Thermodynamic phase noise in passive fiber devices is generally so weak that in most devices, in particular fiber sensors, it has only been observed in fiber lengths in the range of 1 meter or much longer. Here we present a passive fiber strain sensor only 4.5 mm in length in which the noise in the frequency range of 1 kHz to ~12 kHz is limited by thermal phase noise in the fiber. The phase noise could be measured in such a short fiber by utilizing a slow-light fiber Bragg grating (FBG) resonator in which the phase noise is magnified by the resonator's slowing-down factor n<sub>g</sub>/n ≈ 370, where n<sub>g</sub> is the group index. At the same time, the usually dominant laser frequency noise was brought below the level of the phase noise by using a short fiber and a low-noise laser with a linewidth under 200 Hz. At 4 kHz, the total measured noise expressed in units of strain is 110 fε/√Hz, and the phase noise accounts for 77% of it. This sensor resolves a single-pass thermodynamic length fluctuation of only 5 x10<sup>-16</sup> m/√Hz. These measurements provide experimental support for the dependencies of the phase noise on the fiber resonator length and group index predicted by a recent model.
We report a new generation of slow-light FBG strain sensor with a strain resolution (or minimum detectable strain) as
low as 30 fepsilon/√Hz at 30 kHz, which is one order of magnitude lower than the record held by the previous generation. This
sensor has an ultra-stable output (no drift in 4 days) and is capable of resolving an absolute strain of ~250 attostrains by
integrating its output for ~8 hours, which is also a new record for an FBG fiber sensor. These improvements were
accomplished by first maximizing the slope of the slow-light resonances, and hence the strain sensitivity. To this end the
apodized FBG was written in a deuterium-loaded fiber with a femtosecond infrared laser, then thermally annealed. The
three main sources of noise in the sensor system were also carefully reduced. The dominant source of noise, laser
frequency noise, was reduced by interrogating the FBG with an ultra-stable laser (linewidth under 200 Hz) with a low
intensity noise. The phase noise was minimized by selecting the proper FBG length (~25 mm). When used as an acoustic
sensor, the same grating had a measured average pressure resolution of 50 μPa/√Hz between 3 kHz and 6 kHz, one order
of magnitude lower than the previous lowest reported value for an FBG sensor.
This paper reports the generation of record low group velocities, large group delays, and high optical confinements in strong apodized fiber Bragg gratings (FBGs). The gratings were fabricated in deuterium-loaded fiber using an 806-nm femtosecond laser and a phase mask to produce strong apodized index-modulation profiles and low internal loss, followed by annealing to reduce residual losses. In a first FBG of this type with a length of ~25 mm and a non-saturated index modulation we measured a group delay–transmission product of 10.4 ns, the highest ever reported. In a stronger, shorter FBG (12.3 mm in length), a group delay of 42 ns was observed, corresponding to a group velocity of only ~290 km/s and a group index of 1020. In a still shorter and therefore lower loss device (~5 mm) we were able to observe the fundamental mode, and infer a Purcell factor as high as 25.5. These exceptional features are made possible in part by the gratings’ strong index modulation (~2x10<sup>-3</sup>) and ultra-low single-pass loss (~0.01–0.015 dB/cm).
We demonstrate through numerical simulations that a fiber Bragg grating operated in transmission can support much
slower light than previously anticipated. This is accomplished by increasing the grating's index modulation, reducing its
loss, optimizing its length, and apodizing its index profile. With current fiber Bragg grating loss and index modulation,
we predict that group velocities lower than <i>c</i>/1000 are attainable. We validate this concept with a record measured group
index of 130 in a strong apodized grating (index modulation of ~1.1 10<sup>-3</sup>) with a nearly optimized length of 1.2 cm and
an inferred loss coefficient of 1 m<sup>-1</sup>.