Page 129 - Optofluidics Fundamentals, Devices, and Applications

Optofluidic Colloidal Photonic Crystals 109

6-1-2 Photonic Characteristics of Colloidal
Photonic Crystals
In fact, colloidal photonic crystals are a type of photonic crystal. Because
colloidal crystallization is relatively simple and inexpensive—and due
to the absence of an alternative effective technique to create subwave-
length three-dimensional (3D) structures—the crystallization of
colloids has become the most promising technique for preparing 3D
photonic crystals. Unfortunately, typical colloidal photonic crystals,
which are composed of monodisperse silica (with refractive index
n ≈ 1.45) or polymeric particles (n ≈ 1.5), do not show bandgaps
silica polymer
in all directions—so called complete, full, or omnidirectional
bandgaps. Instead, they exhibit “stop” or “pseudo” bands only in
certain directions. In fact, sparkling opal gems composed of silica
nanobeads packed into fcc lattices are natural photonic crystals. The
vivid colors of opals are induced by the reflected lights corresponding
to the bandgaps. As a typical example, the fcc lattice of close-packed
polystyrene nanospheres (n = 1.591) only exhibits a stop band, as is
PS
shown in its energy band structure (Fig. 6-1). The unit cell of the fcc
structure is presented in Fig. 6-1a, where the gray triangle denotes
the (111) plane, the densest hexagonal plane of fcc. In addition,
scanning electron microscopy (SEM) images of the cross section and
top surface of the crystal are shown in Fig. 6-1b and its inset,
respectively, where the crystals are prepared on a glass substrate by
evaporation-induced crystallization during vertical deposition. On
the other hand, the energy band structure presented in Fig. 6-1c,
which was constructed using MIT photonic-bands (MPB) for a water-
filled fcc structure, shows a stop band (called L-gap) in the Γ L
direction normal to the (111) plane [8]. The L-gap is the most useful
stop band in colloidal photonic crystals, because the (111) planes of
the fcc structures are formed along the wall of the confined geometry
during crystallization, and the L-gap has a larger band width
compared to other stop bands.
Tuning of the stop-band position can be achieved by infiltrating
various fluids with different refractive indices into the interstices of the
colloids. As the effective refractive index of the photonic crystal
increases, so does the wavelength of the gap. In addition, a decrease in
the index contrast leads to a reduction of the gap width. These
tendencies are described in the calculation results of Fig. 6-1d, where a
crystal with an fcc lattice composed of polystyrene nanospheres (n =
PS
1.591) with a diameter of 200 nm was infiltrated with various fluids,
going from air (n = 1) to water (n = 1.333), ethanol (n = 1.3614),
tetrahydrofuran (n= 1.4072), chloroform (n= 1.4485), and chlorobenzene
(n = 1.5248). Since 74% of the space is occupied by the particles in an
opaline fcc structure of close-packed spheres, the remaining 26%
is index controllable. A rough estimation gives a wavelength shift of
approximately 90-nm per unit change of the refractive index at