Page 279 - Optofluidics Fundamentals, Devices, and Applications

Optofluidic Dye Lasers 253

the liquid which is refractive index–tuned. In general this can be
expressed by [14]
Δλ = Δn1 + Δn2
λ n1 × f 1 n2 × f 2 (Refractive index tuning) (10-8)

where f represents the device geometry–specific tuning efficiency and
f + f = 1. For Bragg resonators where refractive index n is tuned, f
1 2 1 1
can be estimated to
nL
11
f = ≤ 1 (Bragg) (10-9)
1 nL + n L2
11
2

The laser in Fig. 10-1c is fabricated in an elastomeric material, and
the geometric length of the resonator can be tuned mechanically by
stretching the device [15]. Assuming the induced strain is uniform
across the resonator, that is,
ΔL ΔL ΔL
1 = 2 = (10-10)
L L L
1 2
Δλ ΔL
= (Strain tuning (10-11)
)
λ L
The applied elastomer, PDMS, has a low Young’s modulus, typ-
ically less than 1000 kPa and can take large strain without plastic
deformation. Using this approach, a DFB laser with a grating period,
L = 3 μm, operating on the fifteenth-order Bragg reflection, is wave-
length tuned over 29 nm using a single dye mixture (see Fig. 10-6).

10-7 Dye Bleaching
The organic laser dyes gradually degrade when exposed to visible
and ultraviolet radiation. This is referred to as dye bleaching. Over
time the gain medium will thus turn less active. Typically, the prob-
lem of dye bleaching is compensated by a continuous convective flow
of liquid-dissolved dye molecules, thus compensating the bleaching
dynamics caused by the pump radiation. The required, convective
dye-replenishing flow has been achieved by external fluid-handling
apparatus. As an alternative to ordinary mechanical pumps, one
often relies on syringe pumps for lab-on-a-chip applications. Fabrica-
tion of on-chip micro-fluidic pumps has also been pursued [15,16].
More recently, capillary effects have also been used to generate a con-
vective flow without the need for any complicated pumping schemes.
Finally, considering the microfluidic platform, optofluidic lasers and
other devices may potentially be operated for days by diffusion with-
out the need for a convective flow. Below we give a general account
for the physics related to dye replenishment in optofluidic dye lasers.
The central hypothesis will be that to lowest order the gain will scale
linearly with the concentration C of unbleached dye molecules.