Page 79 - Optofluidics Fundamentals, Devices, and Applications

60 Cha pte r F o u r

Fermat’s principle states that the optical path length must be extre-
mal, that is, it can be either minimal, maximal, or a saddle point). The
optical path length frequently determines the functionality of an opti-
cal component. It is calculated by integration of the incremental prod-
uct of the physical path length and the refractive index of the medium
along the path of the optical ray. Thus, the capability of forming large
variety of geometries and refractive indices provides huge flexibility
in the design and realization of OOCs with desired functionalities. In
addition, the OOCs can be easily tuned by dynamically controlling
their geometry and/or their refractive index. Most of the current OOCs
are made of a soft elastomer, polydimethylsiloxane (PDMS). Besides
the advantage of rapid prototyping, PDMS, being an elastic medium
[typical Young’s modulus < megapascals (MPa)] allows very large
tunability by modifying the geometry of the optical device under the
application of internal (usually in the form of gas pressure) or exter-
nal forces. Flexible elastomer membranes are also key elements in
pressure-actuated microvalves that can be integrated with optoflu-
idic components. Geometrical tuning can also be achieved by the
application of an electric field, resulting a change in the wetting angle
of a liquid droplet via the electrowetting effect. The refractive index
of OOCs is typically controlled simply by replacing the liquid form-
ing the OOC with another liquid having different refractive index.
This can be done either off-chip (e.g., by replacing the content of an
external reservoir), or on-chip, by using a predesigned integrated
mixer allowing the mixing of liquids having different refractive indi-
ces. Liquids are available in wide range of refractive indices spanning
from ~1.33 to ~2.3, offering an incredibly large refractive index tuning
of ~1. Even if the choice is limited to nontoxic liquids, refractive index
tuning of ~0.3 is still achievable, and thus the tunability range of
OOCs is orders of magnitudes larger than that achieved by solid optical
components.
This chapter outlines and discusses some of the of the key OOCs
required for the realization of integrated optofluidic systems, includ-
ing waveguides that are being used for signal delivery, spectral fil-
ters, switches and splitters, and beam-steering devices.

4-2 Optofluidic Waveguides
A basic building block required for the realization of most on-chip
integrated optofluidic systems is the optofluidic waveguide. In con-
trast to conventional waveguides, where the optical mode interacts
with a solid core and with a solid/air clad, the optofluidic waveguide
is based on the interaction (either partially of fully) of the optical
mode with liquid (here we limit the discussion to interaction of light
with liquid, although in broader perspective an optical-guided mode
interacting with gas can also be considered as optofluidic waveguide).