Page 209 - Optofluidics Fundamentals, Devices, and Applications

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range of ±7 degrees with millisecond response time was demon-
strated [49]. High steering efficiency, polarization-independent oper-
ation, and wide steering range were suggested to be of high interest
for laser detection and ranging. According to the author, the same
design with higher index fluids would allow further extension up to
±15 degrees of the steering range.
Even wider range of deflection angles was achieved using membrane-
based micro-mirror [51]. The micro-mirror is mounted to the membrane
and fixed with a thin silicon hinge to the sidewall of the cavity (see
Fig. 8-2b and 8-2c). With application of a differential pressure
between the cavity and ambient pressure, the PDMS membrane is
distended. The hinge limits one degree of freedom, leading to a
tilting motion. The micro-mirror, fixed to the membrane, is
deflected. By varying the pressure, the tilting angles were varied
from 0 to 75 degrees, relative to the substrate surface. Application
to medical devices with a variable mirror setup, used for in vivo
diagnostics, was suggested [51].

8-2 Membrane-Based Tunable Optofluidics
Numerous optofluidic tunable devices based on soft polymer mem-
branes have recently been reported. In such devices the geometry of
the optical element is altered by application of pressure to deform
soft polymer elements. In this chapter we review two types of devices
based on polymer. We start with a tunable polymer lens and continue
the discussion with composite membrane technology. Some review
of the mechanical properties of a thin bending membrane is sug-
gested to provide an insight into more complicated mechanics of
more general structures, such as composite membranes discussed
later in this section.

8-2-1 Mechanics of Pressure Actuated Polymer
Membrane-based devices commonly consist of a chamber with a soft
distensible wall, commonly made of a soft polymer. When a pressure
is applied to the chamber, the wall bends, altering the geometry of the
element. The deflection regime under applied pressure is commonly
(,
described in terms of the middle line ux y) and thickness tx y(, ) of
the bending wall (see Fig. 8-3a).
Depending on the design and the materials used, the bending
wall can be modeled as a shell or a membrane. The major differ-
ence is that a membrane can take bending stresses in addition to
tensile and compressive stresses observed in shells. Some guide-
lines to the model choice can be found in thin plates and shells
theory [52,53]. For the completeness of the chapter we review some
of the results of the theory.