Laser-induced Field Emission from Tungsten Tip: Optical Control of Emission Sites and Emission Process
ABSTRACT Field-emission patterns from a clean tungsten tip apex induced by femtosecond laser pulses have been investigated. Strongly asymmetric field-emission intensity distributions are observed depending on three parameters: (1) the polarization of the light, (2) the azimuthal and (3) the polar orientation of the tip apex relative to the laser incidence direction. In effect, we have realized an ultrafast pulsed field-emission source with site selectivity of a few tens of nanometers. Simulations of local fields on the tip apex and of electron emission patterns based on photo-excited nonequilibrium electron distributions explain our observations quantitatively. Electron emission processes are found to depend on laser power and tip voltage. At relatively low laser power and high tip voltage, field-emission after two-photon photo-excitation is the dominant process. At relatively low laser power and low tip voltage, photoemission processes are dominant. As the laser power increases, photoemission from the tip shank becomes noticeable. Comment: 12 pages, 12 figures, submitted to Physical Review B
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ABSTRACT: Attosecond science is based on steering electrons with the electric field of well controlled femtosecond laser pulses. It has led to the generation of extreme-ultraviolet pulses with a duration of less than 100 attoseconds (ref. 3; 1 as = 10(-18) s), to the measurement of intramolecular dynamics (by diffraction of an electron taken from the molecule under scrutiny) and to ultrafast electron holography. All these effects have been observed with atoms or molecules in the gas phase. Electrons liberated from solids by few-cycle laser pulses are also predicted to show a strong light-phase sensitivity, but only very small effects have been observed. Here we report that the spectra of electrons undergoing photoemission from a nanometre-scale tungsten tip show a dependence on the carrier-envelope phase of the laser, with a current modulation of up to 100 per cent. Depending on the carrier-envelope phase, electrons are emitted either from a single sub-500-attosecond interval of the 6-femtosecond laser pulse, or from two such intervals; the latter case leads to spectral interference. We also show that coherent elastic re-scattering of liberated electrons takes place at the metal surface. Owing to field enhancement at the tip, a simple laser oscillator reaches the peak electric field strengths required for attosecond experiments at 100-megahertz repetition rates, rendering complex amplified laser systems dispensable. Practically, this work represents a simple, extremely sensitive carrier-envelope phase sensor, which could be shrunk in volume to about one cubic centimetre. Our results indicate that the attosecond techniques developed with (and for) atoms and molecules can also be used with solids. In particular, we foresee subfemtosecond, subnanometre probing of collective electron dynamics (such as plasmon polaritons) in solid-state systems ranging in scale from mesoscopic solids to clusters and to single protruding atoms.Nature 07/2011; 475(7354):78-81. · 38.60 Impact Factor
arXiv:1001.5375v1 [cond-mat.mes-hall] 29 Jan 2010
Laser-induced Field Emission from Tungsten Tip:
Optical Control of Emission Sites and Emission Process
Hirofumi Yanagisawa1,∗Christian Hafner2, Patrick Don´ a1, Martin Kl¨ ockner1, Dominik
Leuenberger1, Thomas Greber1, J¨ urg Osterwalder1, and Matthias Hengsberger1
1Physik Institut, Universit¨ at Z¨ urich, Winterthurerstrasse 190, CH-8057 Z¨ urich, Switzerland
2Laboratory for Electromagnetic Fields and Microwave Electronics, ETH Z¨ urich, Gloriastrasse 35, CH-8092 Z¨ urich, Swizerland
(Dated: February 1, 2010)
Field-emission patterns from a clean tungsten tip apex induced by femtosecond laser pulses have
been investigated. Strongly asymmetric field-emission intensity distributions are observed depending
on three parameters: (1) the polarization of the light, (2) the azimuthal and (3) the polar orientation
of the tip apex relative to the laser incidence direction. In effect, we have realized an ultrafast
pulsed field-emission source with site selectivity of a few tens of nanometers. Simulations of local
fields on the tip apex and of electron emission patterns based on photo-excited nonequilibrium
electron distributions explain our observations quantitatively. Electron emission processes are found
to depend on laser power and tip voltage.At relatively low laser power and high tip voltage,
field-emission after two-photon photo-excitation is the dominant process. At relatively low laser
power and low tip voltage, photoemission processes are dominant. As the laser power increases,
photoemission from the tip shank becomes noticeable.
PACS numbers: 79.70.+q, 73.20.Mf, 78.47.J-, 78.67.Bf
Field emission from metallic tips with nanometer
sharpness has been introduced some time ago as highly
bright and coherent electron source [1–8]. Only recently,
pulsed electron sources with high spatio-temporal reso-
lution were realized by laser-induced field emission from
such tips [9–12]. Potentially, spatio-temporal resolution
down to the single atom and the attosecond range ap-
pears to be possible [7, 8, 10].
would be very attractive for applications in time-resolved
electron microscopy or scanning probe microscopy. How-
ever, the interaction of the laser pulses with the sharp
tip and the electron emission mechanism are not yet fully
understood [9, 11–13].
