Supplemental Information
Yu-Hui Chen, Lu Huang, Lin Gan and Zhi-Yuan Li*
Laboratory of Optical Physics, Institute of Physics, Chinese Academy of Sciences,
Beijing 100190, China
*E-mail address:lizy@aphy.iphy.ac.cn
I. Experimental information
Figure S1 | Experimental setup. A quarter-wave plate is placed with its optical axis
oriented at an angle of 45 degree with the vertical line, and then the vertically polarized
incident light becomes circularly polarized. A 60 times Zeiss objective is used to get a
high-intensity incidence and direct the light to the subwavelength hole in the sample. A
100 times Olympus objective is used to collect the scattered light and image its focal plane.
Images are captured by a CCD with lens. The inset shows the laterally imaging process of
a mirror.
Two points must be emphasized. First, a circularly polarized light must be used in
order to read all the structures on the sample; therefore a quarter-wave plate is
indispensable for changing the polarization of incident wave. The reason is
demonstrated in more detail in Section VI of this Supplemental Information (SI).
Second, due to the mirror in front of the CCD, the pictures captured by CCD are
laterally inverted to the image immediately after the imaging objective, i.e., an “L” is
inverted as a “_|”, as illustrated in Figure S1 and its inset. These inverted images are
only shown in the videos of the “L” and “O” samples in the Section IV of SI. In order
to offer a straightforward picture, all the experimental figures in the main text and SI
are the adjusted images instead of the original images, i.e., the images by applying a
left-to-right operation to the original ones.
II. Writing process
Figure S2 | Depiction of the writing process. (a) The propagating field at 10.64 m
away from the “L” source is stored, whose phase distribution 0 is shown on the right panel.
(b) Superposing the phase of the surface wave nkr to 0 (for “L” sample). The black lines
in the right picture show the positions where |0+nkr-2m|0.25.
In our Finite-Difference Time-Domain (FDTD) simulation, we place the “L” source,
as described in Figure S2(a), at z=10=10.64 m with its incident direction along –z
axis, and a monitor is situated at z=0 to collect the field distribution U0. Because the
polarization of the “L” source is along the x axis, we can expect that the major electric
component of U0 is the x component and thus we only extract the x-component phase
information 0, as shown in the right picture of Figure S2(a). In our FDTD simulation,
the information of an 18 m 18 m region with the grid size of 30 nm 30 nm is
stored as 0; therefore 0 is a 601601 matrix. According to the literature [1], the
interferential maxima of the object wave and the surface wave (the interference term
is UOBJUW*, where UOBJ is the object wave and UW is the writing surface wave) occur
at
 0  nkr  2m ,
(1)
where is the phase of object wave, nkr is the phase of writing surface wave, and m
is an integer. However, the conjugate of UOBJ should be used if a real image is desired
[1]
:
( 0 )  nkr  2m  0 .
(2)
In our “L” simulation, we just need to set
0  nkr  2m  0 .
(3)
Noting that nkr is also discretized as a 601601 matrix, we introduce a criterion as
| 0 ( x, y)  nkr  2m | 0.25 to determine which pixel should be etched. If a pixel (xi,
yi) satisfies | 0 ( x, y)  nkr  2m | 0.25 , the local thickness of silver film at (xi, yi) is
set to be 140 nm, otherwise the thickness is 240 nm. Shown in the right panel of
Figure S2(b) is the result of equation (3) under this criterion, according to which we
build our FDTD model and fabricate our sample.
III. Magnified SEM photos
Figure S3 | Magnified SEM Photos. (a) is for “L” sample, and (b) is for “O” sample, with
2-m-scale bars shown in the bottoms. The numbers indicate the positions where the
measured widths are shown.
We randomly choose five positions in Figure S3(a) and measure their widths, whose
values are 0.11, 0.13 0.08, 0.09, and 0.11 m respectively, according to the noted
order. And the measured values of the five positions in Figure S3(b) are 0.10, 0.14,
0.10, 0.09, and 0.09 m respectively. Therefore we make a conclusion that the widths
of grooves are typical /10.
IV. Movies of the imaging process
Taking the plane where the image of the hole is the clearest as the z=0 plane, as shown
in Figure S4, we first set the focal plane of the imaging objective at the z=-10 m, and
then we gradually move the focal plane to the z=30 m plane, therefore we can
monitor the field distributions from the z=-10 m plane to the z=30 m plane in CCD.
