Confining light to deep subwavelength dimensions to enable optical nanopatterning.
ABSTRACT In the past, the formation of microscale patterns in the far field by light has been diffractively limited in resolution to roughly half the wavelength of the radiation used. Here, we demonstrate lines with an average width of 36 nanometers (nm), about one-tenth the illuminating wavelength lambda1 = 325 nm, made by applying a film of thermally stable photochromic molecules above the photoresist. Simultaneous irradiation of a second wavelength, lambda2 = 633 nm, renders the film opaque to the writing beam except at nodal sites, which let through a spatially constrained segment of incident lambda1 light, allowing subdiffractional patterning. The same experiment also demonstrates a patterning of periodic lines whose widths are about one-tenth their period, which is far smaller than what has been thought to be lithographically possible.
Conference Paper: Photoinhibited superresolution lithography: overcoming chemical blur[Show abstract] [Hide abstract]
ABSTRACT: Photoinhibited superressolution (PInSR) lithography is a two--color, one-photon scheme that promises high throughput far-field patterning t deep subwwabvelength scales. Previous work ha shown that the technique susceptible to blurring from active species diffusion, an issue which we have recently overcome with the use of a low-diffiusivity methrylate resist. Here we present out first clear demonstration of superresolution, showing feature spacing 3X better than the 0.2 NA diffraction limit.SPIE Advanced Lithography; 03/2014
- [Show abstract] [Hide abstract]
ABSTRACT: Temperature dependencies of cyclization and cycloreversion processes of a photochromic diarylethene derivative, 1,2-bis(2-methyl-3-benzothienyl)perfluorocyclopentene (BT), were investigated by steady-state spectroscopy and femtosecond laser photolysis methods. Steady-state measurements revealed that the cyclization reaction quantum yield and the fraction of the conformer with C2v symmetry favorable for the cyclization (antiparallel, AP conformer) were independent of temperature in the range of 253–343 K. These results indicated that the cyclization reaction of the AP conformer in the open-ring isomer in the excited state had no apparent temperature dependence and suggested that the fate of the excited AP conformer in the open-ring isomer, such as cyclization or deactivation to the ground state, was determined at the conical intersection. On the other hand, the cycloreversion reaction was dependent on the temperature; the reaction quantum yield increased together with a decrease in the lifetime of the excited state of the closed-ring isomer with increasing temperature. On the basis of the adiabatic energy surface for the reaction profiles, it was deduced that the rapid deactivation into the ground state took place in the S1 state in competition with the activated pathways leading to the conical intersection where the cycloreversion occurred.The Journal of Physical Chemistry C 02/2012; 116(7):4862–4869. · 4.84 Impact Factor
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ABSTRACT: In a large-scale quantum computer, the cost of communications will dominate the performance and resource requirements, place many severe demands on the technology, and constrain the architecture. Unfortunately, fault-tolerant computers based entirely on photons with probabilistic gates, though equipped with "built-in" communication, have very large resource overheads; likewise, computers with reliable probabilistic gates between photons or quantum memories may lack sufficient communication resources in the presence of realistic optical losses. Here, we consider a compromise architecture, in which semiconductor spin qubits are coupled by bright laser pulses through nanophotonic waveguides and cavities using a combination of frequent probabilistic and sparse determinstic entanglement mechanisms. The large photonic resource requirements incurred by the use of probabilistic gates for quantum communication are mitigated in part by the potential high-speed operation of the semiconductor nanophotonic hardware. The system employs topological cluster-state quantum error correction for achieving fault-tolerance. Our results suggest that such an architecture/technology combination has the potential to scale to a system capable of attacking classically intractable computational problems.International Journal of Quantum Information 11/2011; 08(01n02). · 0.99 Impact Factor
, 917 (2009);
et al.Trisha L. Andrew,
to Enable Optical Nanopatterning
Confining Light to Deep Subwavelength Dimensions
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tion times was performed by using a photo-
mask lithographic approach as shown in Fig. 3C,
where resin on a transparent substrate is
irradiated uniformly through the substrate with
the initiating wavelength while being irradiated
by the inhibiting wavelength through a photo-
and becomes insoluble, whereas the unmasked
region remains liquid and is readily washed away.
The fabrication of complex, 3D microstruc-
tures requires that the doughnut of inhibiting
radicals created spatially to refine the polymeri-
zation region be translated in conjunction with
the writing spot without leaving a termination
trail. This desired behavior in turn requires that
absence of the photoinhibition irradiation wave-
length. The rapid cessation of photoinhibition in
the current system is demonstrated in Fig. 3D.
During UV irradiation periods, the polymeriza-
tion slowed dramatically, as evidenced by the
reduced rate of increase in the storage and loss
the polymerization rate underwent an immediate
and marked increase.
To demonstrate that this polymerization rate
control is useful to initiate polymerization below
the optical diffraction limit, as predicted by Fig.