When a focused laser pulse illuminates the tip, optical
electric fields are modified at the tip apex due to the exci-
tation of surface electromagnetic (EM) waves that couple
with collective surface charge excitations to form e.g. sur-
face plasmon polaritons. Interference effects of the result-
ing surface EM waves can lead to local field enhancement
. Depending on the field strength, different electron
emission processes become dominant . For relatively
weak fields, single electron excitations by single- or multi-
photon absorption are dominant, and photo-excited elec-
trons are tunneling through the surface potential barrier;
such processes are termed photo-field emission. On the
other hand, very strong local fields largely modify the
tunneling barrier and prompt the field emission directly,
leading to optical field emission.
emission processes were disputed in the literature, while
the local field enhancement was treated as a static effect
Such electron sources
So far, the different
∗Electronic address: firstname.lastname@example.org
such as the lightening rod effect [9, 10, 15–17]. Hence,
local fields on the tip apex are considered to be symmet-
ric with respect to the tip axis. However, when the tip
size is larger than approximately a quarter wavelength,
dynamical effects are predicted to occur .
Here, we used a tip whose apex was approximately
a quarter wavelength and we investigated laser-induced
field-emission patterns. We have found that dynami-
cal effects substantially influence the symmetries of lo-
cal field distributions and thereby field-emission intensity
distributions.Varying the following three parameters
changes these distributions substantially: (1) the laser
polarization, (2) the azimuthal and (3) the polar orienta-
tion of tip apex relative to the laser incidence direction.
These are effects that had not been observed in earlier
experiments [9, 19]. At the same time, we realized an
ultrafast pulsed field-emission source with emission site
selectivity on the scale of a few tens of nanometers. In
our previous paper, simulations confirm that the photo-
field emission process is dominant in laser-induced field
emission . Here, we further discuss electron emis-
sion processes and their dependence on laser power and
tip voltage by investigating electron emission patterns,
Fowler-Nordheim plots, and calculated electron energy
distributions. At relatively low laser power and high tip
voltage, field emission after two-photon photo-excitation
is the dominant process.At still relatively low laser
power and low tip voltage, multiphoton photoemission
over the surface barrier is dominant. As laser power in-
creases, photoemission from the tip shank contributes.
This manuscript consists of four main sections. In sec-
tion II, we explain our experimental setup and our theo-
retical model. In section III, we discuss the optical con-
trol of field-emission sites and the emission mechanism
based on simulations of local fields on the tip apex and
laser-induced field-emission microscopy (LFEM) images.
In section IV, we discuss the emission processes for vary-
ing laser power and tip voltage based on experimental
and calculated results. In the last section, we present
conclusions and proposals for future experiments.
A. Experimental setup
Fig.1(a) schematically illustrates our experimental
setup. A tungsten tip is mounted inside a vacuum cham-
ber (3 · 10−10mbar). Laser pulses are generated in a
Ti:sapphire oscillator (center wavelength: 800 nm; rep-
etition rate: 76 MHz; pulse width: 55 fs) and intro-
duced into the vacuum chamber. An aspherical lens (fo-
cal length: f = 18 mm) is mounted on a holder that is
movable along the y direction and located just next to
the tip to focus the laser onto the tip apex; the diam-
eter of the focused beam is approximately 4 µm (1/e2
radius) measured by a method with a razor blade .
Linearly polarized laser light was used. The polarization
vector can be changed within the transversal (x, z) plane
by using a λ/2 plate . As shown in the inset, where
the laser propagates towards the reader’s eye as denoted
by the circled dot, the polarization angle θP is defined
by the angle between the tip axis and the polarization
The tip can be heated to clean the apex and also nega-
tively biased for field emission. Although the tip is poly-
crystalline tungsten, heating to around 2500◦C leads to
the tip apex being crystallized and oriented towards the
(011) direction [4, 23]. A position sensitive detector with
a Chevron-type double-channelplate amplifier in front of
the tip is used to record the emission patterns. The spa-
tial resolution of field emission microscopy (FEM) is ap-
proximately 3 nm . The tip holder can move along
three linear axes (x, y, z) and has two rotational axes for
azimuthal (ϕ, around the tip axis) and polar (θ, around
the z axis) angles . The laser propagates parallel to
the horizontal y axis within an error of ± 1 degree. θ is
set so that the tip axis is orthogonal to the laser propaga-
tion axis. The orthogonal angle in θ was determined by
plotting positions of the tip in (x, y) coordinates while
keeping the tip apex in the focus of the laser as schemat-
ically shown in Fig. 1(b). The maximum position in x
gives the orthogonal angle. Experimental data are shown
in Fig. 1(c). The plots were taken in 0.5 degree steps.
The data clearly show the maximum in the x position.
We defined the corresponding angle as θ = 0 for conve-
nience. The precision is estimated to be ± 1 degree. In
these experiments, the base line of the rectangular detec-
tor is approximately 20◦off from the horizontal (y axis)
incidence direction, which means that the laser propaga-
tion axis is inclined by 20◦from the horizontal line in
the observed laser-induced FEM images (see dashed red
arrow in Fig. 3a). All the measurements were done at
FIG. 1: (color online). Schematic diagram of the experimental
setup (a). A tungsten tip is mounted inside a vacuum cham-
ber. Laser pulses are generated outside the vacuum chamber.
An aspherical lens is located just next to the tip to focus
the laser onto the tip apex. Emitted electrons are detected
by a position-sensitive detector in front of the tip. The po-
larization angle θP is defined in the inset, where the laser
beam propagates towards the reader’s eye (see text for fur-
ther description). (b) shows a schematic diagram defining the
orthogonal angle between the laser propagation direction and
the tip axis. The right angle is where x is maximum. (c)
shows tip positions in (x, y) coordinates for different θ, found
while the tip apex is kept in the focus of the laser. The angle
which gives maximum x is defined as θ = 0 for convenience.
