Optically Produced Arrays of Planar Nanostructures inside Fused Silica
V.R. Bhardwaj,1,*E. Simova,1P.P. Rajeev,1C. Hnatovsky,2R.S. Taylor,3D.M. Rayner,1,†and P.B. Corkum1,‡
1Steacie Institute for Molecular Sciences, National Research Council, 100 Sussex Dr, Ottawa, K1A 0R6, Canada
2Department of Physics, University of Ottawa, 150 Louis Pasteur, Ottawa, K1N 6N5, Canada
3Institute for Microstructural Sciences, National Research Council, 1200 Montreal Rd., Ottawa, K1A 0R6, Canada
(Received 28 April 2005; revised manuscript received 11 August 2005; published 7 February 2006)
Linearly polarized femtosecond light pulses, focused inside fused silica to an intensity that leads to
multiphoton ionization, produce arrayed planes of modified material having their normal parallel to the
laser polarization. The planes are ? 10 nm thick and are spaced at ??=2 in the medium for free space
wavelengths of both 800 and 400 nm. By slowly scanning the sample under a fixed laser focus, order is
maintained over macroscopic distances for all angles between the polarization and scan direction. With
the laser polarization parallel to the scan direction we produce long-range Bragg-like gratings. We discuss
how local field enhancement influences dielectric ionization, describe how this leads to nanoplane growth,
why the planes are arrayed, and how long-range order is maintained.
DOI: 10.1103/PhysRevLett.96.057404PACS numbers: 78.67.?n, 33.80.Rv, 73.20.Mf, 81.16.Rf
We observe arrayed ?10 nm wide nanoplanes inside
fused silica formed in the focal region of a ?50 femto-
second Ti:sapphire laser beam. These structuresare formed
despite the fact that the focal spot of a laser beam is limited
in free space optics to about a wavelength. We propose that
local field enhancements play a critical role in their for-
mation. In nanoplasmonics, the local field enhancement
near a metal-dielectric interface [1,2] overcomes the dif-
fraction limit of light. Electric fields can be concentrated to
nanometer scale leading to light confinement well below
High intensity femtosecond laser pulses focussed inside
the bulk material lead to plasma formation through multi-
photon ionization. The plasma density grows during the
laser pulse. During much of the critical growth period the
plasma is underdense . Any inhomogeniety in the
plasma formation will lead to local field enhancements
that must influence subsequent growth. If the inhomegen-
ities are highly localized, they lead to the formation of
nanoplasmas in the dielectric. The nanoplasmas drive
structural changes that are imprinted in the material.
Nanoplasmonics has not been considered in conven-
tional models of dielectric breakdown with short  or
ultrashort  pulses—nanostructures are hard to observe
inside dielectrics and plasmas are hard to diagnose. We
observe the nanostructures by cutting or grinding the di-
electric to the modified zone and polishing and etching
the surface before imaging it with an atomic force micro-
scope (AFM)  or a scanning electron microscope
(SEM). These techniques reveal the modification through
the differential etch rate between the modifiedand unmodi-
fied regions. They have a resolution of 20 and 5 nm,
Evidence of nanostructures has been previously found
for a stationary focus by polishing to reveal a cross section
of the laser-modified regions and imaging them by electron
backscattering . Modified stripes were found that sug-
gested planar structures. The stripes were perpendicular to
the laser field direction. Their spacing was found to depend
on the pulse energy, and the number of laser pulses.
We confirm that the stripes are projections of planes.