1D, we implemented the direct-write lithography
scheme shown in Fig. 1A. Polymer voxels were
created on a glass substrate and imaged by
scanning electron microscopy (SEM) after sol-
vent wash, as shown in Fig. 4A. As predicted in
Fig. 1D, increasing the UV power, and therefore
the photoinhibition rate, of the GL mode
progressively reduces the voxel diameter in a
controllable manner. In the sequence shown, the
constant-power, 1.3-mm (full width to 1/e2) blue
focus has written polymer voxels with diameter
varying from 3.6 mm with no UV down to 200
nm for strong UV inhibition at 100 mW UV
irradiation power. This resolution is typical of
two-photon initiation using ~1.4 numerical
aperture (NA) lenses (2, 5) with aberration-
limited depth ranges of tens of mm; the much
lower NA demonstrated here enables mm-scale
thicknesses. In Fig. 4B we show the ability to
create 110-nm voxels full width and 65 nm full
width at half maximum by using a 1.3-NA lens
and measured by SEM, approaching the size of
the smallest features produced with use of two-
ing under these conditions with the superimposed
Gaussian/GL irradiation scheme is shown in Fig.
of voxel diameters using this irradiation scheme
could be effected in other materials such as those
containing reversibly photodimerizable functional-
ities, where dimers are created by irradiation at one
wavelength and cleaved by irradiation at a
different wavelength; however, photoreversibil-
ity precludes translation of a writing spot and
disallows fabrication of dense, 3D structures.
Two-photon photopolymerization has been
described as the only microprocessing approach
with intrinsic 3D fabrication capability (18).
produces confinement of the polymerized region
along only two axes, manipulation of the photo-
inhibiting wavelength into a bottle beam profile
(19) would induce confinement along the third
axis, thus allowing fabrication of 3D structures
with sub–100-nm isotropic resolution. Because
single-photon absorption cross sections are often
sections, this photoinitiation-photoinhibition sys-
tem facilitates the use of inexpensive continuous
wave (CW) diode lasers and very high write
velocities. Thus, this single-photon approach to
nanolithography uses dramatically cheaper hard-
ware and scales to much higher throughput.
References and Notes
1. A. C. Sullivan, M. W. Grabowski, R. R. McLeod, Appl. Opt.
46, 295 (2007).
2. S. Kawata, H.-B. Sun, T. Tanaka, K. Takada, Nature 412,
3. B. H. Cumpston et al., Nature 398, 51 (1999).
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8. K. Ichimura, M. Sakuragi, J. Polym. Sci. Polym. Lett. Ed.
26, 185 (1988).
9. S.-K. Lee, D. C. Neckers, Chem. Mater. 3, 852 (1991).
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J. Appl. Phys. 63, 4841 (1988).
12. S. K. Soh, D. C. Sundberg, J. Polym. Sci. Polym. Chem.
Ed. 20, 1299 (1982).
13. G. Donnert et al., Proc. Natl. Acad. Sci. U.S.A. 103,
14. Materials and methods and a study examining the effect
of exposure time on polymerized feature size are detailed
in supporting material available on Science Online.
15. P. J. Flory, in Principles of Polymer Chemistry
(Cornell Univ. Press, Ithaca, NY, 1953).
16. L. G. Lovell, B. J. Elliott, J. R. Brown, C. N. Bowman,
Polymer 42, 421 (2001).
17. F. Chambon, H. H. Winter, J. Rheol. 31, 683 (1987).
18. H. B. Sun, S. Kawata, in NMR - 3D Analysis -
Photopolymerization (Springer, Berlin, 2004), vol. 170,
19. J. Arlt, M. J. Padgett, Opt. Lett. 25, 191 (2000).
20. Supported by NSF programs IIP-0750506, IIP-0822695,
and ECS-0636650, NIH grant DE10959, and the
University of Colorado Innovative Seed Grant Program.
A preliminary patent based on this technology has been
filed by T.F.S., A.C.S., C.N.B., and R.R.M.
Supporting Online Material
Materials and Methods
23 October 2008; accepted 24 March 2009
Published online 9 April 2009;
Include this information when citing this paper.
Confining Light to Deep
to Enable Optical Nanopatterning
Trisha L. Andrew,1Hsin-Yu Tsai,2,3Rajesh Menon3,4*
In the past, the formation of microscale patterns in the far field by light has been
diffractively limited in resolution to roughly half the wavelength of the radiation used.
Here, we demonstrate lines with an average width of 36 nanometers (nm), about
one-tenth the illuminating wavelength l1= 325 nm, made by applying a film of thermally
stable photochromic molecules above the photoresist. Simultaneous irradiation of a second
wavelength, l2= 633 nm, renders the film opaque to the writing beam except at nodal sites,
which let through a spatially constrained segment of incident l1light, allowing subdiffractional
patterning. The same experiment also demonstrates a patterning of periodic lines whose
widths are about one-tenth their period, which is far smaller than what has been thought to
be lithographically possible.