Although the field emission is a quantum mechanical
phenomenon, the interaction between the optical fields
and the tungsten tip apex can be treated classically by
solving Maxwell equations. Such an interaction can be
understood by a mechanistic picture as shown in Fig.
2(a). When a laser pulse illuminates the metallic tip,
surface EM waves are excited, which propagate around
the tip apex. As a result of the interference among the
excited waves, the optical fields are modulated. To sim-
ulate the superposition of surface EM waves and the re-
sulting local field distributions on the tip apex, we used
the Multiple Multipole Program (MMP) [25–27], which
is a highly accurate semi-analytic Maxwell solver, avail-
able in the package MaX-1  and in the open source
project OpenMaX [29, 30].
A droplet-like shape was employed as a model tip as
shown in Fig. 2(b), with a radius of curvature of the
tip apex of 100 nm, which is a typical value for a clean
tungsten tip. Atomic structures were not included in the
model becasue the tip apex can be regarded as a smooth
surface on this length scale given by the tip dimensions
and the wavelength of the laser field. The dielectric func-
tion ǫ of tungsten at 800 nm was used, i.e. a real part
Re(ǫ) = 5.2 and an imaginary part Im(ǫ) = 19.4 .
Note that accuracy of the dielectric functions does not
affect our conclusion, which will be demonstrated in sec-
FIG. 2: (color online).
tation and interference of surface EM waves (a) and of the
model tip (b). The radius of curvature of the tip apex is
100 nm, and the length is 700 nm. (c) represents the field
distribution of the focused beam used in the simulation at a
certain time. The beam waist is 1 µm and the wavelength is
800 nm. Small arrows indicate the field direction, and field
strength is represented by a linear color scale: highest field
values are represented in yellow (brightest color). The calcu-
lated time-averaged field distribution around the model tip is
shown in (e) for θP = 0◦together with a magnified picture in
the vicinity of the tip apex. (e) shows the time-averaged field
distribution around a longer model tip together with a mag-
nified picture in the vicinity of the tip apex; the tip length is
twice as large as that of (d). (f) represents the time-averaged
field distributions around the model tip simulated by incident
laser light with wavelengths of 750 nm, 800 nm and 850 nm.
Schematic illustration of the exci-
tion III B by comparing with local fields on a gold tip.
A focused laser with a beam waist of 1 µm and a wave-
length of 800 nm was used as shown in Fig. 2(c). The
model tip was set so that its apex is at the center of the
By using different droplet sizes it was verified that the
model tip is long enough so as to mimick the infinite
length of the real tip; the fields at the truncated side
of the tip are substantially weaker so that the excited
surface EM waves propagating arond the whole tip do
not affect the induced field distribution at the tip apex.
Figure 2(d) shows the calculated time-averaged field dis-
tribution around the model tip of Fig. 2(b). Fig. 2(e)
shows the same calculated field distribution for a longer
tip with the same radius of curvature of the tip apex of
100 nm. In both cases, the laser is propagating from left
to right, where the polarization vector has been chosen
parallel to the tip axis (θP = 0◦). The magnified pictures
around the tip apex of Fig. 2(d) and 2(e) show that the
local field distributions of the two are basically the same,
indicating the length of the model tip in Fig. 2(b) to be
In the simulations, we only used a center wavelength of
800 nm, even though the laser pulse has a spectral width
of ∆ = 25 nm with respect to the center wavelength. Jus-
tification of the use of only a center wavelength is done
by simulating the local electric fields with laser light of
wavelengths of 750 nm and 850 nm. Fig. 2(f) shows
the time-averaged field distributions around the model
tip obtained by excitation with these three wavelengths.
They are almost the same, which indicates that the sub-
stantial spectral width of the light around 800 nm would
not affect the position of the maximum local electric fields
simulated with the wavelength of 800 nm.
III. OPTICAL CONTROL OF FIELD-EMISSION
SITES AND EMISSION MECHANISM
A. Experimental Results
The field emission pattern from the clean tungsten tip
apex which orients towards the (011) direction is shown
in Fig. 3(a). The most intense electron emission is ob-
served around the (310)-type facets, and weaker emission
from (111)-type facets. These regions are highlighted by
green areas with white edges on the schematic front view
of the tip apex in the inset of Fig. 3(a). The intensity
map roughly represents a work function map of the tip
apex: the lower the work function is, the more electrons
are emitted. The relatively high work functions of (011)-
and (001)-type facets  suppress the field emission from
The laser-induced FEM (LFEM) image in Fig. 3(b),
taken with the light polarization oriented parallel to the
tip axis (θP= 0), shows a striking difference in symmetry
compared to that of the FEM image in Fig. 3(a). Emis-
sion sites are the same in both cases, but the emission
pattern becomes strongly asymmetric with respect to the
FIG. 3: (color online). Electron emission patterns for two
orthogonal azimuthal orientations (ϕ) of the tip without laser
[ϕ = 0◦(a) and ϕ = 90◦(c)], and with laser irradiation
[ϕ = 0◦(b) and ϕ = 90◦(d)]. Vtip indicates the DC potential
applied to the tip and PL indicates the laser power measured
outside the vacuum chamber. The insets of (a) and (c) show
the front view of the atomic structure of a tip apex with a cur-
vature radius of 100 nm, based on a ball model, in which green
areas with white edges indicate the field emission sites and the
red arrow indicates the laser propagation direction. The inset
of (b) shows a schematic side view of the laser-induced field
emission geometry, in which green vectors indicate intensities
of electron emission and the white arrow indicates the laser
propagation direction. A dashed white line denotes a mirror
symmetry line of the atomic structure in each picture. In
(c) and (d) specific regions of interest, marked by dashed red
rectangles, are blown up on the right hand side.
shadow (right) and exposed (left) sides to the laser inci-
dence direction. The most intense emission is observed
on the shadow side as illustrated in the inset of Fig. 3(b).
