• Chinese Optics Letters
  • Vol. 21, Issue 12, 120601 (2023)
Zhigang Han1,2,*, Junbo Li1,2, Siliang Liu1,2, Fangxin Li1,2..., Zhenying Yang1,2, Qi Wang1,2, Jiuduo Rui1,2, Hua Shen1,2 and Rihong Zhu1,2|Show fewer author(s)
Author Affiliations
  • 1School of Electronic Engineering and Optoelectronic Technology, Nanjing University of Science and Technology, Nanjing 210094, China
  • 2MIIT Key Laboratory of Advanced Solid Laser, Nanjing University of Science and Technology, Nanjing 210094, China
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    DOI: 10.3788/COL202321.120601 Cite this Article Set citation alerts
    Zhigang Han, Junbo Li, Siliang Liu, Fangxin Li, Zhenying Yang, Qi Wang, Jiuduo Rui, Hua Shen, Rihong Zhu, "Simultaneous determination of polarization states and mode coefficients of fiber LP modes with four-channel off-axis holography," Chin. Opt. Lett. 21, 120601 (2023) Copy Citation Text show less

    Abstract

    Four-channel off-axis holography is proposed to simultaneously understand the polarization states and the mode coefficients of linearly polarized (LP) modes in few-mode fiber. Far-field off-axis holograms in the four polarization directions of the fiber laser were acquired at the same moment through a four-channel holographic device. The weights, the relative phase differences, and the polarization parameters of the vector fiber laser mode can be solved simultaneously. The simulated and experimental mode analysis of the laser output by 1060-XP fiber with 6 LP modes at 632.8 nm is conducted, which shows that the similarity of the total intensity distribution of the laser before and after mode analysis is above 0.97. The mode polarization states, the mode weights, and the relative phase differences of the few-mode laser can be determined simultaneously in a single shot by four-channel off-axis holography.

    E(x,y)=a·m=1M(ρm·eiϑm)·Em(x,y)·Pm,

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    Pm=1Am2+Bm2[AmBmeiφm],

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    Iintp(x,y)=Ap(x,y)+Cp(x,y)cos[φp(x,y)+w1·x+w2·y],

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    Ip_in(x,y)=Ip_FT(x,y)IÌŒp(x,y),

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    Epin(x,y)=Ip_in(x,y)exp[iφp_FFT(x,y)].

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    cmp=Ep(x,y)Em(x,y)dxdy(|Ep(x,y)|2dxdy)|Em(x,y)|2dxdy,

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    θmp=arctan[Im(cmp)Re(cmp)],

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    rhomp=Re(cmp)2+Im(cmp)2,

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    ERmp(x,y)=Kp·rhomp·eiθmp·Em(x,y),

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    S(x,y)=[S0(x,y)S1(x,y)S2(x,y)S3(x,y)]=[I0°(x,y)+I90°(x,y)I0°(x,y)I90°(x,y)I45°(x,y)I135°(x,y)IRight(x,y)ILeft(x,y)],

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    S0m=I0°+I90°rhom1·K1+rhom3·K3,(11a)

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    S1m=I0°I90°rhom1·K1rhom3·K3,(11b)

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    S2m=I45°I135°rhom2·K2rhom4·K4,(11c)

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    |S3m|=S0m2S1m2S2m2.(11d)

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    S0m=Am2+Bm2,(12a)

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    S1m=Am2Bm2,(12b)

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    S2m=2AmBmcos(φm),(12c)

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    S3m=2AmBmsin(φm).(12d)

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    Am=S0m+S1m2=rhom1·K1,(13a)

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    Bm=S0mS1m2=rhom3·K3,(13b)

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    |φm|=arccos(S2m2AmBm)=arccos(rhom2·K2rhom4·K42rhom1·K1·rhom3·K3)[0,π).(13c)

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    ϑmm1,(14a)

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    ρmrhom1·K1+rhom3·K3,(14b)

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    Zhigang Han, Junbo Li, Siliang Liu, Fangxin Li, Zhenying Yang, Qi Wang, Jiuduo Rui, Hua Shen, Rihong Zhu, "Simultaneous determination of polarization states and mode coefficients of fiber LP modes with four-channel off-axis holography," Chin. Opt. Lett. 21, 120601 (2023)
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