IEEE Robotics & Automation Magazine - June 2013 - 85

formed gold nanoparticles will be
addressed elsewhere.

Pressure

Basic Physical Principle: EM
Coupling by Applied Pressure
PDMS Gold Nanocomposite Gold Nanoparticles
and Experimental Observations
The gold nanoparticles formed in the
Light
Transmitted
PDMS material are expected to
Source
Light
increase the effective refractive index of
the PDMS and support EM coupling
with the tapered region of the fiber
Tapered Fiber
since the transmitted light tends to
(a)
preferentially propagate into regions
with a high refractive index. As shown
Pressure
in Figure 5(a), the pressure applied to
the GNM introduces a displacement of
Equivalent PDMS Gold Nanocomposite Higher Effective
nanoparticles along its interface with
Lower Effective
Refractive Index
the tapered fiber increasing the light
Refractive Index
Coupled Light
scattering; the nanoparticles thus
Transmitted
Light
increase the coupling of light with the
Light
Source
GNM, reducing the transmitted light
intensity of the optical fiber.
Regarding the modifications of the
Tapered Fiber
optical properties of the GNM, the
(b)
effect of nanoparticle displacements due
to the applied pressure is to change the Figure 5. (a) Light coupling in GNM and light scattering process due to the gold
effective refractive index of GNM as a micro/nanoparticles. (b) Equivalent nanocomposite material as a gradual variation
function of the gold concentration. In of the effective refractive index.
particular, we can model the gradual
variation of the GNM effective refractive index, as illustrated in Figure 5(b), where the region with a higher refractive index is near the contact interface of the tapered fiber
and the region with a lower effective refractive index is
toward the pressure contact surface. This variation of the
effective refractive index can be approximately estimated
Contact Surface of the Tapered Fiber
assuming spherical gold nanoparticles in the PDMS mate(a)
rial. In this case, the effective dielectric function f eff for
spherical gold particles having dielectric function f m,
which varies with the optical working wavelengths [26],
embedded in a medium f s is defined by [27]-[28] as
E eff = E s

E m (1 + 2z) + 2E s (1 - z)
,
E m (1 - z) + E s (2 + z)

(b)

(1)

where z indicates the gold concentration.
The displacement of the gold nanoparticles in PDMS due
to a uniformly applied force are schematically indicated by the
bidimensional (2-D) FEMsimulation of Figure 6(a): the particles that are on the top of the GNM microcell region tend to
accumulate near the contact interface by increasing the effective dielectric function of f eff due to the increment of z, as
schematized in Figure 5(b). The exact distribution of the function f eff during the applied force is difficult to model. To
explain the basic principles through an approximated model,
we assume high gold concentration for the region with higher
effective permittivity in contact with the tapered region and a

Figure 6. (a) 2-D mechanical FEM modeling of a GNM microcell:
gold nanoparticle density correlated to the applied force. The
simulated particles have a diameter of 120 nm. (b) 2-D FEM
modeling: simulated modeling of Figure 5, where the results are
obtained by reducing the value of the effective permittivity step
by step by a factor two (corresponding to a theoretical reduction
of gold concentration). The light coupling effect is strong in
proximity of the tapered fiber interface.

reduction of f eff to a different extent. The 2-D FEM simulation of Figure 6(b) shows that the EM energy is confined to
where the effective permittivity is higher (pressure effect) by
reducing the transmitted light intensity at the output of the
fiber. The parameters used in the FEM simulation are
june 2013

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IEEE ROBOTICS & AUTOMATION MAGAZINE

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