Figs. 3(c) and 3(d) give the same comparison for a dif-
ferent azimuthal orientation of the tip as shown in the
inset of Fig. 3(c). In the magnified image of Fig. 3(c),
two emission sites can be identified which are separated
by approximately 30 nm. The strong emission asymme-
try is observed even over such short distances, as shown
in Fig. 3(d). Actually, the laser pulses arrive at an an-
gle of 20◦off the horizontal line in both LFEM images,
as indicated by the dashed red arrow in the inset of Fig.
3(a). This oblique incidence slightly affects the symmetry
with respect to the central horizontal line in the observed
LFEM images (see below).
The asymmetry in LFEM images can be controlled fur-
ther by changing θ. In Fig. 4, the θ-dependence of LFEM
images at [ϕ = 0◦, θP = 0◦] is shown, which were taken
at Vtip = -1500 V and PL = 20 mW. θ is varied from
θ = −12◦to θ = 12◦by 4 degree steps. Schematic di-
agrams for the experimental configuration are shown at
the top, in which red arrows indicate the laser propaga-
tion direction. The corresponding FEM images, which
were taken at Vtip= -2200 V, are also shown. As θ in-
creases, the asymmetry of the LFEM images becomes
clearly enhanced. At θ = 12◦, electrons are emitted al-
most only from right-side emission sites. Among these θ
FIG. 4: (color online).
[ϕ = 0◦, θP = 0◦], which were taken at Vtip = -1500 V and
PL = 20 mW. θ is varied from θ = −12◦to θ = 12◦by 4◦
steps. Schematic diagrams for the experimental configuration
are shown at the top, in which red arrows indicate the laser
propagation direction. The corresponding FEM images are
also shown below, which were taken at Vtip = -2200 V. The
white dashed lines in the pictures denotes a mirror symmetry
line of the atomic structure. The total yield Srightfrom right
side of each image and the total yield from left side Sleftwith
respect to the white dashed line were taken. The ratio of
Sright to Sleft are plotted in the graph. Blue circles are for
LFEM and black squres are for FEM.
θ-dependence of LFEM images at
FIG. 5: (color online). Comparison of measured and simulated laser-induced FEM (LFEM) images for different light polarization
angles θP and for different azimuthal orientations ϕ of the tip. The leftmost column gives the FEM images without laser
irradiation for four different azimuthal angles (Vtip = -2250 V). For the same azimuthal angles, observed LFEM images are
shown as a function of polarization angle θP in 30◦steps (Vtip ≈ -1500 V and PL = 20 mW). The simulated LFEM images
from the photo-field emission model, in which Vtip and PL were set as in the corresponding experiments, are shown on the
right-hand side of the observed LFEM images. The color scale and laser propagation direction are the same as in Fig. 3.
values, the symmetry of the FEM images changed only
slightly due to a change of the DC field distribution on
the tip apex. To distinguish between the contributions
of DC and laser field distributions to the asymmetry of
the LFEM images, we evaluated the change in symme-
try quantitatively. The total yield Srightfrom the right
side of each image and the total yield from the left side
Sleftwere obtained from each image with respect to the
white dashed line. Then the ratios of Srightto Sleftare
plotted in the graph: high values indicate large asym-
metries. The asymmetry is clearly enhanced in LFEM
with respect to FEM, which indicates that the laser fields
mainly contribute to enhance the asymmetry for higher
We also found experimentally a strong dependence of
the electron emission patterns on the laser polarization
direction and on the azimuthal tip orientation. Fig. 4
shows the LFEM patterns for different values of θP in
30◦steps, and for four different azimuthal orientations
ϕ of the tip. The corresponding FEM images are also
shown in the left-most column; they show simply the
azimuthal rotation of the low work function facets around
the tip axis. Throughout the whole image series, the
emission sites do not change, but intensities are strongly
modulated resulting in highly asymmetric features. For
instance, for [ϕ = 0◦, θP= 0◦] the intense emission sites
are located on the right-hand (shadow) side of the tip,
but for [ϕ = 0◦, θP = 60◦] the emission sites on the left-
hand side become dominant. LFEM images recorded for
θP = 180 (not shown) are exactly the same as those for
θP= 0◦, and all the LFEM images are well reproducible.
B.Simulations of Local fields
When a laser pulse illuminates the metallic tip, surface
EM waves are excited, which propagate around the tip
apex as illustrated schematically in Fig. 2(a). Due to
the resulting interference pattern, the electric fields show
an asymmetric distribution over the tip apex, depending
also on the laser polarization. Fig. 6(a) shows the time
evolution of laser fields at 800 nm wavelength over a cross
section of the model tip while propagating through the
tip apex from left to right, where the polarization vector
has been chosen parallel to the tip axis (θP= 0◦). It can
be seen that a surface EM wave is propagating around the
tip apex indicated by white arrows and enhanced at the
tip apex. The calculated time-averaged field distribution
around the tip apex is shown in Fig. 6(b). The field
distribution is clearly asymmetric with respect to the tip
axis, with a maximum on the shadow side of the tip. The
field enhancement factor of the maximum point is 2.5
with respect to the maximum field value of the incident
laser, and 1.7 for the counterpart of the maximum point
on the side exposed to the laser. This is consistent with
our observations in Fig. 3(b) and 3(d) where the field
emission is enhanced on the shadow side.
