  Liquid phase sensing applications at 1550~nm are highly desirable due to
widely available off-the-shelf components. Generally, liquids at 1550~nm induce
a high absorption loss that limits the overall sensor's sensitivity and
detection limit. One solution is to use an active fiber loop in conjunction
with cavity ring down spectroscopy to overcome these absorption losses.
However, the amplifier inside the fiber loop suffers from inherent gain
fluctuations that limit the sensing system's overall performance. Here, we
provide a novel sensor using the wavelength-scanned phase shift-cavity ring
down spectroscopy (PS-CRDS) in conjunction with a linear active fiber cavity
that potentially offers a more sensitive solution than traditional fiber loop
sensors. We use a tapered fiber as a sensing head inside the active cavity
built from fiber Bragg gratings. We derive a theoretical phase shift expression
for our system and simulate it using the finite element method to determine
optimum tapered fiber diameter for glucose sensing in DI water. Compared to a
non-amplified system, we find that our amplified system can increase the
sensitivity by fourteen times via the amplifier gain tuning. We also conduct
experimental measurements using 0-15.5~mM glucose solutions and find them in
excellent agreement with our theoretical predictions. Experimentally we obtain
the sensor's sensitivity of 0.768~$^o$/mM (1164~$^o$/RIU) and detection limit
of 0.75~mM ( 4.5~$\times$~10$^{-4}$~RIU) without any temperature stabilization
in the system. We anticipate that the present work will find a wide range of
sensing applications in fiber cavities, ring resonators, and other microcavity
structures.
