• Photonics Research
  • Vol. 13, Issue 4, 875 (2025)
Ruimin Jie1, Jie Huang1,2, and Chen Zhu1,*
Author Affiliations
  • 1Department of Electrical and Computer Engineering, Missouri University of Science and Technology, Rolla, MO 65409, USA
  • 2e-mail: jieh@mst.edu
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    DOI: 10.1364/PRJ.542584 Cite this Article Set citation alerts
    Ruimin Jie, Jie Huang, Chen Zhu, "Transforming optical Vernier effect into coherent microwave interference towards highly sensitive optical fiber sensing," Photonics Res. 13, 875 (2025) Copy Citation Text show less

    Abstract

    The optical Vernier effect has garnered significant research attention and found widespread applications in enhancing the measurement sensitivity of optical fiber interferometric sensors. Typically, Vernier sensor interrogation involves measuring its optical spectrum across a wide wavelength range using a high-precision spectrometer. This process is further complicated by the intricate signal processing required for accurately extracting the Vernier envelope, which can inadvertently introduce errors that compromise sensing performance. In this work, we introduce a novel approach to interrogating Vernier sensors based on a coherent microwave interference-assisted measurement technique. Instead of measuring the optical spectrum, we acquire the frequency response of the Vernier optical fiber sensor using a vector network analyzer. This response includes a characteristic notch that is highly sensitive to external perturbations. We discuss in detail the underlying physics of coherent microwave interference-based notch generation and the sensing principle. As a proof of concept, we construct a Vernier sensor using two air-gap Fabry–Perot interferometers arranged in parallel, demonstrating high-sensitivity strain sensing through microwave-domain measurements. The introduced technique is straightforward to implement, and the characteristic sensing signal is easy to demodulate and highly sensitive, presenting an excellent solution to the complexities of existing optical Vernier sensor systems.
    R(ω)=S(ω)·{CV1cos(ωc·2L1)V2cos(ωc·2L2)+V3cos[ωc·2(L1L2)]},

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    H(Ω)=R(ω)[mH*(ω)·H(ω+Ω)+mH(ω)·H*(ωΩ)]dω,

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    f1=1DDCFFSR1,f2=1DDCFFSR2,f3=|FSR1FSR2|DDCFFSR1FSR2,

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    H(Ω,ω0)=(m·ejβL2Ω2+m·ejβL2Ω2)·ejΩ[τ(ω0)+βLω0]·HRF(Ω),

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    HRF(Ω)=R(ω)·ejβLωΩdω,

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    S1(ω)=S1(ω+ω0).

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    R(ω)=S1(ωω0)·{CV1cos(ωc·2L1)V2cos(ωc·2L2)+V3cos[ωc·2(L1L2)]}.

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    H+(Ω)=2πmcos(βL2Ω2)·eiΩ[τ(ω0)+βLω0]·[V1S1f(βLΩ2L1c)eiω0(βLΩ2L1c)+V2S1f(βLΩ2L2c)eiω0(βLΩ2L2c)],

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    M=|M|eiφ=M1+M2,|M|=A12+A22+2A1A2cos(φ2φ1)=A12+A22+2A1A2cos[2ω0c(L2L1)],φ=arctanA1sinφ1+A2sinφ2A1cosφ1+A2cosφ2,

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    |M|=2A0|cosφ2φ12|=2A0|cos(ω0c(L2L1))|.

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    |M|L2=±2A0ω0csin[ω0c(L2L1)].

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    L2L1=2k+14λ0,

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    f=1DDCFFSR=1DDCF·OPLλ2,

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    fOPL=1DDCF·1λ2.

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    L2L1=k2λ0.

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    R(ξ)=2πS1f(ξ)Ceiω0ξ2πV12[S1f(ξ2L1c)eiω0(ξ2L1c)+S1f(ξ+2L1c)eiω0(ξ+2L1c)]2πV22[S1f(ξ2L2c)eiω0(ξ2L2c)+S1f(ξ+2L2c)eiω0(ξ+2L2c)]++2πV32{S1f[ξ2(L1L2)c]eiω0[ξ2(L1L2)c]+S1f[ξ+2(L1L2)c]eiω0[ξ+2(L1L2)c]}.(A1)

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    M1=A1eiφ1,A1=2πmV1cos(βL2Ω2)S1f(βLΩ2L1c),φ1=τ(ω0)Ω+ω02L1c;(A2)

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    M2=A2eiφ2,A2=2πmV2cos(βL2Ω2)S1f(βLΩ2L2c),φ2=τ(ω0)Ω+ω02L2c.(A3)

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    Ruimin Jie, Jie Huang, Chen Zhu, "Transforming optical Vernier effect into coherent microwave interference towards highly sensitive optical fiber sensing," Photonics Res. 13, 875 (2025)
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