Additionally, we would like to note that a similar asym-
metric distribution can also be seen even for a metal with
a dielectric function which is largely different from that
of tungsten. For example, we performed a simulation for
gold using a real part Re(ǫ) = −24 and an imaginary
part Im(ǫ) = 1.5 . Fig. 6(c) shows the time-averaged
field distribution on the gold tip apex. The field distribu-
tion shows a similar asymmetry as for tungsten. It should
also be mentioned that surface EM waves are classified in
terms of the dielectric functions of the interacting mate-
rial  though some authours do not distinguish. If the
real part of the dielectric function is negative, then the
surface EM waves are proper surface plasmon polaritons.
On the other hand, if the real part is positive and the
imaginary part is large, the term Zenneck waves is more
appropriate.The dielectric functions of tungsten and
gold between 700 nm and 900 nm are plotted by black
FIG. 6: (color online). Time evolution of laser fields over
a cross section of the model tip while propagating through
the tip apex from left to right (a). The polarization vector
is parallel to the tip axis (θP = 0◦).
indicate the field direction, and field strength is represented
by a linear color scale: highest field values are represented in
yellow (brightest color). The time-averaged field distribution
for tungsten and gold tips are shown in (b) and (c) where the
model tip of Fig. 2(b) is employed for both. The dielectric
function of tungsten and gold for the wavelengths between
700 nm and 900 nm are plotted by black dots in (d) and the
values at 800 nm are highlighted by red circles. (e) shows the
time-averaged field distributions around the tungsten tip for
three different polar angles: θ = −12◦, θ = 0◦, and θ = 12◦.
In (f) the time-averaged field distributions are given in a front
view of the model tip for different polarization directions θP
(θ = 0◦). The laser propagation direction is indicated by red
arrows, and is the same as in the experiment.
Small black arrows
dots in Fig. 6(d), where the values at 800 nm are high-
lighted by red circles. From Fig. 6(d), strictly speaking,
the excited surface EM waves on tungsten are Zenneck
waves and those on gold are surface plasmon polaritions.
Figs. 6(b) and (c) also indicate that different kinds of
surface EM waves do not show substantial difference in
the resulting field distribution.
The asymmetric local field distribution can be con-
trolled by changing the polar angle θ and the laser po-
larization angle θP. Fig. 6(e) shows time-averaged field
distributions on the tungsten tip apex with different laser
incidence directions relative to the polar orientation of
the tip apex. As θ increases, the asymmetry becomes
stronger. This is consistent with our observation in Fig.
4 where the most asymmetric emission is observed at
θ = 12◦. Fig. 6(f) shows, in a front view, time-averaged
field distribution maps from the white dashed line region
of the model tip in Fig. 6(b). This area corresponds
roughly to the observed area in our experiments. The
red arrows indicate the laser propagation direction which
has been set to the same as in our experimental situation.
The field distribution changes strongly depending on the
polarization angle. While the maximum field is located
directly on the shadow side of the tip for θP = 0◦, the
maximum moves towards the lower side of the graphs in
concert with the polarization vector for θP = 30◦and
θP= 60◦, and reappears on the upper side for θP = 120◦
and θP = 150◦. For θP = 90◦the polarization vector
is perpendicular to the tip axis and produces two sym-
metric field lobes away from the tip apex. In general the
observed LFEM images show the same intensity modu-
lations (Fig. 5): each LFEM pattern at θP = 30◦and
60◦shows pronounced emission at the lower side of the
image, while each LFEM pattern at θP = 120◦and 150◦
has maximum emission at the upper side of the image.
C.Simulations of LFEM by the photo-field
From the calculated local fields, we further simulated
the LFEM images by considering the photo-field emission
mechanism. The current density jcalc of field emission
can be described in the Fowler-Nordheim theory based
on the free-electron model as follows [4, 5, 35, 36],
Here, e is the electron charge and m the electron mass,
−Wais the effective constant potential energy inside the
metal, W is the normal energy with respect to the sur-
face, and E is the total energy. Important factors are
D(W,Φ,F) and f(E). D(W,Φ,F) is the probability that
an electron with the normal energy W penetrates the sur-
face barrier. It depends exponentially on the triangular-
shaped potential barrier above W, as indicated by the
cross-hatched area in Fig. 7(a) where field emission with
energy W occurs. The cross-hatched area is determined
by the work function Φ and the electric field F just out-
side the surface. f(E) is an electron distribution func-
tion. In the case of field emission we have F = FDC,
where FDC is the applied DC electric field, and f(E) is
the Fermi-Dirac distribution at 300 K as shown in Fig.
7(a). In the photo-field emission model, F still equals
FDC, but the electron distribution is strongly modified
by the electron-hole pair excitations due to single- and
multi-photon absorption, resulting in a nonequilibrium
distribution characterized by a steplike profile, as illus-
trated in Fig. 7(c) [13, 37]. For example, one-photon ab-
sorption creates a step of height S1from EFto EF+hν by
exciting electrons from occupied states between EF−hν
and EF. Absorption of a second photon creates a step
FIG. 7: (color online). A schematic diagram of field emission
from a Fermi-Dirac distribution (a), where an electron with a
normal energy W is emitted. The surface barrier above W is
shown by a cross-hatched area. (b) shows the logic diagram
for obtaining work function and absolute DC field maps. (c)
and (d) show schematic diagrams of photo-field emission from
a nonequilibrium electron distribution and optical field emis-
sion from a Fermi-Dirac distribution, respectively.
of height S2from EF+hν to EF+2hν, where S2≈ S2
We included absorption of up to four photons. The step
height S1is proportional to the light intensity I. In the
vicinity of the tip we have I ∝ F2
the enhanced optical electric field that varies over the tip
apex as illustrated in Fig. 6(f) .