The far-field diffraction barrier limits the reso-
lution of optical systems to approximately half
ptical patterning is the primary enabler
of microscale devices. However, the
Achilles heel of optics is resolution.
the wavelength (1) and therefore restricts nano-
scale patterning at visible wavelengths. Scan-
ning electron beam patterning has thus become
the preferred method for fabricating nano-
structures. However, electrons are affected by
extraneous electromagnetic fields, limiting the
accuracy with which patterns can be placed
relative to one another (2). Furthermore, elec-
tron flux is limited by mutual repulsion effects,
constraining the patterning speed (3). The vac-
uum environment and electron lenses increase
system complexity and cost. Alternatively, the
diffraction barrier can be overcome in the optical
1Department of Chemistry, Massachusetts Institute of Tech-
nology (MIT), Cambridge, MA 02139, USA.2Department of
Electrical Engineering and Computer Science, MIT, Cam-
bridge, MA 02139, USA.3Research Laboratory of Electronics,
MIT, Cambridge, MA 02139, USA.4LumArray, Somerville, MA
*To whom correspondence should be addressed. E-mail:
VOL 32415 MAY 2009
on May 15, 2009
near field (4). The high spatial frequencies
present in the optical near field are evanescent,
and hence the recording medium needs to be
placed at a precisely controlled nanometric dis-
tance from the source of the optical near field
(5–7). By placing a prepatterned photomask in
intimate contact with the photoresist, the op-
tical near field may be recorded (8). In this
case, high resolution is achieved at the expense
of an inflexible and costly photomask and the
high probability of contamination of the con-
tacted surfaces. An alternative approach scans
one or many nanoscale tips in close proximity
to the sample (9). Precisely maintaining the
gap between the tip (or tips) and the sample is
problematic, especially when patterning over large
areas or with multiple near-field probes (10).
Plasmonic lenses can alleviate some of these
problems (11), but they still require gaps of
<100 nm and nanometric gap control (12, 13).
To overcome these limitations, we used a
thin photochromic film on top of the record-
ing photoresist layer. The molecules chosen to
comprise the film adopt two isomeric forms
that interconvert on respective absorptions of
light at ultraviolet (l1) and visible (l2) wave-
lengths (14). We simultaneously applied both
colors in an interference pattern that overlaps
peaks at l1with nodes at l2. Absorption at
l1generates the isomer transparent at that wave-
length, but regions exposed to l2revert to the
initial isomer and continue to absorb at l1,
protecting the photoresist. Only at the l2nodes
does a stable transparent aperture form (Fig.
1A) (15). Photons at l1penetrate this aperture,
forming a nanoscale writing beam that can
pattern the underlying photoresist. The size of
the aperture decreases as the ratio of the in-
tensity at l2with respect to that at l1increases
(15, 16). This technique, which we refer to as
absorbance modulation, can therefore confine
light to spatial dimensions far smaller than the
Furthermore, because the photochromic mol-
ecules recover their initial opaque state, spatial
periods smaller than the incident wavelengths
can be achieved by repeated patterning (17). In
Fig. 1B, we plot the simulated full width at
half maximum (FWHM) of the transmitted
light at l1as a function of the ratio of in-
tensities at the two wavelengths, illustrating
that the transmitted light is spatially confined
to dimensions far below the wavelength. In
other words, optical near fields are generated
without bringing a physical probe into close
proximity with the sample. In the past, we
used an interferometric setup to illuminate an
azobenzene polymer–based photochromic film
with a standing wave at l2and uniform illumi-
nation at l1(16). Although linewidths as small
as l1/4 were demonstrated, the thermal in-
stability of the azobenzene polymer as well as
the nonnegligible sensitivity of the underlying
photoresist to l2prevented further scaling below
For optimum performance, it is essential
that the photochromic molecules are thermally
stable; otherwise, the size of the writing beam
becomes dependent on the absolute intensities
rather than their ratio alone. If the photochro-
mic molecule in the transparent state is ther-
mally unstable, then at low-l1intensities the
thermal back-reaction overwhelms the forward
(opaque-to-transparent) reaction, essentially clos-
ing the aperture. The FWHM of the resulting
beam shows a minimum. This is illustrated in
Fig. 1B, in which the photochromic parame-
ters of 1,2-bis(5,5′-dimethyl-2,2’-bithiophen-yl)
perfluorocyclopent-1-ene (compound 1) (Fig.
1C) were assumed (18). A thermal rate constant
of 5 × 10−4s−1was assumed for the dashed
curve. The incident illumination is modeled as
standing waves with a period of 350 nm (l2=
633 nm) and 170 nm (l1 = 325 nm). Both
curves were calculated by decreasing the peak
Fig. 1. The scheme of absorbance modulation. (A) The photochromic layer turns transparent upon
exposure to l1and opaque upon exposure to l2. When illuminated with a node at l2coincident
with a peak at l1, a subwavelength transparent region (or aperture) is formed through which
photons at l1penetrate, forming a nanoscale optical writing beam. (B) FWHM of the intensity
distribution at l1directly beneath the photochromic layer as a function of the ratio of the peak
intensities at the two wavelengths. When the photochromic molecules are thermally stable [the
thermal rate constant (k) = 0], the size of the writing beam decreases monotonically, far below the
wavelength. However, when a thermal instability is present (k = 5 × 10−4s−1), the smallest beam
size is limited, as shown by the dashed line. (C) Structures of the open- and closed-ring isomers of
compound 1. (D) Absorbance spectra of compound 1 in the open and closed forms in hexane. e is
the decadic molar absorptivity.