They extend over the full depth of the modified zone and
can be organized over long distances when the sample is
scanned under a fixed laser focus. We show that the laser
electric field direction controls their alignment for anyscan
direction. We find that self-organized nanostructures are
formed over a specific pulse energy range. Below this
range the modification is uniform  and above it the
modification is disordered. The nanoplanes are spaced by
?0=2n,wherenisthe refractiveindexoffusedsilica and?0
is the free space wavelength, for both 800 and 400 nm light
independent of pulse energy. The planes are ? 10 nm in
Our experiment used 50 fs, 800 nm pulses containing a
peak energy of up to 3 ?J and produced at a repetition rate
of 100 kHz. The beam could be frequency doubled to
produce 400 nm light. The beam was focused with a 0.45
or 0.65 NA microscope objective 100 ?m below the sur-
face of the sample. We produced extended modified re-
gions by translating the sample at 30 ?m=s perpendicular
to the direction of propagation of the laser beam. Any
exposed region experienced a few thousand shots.
We varied the average laser power from 5 –150 mW by
attenuating the laser beam with a variable density filter. We
used a ?=4 waveplate followed by a polarizer to change the
laser polarization with respect to the scan direction. The
advantage with this arrangement is that the electric field
remains constant and the pulse duration is not affected as
the polarization is rotated. The beam was precompensated
for dispersion in the optical elements.
The AFM scans in Fig. 1 show two different projections
ofa periodic nanostructure array.Figure 1(a) is obtained by
cutting the dielectric block inthe XZ plane asdefinedinthe
inset. The electric field (E) of the laser pulse is polarized
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© 2006 The American Physical Society
close to the X direction, approximately perpendicular to
the scan direction. This end view shows that the planes
extend over ?20 ?m in the direction of laser light propa-
gation. We expect the modification to occur preferentially
in the region before the laser focus due to depletion of the
pulse energy by nonlinear absorption .
Figure 1(b) is obtained by grinding and polishing the
dielectric block in the XY plane. This top view shows that
the planes extend several tens of microns, limited by the
slight angle between E and the X axis.
We now demonstrate directly that changing the polar-
ization of the laser with respect to the writing direction
controls the orientation of the nanoplanes. Figure 2(a)
shows an AFM image (viewed from the top of the sample)
of modified planes obtained for linearly polarized light
with E pointed along the scan direction. A long-range
grating pattern is formed over the entire 1=2 cm writing
range. This is remarkable because the sample moves es-
sentially continuously, yet the grating pattern has not
washed out. Instead, the coherence of the grating is con-
tinuously transferred as the sample is scanned. The average
grating spacing is 242 ? 10 nm while ?0=2n ? 276 nm
(?0? 800 nm; n ? 1:45, the refractive index of fused
silica). The spacing is independent of pulse energy as
shown in Fig. 3 .
Figure 2(b)is an AFMimage (viewedfrom the top of the
sample) of modified planes obtained for linearly polarized
light with E directed at ?45?to the scan direction. Long-
range order is again evident, but the grating planes are
tilted with their normal aligned to the polarization direc-
tion. This emphasizes the degree of control that the laser
polarization gives over the grating alignment. Gratings are
not produced with circularly polarized light.
The images in Figs. 1 and 2 do not reveal the true width
of the nanoplanes. AFMdepth profiles showthat the planes
are <20 nm wide, the resolution limit of the measurement.
SEM images of very gently etched structures show the
width to be <10 nm [Fig. 4(a)]. SEM images of structures
that have been etched more strongly [Figs. 4(b) and 4(c)]
provide a further demonstration of the 3-dimensional struc-
ture of the arrayed nanoplanes.
The structures shown in Fig. 2(a) are self-organized
Bragg gratings. The material between the planes shows
almost no modification with an etch rate less than 10% of
the rate inside the planes—often much less [Fig. 3(a)]. It
has been shown  that the etch rate in fs-laser-modified
fusedsilica is proportional to the refractive indexchange of
the material. If this still holds for the nanoplanes, then the
index modulation in the grating is more than an order of
chemically etched (4 min in 1% HF) modified regions with laser
polarization at 0?(a) and 45?(b), and (c) with respect to the scan
direction. Images (a) and (b) were obtained with 800 nm irra-
diation and with 400 nm in (c). The pulse energy was 300 nJ at
800 nm and 150 nJ at 400 nm.
