• Optics and Precision Engineering
  • Vol. 30, Issue 21, 2655 (2022)
Jinlong ZHANG*, Fumei WANG, Shenghuan FANG, Hongfei JIAO..., Xinbin CHENG and Zhanshan WANG|Show fewer author(s)
Author Affiliations
  • Institute of Precision Optical Engineering, MOE Key Laboratory of Advanced Micro-Structured Materials, Shanghai Frontiers Science Center of Digital Optics, Shanghai Professional Technical Service Platform for Full-Spectrum and High-Performance Optical Thin Film Devices and Applications,School of Physics Science and Engineering, Tongji University, Shanghai200092, China
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    DOI: 10.37188/OPE.20223021.2655 Cite this Article
    Jinlong ZHANG, Fumei WANG, Shenghuan FANG, Hongfei JIAO, Xinbin CHENG, Zhanshan WANG. Scattering and mechanical loss of ultra-low loss laser coatings[J]. Optics and Precision Engineering, 2022, 30(21): 2655 Copy Citation Text show less

    Abstract

    Ultralow-loss laser coatings have important applications in precision measurement fields such as gravitational wave detection, optical atomic clocks, and optical cavity ring-down spectroscopy. The cavity length stability and total optical loss of the laser resonator determine the sensitivity and signal-to-noise ratio of the measurement system. With the development of thin-film materials, fabrication processes and detection techniques, significant progress has been achieved in thin-film optical loss and thermal noise research. As regards optical loss, the absorption of the thin film can be controlled at the sub-ppm level, and the scattering of the thin film has become the main contributing factor of optical loss. This paper focuses on defect-induced scattering and interface scattering and presents the research ideas and achievements of thin-film scattering control. The interface scattering of thin films is reduced through optical factor design and interface power spectral density control. The theoretical analysis model of nodule defect-induced scattering is established, and the physical mechanism and the control technology of the defect-induced scattering are proposed. With regard to thermal noise research, this paper primarily introduces the physical mechanism of thin-film mechanical loss, presents the mechanical loss reduction of reflective coating through thin-film material optimization, and the corresponding improvement in the characterization method of mechanical loss.
    STIPsP0+PS=1-exp-4πcosθiσ/λ2PsP04πσλ,(1)

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    ARSθsi=0Nj=0NFiFj*PSDijf(2)

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    PSDij=PSDnormale-2πi×fzi-zjtanβcosφs+δ(3)

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    ARS=i=0Nj=0NFiFj*PSDnormalfx,fy×e-2πi×fzi-zjtanβcosφs+δ,(4)

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    ARS(θi,π,θi)=k4π2cos3θir(θi)2PSD(2ksinθi).(5)

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    ARS(θs,θi)=1QidQsdΩ=|A(θs,θi)|2Scosθi(6)

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    A(θs,θi)=AML(θs,θi)+ABL(θs,θi),sinθs=sinθi+λνx,(7)

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    AML(θs,θi)=k24πj=02N(εj-εj+1)Ej(θi)Ej(θs)ζjF(v),(8)

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    ABL(θs,θi)=k24πj=-2-1(εj-εj+1)Ej(θi)Ej(θs)ζjF(ν)(9)

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    ABL(θs=-θi=45)k24π(1-εL)E02(θi)κHκL2eiηBLζMLF(ν).(10)

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    A(θi=-θs=45)=k24π1-εLE02(θi)κH2κL2e2iηBL1-e-iηMLκL2/κH2ζMLF(ν)×1-εL-sin2θiεH-sin2θie-iηML+εH-εLεL-1e-iηBL=0.(11)

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    F=1-εL-sin2θiεH-sin2θie-iηML+εH-εLεL-1e-iηBL=0(12)

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    ηML=arccos12×εL-sin2θiεH-sin2θi1-εH-εLεL-12+12×εH-sin2θiεL-sin2θi(13)

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    ηBL=-arcsinεL-1εH-εLsinηML,(14)

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    tan βML=ληML4π(dH+dL)sinθi(15)

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    tan βBL=ληBL4π(dH+dL)sinθi(16)

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    ARScorrj=0NFj2PSDf(17)

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    ARSuncorrj=0NFj2PSDf(18)

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    Fj=εj-εj-1Ezj,θ0Ezj,θs(19)

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    S(f)kBT2πfdω2φC(f)(20)

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    ϕ=γ2Y00ωτ1+ω2τ2sech2Δ2kBT1kBT×f(Δ)g(V)dΔdV,(21)

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    φ=πfτ-1(22)

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    φcoating=φcoated+D-1φsubstrateD(23)

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    D=EcoatingEcoating+Esubstrate(24)

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    Jinlong ZHANG, Fumei WANG, Shenghuan FANG, Hongfei JIAO, Xinbin CHENG, Zhanshan WANG. Scattering and mechanical loss of ultra-low loss laser coatings[J]. Optics and Precision Engineering, 2022, 30(21): 2655
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