The files named Movie_L.avi and Movie_O.avi are the movies of such process for the
“L” sample and the “O” sample, respectively. In each movie, a pause is set where the
image of “L” or “O” is the clearest.
Figure S4 | Images at the z=0 plane. (a) is for the “L” sample and (b) is for the “O”
sample. The 6 m ruler is also shown. The asymmetry of the central hot spots is ascribed
to the misalignment of the focal spot of the focusing objective to the hole in the silver film.
V. Effect of the widths and depths of the grooves on the image position
Because which pixel should be etched is decided according to the criterion that
| 0 ( x, y)  nkr  2m | 0.25 , the width of a groove is not homogeneous, e.g., at
position A, only one pixel is etched, while three or four pixels are etched at position B.
Therefore the widths shown in Section III above are position dependent. However,
one can change the widths of grooves as a whole by the choice of the criterion. When
we set the criterion as | 0 ( x, y)  nkr  2m | 0.2 , the image intensity varies a little,
whereas the image position is almost unchanged. Similar conclusion applies to the
effect of the groove depth on the image. A series of FDTD simulations indicate that
the influence of changing the depth is more significant on the intensity of the image
than on its position. In the experiment, we fabricate a series of samples with different
depths by changing the focused ion beam etching dwell time from 2 min to 2.5 min,
and the positions of the clearest images are approximately 14.5 m for all “L”
and ”O” samples. In a word, the image position is insensitive to the grooves’ width
and depth.
VI. Polarization dependence of surface wave holography
Figure S5 | Field distribution of a “_” source. (a) The patterns of a strip-like source with
uniform field distribution. The black arrow indicates the polarization, i.e., x polarization.
The length of the strip is 6 m, and the width of the strip is 0.4 m. (b) The FDTD
simulated field distribution pattern at 10.64 m away from the “_” source. The simulated
results are normalized relative to the amplitude of the incident wave.
Figure S5 shows that when monitored at a distance of 10.64 m away, the radiation
field from a strip-like source is widely dispersed along the short axis due to the light
diffraction effect, while little along the long axis, i.e., little energy in the region where
x<-3 m and x >3 m in Figure S5(b).
Figure S6 | Reconstructed image for y polarized incidence. (a1) and (b1) are the
FDTD calculated field distributions at 10.64 m above the front faces of the samples,
while the incident light is y polarized. (a1) is for the “L” sample and (b1) is for the “O”
sample. The amplitude of the incident y polarized wave is set to be one. The calculated
ranges here are also 18 m 18 m. (a2) and (b2) are experimental photos when
y-polarized illumination is used. (a2) is for the “L” sample and (b2) is for the “O” sample.
The 6 m ruler is also shown.
Figure S6 shows the simulated and experimental results for setting the incident
wave as y-polarized. Compared with Figure 2 (noting that all the incident waves in
Figure 2 are circularly polarized), the panels in Figure S6 has only a half of their
counterparts, which is ascribed to the fact that the surface wave excitation is
polarization selective, i.e., SPPs are excited much more effectively by the p-polarized
waves [2]. Intuitively, if we use a “” to divide our hologram sample [Figure 2(a2) and
(b2)] into four quarters, only at the upper and lower quarters (but not the left and right
quarters) can SPP be excited by a y-polarized incidence (approximately), and thus
only the upper and lower quarters of the hologram structure can be read out. For the
case of the “L” sample whose reconstructed image is a “_” here, these two quarters
are the main structures that are responsible for the reconstruction of the “_” strip. The
radiation energy of a strip-like rectangle source is diffracted mainly along its short
axis instead of the long axis, as shown in Figure S5; therefore the contribution of the
“_” strip source and the “|” source to 0 are different in the writing process. When
tracing back to the writing process, only the “_” strip source contributes remarkably to
the upper and lower quarters of U0 and 0. After the superposition of 0 and nkr, the
upper and lower quarters of the structure mainly store the information of “_” instead
of “|”. As a result, only the “_” strip can be reconstructed when the reading surface
wave reads these parts of structure. Another thing given by the comparison of Figure
2 and Figure S6 is that different-polarization components of the scattered wave
propagate independently. Such polarization selective excitation and independent
propagation of each polarized component should be kept in mind when designing
wave-manipulation functionalities.
Reference:
1. Chen YH, Fu JX, Li ZY. Surface wave holography on designing subwavelength metallic structures.
Opt Express 2011; 19: 23908-23920.
2. Maier SA, Plasmonics : fundamentals and applications. Springer, Bath ; New York, 2006.