15 MAY 2009VOL 324
on May 15, 2009
intensity of the l1standing wave while main-
taining the peak intensity of the l2standing
wave equal to 1 kW m–2and repeating the
numerical simulation for each intensity ratio.
Although this deleterious effect can be over-
come by using higher intensities at both wave-
lengths while maintaining the required intensity
ratio, it is highly desirable to achieve nanoscale
resolution at low intensities. For this reason, we
turned our attention to thermally stable classes
of photochromes, such as fulgides (19) and
diarylethenes (20). In both of these classes of
photochromes, photoinduced electrocyclic rear-
rangements transform a colorless (UV-absorbing)
triene system into a highly colored cyclohexadiene
photoproduct and vice versa. Because covalent
bonds are either formed or broken during the
photoisomerization process, conversion between
the open-ring and closed-ring isomers is primar-
ily photoinitiated, and the thermal contribution
to this isomerization is negligible.
Initial investigations of furyl fulgide (21)
as the active component in the absorbance-
modulation layer (AML) revealed a suscepti-
bility to photodegradation that significantly
reduced the concentration of this photochrome
in the AML with prolonged irradiation. Cursory
analysis of some fulgides reported in the chem-
ical literature confirmed that many fulgides dis-
play a lack of fatigue resistance because of
photooxidation of either their triene or hetero-
cyclic moieties (19). Therefore, we explored a
comparatively photostable class of thiophene-
substituted fluorinated cyclopentenes as poten-
tial photochromes for absorbance modulation.
The perfluorinated bridge in these systems pre-
vents photooxidation of the active triene moiety
and suppresses competing nonproductive isom-
erization pathways. Specifically, compound 1
(Fig. 1C) was chosen for use in the AML be-
cause it displayed an absorption band centered
at 313 nm in the open state and one centered at
582 nm in the closed state (Fig. 1D). These spec-
tral features allowed the use of the 325-nm line
of the helium-cadmium laser and the 633-nm
line of the helium-neon laser for the writing and
the confining beams, respectively. High inten-
sities could be applied at the nodal wavelength
l2because 633-nm light has no effect on most
Pertinent photophysical constants, such as
absorption coefficients and photoreaction quan-
tum yields, were measured for compound 1 at
room temperature in hexane solution [table S1
and supporting online material (SOM) text].
In order to spin-cast the photochromic layer,
we used a 30 mg ml–1solution of poly(methyl
methacrylate) (PMMA) in anisole doped with
92 weight percent compound 1 (with respect
to PMMA) (20). The photochromic layer was to
be placed atop a photoresist layer in order to
record the transmitted light at l1. The solvent
for the PMMA matrix, anisole, distorts the de-
velopment rate of the photoresist. Therefore, a
barrier layer of polyvinyl alcohol (PVA) was
placed in between the two layers. The barrier
layer also prevents any interdiffusion between
the two layers. Because the high–spatial fre-
quency content of the nanoscale writing beam is
evanescent, it is important to keep the thickness
of the PVA layer as small as possible.
In order to illustrate the effect of the thick-
ness of the PVA layer on the linewidth of the
pattern, we simulated the transmission of light
through a subwavelength aperture in a metal
Fig. 2. Effectof barrier-layer thicknesson the patterned linewidth. (A)
FDTD simulation of light transmission through a one-dimensional
subwavelength aperture. The incident light was assumed to be a
was placed in air. (B) Cross sections of the normalized intensity
distributions at different distances from the aperture. The evanescent
high spatial frequencies die away from the aperture, and the linewidth
(defined by the FWHM) increases.
Fig. 3. Scanning elec-
tron micrographs of cross
sections of exposed and
developed lines in pho-
toresist in which the PVA
barrier layer thickness was
(A) 25 nm and (B) 8 nm,
respectively. The thinner the
PVA layer is, the straighter
is the resist sidewall and
In both cases, the period
of the lines is 350 nm,
corresponding to the pe-
riod of the l2standing wave.
VOL 324 15 MAY 2009
on May 15, 2009
film using custom software that implements the
finite-difference time-domain (FDTD) method
(22). When a subwavelength aperture is illumi-
nated, the transmitted light is primarily composed
of evanescent high–spatial frequency compo-
nents. These components decay exponentially
away from the aperture, increasing the FWHM
of the transmitted light. The illumination of a
one-dimensional aperture with a width of 75 nm
was simulated with a plane wave with a wave-
length of 325 nm, as shown in the schematic in
Fig. 2A. The electric field of the incident wave
was polarized normal to the plane of the figure.
The time-averaged intensity of the scattered light
was calculated at steady state. Cross sections of
the normalized intensity distribution in planes
parallel to the aperture at varying distances from
the aperture were computed and plotted in Fig.
2B. Clearly, the transmitted light is substantially
broadened with distance from the aperture.
Furthermore, the peak intensity at the center of
the line also falls exponentially with distance
from the aperture.
