Page 273 - Optofluidics Fundamentals, Devices, and Applications

Optofluidic Dye Lasers 247

In the actual device, the μm scale mirror separation yields mode spac-
ings ~10 nm in the relevant wavelength range, 570 to 600 nm.
For integration it would be an advantage to have a lateral emis-
sion of laser radiation. A laterally emitting Fabry-Perot optofluidic
laser was realized in a hybrid approach, where two cleaved, end-face
metallized optical fibers were aligned face-to-face in a microfluidic
channel in a polymer device [9].
Figure 10-1b shows a laterally emitting distributed feedback
(DFB) optofluidic laser. The DFB resonator is formed by placing a
periodic array of polymer walls inside the microfluidic channel. Light
traversing the microfluidic channel at the resonator will experience a
periodic refractive index modulation. For simplicity we treat this as a
one-dimensional problem by considering a periodic stack of liquid
and polymer layers with the refractive index varying between n =
1
1.36 in the liquid dye and n = 1.59 in the polymer. Commensurability
2
between the period L of the structure and the wavelength of light will
give rise to resonances and standing waves according to the Bragg
condition for the free-space wavenumber:

k (n L + n L ) = Nπ, N = 1, 2, 3,… (Bragg) (10-4)
N 1 1 2 2
with L = L + L , where L is the width of the fluidic channels and L is
1 2 1 2
the width of the polymer walls. At resonance, a standing wave is
formed along the periodic structure. Partial reflection of light at the
liquid polymer interfaces yields a distributed optical feedback across
the entire structure, as opposed to feedback between the two discrete
mirrors in the Fabry–Perot cavity. The optofluidic DFB laser device in
Fig. 10-1b has a mode spacing of a few nanometers and operates in a
high Bragg order.
For simplicity we could consider to realize a “symmetric” struc-
ture L = L = L / 2, of the same materials as the device in Fig. 10-1b:
1 2
n = 1.36 and n = 1.59. To build a first-order optofluidic DFB laser N = 1
1 2
emitting at a vacuum wavelength λ around 600 nm, a grating period
L below 200 nm is required.
In the one-dimensional treatment previously, we have neglected
the finite transverse dimensions, for example, the finite height of the
microfluidic channel. If we consider the full three-dimensional struc-
ture, we note that the liquid dye has a lower refractive index n =
dye
1.36 than the surrounding polymer n = 1.59, that is, the light is
polymer
not confined in the liquid by total internal reflection.
This issue is addressed in the device shown in Fig. 10-1c [10],
where light confinement in the liquid dye is enabled by choosing a
dye solvent of high refractive index (mixture of ethanol and ethylene
glycol n = 1,409) in combination with a lower refractive index poly-
mer (PDMS n = 1.406) for the device. The low index contrast between
liquid core and polymer cladding allows single mode waveguiding
at wavelength λ ~600 nm even when the channel cross section