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We put forward a new fiber optic sensor for measuring linear velocity withpicometer/second sensitivity with Weak-value amplification based on generalizedSagnac effect [Phys. Rev. Lett.\textbf{93}, 143901(2004)].The generalizedSagnac effect was first introduced by Yao et al, which included the Sagnaceffect of rotation as a special case and suggested a new fiber optic sensor formeasuring linear motion with nanoscale sensitivity. By using a different schemeto perform the Sagnac interferometer with the probe in momentum space, we havedemonstrated the new weak measure protocol to detect the linear velocity byamplifying the phase shift of the generalized Sagnac effect. Given the maximumincident intensity of the initial spectrum, the detection limit of theintensity of the spectrometer, we can theoretically give the appropriatepre-selection, post-selection, and other optical structures before theexperiment. Our numerical results show our scheme with Weak-value amplificationis effective and feasible to detect linear velocity with picometer/secondsensitivity which is three orders of magnitude smaller than the result$\nu$=4.8 $\times$ $10^{-9}$ m/s obtained by generalized Sagnac effect withsame fiber length.

the european physical journal. d, atomic, molecular and optical physics/the european physical journal. d, atomic, molecular, optical and plasma physics

The design of a new fiber optic sensor for measuring linear velocity with pico meter/second sensitivity based on Weak-value amplification