Page 184 - Optofluidics Fundamentals, Devices, and Applications

Optofluidic Photonic Crystal Fibers: Pr operties and Applications 159

provides an advantage over index-guided fluidic fibers. Further-
more, our specific choice of a PBGF consisting of an array of high
index rods in a low index background is amenable to a quasi-analytic
model based on the resonant scattering spectrum of a single high
index rod [59,91–94] (an analogous, though nonanalytic, model exists
for hollow PBGFs with a honeycomb PC cladding [95]). This is
closely linked to the analytic waveguide theory of dielectric cylin-
ders [59,92–94,96,97] and makes it very easy to design the transmis-
sion properties of the fiber, and by extension, the tuning properties
of devices formed from such fibers [98,99].
Representative transmission spectra of fluidic PBGFs are shown
in Fig. 7-20a, where the high transmission regions correspond to
photonic bandgaps of the cladding. As we mentioned, this fiber is
inherently a bandpass filter, and since the center frequency of the
bandgaps depends on the index contrast (see Sec. 7-3), we can tune
the passbands by appropriate choice of filling fluid using the same
PCF template. The thermo-optic coefficients of most fluids are very
large relative to that of silica (~10–100× greater), so one can make the
PBGF into a tunable filter by uniformly heating it [100]. In a variant
on this design, one applies a thermal gradient to the fiber, so that the
center frequencies of the bandgaps vary as a function of propagation
distance along the fiber [101]. Only those wavelengths that lie in the
bandgap of both the hottest and coldest points of the fiber are trans-
mitted, so by increasing the thermal gradient, one can reversibly nar-
row the passbands or completely close them off (Fig. 7-20b). From a
resonant scattering point of view, axial variations in the diameter of
the high-index inclusions are equivalent to variations in the index
contrast, so one may also shape the passbands by weakly tapering
the fiber [102]. Highly tunable filtering based on dual-core fluidic
PBGF directional couplers has also been demonstrated [103]. One
may further enhance the functionality by employing fluidic PBGF
filters based on liquid crystals (LCs), which have far stronger ther-
mal tunability than isotropic fluids [102,104–108] and can be tuned
electrically [108–110] or photochemically [110].
Though we have focused thus far on bandpass filtering, we can
make a fluidic PBGF band rejection filter by using an LPG, as shown
in Fig. 7-21. Silica/fluid fibers are not photosensitive like germanosili-
cate in SMF or grapefruit fiber, but LPGs can be formed in fluidic
PBGFs by applying spatially periodic mechanical stress [111,112], elec-
tric arcs [113], or electric fields (in the case of LC-PBGFs) [112], or by
launching an acoustic wave along the fiber [114]. LPGs are of interest
for their own sake in that they allow one to experimentally probe the
cladding mode and higher order mode properties of PBGFs [111,115]
that are very different from those of index-guided fibers. From a device
perspective, fluidic PBGF LPGs have very large thermal or index sen-
sitivity [116] (~1.5 nm/ºC, or ~3500 nm/R.I.U., has been demonstrated
for isotropic fluids, even larger for LC-PBGFs [112]) owing not so