ground scattering is reduced with a larger tip. Figures 3~e!
and 3~f! show how the image intensity changes for featuresDownloaded 03 Apr 2006 to 131.215.225.171. Redistribution subject twith different indices of refraction. These images show
clearly that the dipole model can image differences in optical
properties.
Experimental images with polarization dependent fea-
tures are shown in Fig. 4. The samples being imaged are two
200 nm polystyrene spheres adsorbed on a glass substrate.
The optical images in Figs. 4~b!–4~f! show the lower inten-
sities above the sample due to destructive interference be-
tween the near field of the sample and the external laser
shown in the simulations. As the direction of linear polariza-
tion of the external laser is changed, stark differences in
contrast are evident. For example, the bright area in the im-
age in Fig. 4~d! is no longer apparent with the orthogonal
polarization shown in Fig. 4~f!, resembling the polarization
dependence shown in the simulations in Figs. 3~a! and 3~b!.
In conclusion, we have used a simple dipole–dipole
scattering model to demonstrate that our apertureless tech-
nique can, in theory, image information about a sample that
is indeed optical in nature. Our model contains no fitting
parameters; all physical constants used are well known or
easily measured. Initial experiments show a strong polariza-
tion dependence in the images, as well as destructive inter-
ference lowering the signal intensity when the tip is above
the sample. We conclude that many features of the dipole
coupling model are in qualitative agreement with experimen-
tal data.
This work was supported under Office of Naval Re-
search Contract No. N00014-98-1-0567 and by a grant from
Hughes Research Laboratories, Inc., LLC.
1 H. K. Wickramasinghe and C. C. Williams, Apertureless Near Field Op-
tical Microscope, U.S. Patent No. 4,947,034 ~April 28, 1989!.
2 F. Zenhausern, M. P. O’Boyle, and H. K. Wickramasinghe, Appl. Phys.
Lett. 65, 1623 ~1994!.
3 B. Hecht, H. Bielefeldt, Y. Inouye, L. Novotny, and D. W. Pohl, J. Appl.
Phys. 81, 2492 ~1997!.
4 P. M. Bridger and T. C. McGill, Opt. Lett. 24, 1005 ~1999!.
5 J. D. Jackson, Classical Electrodynamics, 2nd ed. ~Wiley, New York,
1975!.o AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp


Scanning apertureless microscopy below the diffraction limit: Comparisons between theory and experiment

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Scanning apertureless microscopy below the diffraction limit: Comparisons between theory and experiment

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