These theoretical predictions were qualita-
tively confirmed by our experimental results.
Figure 3, A and B, shows scanning electron
micrographs of the cross sections of exposed
and developed photoresist with PVA barrier
layer thicknesses of 25 nm and 8 nm, respec-
tively. With the 25 nm layer, the exposed line
exhibits considerable broadening with depth into
the photoresist. The sidewall profile bears a quali-
tative resemblance to the intensity contours in
Fig. 2A. With the thinner PVA, this linewidth
broadening is noticeably curtailed, and the pho-
toresist exhibits vertical sidewalls. This result
also suggests that an ultrathin photoresist layer
may be necessary to faithfully record the high
spatial frequencies in the near field, which is in
agreement with earlier work (23).
To minimize this effect of line broadening,
we used a PVA film thickness of 8 nm, which
was found to be sufficient to protect the photo-
resist from the solvent for the photochromic
layer. Samples consisted of a silicon substrate
spin-coated with 200 nm of anti-reflection coat-
ing, 200 nm of photoresist, 8 nm of PVA, and
410 nm of the photochromic layer. After expo-
sure, the samples were rinsed in de-ionized water
in a sonicator for about 5 min, which removed
the PVA layer as well as the photochromic over-
layer. The photoresist was baked on a hotplate at
120°C for 90 s and developed in 0.26 N tetra-
methyl ammonium hydroxide for 60 s. The re-
sulting patterns were inspected in a scanning
electron microscope after sputter-coating them
with ~2 nm of a palladium/gold alloy.
The exposure system was a modified Lloyd’s-
mirror interferometer (fig. S5), consisting of a
mirror at right angles to a vacuum chuck that
held the sample. This configuration was illumi-
nated at l1= 325 nm and l2= 633 nm. The
angles of incidence of the two wavelengths were
adjusted so that the resulting standing waves on
the sample had periods of 350 nm at l2= 633 nm
and 170 nm at l1= 325 nm (18). As illustrated
in Fig. 4A, the nodes of the l2standing wave
approximately coincide with every other peak of
the l1standing wave. Photokinetic simulation
using the extracted photochromic parameters re-
veal that the transmitted light at l1is substan-
tially narrower than the diffraction limit. The
scanning electron micrograph in Fig. 4B shows
that the average width of the lines recorded in
the photoresist was 36 nm close to one tenth of
l1. Furthermore, the narrow lines were spaced
by 350 nm, which corresponds to the period of
the l2standing wave. We separately confirmed
that the photoresist is not sensitive to the l2
photons. Those l1peaks that coincide with the
l2peaks are suppressed beyond the photochro-
mic layer. We confirmed this experimentally by
recording lines at lower intensity ratios and ex-
amining their cross sections in the scanning
electron microscope (fig. S6). In our current set-
up, in order to maintain high intensity in the
l2peaks, it was necessary to forgo spatial fil-
tering of the l2illumination. High-frequency
noise therefore persisted in the l2 standing
wave, causing line edge roughness as well as
the line-width variation in the photoresist pat-
terns. Nevertheless, these results clearly demonstrate
the feasibility of deep subwavelength localiza-
tion of light by using absorbance modulation.
Furthermore, these results also demonstrate
the feasibility of patterning periodic lines far
smaller than their spatial period. Because the ab-
sorbance of the AML is reversible, interspersed
multiple exposures could pattern lines spaced
apart by a distance far smaller than the far-field
diffraction limit of the optical system. Although
the current demonstration utilized one-dimensional
standing waves, we anticipate straightforward
extension to two-dimensional peaks and nodes,
which can be generated with diffractive micro-
optics (24, 25). Furthermore, such nanoscale
optical beams may also be useful for optical nano-
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λ1 = 325nm
λ2 = 633nm
direction of propagation
Fig. 4. Deep subwavelength patterning using absorbance modulation. (A) The photochromic layer is
illuminated by two overlapping standing waves with periods of 350 nm (l2= 633 nm) and 170 nm (l1=
325 nm), respectively. Simulating the transmitted light at l1supported narrow lines where the peaks of
the l1standing wave coincided with the nodes of the l2standing wave. (B) Scanning electron micrograph
of lines exposed in photoresist. Although the photoresist is underexposed, the lines represent a recording
of the aerial image that is consistent with simulation.
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on May 15, 2009
25. H.-Y. Tsai, H. I. Smith, R. Menon, Opt. Lett. 33, 2916
26. S. W. Hell, Nat. Biotechnol. 21, 1347 (2003).
27. We thank F. Stellacci and T. Swager for advice on
synthesis of the photochromic molecules, H. Koh for the
ellipsometric measurements, T. O’Reilly for assistance with
the Lloyd’s-mirror interferometer, and H. Smith for
suggestions on the manuscript. T.L.A. was partially funded
by a subcontract (6916866) from LumArray. H.-Y.T. was
partially funded by an ignition grant from the MIT
Deshpande Center for Technological Innovation. R.M.
was partially funded by a Defense Advanced Research
Projects Agency Small Business Innovation Research
award (W31P4Q-05-C-R156). Three patents have been
filed through MIT based on the work presented herein.
