The first fiber Bragg grating (FBG) accelerometer using direct transverse forces is demonstrated by fixing the FBG by its two ends and placing a transversely moving inertial object at its middle. It is very sensitive because a lightly stretched FBG is more sensitive to transverse forces than axial forces. Its resonant frequency and static sensitivity are analyzed by the classic spring-mass theory, assuming the axial force changes little. The experiments show that the theory can be modified for cases where the assumption does not hold. The resonant frequency can be modified by a linear relationship experimentally achieved, and the static sensitivity by an alternative method proposed. The principles of the over-range protection and low cross axial sensitivity are achieved by limiting the movement of the FBG and were validated experimentally. The sensitivities 1.333 and $0.634\mathrm{nm}/\mathrm{g}$ were experimentally achieved by 5.29 and 2.83 gram inertial objects at 10 Hz from 0.1 to 0.4 g ($\mathrm{g}=9.8\mathrm{m}/{\mathrm{s}}^2$), respectively, and their resonant frequencies were around 25 Hz. Their theoretical static sensitivities and resonant frequencies found by the modifications are $1.188\mathrm{nm}/\mathrm{g}$ and 26.81 Hz for the 5.29 gram one and $0.784\mathrm{nm}/\mathrm{g}$ and 29.04 Hz for the 2.83 gram one, respectively.

Fiber Bragg grating (FBG) is inherently sensitive to temperature and strain. By modulating FBG’s strain, various FBG sensors have been developed, such as sensors with enhanced or reduced temperature sensitivity, strain/displacement sensors, inclinometers, accelerometers, pressure meters, and magnetic field meters. This paper reviews the strain modulation methods used in these FBG sensors and categorizes them according to whether the strain of an FBG is changed evenly. Then, those even-strain-change methods are subcategorized into (1) attaching/embedding an FBG throughout to a base and (2) fixing the two ends of an FBG and (2.1) changing the distance between the two ends or (2.2) bending the FBG by applying a transverse force at the middle of the FBG. This review shows that the methods of “fixing the two ends” are prominent because of the advantages of large tunability and frequency modulation.

We demonstrate the first biaxial fiber Bragg grating (FBG) accelerometer using axial and transverse forces. An inertial object is fixed at the middle of two FBGs inscribed in one fiber. The difference between the resonant wavelengths of the two FBGs can distinguish the acceleration in the axial direction, while being insensitive in the transverse direction. The average of the resonant wavelengths of the two FBGs can distinguish the acceleration in the transverse direction, while being insensitive in the axial direction. In the experiments, when the transverse direction was vertical, the crest-to-trough sensitivity at 5 Hz and resonant frequency of the average were 0.545 nm/g and 34.42 Hz, respectively. When the axial direction was vertical, those of the difference were 0.0454 nm/g and 900 Hz, respectively. For each FBG, the crest-to-trough sensitivity at 5 Hz and resonant frequency in the transverse/vertical direction were 24 and 1/26 times those in the axial/vertical direction, respectively.

The only effective method of fiber Bragg grating (FBG) strain modulation has been by changing the distance between its two fixed ends. We demonstrate an alternative that is more sensitive to force based on the nonlinear amplification relationship between a transverse force applied to a stretched string and its induced axial force. It may improve the sensitivity and size of an FBG force sensor, reduce the number of FBGs needed for multiaxial force monitoring, and control the resonant frequency of an FBG accelerometer.

Reducing the size of an accelerometer overcomes the tradeoff between its sensitivity and resonant frequency, and the theoretical relationships are analyzed. A fiber Bragg grating (FBG) accelerometer with the shortest vibration arm, 7 mm, among FBG accelerometers using the optical fiber to hold its inertial object is demonstrated here. The inertial object was 4.41 g. The experimental crest-to-trough sensitivity and resonant frequency, 244 pm/g and 90 Hz, disagree with the theoretical values, 633 pm/g and 67 Hz, perhaps due to the friction between the inertial object and shell. In order to find the theoretical values, a method to find the pre-stretch of the FBG is also presented here, based on the stretch of the FBG at equilibrium and the mass of the inertial object. The FFT program, experimental data and theoretical calculations are presented in detail in the ^{Supplementary Material}.