• Advanced Photonics
  • Vol. 5, Issue 5, 056003 (2023)
Hongya Wang1、2, Jianzhou Ai1、2, Zelin Ma3, Siddharth Ramachandran3, and Jian Wang1、2、*
Author Affiliations
  • 1Huazhong University of Science and Technology, Wuhan National Laboratory for Optoelectronics and School of Optical and Electronic Information, Wuhan, China
  • 2Optics Valley Laboratory, Wuhan, China
  • 3Boston University, Boston, Massachusetts, United States
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    DOI: 10.1117/1.AP.5.5.056003 Cite this Article Set citation alerts
    Hongya Wang, Jianzhou Ai, Zelin Ma, Siddharth Ramachandran, Jian Wang. Finding the superior mode basis for mode-division multiplexing: a comparison of spatial modes in air-core fiber[J]. Advanced Photonics, 2023, 5(5): 056003 Copy Citation Text show less

    Abstract

    Diverse spatial mode bases can be exploited in mode-division multiplexing (MDM) to sustain the capacity growth in fiber-optic communications, such as linearly polarized (LP) modes, vector modes, LP orbital angular momentum (LP-OAM) modes, and circularly polarized OAM (CP-OAM) modes. Nevertheless, which kind of mode bases is more appropriate to be utilized in fiber still remains unclear. Here, we aim to find the superior mode basis in MDM fiber-optic communications via a system-level comparison in air-core fiber (ACF). We first investigate the walk-off effect of four spatial mode bases over 1-km ACF, where LP and LP-OAM modes show intrinsic mode walk-off, while it is negligible for vector and CP-OAM modes. We then study the mode coupling effect of degenerate vector and CP-OAM modes over 1-km ACF under fiber perturbations, where degenerate even and odd vector modes suffer severe mode cross talk, while negligible for high-order degenerate CP-OAM modes based on the laws of angular momentum conservation. Moreover, we comprehensively evaluate the system-level performance for data-carrying single-channel and two-channel MDM transmission with different spatial mode bases under various kinds of fiber perturbations (bending, twisting, pressing, winding, and out-of-plane moving). The obtained results indicate that the CP-OAM mode basis shows superiority compared to other mode bases in MDM fiber-optic communications without using multiple-input multiple-output digital signal processing. Our findings may pave the way for robust short-reach MDM optical interconnects for data centers and high-performance computing.
    HEl+1,modd=Fl,m(r)[x^sin(lϕ)+y^cos(lϕ)]exp(iβHE,z·z),(1a)

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    HEl+1,meven=Fl,m(r)[x^cos(lϕ)y^sin(lϕ)]exp(iβHE,z·z),(1b)

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    EHl1,modd=Fl,m(r)[x^sin(lϕ)y^cos(lϕ)]exp(iβEH,z·z),(1c)

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    EHl1,meven=Fl,m(r)[x^cos(lϕ)+y^sin(lϕ)]exp(iβEH,z·z),(1d)

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    LPl,mx,odd=EHl1,modd+HEl+1,modd,(2a)

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    LPl,mx,even=EHl1,meven+HEl+1,meven,(2b)

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    LPl,my,even=EHl1,moddHEl+1,modd,(2c)

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    LPl,my,odd=EHl1,mevenHEl+1,meven,(2d)

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    LPl,mx,odd=2Fl,m(r)x^sin(lϕ)exp(iβz·z),(3a)

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    LPl,mx,even=2Fl,m(r)x^cos(lϕ)exp(iβz·z),(3b)

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    LPl,my,even=2Fl,m(r)y^cos(lϕ)exp(iβz·z),(3c)

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    LPl,my,odd=2Fl,m(r)y^sin(lϕ)exp(iβz·z).(3d)

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    OAMl,mx=LPl,mx,even+iLPl,mx,odd=2Fl,m(r)x^exp(ilϕ)exp(iβz·z)=EHl1,meven+HEl+1,meven+iEHl1,modd+iHEl+1,modd,(4a)

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    OAMl,mx=LPl,mx,eveniLPl,mx,odd=2Fl,m(r)x^exp(ilϕ)exp(iβz·z)=EHl1,meven+HEl+1,meveniEHl1,moddiHEl+1,modd,(4b)

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    OAMl,my=LPl,my,eveniLPl,my,odd=2Fl,m(r)y^exp(ilϕ)exp(iβz·z)=EHl1,moddHEl+1,moddiEHl1,meven+iHEl+1,meven,(4c)

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    OAMl,my=LPl,my,even+iLPl,my,odd=2Fl,m(r)y^exp(ilϕ)exp(iβz·z)=EHl1,moddHEl+1,modd+iEHl1,meveniHEl+1,meven,(4d)

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    OAMl,mσ+=HEl+1,meven+iHEl+1,modd=Fl,m(r)(1i)exp(ilϕ)exp(iβHE,z·z),(5a)

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    OAMl,mσ=HEl+1,meveniHEl+1,modd=Fl,m(r)(1i)exp(ilϕ)exp(iβHE,z·z),(5b)

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    OAMl,mσ=EHl1,meven+iEHl1,modd=Fl,m(r)(1i)exp(ilϕ)exp(iβEH,z·z),(5c)

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    OAMl,mσ+=EHl1,meveniEHl1,modd=Fl,m(r)(1i)exp(ilϕ)exp(iβEH,z·z),(5d)

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    Pu,v=ω2c2Φ(βuβv)·(Eu*TpertEvrdrdϕ)2,

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    Φ(βuβv)=πσrms2Lcexp{[Lc(βuβv)/2]2},

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    Tpert(r,ϕ)=n=tn(r)exp(inϕ),

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    Pu,vexp{[Lc(βuβv)/2]2}·{n=tn02πexp[i(lvlu+n)ϕ]dϕ}2.

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    Φgp(C)=σ·Ω(C),

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    Φgp(C)=(σ+l)·Ω(C).

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    OAMl,mσ+¯=OAMl,mσ+·exp(iΦgp1),(12a)

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    OAMl,mσ¯=OAMl,mσ·exp(iΦgp1),(12b)

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    OAMl,mσ=OAMl,mσ·exp(iΦgp2),(12c)

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    OAMl,mσ+¯=OAMl,mσ+·exp(iΦgp2),(12d)

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    HEl+1,meven¯=12(OAMl,mσ+¯+OAMl,mσ¯)=cosΦgp1·HEl+1,mevensinΦgp1·HEl+1,modd,(13a)

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    HEl+1,modd¯=12i(OAMl,mσ+¯OAMl,mσ¯)=cosΦgp1·HEl+1,modd+sinΦgp1·HEl+1,meven,(13b)

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    EHl1,meven¯=12(OAMl,mσ¯+OAMl,mσ+¯)=cosΦgp2·EHl1,mevensinΦgp2·EHl1,modd,(13c)

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    EHl1,modd¯=12i(OAMl,mσ¯OAMl,mσ+¯)=cosΦgp2·EHl1,modd+sinΦgp2·EHl1,meven.(13d)

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    Hongya Wang, Jianzhou Ai, Zelin Ma, Siddharth Ramachandran, Jian Wang. Finding the superior mode basis for mode-division multiplexing: a comparison of spatial modes in air-core fiber[J]. Advanced Photonics, 2023, 5(5): 056003
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