Supporting Online Material
Materials and Methods
Figs. S1 to S6
27 October 2008; accepted 24 February 2009
Published online 9 April 2009;
Include this information when citing this paper.
Size and Shape of Saturn's
Howard A. Zebker,1* Bryan Stiles,2Scott Hensley,2Ralph Lorenz,3
Randolph L. Kirk,4Jonathan Lunine5
Cassini observations show that Saturn’s moon Titan is slightly oblate. A fourth-order spherical
harmonic expansion yields north polar, south polar, and mean equatorial radii of 2574.32 T
0.05 kilometers (km), 2574.36 T 0.03 km, and 2574.91 T 0.11 km, respectively; its mean radius is
2574.73 T 0.09 km. Titan’s shape approximates a hydrostatic, synchronously rotating triaxial
ellipsoid but is best fit by such a body orbiting closer to Saturn than Titan presently does.
Titan’s lack of high relief implies that most—but not all—of the surface features observed with the
Cassini imaging subsystem and synthetic aperture radar are uncorrelated with topography and
elevation. Titan’s depressed polar radii suggest that a constant geopotential hydrocarbon table could
explain the confinement of the hydrocarbon lakes to high latitudes.
turn surface elevation data from a nadir-pointing
radar altimeter (1) and a multiple-beam synthetic
aperture radar (SAR) imaging system (2, 3). We
have used these radar instrument modes to
estimate the surface elevation by measuring the
time delay of the altimeter echoes and the pre-
cise radar look angle to points on the surface by
processing the multibeam SAR images with
monopulse methods (Fig. 1) (4).
In the radar altimeter mode, the instrument
transmits energy nearly vertically to the plane-
tary surface below and records the received echo
as a function of time; we corrected the data for
biases due to mis-pointing errors (1). The Cassini
altimetry data products record both the leading-
edge location and the average delay of the return
echo, but we used the mean return in order to
estimate the mean surface height.
The SAR imaging system on Cassini com-
prises five parallel beams that produce a much
wider ground swath than would have been pos-
sible with the use of a single beam. Each beam
he Cassini spacecraft has been orbiting
Saturn for 4 years, observing Titan pe-
riodically. When close to Titan, it can re-
is time-shared in order to maintain a contiguous
swath on the ground (5, 6), so we sacrificed along-
track resolution, averaging, and signal-to-noise
ratio for the sake of the increased swath width.
This is the burst-mode or ScanSAR imaging con-
figuration, and it returns five overlapping obser-
vation swaths from the surface. The differencing
of power images from the overlapped sections
of adjacent beams forms an amplitude mono-
pulse system to measure the precise angle to a
given point on the ground (4, 7), which, combined
with knowledge of the spacecraft imaging ge-
ometry, yields a surface height measurement.
Hence, under this analysis, most of the SAR im-
aging passes also provide estimates of the ele-
vation at the beam overlap regions. Although
this method is more elaborate than altimetry, it
provides wider coverage because SAR imag-
ing is used more often. We used all possible
beam overlaps containing pixels sufficiently
bright that the intensity differences were mean-
ingful. The effective footprint of each measure-
ment is roughly the SAR resolution (0.5 km) in
the range direction and 10 km in the along-track
These techniques show that the poles of
Titan lie at lower elevations than the equator and
that the topography also varies longitudinally
(Fig. 1). Measurements in the polar regions yield
elevations of about –600 to –700 m, referenced
to a 2575-km-radius sphere, whereas Titan’s
1Departments of Geophysics and Electrical Engineering,
Stanford University, Stanford, CA 94305, USA.2Jet Propulsion
Laboratory (JPL), California Institute of Technology, 4800 Oak
Grove Drive, Pasadena, CA 91109, USA.
Laboratory, Johns Hopkins University, 11100 Johns Hopkins
Road, Laurel, MD 20723, USA.4U.S. Geological Survey, 2255
North Gemini Drive, Flagstaff, AZ 86001, USA.5Departments
of Planetary Science and Physics, University of Arizona,
Tucson, AZ 85721, USA.
*To whom correspondence should be addressed. E-mail:
West longitude (deg)
North latitude (deg)
Fig. 1. Titan elevations observed with altimeter and SAR monopulse radar modes, cylindrical projection,
displayed as deviation from an ideal 2575 km sphere located at Titan’s barycenter. Locations on the figure
give the latitude and west longitude of each measurement. Far more coverage is available from the
monopulse mode than from altimetry, but these data are not as accurate as the altimeter measurements.