There are three adjustable parameters in our calcu-
lations of jcalc: Φ, FDC, and S1.
tions of position on the tip apex. Φ and FDC maps on
the tip apex were obtained from the measured FEM im-
ages by following the logic diagram shown in Fig. 7(b).
The measured FEM images, which were symmetrized to
have the ideal two-fold symmetry, represent the current
density jexp as a function of position on the tip apex,
laserwhere Flaser is
They are all func-
TABLE I: Table of work functions of tungsten for several
faces. An error in experimental values can be as much as
± 0.3 eV .
FIG. 8: (color online). The calculated DC field distribution
around the model tip is shown in (a). A wire-like shape was
employed for the simulation of relative DC fields. The color
scale is the same as in Fig. 6. The relative DC field distribu-
tion at the tip apex of (a) is shown as a function of angle θc,
which is defined in (a). The obtained work function profile
along a (001)-(011)-(010) curve is shown in (c) as a function
because the electrons follow closely the field lines from
the tip apex to the position sensitive detector. In prac-
tice we assumed a radius of curvature of the tip apex of
100 nm and used the FEM image at ϕ = 45◦shown in
Fig. 5. Second, a relative DC field FDC relativedistribu-
tion was generated by MaX-1. We used a more wire-like
tip shape for this purpose as shown in Fig. 8(a), and a
grounded plate was set 1 cm away from the tip, which is
close to that in our experimental setup. The simulated
FDC relative is shown in Fig. 8(b), which is normalized
by the value at tip apex. Going away from the tip apex
FDC relativedecreases. A scaling factor α is introduced,
which determines FDC by FDC = α · FDC relative. We
then obtained the Φ map by inserting FDCinto Eq. (1)
and postulating jexp− jcalc = 0. The resulting Φ map
was compared to known values for several surface facets
of tungsten. The scaling factor α was changed and the
procedure was iterated until reasonable work functions
were obtained. Thus, a full Φ map and absolute values
for FDCwere determined.
A line profile of the resulting Φ map along the (001)-
(011)-(010) curve is shown in Fig. 8(c). The work func-
tion has local curve maxima at the (011)- and (001)- type
facets and local minima at (310)- type facets, which is in
line with the observed field emission intensity distribu-
tion seen in Fig. 3(a); the higher the work function, the
lower the intensity. The resulting Φ values are summa-
rized for several facets and compared with known experi-
mental values in Table 1. They are in fair agreement with
each other. A field strength FDC of 2.15 V/nm results
at the tip apex center for the FEM image taken with
Vtip= −2250 V, which is a typical value for FEM. The
LFEM experiments were carried out with a reduced tip
voltage Vtip≈ −1500 V. Therefore we used a down-scaled
value of 1.43 V/nm in the LFEM simulations. Note that
the uncertainty in the Φ values is not important for our
conclusions which will be discussed below: we have also
checked the whole discussion in this section with a differ-
ent work function map using 4.6 eV, 4.32 eV, 4.20 eV for
(011), (001) and (310) facets, respectively, but the main
outcome does not change.
Substituting the obtained Φ and F distribution maps
into Eq. (1), and using a nonequilibrium electron distri-
bution f(E), the absolute values of S1over the tip apex
were determined by fitting the measured total current
from the (310) facet on the right-hand side of the LFEM
image in Fig. 3(b). The resulting maximum value for
S1 was 1.6 · 10−6. By substituting all the adjusted pa-
rameters into Eq. (1), we could simulate all the LFEM
images. The calculated current densities on the tip apex
were projected to the flat screen by following the static
field lines. The simulated images can now directly be
compared to the experimental images (Fig. 5): they are
in excellent agreement in every detail. This comparison
clearly demonstrates that the observed strongly asym-
metric features originate from the modulation of the local
D.Simulations of LFEM by the optical field
We also simulated the LFEM images for the optical
field emission process and compared the resulting in-
tensity distributions to those of the photo-field emission
model. In the optical field emission model schematically
shown in Fig. 7(d), the Fermi-Dirac distribution is not
modified, but instead the electric field F in Eq. (1) is
expressed as F = FDC+ F⊥
mal component of Flaserat each point of the tip surface.
The absolute values for F⊥
laseron the tip apex were de-
termined in the same way as described above for S1. The
resulting maximum value for F⊥
Fig. 9(a) shows the LFEM image for the optical field
emission process together with experimentally obtained
LFEM and the simulated LFEM image based on the
photo-field emission model at [ϕ = 0◦, θP = 0◦]. The op-
tical field emission model results in an even more strongly
asymmetric pattern as compared to the photo-field emis-
sion model. This contrasts with the experimental data.
Fig. 9(b) shows line profiles extracted from the observed
FEM and LFEM images, and from the corresponding
simulations for both models, which are all normalized
to their maximum value. The measured LFEM profile
clearly shows the asymmetric feature observed in the re-
gions B and D. The photo-field emission model catches
this asymmetry much more quantitatively than the op-
tical field emission model, as can be best seen in region
D. Therefore, the local fields in our experiment are still
laseris the nor-
laserwas 0.71 V/nm.