AFM images (viewed from top of the sample) of
200 400 6008001000
Pulse energy (nJ)
Distance ( m)
direction obtained from the scan shown in Fig. 2(a). (b) Nano-
plane spacing as a function of pulse energy for E ? S (?) and
E k S (5). The spacings and their variance was obtained from
line profiles similar to that shown in (a). The variance for E ? S
is shown as the vertical bars. For E k S it is ?10 nm.
Nanoplane spacing. (a) AFM line profile along the scan
(4 min in 1% HF) laser-modified regions. The laser polarization
is perpendicular to the scan direction. K is the direction of
propagation of the laser radiation, E is the direction of electric
field of the laser, and S is the scan direction. (a) Cross sectional
view (in the XZ plane) of the laser-modified region. (b) Top view
(in the XY plane) along the length of the modified region. The
pulse energy is 250 nJ. The inset in (a) gives the experimental
configuration and defines the coordinate axes.
Atomic force microscope images of chemically etched
PRL 96, 057404 (2006)
10 FEBRUARY 2006
magnitude larger than index changes generally made in
UV-laser fabricated Bragg gratings. The relatively high
etch rate may be indicative of severe local changes in the
dielectric structure and may even imply dislocations.
The existence of ordered nanoplanes requires major
modifications in the standard ideas of how dielectrics
breakdown [4,5]. One proposal is that the planes result
from interferences between the light and plasma waves
. The spacing is predicted to be dependent on the plasma
Te??107K? and NE(asymtotically close to the critical
density, Ncr? 1:75 ? 1021cm?3) conditions implied by
this model are not consistent with the energy budget that
arises from our 3D characterization of the modified region.
There is just insufficient energy in the laser pulse to reach
even close to the implied Te. Estimating the volume of the
modification as 30 ?m3from Fig. 1, a pulse energy of
11 ?J is required to reach Te? 107K at Ne? 1:7 ?
1021cm?3. The structures are formed with energies as
low as 200 nJ. The low threshold is consistent with our
expectation that electron-ion collisions restrict Teto the
order of the band gap (?10 eV).
We propose that the planes arise from local field en-
hancements that occur during inhomogeneous breakdown.
This is based on ideas arising from nanoplasmonics. The
very existence of nanoplanes that develop over thousands
oflaser shotsrequiresthat there isa memory inthe material
that can feed back to the breakdown. Such a memory could
arise from metastable color centers  or permanent
changes in electronic structure associated with chemical
reorganization . Either of these processes could seed
localized ionization around areas that have already been
modified. Without the memory, the ionization would be
Compared to themetal structuresnormally considered in
nanoplasmonics, breakdown nanoplasmas start as under-
dense plasmas, they have no fixed boundaries and have a
density gradient at the boundary. The internal electric field
inside an underdense plasma exceeds the laser field. This
enhances the local nature of the breakdown. There is
positive feedback since the rate of plasma formation in-
creases as the density increases. Shot to shot memory
allows the feedback to work over many pulses. Thus nano-
plasmas may grow even from thermal noise.
It is possible that the breakdown is inhomogeneous
even on the first shot for two reasons. Natural inhomogen-
eties in the dielectric such as color centers and defects
might form nucleation centers for nanoplasmas. In addi-
tion, the ‘‘forest-fire’’ multiphoton and avalanche ioniza-
tion model, recently calculated for argon clusters, could
form highly inhomogeneous plasmas .
Nanoplasmas naturally grow into nanoplanes when
formed by linearly polarized electric fields. Consider an
underdense spherical nanoplasma (Fig. 5). The boundary
conditions require that the electric field around the equator
(as defined in the figure) is enhanced and the electric field
at the poles issuppressed[13,14].When the plasma density
is half the critical value  the relative field enhancement
is a factor of 2 and increases significantly as the critical
density is approached. Even small changes in the field have
a large effect on highly nonlinear multiphoton ionization.
