Page 142 - Optofluidics Fundamentals, Devices, and Applications

120 Cha pte r S i x

Colloidal-Crystal Lasers
Many applications of colloidal crystals are based on the selectively
reflected light (i.e., L-gap) induced by Bragg diffraction from the (111)
plane of the fcc structure. On the other hand, if light emitters exist in
the colloidal crystals, the situation becomes totally different because
a periodic modulation of the refractive index in space can induce a
different electromagnetic density of states within the crystals.
According to Fermi’s golden rule, the transition rate from one energy
eigenstate to another is proportional to the density of the final states.
Therefore, emitters, such as dye molecules or quantum dots embedded
in the colloidal crystals, can show emission spectra that are quite dif-
ferent from those of the bulk. The density of states is low at the
bandgap but high at the band edge or at defect modes. Therefore,
spontaneous emission from the emitter in colloidal crystals is inhibited
at the stop band but enhanced at the band edge. Especially, emission
at the band edge can be stimulated, thus inducing lasing due to the
high density of states and the low group velocity at the band edge.
Shkunov et al. reported lasing phenomena at the band edge of a silica
opal immersed in a dye solution (Fig. 6-4c and d) [24]. The silica opal
was prepared slowly by sedimentation of silica particles. Due to the
long attenuation length of the Bragg diffraction at small index
contrasts (of the order of 10 ), the thickness of the crystal should be
−2
on the millimeter scale. Also, Furumi et al. reported lasing at the
defect mode of colloidal photonic crystals. Here, dye molecule-
incorporated thin film is sandwiched with polydimethylsiloxane
(PDMS)-infiltrated PS colloidal crystals [25].
These colloidal crystals for lasing applications can be incorporated
into microfluidic devices. If the dye solution flows though the
interstices of the colloidal crystal in the channel, the problem of dye
bleaching, which is the major drawback of solid-state dye lasers, can
be solved. In addition, tuning of the lasing wavelength can be
achieved by changing the refractive index of the dye-laden fluid.
More importantly, the emitted lasers can be directly used as light
sources in optofluidics or micro-TAS (total analysis systems) applica-
tions by integration with other components.

6-3 Optofluidic Synthesis of Spherical Photonic Crystals
Colloidal crystals integrated in microfluidic chips exhibit an fcc
structure with the (111) plane facing the wider walls of the
microchannel. Thus, in a conventional rectangular channel, the (111)
surfaces are aligned along the horizontal planes. According to Bragg’s
law, the angle of the incident light on the stacked planes determines
the optical path length, and thus, the wavelength of constructive
interference. Therefore, the colloidal crystals produced in the channel
exhibit optical anisotropy. On the other hand, if spherical emulsion