Page 230 - Optofluidics Fundamentals, Devices, and Applications

Bio-Inspir ed Fluidic Lenses for Imaging and Integrated Optics 205

9-1-2 Curvature-Tunable Fluidic Lens
In contrast to fluidic lens that tunes its index or refraction gradient,
the other major type of fluidic lens changes its curvature. To change the
curvature, different physical mechanisms can be used. Among them
are electrowetting effect, dielectrophoretic effect, surface tension, and
the structure of fluid-filled chamber covered by an elastomer mem-
brane, to name a few.
The effect of electrowetting is manifested by the change of contact
angle of a liquid droplet by an applied electric field. Lippman-Young
equation is the governing equation:

εε
cos( ) = cos( ) + 0 V 2
θ
θ
0 γ 2 d
LG
where θ = the contact angle
θ = initial contact angle with zero voltage applied
0
ε = dielectric constant of the dielectric layer
ε = permittivity of vacuum
0
γ = interfacial energy between the droplet and the ambient
LG
d = thickness of the dielectric layer
V = voltage applied between the substrate and the droplet.
When the contact angle of the droplet changes, the curvature of
the lens changes [18–23]. An example of such structure is shown in
Fig. 9-2.

On Off
~ ~
Electrostatic
+ Electrostatic pressure
+ pressure
–
–
Oil Optical Water oil Optical axis
axis

–
–
Window + + Window Window Window
Metal Metal Metal Metal
Insulation Insulation
FIGURE 9-2 Electrowetting liquid lens. First, a water drop is deposited on a substrate
made of metal, covered by a thin insulating layer. The voltage applied to the substrate
modifi es the contact angle of the liquid drop. The liquid lens uses two isodensity
liquids, one is an insulator while the other is a conductor. The variation of voltage
leads to a change of curvature of the liquid-liquid interface, which in turn leads to a
change of the focal length of the lens. (http://www.varioptic.com/en/index.php.)