Thus, underdense nanoplasmas must grow into nanosheets
orientated with their normal parallel to the laser polariza-
tion, just as we observe. Since the plasma is unconstrained,
growth will continue at the edges without limit. It may
appear that this peripheral growth would halt when the
plasma density exceeds the plasma resonance (the critical
density for a bulk plasma or for a large plasma sheet).
ε′ + 2
ε′ + 2
nanoplasma. K denotes the direction of propagation of the laser
beam and E the electric field. EEand EPare the local fields
found at the equator and poles of the sphere, respectively, for an
overall field E. "0is the ratio of the permitivities of the nano-
sphere and the dielectric medium. When "0< 1 (i.e., when the
plasma density is less than the critical density), field enhance-
ment occurs around the equator and the spherical nanoplasma
expands to form an oblate ellipsoid that evolves into a nano-
Schematic showing local field enhancement outside a
etched laser-modified regions that have been overlayed with
1.5 nm Pt to avoid surface charging. (a) High resolution image
of a weakly etched (20 s in 1% HF) structure written with E
perpendicular to the scan direction, S; (b) and (c) are arrayed
nanostructures written with E ? S and E k S, respectively, after
extensive etching (20 min in 1% HF) and disruption by ultra-
Scanning electron microscope images of chemically
PRL 96, 057404 (2006)
10 FEBRUARY 2006
However, this is not true. In unconstrained plasmas, the Download full-text
plasma boundaries are graded and the critical density is
never exceeded at any boundary.
We have extended our nonlinear absorption measure-
ments made on borosilicate glass  to fused silica. We
find that, at the threshold for nanoplane formation (200 nJ),
50% of the beam is absorbed. From this we estimate that
the average carrier density is 1021cm?3, assuming that the
light is absorbed in the volume of the modified region in
Fig. 1, that the electron temperature is the band gap energy
(?9 eV) and that recombination plays no role on these
short time scales. If the planes are ?10 nm thick and
absorption is confined to the planes, this implies that the
plasma density within the sheets reaches 2:5 ? 1022cm?3.
At such densities recombination could be very fast—the
rates are not known. However, it seems safe to assume that
the critical density is exceeded. In this case the sheets must
affect light propagation; for a single sheet, surface plas-
mons will be excited and for multiple sheets, the light must
adopt modes similar to those established in planar metallic
The order naturally evolves from a random distribution
of nanoplasmas over many shots due to the memory
mechanism and mode selection. Planes will be favored
only if they support modes whose field distribution rein-
forces their own growth. Although a great deal of work is
required to understand this in detail, the ?0=2n plane
spacing is reminiscent of the minimum spacing required
in a planar metal waveguide to support such modes having
field maxima at the metal-dielectric interface. It is likely
that transient plasma based planar waveguides have similar
properties favoring their development from an initially
random nanoplasma distribution.
Inconclusion,the nanoplasmonic model that wepropose
explains many observations. First, the formation of nano-
planes and their orientation is easily understood in terms of
local field enhancements. Second, the scaling of the array
spacing with ? follows naturally if the order is imposed by
modes related to planar waveguides. Third, since the spac-
ing is imposed by the mode structure, a dependence on
pulse energy is not expected. Finally, as the laser focus
moves, order is imposed in the newly exposed material by
the modes of the plasma grating seeded by the existing
Our results highlight the need for fundamental measure-
ments on high-density plasmas in transparent media. For
example, even such fundamental properties as Auger and
other recombination rates are not measured at densities
approaching those that are important for dielectric modifi-
cation. Electrons interacting with solids in the presence of
strong laser fields are poorly understood. Modes in non-
metallic lossy, transient waveguides have not been
We thank M. Stockman and M. Yu. Ivanov for valuable
discussions. This work was supported in part by NRC-
British Council Collaboration.
*Present address: Department of Physics, University of
Ottawa, 150 Louis Pasteur, Ottawa, K1N 6N5, Canada.
†Electronic address: firstname.lastname@example.org
‡Electronic address: email@example.com
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