VOL 32415 MAY 2009
on May 15, 2009
Supporting Online Material for
Confining Light to Deep Subwavelength Dimensions to Enable Optical
Trisha L. Andrew,1 Hsin-Yu Tsai,2,3 Rajesh Menon3,4*
*To whom correspondence should be addressed. E-mail: firstname.lastname@example.org
Published 9 April 2009 on Science Express
This PDF file includes:
Materials and Methods
Figs. S1 to S6
Supporting Online Material (SOM)
1. Sample preparation.
A silicon wafer was spin-coated with a solution of BarLi anti-reflection coating at 6000
rpm for 60 seconds and baked on a hot-plate at 175 degrees Celsius for 90 seconds to form
a 200nm layer. Then, the sample was spin-coated with the photoresist at 4000 rpm for 60s
and baked on a hot-plate at 90 degrees Celsius for 90 seconds to form a 200nm layer. The
photoresist was comprised of a blend of a chemically amplified positive-tone photoresist,
TDUR-P308 (Tokyo Ohka Kogyo Co. Ltd.) and a photoacid generator, CGI-725 (CIBA
Specialty Chemicals, Inc.) in the ratio of approximately 5:1 by weight. Then, the sample
was spin-coated with a solution of poly-vinyl alcohol in water (5.7μg/ml) at 6000 rpm and
air-dried for 5 minutes to form a film of thickness 8nm. Finally, the sample was spin-coated
with the PMMA solution doped with the photochromic molecules at 500rpm and air-dried
for 5 minutes to form a layer of thickness 410nm. The results shown in Fig. 3 were
conducted in the same manner, except that the photoresist comprised of a blend of TDUR-
P308 (Tokyo Ohka Kogyo Co. Ltd.) and a photoacid generator, Irgacure PAG-103 (CIBA
Specialty Chemicals, Inc.) in the ratio 20:1 by weight. The thickness of this photoresist
layer was 73nm.
2. Photochrome Synthesis and Characterization
Furyl fulgide was synthesized according to a literature procedure (S1). 4-Bromo-5,5’-
dimethyl-2,2’-bithiophene was synthesized via a conventional Negishi cross-coupling
reaction. Compound 1o was then synthesized from this starting material as shown in
Scheme S1 following a literature procedure (S2) and isolated in 30% yield.
Scheme S1: Synthesis of 1o
1o was recrystallized from pentanes and stored in the dark to exclude formation of
1c. The 1H-NMR and 13C-NMR spectra and HRMS (ESI) of the photochrome obtained in
our hands matched those reported in the literature (S3). Compound 1c was synthesized by
irradiating a degassed solution ofcompound 1o in hexanes for 30 minutes at 313 nm and by
purifying the resulting reaction mixture via high performance liquid chromatography
Ultraviolet-visible absorption spectra were measured with an Agilent 8453 diode
array spectrophotometer and corrected for background signal with either a solvent-filled
cuvette (solutions) or a microscope slide (films).
The decadic molar absorption coefficients of the open and closed forms of
compound 1 at 325 (λ1) and 633 nm (λ2) (ε1open, ε1closed, ε 2open, ε 2closed) were calculated
using the integrated form of the Beer-Lambert Law (α = εlc, where α is absorbance, l is the
optical path length and c is the concentration) as follows. A known quantity of pure
compound 1 (open) and compound 1 (closed) was dissolved in hexanes in the dark.
Approximately 3 mL of these two solutions were placed in quartz cuvettes with an optical
path length of 1 cm and the absorbance spectrum recorded. The absorbance values thus
obtained at 313, 325 and 633 nm were used in the integrated Beer-Lambert equation to
calculate the experimental absorption coefficients.
The quantum yield of cyclization was defined as the moles compound 1 (closed)
formed per mole photon absorbed by the sample. Cyclization quantum yields were obtained
by irradiating hexane solutions (of known concentrations) of compound 1 (open) at 313 or
325 nm and monitoring the change in absorbance at 633 nm at 5s intervals. Fig. S1(a)
shows the absorbance profile of the photocylization reaction recorded every 5 seconds. A
500 W Xenon arc lamp was used as the light source and the irradiation wavelength isolated
by passing the light through two monochromators. The irradiation density was measured
using a power meter and this value converted to moles photons sec-1 using Einstein’s
equation (Emol = NAhν, where NA is Avogadro’s number). The moles of photons absorbed
by the compound 1 sample was calculated from the irradiation duration and corrected with
the α313 or α325 of the solution immediately prior to irradiation. The moles of compound 1
(closed) formed were calculated from α633 using the integrated Beer-Lambert equation and
the ε2closed obtained above.
The quantum yield of ring-closing was defined as the moles compound 1 (open)
formed per mole of photon absorbed. Ring-opening quantum yields were obtained in a
similar fashion to cyclization quantum yields, by irradiating solutions of compound 1
(closed) with 633 nm light and monitoring the change in absorbance at 313 nm. The moles
of compound 1 (open) formed were calculated using the integrated Beer-Lambert equation
and the absorption coefficient of compound 1 (open) at 313 nm obtained above. Fig. S1(b)
shows the absorption profile of the ring-opening photoreaction recorded every 50 minutes.
Figure S1: (a) Absorbance profile of the photocyclization reaction of compound 1 (open)
recorded every 5 seconds. (b) Absorbance profile of the ring-opening photoreaction of
compound 1 (closed) recorded every 50 minutes.
The photochromic film was spun-cast under yellow light in a class 10 clean-room.
