IEEE Robotics & Automation Magazine - June 2013 - 86

Table 1. Parameters used in the FEM simulation.
Broad Lamp
Source
Multimode
Fiber

Parameter

Description

Value

m0

Working wavelength

1.3 µm

E fiber

Relative dielectric permittivity of the core of the
tapered fiber

3.17

Es

Relative dielectric permittiv- 2.25
ity of PDMS

E eff

Real part of the relative
dielectric permittivity of the
gold nanoparticle with z
= 0.5 [first layer of GNM of
Figure 5 (b)]

10

t gold

Density of gold

19,300 kg/m3

t PDMS

Density of PDMS

970 kg/m3

E gold

Young's modulus of gold

70 # 109 Pa

E PDMS

Young's modulus of PDMS

500 # 103 Pa

v gold

Poisson's ratio of gold

0.44

v PDMS

Poisson's ratio of PDMS

0.5

Sensor

OMA

Figure 8. A schematic plot of the used experimental setup that
includes a broad lamp source and an OMA.

reported in Table 1. We have used a properly designed FEM
tool oriented on micro-EM issues [29]. To highlight the
importance of GNM for light coupling, we simulate and measure the coupling effect by considering PDMS and PDMS
GNM, simply positioned on the tapered profile (without
applied forces). Figure 7 shows the comparison between the
transmitted optical intensities, taking into account the light

transmitted in the tapered Si fiber [Figure 7(a)], the light
transmitted and coupled for a fiber/PDMS system [Figure 7(b)], and the light transmitted and coupled for a fiber/
GNM system [Figure 7(c)], respectively. A remarkable reduction of the transmitted light, due to coupling with GNM, is
experimentally observed in the spectral range between 1,280
and 1,320 nm. Besides, no considerable variations are found
in the same range by comparing the case of the tapered Si
fiber and fiber/PDMS system. The same behavior of light
intensity reduction is predicted by FEM simulations (see inset
of Figure 7). Due to the multimodal propagation of light in
the fiber, the variations of the transmitted light intensities are
enhanced in specific frequency band regions. One of these
regions is shown in Figure 7.

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0

1,

32
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1,

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0

1,

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0
30
0

IEEE ROBOTICS & AUTOMATION MAGAZINE

1,

1,

70

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0

1,

60

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2

1,
2

1,
2

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Intensity (a.u.)

Measurements and Discussions
The measurements presented in Figure 7 and the ones of
optical characterization of the proposed sensor upon pressure are performed using the experimental setup shown in
Figure 8. An optical multichannel
analyzer (OMA) is connected with
the output of the multimode tapered
fiber. The pressure sensor sample is
40,750
Working Wavelength
fixed on a system that assures the
40,500
mechanical stability during the
40,250
application of the pressure forces.
40,000
(a)
The input of the fiber is connected
39,750
39,500
to a broad lamp source. We observe
39,250
that the proposed technology is suit(b)
39,000
able for pressure sensors that can
38,750
detect forces that are applied by dif(c)
38,500
ferent weights ranging from a few
38,250
grams (0.01 N) to 200 (1.9 N) and
38,000
400 g (3.9 N). In each case, by apply37,750
ing different weights to the sensors a
significant variation of the transmitted light intensity occurs. An examm (nm)
ple of real-time response is shown in
(a)
Tapered Fiber
Figure 9, where the optical response
(b)
Tapered Fiber + PDMS
returns to the initial configuration
(c)
Tapered Fiber + gold/PDMS
after the measurements and the fast
light transmittivity response is thus
Figure 7. Experimental characterization of the light coupling without applied pressureforces:
verified. We experimentally observe
part of the transmittivity optical spectrum for (a) tapered fiber, (b) tapered fiber with PDMS
a quasi-simultaneous return to the
material placed on the tapered region, and (c) tapered fiber with gold/PDMS material. Inset:
2-D FEM results. (a) FEM example of light coupling in an Si-tapered fiber, (b) small coupling
initial spectrum as soon as we
effect by positioning a PDMS material on the tapered surface, and (c) high light coupling
remove the weights (a response time
effect performed by placing it on the tapered region of the GNM. The working wavelength is
less than 1 s is checked).
m 0 = 1.298 nm. The inset proves the experimental results reported in the figure.
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