FIG. 9: (color online). (a) experimentally obtained LFEM
image and simulated LFEM image at [ϕ = 0◦, θP = 0◦] for
both photo-field emission and optical field emission models.
(b) shows line profiles extracted from the observed FEM im-
ages (red line with squares), LFEM images (blue line with
circles), and from LFEM images simulated by the photo-field
emission model (green solid line) and the optical field emission
model (black dashed line) at [ϕ = 0◦, θP = 0◦]. The whole
scanned line corresponds to the unfolded rectangle indicated
by the dashed blue line in the FEM figures above, and the
corresponding sides are indicated by white arrows. Each line
profile has been normalized by the maximum value.
weak enough such that the photo-field emission process
is the dominant one.
IV.VOLTAGE- AND POWER- DEPENDENCE
OF EMISSION PROCESSES
A.Lower laser power
In this section, we futher discuss the details of elec-
tron emission processes and their dependence on laser
power and tip voltage by investigating electron emission
patterns and Fowler-Nordheim plots, and by simulating
electron energy distributions. Figure 10 shows the de-
pendence of LFEM images at [ϕ = 0◦, θP = 0◦] on the
average laser power PLand the tip voltage Vtipapplied
to the tip. Throughout the whole seriese of pictures, the
intensity of each image was normalized by the maximum
intensity. Normally, total yields decrease as either laser
power or tip voltage decrease. As can be seen, the left-
right asymmetry is present in all images below a laser
power of 60 mW except when PL= 0 mW (FEM). Nev-
ertheless, the images show a trend: the outlines of emis-
sion facets become diffuse in the lower tip voltage region,
see e.g. the 20 mW row surrounded by a white dashed
line. In these experiments, electron emission is consid-
ered to be a concerted action of photoemission and field
FIG. 10: (color online). Laser power and tip voltage dependence of the electron emission patterns at [ϕ = 0◦, θP = 0◦]. On the
vertical axis laser power, on the horizontal axis tip voltage are plotted. The inset shows the electron emission patterns where
the laser beam is displaced from the tip apex downwards by a distance of 1 µm and 16 µm, taken at the 90 mW laser power.
The definition of distance d is also shown on the right-hand side of the inset. The time-averaged field distribution around the
tip when the laser beam is displaced by a distance of 0.5 µm is also shown in the inset, where the longer model tip shown in
Fig. 2(e) was used. The green dashed circles highlight the left-side electron-emission sites (see section IV B).
emission. In the case of field emission, the emitted elec-
trons strongly feel the work function corrugation on the
nanometer scale, which generates a sharp contrasts at the
border of each emission facet. In the case of photoemis-
sion, the excited electrons encounter a much narrower
surface barrier and appear thus to be less sensitive to
the work function corrugation, hence showing a smeared
contour of the emission sites. At lower tip voltage, mul-
tiphoton processes will be enhanced since field emission
is suppressed. Eventually, photoemission from 3PPE or
4PPE will contribute, with energies above the vacuum
level. Therefore, the outline of each emission facet be-
comes diffuse in the lower tip voltage region. This is
confirmed by simulations of energy distribution curves
and emission patterns.
We have simulated the energy distribution of field-
emitted electrons with the parameters representing the
emission site where maximum intensity can be seen in
the simulated image in Fig. 5 at [ϕ = 0◦, θP = 0◦]: the
work function at this point is 4.45 eV, the DC field is 1.32
V/nm and S1is 1.6·10−6, which should correspond to the
conditions where the most intense point can be seen in
FIG. 11: (color online). Simulated electron energy distribu-
tion curves (a). The spectrum at the top of (a) shows the sim-
ulated electron energy distribution of field-emitted electrons
with the parameters representing the point where maximum
laser intensity can be observed for ϕ = 0◦, θP = 0◦. The
parameters are the following: the work function is 4.45 eV , a
DC field of 1.32 V/nm corresponds to a tip voltage of -1500 V
and S1 is 1.6·10−6for 20 mW laser power. The energy distri-
bution for lower DC fields but the same laser power are also
shown in (a). The vacuum level Evac is defined as 0 eV, and
the Fermi level EF is 4.45 eV below Evac. The energies cor-
responding to one-, two- and three-photon excitations from
EF (1PPE, 2PPE and 3PPE) are also indicated by vertical
dashed lines. The simulated LFEM images at corresponding
tip voltage and laser power are shown in (b).
the image at 20 mW laser power and -1500 tip voltage in
Fig. 10. Figure 11(a) shows the corresponding simulated
energy spectrum at the top, and underneath, spectra for
various lower tip voltages. We find that field emission
from two-photon processes is strongly dominant at the
higher DC fields. For lower DC voltage, the calculated
energy distributions clearly show that field-emission from
the 2PPE line is suppressed and photoemission from the
3PPE line is enhanced. The simulated LFEM images at
corresponding tip voltage are shown in Fig. 11(b). As the
DC voltages decrease, the outlines of emission sites be-
come diffuse due to the fact that photoemission processes
become dominant. This is in line with the experimental
observations described above.
Experimental Fowler-Nordheim (FN) plots give further
suppports for the suggested emission mechanism. Fig.