Since the closed form is accessible only via photo-reaction, this ensures that the thin film
contains predominantly the open form. The spectrophotometer used in the above
measurements was not suitable for measuring absorbance values above 3. Hence, the
dispersion curve of the film was measured using a spectroscopic ellipsometer (Fig. S2). The
thickness of the film was estimated from the dispersion curve as 410nm. The absorbance of
this film was calculated using the equation, α = 4πk/λ, where k is the imaginary part of the
refractive index. The integrated form of the Beer-Lambert law was then used to calculate
the initial concentration of the open form in the film.
Figure S2: Dispersion curve of the photochromic film (primarily open form of compound 1
in a PMMA matrix). The real part (n) and the imaginary part (k) of the refractive index are
plotted in blue and green colors, respectively. The absorbance is plotted in red.
In order to check the thermal stability of compound 1, solutions of 1o and 1c in
toluene were heated to 100oC in the dark for 60 min and their absorbance spectra were
recorded every 10 minutes. Additionally, thin films of ca. 92 wt% 1o or 1c in PMMA were
heated to 120oC for 60 minutes and their absorption spectra recorded every 10 minutes. No
changes in absorbance spectra were observed within the measurement error of our
spectrophotometer (~ 0.01 O. D.). Considering the 60mins of observation time, we
conclude that the thermal reaction rate constant, κ, is less than ~3 X 10-6s-1. For the sake of
simplicity, κ is set to 0s-1 for all the simulations, unless stated otherwise.
The calculated photochromic parameters are listed in table S1.
Table S1: Photochromic parameters of compound 1. ε’s are the decadic molar
absorptivities, φ’s are the quantum efficiencies, κ is the thermal rate constant, and [open0]
is the initial concentration of the open form of compound 1 in the photochromic film.
ε1open = 31136 liters/mol-cm
ε1closed = 10521 liters/mol-
ε2closed = 20035 liters/mol-
φclosed->open = 8.8X10-4
[open0] = 2.99 mol/liter
ε2open = 158 liters/mol-cm
φopen->closed = 0.24
κ < 3X10-6s-1
3. Photokinetic Simulation
Compounds 1o and 1c are thermally stable and are not observed to interconvert at elevated
temperatures (T<120oC). The absorption onset value for compound 1o is approximately
370 nm, which corresponds to an excitation energy of 3.35 eV. In other words, photons
with energy of at least 3.35 eV are necessary to excite 1o and effect cyclization to form 1c.
Since 633 nm photons correspond to an energy of 1.96 eV, we can effectively conclude that
cyclization does not occur when 1o is irradiated at 633 nm.
As for the retrocyclization of 1c to 1o, we assume that the quantum yield of ring-
opening is constant across all absorbed wavelengths because of Kasha’s rule (S4). Kasha’s
rule states that for photochemical reactions we need consider only the lowest excited singlet
(S1) or the lowest triplet (T1) state as likely candidates for the initiation of a reaction
because rapid radiationless conversion from higher excited states (Sn>1 or Tn>1) to S1 or T1
competes favorably with higher-order processes; specifically, for most organic molecules
the rate of internal conversion from Sn>1→S1 falls in the range of 1011-1013 sec-1. The
absorption onset for 1c occurs at 700 nm (1.77 eV) and therefore, photons with energy of at
least 1.77 eV are necessary to excite 1c. Assuming that the lowest energy absorption band
centered at 582 nm corresponds to the S0→S1 transition of 1c, we can claim that the
quantum yield of ring-opening from the S1 state is 8.8x10-4. Upon absorption of higher-
energy 325 nm photons, 1c can access the S2 (or higher) state, but subsequent relaxation to
the S1 state via internal conversion should be faster than ring-opening; thus, although
different excited states can be accessed at different wavelengths, ring-opening is most
likely to occur from the comparatively long-lived S1 state. Therefore, we assume that the
quantum yield of ring-opening is independent of wavelength.
Figure S3: Schematic of the chemical reactions.
The rate equation for the reactions (Fig. S3) is:
where [ ] denote concentrations of the corresponding species. Assuming that the initial state
is composed of only the open form,
[open] + [closed] = [open0], (2)
where [open0] is the initial concentration.
The differential form of the Beer-Lambert law gives us:
∂z= −ln(10) ε1openopen
I1 ) (3)
∂z= −ln(10) ε2openopen
I2 ) , (4)
where ln() refers to the natural logarithm.
The boundary conditions are set by the incident intensity distributions.
Furthermore, at the photostationary state, equation (1) is set to 0. Then we can
numerically solve for I1 as a function of the lateral coordinate, x and the axial co-ordinate, z
as shown in Fig. S4. The full-width at half-maximum (FWHM) of the transmitted light is
obtained from the cross-section of the intensity at the bottom of the photochromic layer as
shown. This simulation was performed with the photochromic parameters listed in table S1
(κ was set to 0s-1). The peak intensities at λ1 and λ2 were assumed to be 0.365W/m2 and
1KW/m2, respectively (the same as the experimental conditions).
Figure S4: Simulation of beam propagation through the photochromic layer. Color image
is the simulated intensity distribution at λ1 in the photochromic layer after the
photostationary state is reached. The color bar is intensity in arbitrary units. Incident light