Page 272 - Optofluidics Fundamentals, Devices, and Applications

246 Cha pte r T e n

10-4 From Macro to Micro
In microfluidic devices, the 100 mm/s flow velocities would imply
excessive pressure gradients, due to the large flow resistance. The
hydraulic resistance of a tube of circular cross section is given by [7]

8 1
Rhyd = η L (10-1)
π a 4

where a = inner radius
L = length
η = viscosity of the liquid flowing through the tube

The Hagen–Poiseuille law
Δp = R Q
hy d (10-2)

can be used to calculate the pressure gradient −Δp/L for the flow rate
2
Q =πa v . With a pressure drop of 1 atm over a 10-mm-long
0
microfluidic channel of inner radius a = 10 μm, a maximum average
flow velocity of v = 100 mm/s can be achieved.
0
The low flow velocities attainable in microfluidic devices have
hindered CW operation of optofluidic dye lasers. Instead, triplet exci-
tation is minimized by pulsing the optical pump radiation, with a
pulse length typically below 10 ns.
The limitations on flow velocity are a first illustration that
optofluidic dye lasers involve more than straightforward miniatur-
ization. In the rest of the chapter we will discuss three main chal-
lenges and their potential solutions.

10-5 Laser Resonators
An optofluidic laser is basically a microfluidic channel with an
embedded optical resonator, as illustrated in Fig. 10-1. The first
optofluidic laser [8], (see Fig. 10-1a), was a vertically emitting device,
where a Fabry–Perot optical resonator was embedded in a 10-μm-
high microfluidic channel by placing thin-film gold mirrors in the
floor and ceiling of the channel. The mode-spacing of the Fabry–Perot
resonator is determined by the condition for standing waves:

k nL = Nπ, N = 1, 2, 3,… (Fabry−Perot) (10-3)
N

where k = 2π/λ is the vacuum wavenumber
n = refractive index of the liquid in the cavity