12 shows FN plots of FEM and LFEM, where the elec-
tron count rate i devided by V2
scale versus the inverse of Vtip. The count rate was taken
by integrating the electron emission from the right-hand
(310) type facet in Fig. 10. According to the FN the-
ory, the linearity of such plots indicates that the electrons
are emitted through field emission processes . The FN
plots of FEM data in Fig. 12 clearly show linear be-
havior, and linearity can be seen also for LFEM at 10
mW and 20 mW, which are shown together with approx-
imated exponential functions (black solid lines). The FN
tipis displayed on a log
FIG. 12: (color online). Fowler-Nordheim (FN) plots for FEM
and LFEM (PL = 10 mW, 20 mW, 30 mW, 40 mW, 50 mW).
The vertical axis is signal i over the V2
scale. The signal i is the total yield of electron emission from
the right hand (310) type facet of each image in Fig. 10. The
horisontal axis is 1/Vtip.
tipon a logarithmic
plots for 20 mW show non-linear behavior at low bias
voltage. This indicates that photoemission processes be-
come dominant at low voltage as discussed above. Sim-
ilar behavior is also observed in the case of higher laser
power, 30 mW, 40 mW and 50 mW.
The slope of the straight sections is proportional to
Φ3/2.From this fact, we can estimate the effec-
tive barrier height ΦLFEM(10mW) and ΦLFEM(20mW)
at PL = 10 mW and 20 mW, respectively, which
an emitted electron feels in the case of LFEM. First,
the barrier height ratios were derived from the propor-
tionality constants: ΦLFEM(10mW)/ΦFEM = 0.24 and
ΦLFEM(20mW)/ΦFEM = 0.2.
tion of (310) type facets of 4.35 eV for ΦFEM, thus
ΦLFEM(10mW)= 1.05 eV and ΦLFEM(20mW)= 0.85 eV
were obtained. The energy difference between ΦLFEM
and ΦFEM should corresponds to the energy of emit-
ted electrons measured from the Fermi level in LFEM.
Here we obtain ΦLFEM(10mW)- ΦFEM = 3.3 eV and
ΦLFEM(20mW) - ΦFEM = 3.5 eV, which is close to
the electron energy after two-photon excitation, i.e. 3.1
eV. These values corroborate the two-photon photo-field
emission processes, which is consistent with the simu-
lated electron energy distributions for higher voltage in
Taking the work func-
B.Higher laser power
For this discussion, we would like to point out the
electron emission from the shank side of the tip in the
higher laser power range. As in the previous sections,
the electron emission from the tip apex is dominant in
the emission pattern at low laser power because of the
local field enhancement at the tip apex even though the
surface area exposed to the laser beam is much larger for
the shank than for the apex. At the higher laser power,
however, the electron emission from the shank side be-
comes noticiable because of the nonlinear dependence of
the electron emission intensities on the laser power.
In the column of Vtip= −100V of Fig. 10, the left-side
electron-emission features highlighted by green dashed
circles becomes suddenly very strong for laser powers ex-
ceeding 70 mW. At 90 mW, the intensity of left-side elec-
tron emission is comparable to that on the right-side. It
remains even when the position of the tip in the beam
waist is varied. The insets of Fig. 10 show electron emis-
sion patterns at 90 mW laser power where the laser beam
is displaced from the tip apex downwards by distance of
1 µm and 16 µm. In the two images, right-side emission
sites disappear, but the left-side emission remains, indi-
cating that it originates from the shank side of the tip.
Such an electron emission should be dominated by pho-
toemission over the surface barrier because DC fields on
the shank side are significantly weak with respect to the
tip apex. Since the laser pulses arrive at an angle of 20◦
off the horizontal line in both LFEM images, the position
of the electron emission from the shank is also deviated
from the horizontal line. In the inset, we also show the
time-averaged field distribution around the tip when the
laser beam is displaced downwards from the tip apex by
a distance of 0.5 µm: the longer model tip shown in Fig.
2(e) was used. The maximum field can be observed at
the side exposed to laser, which is consistent with our
We have observed laser-induced modulations of field
emission intensity distributions resulting in strong asym-
metries, which originate from the laser-induced local
fields on the tip apex. By varying the laser polariza-
tion and the laser incidence direction relative to both
azimuthal and polar orientation of the tip apex, we have
demonstrated the realization of an ultrafast pulsed field-
emission source with convenient control of nanometer
sized emission sites. These experimental observations
are quantitatively reproduced by using simulated local
fields for the photo-field emission model. We discussed
the emission processes further and found field-emission
after two photon photo-excitation to be the dominant
process in laser-induced field emission. From experimen-
tal data and simulations, the dependence of the emission
processes on laser power and tip voltage could be under-
This type of electron source is potentially useful for
many applications such as time-resolved electron mi-
croscopy, spatio-temporal spectroscopy, near-field imag-
ing techniques, surface-enhanced Raman spectroscopy, or
coherent chemical reaction control. Maybe the most in-
teresting applications will arise when two laser pulses
with different polarizations or paths are used for the emis-
sion of two independent electron beams from two differ-
ent sites on the tip, spaced only a few tens of nanometers
apart, and with an adjustable time delay between the two
electron pulses. Since field emission electron sources pro-
duce highly coherent electron beams due to their inher-
ently small source size, comparable to the finite spatial
extent of electron wave packets inside the source [2, 3], we
could expect two spatially and temporally coherent elec-
tron beams to be available within the coherence time.
This should create new opportunities for addressing fun-
damental questions in quantum mechanics such as anti-
correlation of electron waves in vacuum , or for new
directions in electron holography .
We acknowledge many useful discussions with Prof. H.
W. Fink, Dr. C. Escher, Dr. T. Ishikawa, and Dr. K.
Kamide. This work was supported in part by the Japan
Society for the Promotion of Science (JSPS), and the
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