Dielectric versus topographic contrast
in near-field microscopy
Olivier J. F. Martin
Laboratory for Field Theory and Microwave Electronics, Swiss Federal Institute of Technology, ETH-Zentrum,
8092 Zurich, Switzerland
Christian Girard
Laboratoire de Physique Mole
´
culaire, Unite
´
de Recherche Associe
´
e au Centre de la Recherche Scientifique 772,
Universite
´
de Franche–Comte
´
, 25030 Besanc¸on, France
Alain Dereux
Equipe Submicronique, Unite
´
de Recherche Associe
´
e au Centre de la Recherche Scientifique 1796,
Laboratoire de Physique, Universite
´
de Bourgogne, BP 138, 21004 Dijon Cedex, France
Received October 30, 1995; accepted January 22, 1996
Using a fully vectorial three-dimensional numerical approach (generalized field propagator, based on Green’s
tensor technique), we investigate the near-field images produced by subwavelength objects buried in a dielec-
tric surface. We study the influence of the object index, size, and depth on the near field. We emphasize the
similarity between the near field spawned by an object buried in the surface (dielectric contrast) and that
spawned by a protrusion on the surface (topographic contrast). We show that a buried object with a negative
dielectric contrast (i.e., with a smaller index than its surrounding medium) produces a near-field image that is
reversed from that of an object with a positive contrast. © 1996 Optical Society of America.
1. INTRODUCTION
With a resolution far beyond the diffraction limit, scan-
ning near-field optical microscopy (SNOM) is becoming an
extremely powerful technique for the analysis of surface
structures at the mesoscopic scale.
1
[SNOM as used in
this paper also covers near-field scanning optical micros-
copy (NSOM), photon scanning tunneling microscopy
(PSTM), and scanning tunneling optical microscopy
(STOM).]
The imaging properties of the topographic variations of
a surface (protrusions, surface roughness) have been in-
vestigated from a theoretical point of view with different
numerical methods, and the relationship between a topo-
graphic object and its near-field image is understood to a
certain extent.
2–9
Recently, procedures have also been
proposed for solving the important inverse problem, i.e.,
the reconstruction of the topographic profile from the
near-field data.
10–13
On the other hand, to the best of our
knowledge, pure dielectric contrast has been investigated
only in two-dimensional systems or by means of a pertur-
bative approach,
14–16
and no self-consistent calculations
have yet been presented on pure dielectric contrast for
three-dimensional (3D) defects buried in a dielectric sur-
face. In this paper we address this problem and investi-
gate the near field spawned by a perfectly flat surface dis-
playing 3D index variations.
The physical system considered and the formalism
used are described in Section 2. In Section 3 we study
the influence on the near field of different physical param-
eters (index contrast, size, and depth of the perturbation).
These results are summarized in Section 4.
2. MODEL
Local index variations of a flat dielectric surface are com-
monly used in integrated optics to define buried
waveguides. Such diffused waveguides represent key
components for advanced photonic integrated circuits
(PIC’s). Depending on the substrate material used, they
can be produced by different techniques: ion exchange,
flame hydrolysis, or chemical vapor deposition.
17,18
It is
important to note that all these techniques produce
extremely weak index variations in the surface,
Dn < 0.01.
19
The analysis and monitoring of photonic integrated cir-
cuits indisputably provides an extremely promising appli-
cation field for SNOM.
20–22
We will therefore place the
present study in this context and investigate SNOM’s im-
aging properties of weak index variations, similar to those
used for diffused waveguides in PIC’s.
In this paper we consider a flat dielectric surface
(n 5 1.500) with localized 3D index variations
Dn
,
0.01. The surface is illuminated from below by total
reflection (Fig. 1). For such a glass–air interface, the to-
tal reflection angle is 42°; we take for our calculations an
incident angle of 50°. We investigate two different inci-
dent polarizations: s polarization, where the incident
electric field is parallel to the glass–air interface, and p
polarization, where it is in the plane of incidence (Fig. 1).
Martin et al. Vol. 13, No. 9/ September 1996 /J. Opt. Soc. Am. A 1801
0740-3232/96/0901801-08$10.00 © 1996 Optical Society of America
The electric near field spawned above the surface is
computed with the generalized field propagator; this fully
vectorial formalism, based on Green’s tensor technique,
allows simultaneous computation of the responses of a
physical system to different incident fields.
23
In this
way, different polarizations and incident field directions
can be investigated simultaneously. For all the results
presented in this paper, we consider an illumination
wavelength of 633 nm in vacuum and a 53535nm
3
dis-
cretization mesh for the inhomogeneities of the system.
24
3. RESULTS
To compare topographic and dielectric contrasts, let us
first consider a pure topographic case, where a 20320310
nm
3
protrusion with the same index is placed on the sur-
face (Fig. 1). In this figure we report the relative total
electric field intensity in a plane parallel to the surface,
located 5nm above the protrusion. The field intensity I
is normalized to the intensity I
0
that would be measured
without a protrusion.
For p polarization [Fig. 1(a)] we observe a strong field
confinement that reproduces the object shape.
5
The fact
that an object much smaller than the wavelength can
spawn a confined field that perfectly reproduces its shape
explains how SNOM achieves a resolution far beyond the
diffraction limit. Indeed, such a confined field can be de-
tected by a SNOM probing tip.
For s polarization, the field intensity no longer repro-
duces the object, but strong field gradients appear along
the object sides that are orthogonal to the incident field,
whereas the object itself appears in reversed contrast: A
depletion in the field intensity is observed above the ob-
ject [Fig. 1(b)].
This difference of behavior between s and p polariza-
tions, which is also observed experimentally,
25
is easily
understood if one recalls the fact that a small volume of
matter, such as the protrusion in Fig. 1, generates a de-
polarization field E
d
when it is submitted to an external
field E
0
. This depolarization field is such that the total
field E 5 E
0
1 E
d
fulfills the boundary conditions re-
quired by Maxwell equations.
26
For s polarization the
discontinuity of the total field along the protrusion sides
orthogonal to the incident field imposes strong variations
of the depolarization field along these sides [Fig. 1(b)].
On the other hand, the incident field already satisfies
Fig. 1. Relative total field intensity I/I
0
, above a dielectric surface (n 5 1.500) with a 20 3 20 3 10 nm
3
protrusion of same index.
The field intensity I is computed 5 nm above the protrusion (i.e., 15 nm above the surface) and normalized with the value I
0
that would
be obtained without a protrusion. The surface is illuminated by total reflection with a wave propagating in the k direction. Two dif-
ferent incident polarizations are investigated: (a) p polarization (incident electric field E
p
0
) and (b) s polarization (incident electric field
E
s
0
).
Fig. 2. Same geometry as in Fig. 1 but with another propagation direction for the incident field.
1802 J. Opt. Soc. Am. A / Vol. 13, No. 9 / September 1996 Martin et al.
these boundary conditions along the protrusion sides par-
allel to the incident field, and no depolarization effect is
observed along these sides. When the orientation of the
incident field changes, the depolarization effects appear
along other protrusion sides, as is visible in Fig. 2(b).
For p polarization the incident field is mainly vertical,
and the dominant depolarization effects occur along the
top protrusion face. Because we compute the field in a
plane parallel to that top face, we cannot observe these
vertical depolarization effects, and we measure only the
field enhancement caused by the entire protrusion. Note
that, in spite of the small protrusion volume, this en-
hancement is significant, and the field intensity reaches
1.3 times its value without a protrusion [Fig. 1(a)]. Be-
cause this field confinement effect is related to the verti-
cal field component, it does not depend on the propagation
direction of the incident field, and the total field intensity
always reproduces the surface defect, as can be seen in
Figs. 1(a) and 2(a). Nonetheless, let us emphasize that if
we considered only the minor horizontal field component
that also exists for that p polarization, we would of course
observe a horizontal depolarization effect similar to that
observed for s polarization; but, for our illumination
mode, the total field in p polarization is dominated by the
vertical field component, and this horizontal depolariza-
tion effect is not visible. For all that, it is important to
keep in mind that in a practical SNOM experiment, the
polarization sensitivity of the signal-collecting scheme
(optical fiber, aperture, etc.) can strongly influence the re-
corded image. In this way, the experimental image can
be dominated by the intensity of a given field component
and not reproduce the total near-field intensity.
Let us now turn to a pure dielectric contrast case. We
show in Fig. 3 the near-field intensity 5nm above a per-
fectly flat surface with four buried pads with indices
slightly different from the surface. The top face of each
pad coincides with the surface, so that the system is per-
fectly flat.
The topography of the field intensity produced by such
a buried pad is similar to that obtained for the protrusion
on the surface: field confinement above the pad for p po-
larization [Fig. 3(a)] and inverse contrast and field gradi-
ents along the object sides for s polarization [Fig. 3(b)].
In Fig. 3 the amplitude of the signal above a buried pad
increases with the contrast of index (difference between
pad index n
pad
and surface index n
surf
). This effect is em-
phasized in Fig. 4, where we show the relative total field
intensity above the center of a buried pad as a function of
the pad index. Note the field enhancement for p polar-
ization and the field depletion for s polarization. For a
small contrast index (n
pad
5 1.5...1.6), the relative to-
tal field intensity varies mainly linearly with the pad in-
dex (Fig. 4). For a larger contrast, the intensity con-
verges to a limiting value that depends on the pad shape.
This effect is similar to the scattering by a sphere of index
n
sp
and radius r embedded in a homogeneous medium of
index n
med
. For such a system, the scattered field is pro-
portional to the mean polarizability
a
of the sphere. For
Fig. 3. Relative total field intensity I/I
0
, 5 nm above a perfectly flat surface (n 5 1.500) with four 20 3 20 3 10 nm
3
buried pads of
different indices (see inset). The total field intensity I is normalized to the value I
0
measured without buried pads. Same incident
fields as in Fig. 1.
Fig. 4. Relative total field intensity I/I
0
, 5 nm above the center
ofa203 20 3 10 nm
3
pad of varying index, buried in a perfectly
flat surface (n 5 1.500). The total field intensity I is computed
for the two polarizations depicted in Fig. 1 and normalized to the
value I
0
measured without a buried pad.
Martin et al. Vol. 13, No. 9/ September 1996 / J. Opt. Soc. Am. A 1803
Fig. 5. Same geometry as in Fig. 3 but with a negative index contrast (the indices of the pads are smaller than the surface index). This
negative index contrast leads to the reversed (upside down) image of Fig. 3.
Fig. 6. Relative total field intensity I/I
0
, 5 nm above a perfectly flat surface (n 5 1.500) with four 20 3 20 3 10 nm
3
pads
(n 5 1.508) buried at different depths. The distance between the top face of each pad and the substrate–air interface is given in the
inset. The total field intensity I is normalized to the value I
0
measured without buried pads. Same incident fields as in Fig. 1.
Fig. 7. Relative total field intensity I/I
0
, 5 nm above a perfectly flat surface (n 5 1.500) with four 20 3 20 3 h nm
3
buried pads
(n 5 1.508) of varying height: h 5 10, 20, 30 and 40 nm. The total field intensity I is normalized to the value I
0
measured without
buried pads. Same incident fields as in Fig. 1.
1804 J. Opt. Soc. Am. A / Vol. 13, No. 9 / September 1996 Martin et al.
a given embedding medium and sphere radius, this mean
polarizability, given by the Lorentz–Lorenz formula
27
a
5
n
sp
2
2 n
med
2
n
sp
2
1 2n
med
2
r
3
, (1)
also converges to a constant value (
a
5 r
3
) for large
sphere indices.
It is important to note that the intensity of the signal
measured in Fig. 3 is 100 times smaller than in the topo-
graphic contrast case studied in Fig. 1. We will address
this problem at the end of this section.
The dielectric contrast investigated in Fig. 3 is positive
(the index is higher in the pad than in the surface). If we
consider the opposite case, where the pad index is smaller
than the surface index, we obtain a reversed field inten-
sity pattern, as is visible in Fig. 5. Note the reversed
peak for p polarization and the reversed depletion that
leads to a broad peak above each pad for s polarization.
If we place the buried pads not directly below the sur-
face but at a certain depth, we observe a strong decrease
of the measured intensity, as can be seen in Fig. 6. When
the pad is only 10 nm below the surface, the correspond-
ing peak in p polarization reaches only one third of the
value measured when the pad was just at the surface
[Fig. 6(a)].
This extremely rapid reduction of the field intensity as
a function of the pad depth is caused by the strong decay
of the evanescent-field components responsible for the
near-field intensity. This decay is easily understood if
one recalls the form of Green’s tensor G
0
used for the cal-
culation of the scattered field in our formalism [see, e.g.,
Eq. (9) of Ref. 23]. Indeed, in addition to the 1/R term
that dominates the far field, G
0
also contains 1/R
2
and
1/R
3
terms that account for the near field and are respon-
sible for the rapid intensity decay observed in Fig. 6 when
the pad depth increases (R can be viewed as the distance
between the pad and the point where the field is com-
puted).
When we maintain the pad just below the surface and
increase its height, thereby increasing its volume, the
measured intensity rises (Fig. 7). However, the intensity
is not simply proportional to the pad height, and for very
high buried pads the intensity saturates. This is due to
Fig. 8. Relative total field intensity I/I
0
, 5 nm above a perfectly flat surface (n 5 1.500) with four 10-nm-thick buried pads
(n 5 1.508) of varying area (10 3 10, 20 3 20, 30 3 30, and 40 3 40 nm
2
). The total field intensity I is normalized to the value I
0
measured without buried pads. Same incident fields as in Fig. 1.
Fig. 9. Relative total field intensity I/I
0
above a surface (n 5 1.500) with a 20 3 20 3 10 nm
3
pad (n 5 1.508) buried in the surface
anda203 20 3 10 nm
3
protrusion on the surface. The field intensity is computed 5 nm above the protrusion. The total field intensity
I is normalized to the value I
0
measured on a perfectly flat surface. Same incident fields as in Fig. 1.
Martin et al. Vol. 13, No. 9/ September 1996 / J. Opt. Soc. Am. A 1805
