Review of Space Division Multiplexing Fibers

Fig. 1. Reasons that make the capacity of single-mode fiber approach Shannon limit. (a) Nonlinear Shannon limit^[3]; (b) fiber fuse damage phenomenon^[4]; (c) transmission window of fused-silica fibers, where black region represents the standard optical amplification band^[5]

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Fig. 2. Comparison of crosstalk between Homo-MCF and Hetero-MCF. (a) Crosstalk of Homo-MCF dependence on bending radius and change of effective index under bending condition; (b) crosstalk of Hetero-MCF dependence on bending radius and change of effective index under bending condition

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$Classification of single-mode multi-core fiber based on the assisted structure around core[20]. (a) Refractive index profile of trench-assisted core; (b) cross-section of trench-assisted multi-core fiber; (c) refractive index profile of air-hole-assisted core; (d) cross-section of air-hole-assisted multi-core fiber; (e) refractive index profile of photonic crystal core; (f) cross-section of photonic crystal multi-core fiber$

Fig. 3. Classification of single-mode multi-core fiber based on the assisted structure around core^[20]. (a) Refractive index profile of trench-assisted core; (b) cross-section of trench-assisted multi-core fiber; (c) refractive index profile of air-hole-assisted core; (d) cross-section of air-hole-assisted multi-core fiber; (e) refractive index profile of photonic crystal core; (f) cross-section of photonic crystal multi-core fiber

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Fig. 4. Core selection of outer core 1^[42]. (a) Cross-section of a Hetero-TA-7-core fiber; (b) n_eff and A_eff as functions of r₁ and Δ₁ at λ =1550 nm and Λ=35 μm for the first outer cores in Hetero-TA-7-core fiber

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Fig. 5. Core selection of outer core 2^[42]. (a) Cross-section of a Hetero-TA-7-core fiber; (b) n_eff and A_eff as function of r₁ and Δ₁ at λ=1550 nm and Λ=35 μm for the second outer cores in Hetero-TA-7-core fiber

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$XT between core 1 and the undetermined core as a function of neff,q and K[42], where neff,p and neff,q in Eq. (5) are effective indexes of refraction of core 1 and the undetermined core, respectively$

Fig. 6. XT between core 1 and the undetermined core as a function of n_eff,_q and K^[42], where n_eff,_p and n_eff,_q in Eq. (5) are effective indexes of refraction of core 1 and the undetermined core, respectively

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Fig. 7. n_effand A_effas functions of r₁ and Δ₁ at λ=1550 nm and λ=35 μm with CSR of center core 2 in Hetero-TA-7-core fiber^[42], where ${l_{XT}}_{, \max}$

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Fig. 8. Conversion relationship between OAM, CV and LP modes

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Fig. 9. Reported inner-depressed step-index few mode fibers with the weak coupling. (a) Inner-depressed step-index 6-LP-mode fiber with the weak coupling^[49]; (b) inner-depressed step-index 7-LP-mode fiber with the weak coupling^[50]; (c) inner-depressed step-index 4-LP-mode fiber with the weak coupling^[51]; (d) inner-depressed step-index 6-LP-mode fiber wi

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$Fiber solutions for reducing DMGD between modes. (a) Trench-assisted dual-cladding step fiber with low refractive index[54]; (b) trench-assisted graded-index fiber with low refractive index[55]; (c) 0DMGD compensation method to connect positive DMGD fiber (p) and negative DMGD fiber(n) with low refractive index [57]$

Fig. 10. Fiber solutions for reducing DMGD between modes. (a) Trench-assisted dual-cladding step fiber with low refractive index^[54]; (b) trench-assisted graded-index fiber with low refractive index^[55]; (c) 0DMGD compensation method to connect positive DMGD fiber (p) and negative DMGD fiber(n) with low refractive index^[57]

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Fig. 11. OAM mode groups multiplexing transmission system. (a) Low crosstalk and low attenuation ring-core fiber with 4×4 MIMO based OAM multiplexing transmission experiment involving ten wavelengths and eight OAM modes over a distance of 100 km, transmitting 16-Gbaud QPSK signals over all 80 channels^[65]; (b) graded-index multi-mode fiber without MIMO based OAM multiplexing transmission over 2.6 km transmitting 4 OAM mode groups^{[Download full size}

$Cross-section, refractive index distribution and dispersion curves of step-index fiber. (a) Cross-section and refractive index distribution of step-index fiber; (b) dispersion curves of weakly-guiding step-index fiber[68]$

Fig. 12. Cross-section, refractive index distribution and dispersion curves of step-index fiber. (a) Cross-section and refractive index distribution of step-index fiber; (b) dispersion curves of weakly-guiding step-index fiber^[68]

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$Cross-section, refractive index distribution and dispersion curves of ring-core fiber[68]. (a) Cross-section and refractive index distribution of ring-core fiber; (b) dispersion curves of weakly-guiding ring-core fiber, when d/(2a)=0.20; (c) dispersion curves of weakly-guiding ring-core fiber, when d/(2a)=0.25; (d) dispersion curves of weakly-guiding ring-core fiber, when d/(2a)=0.30$

Fig. 13. Cross-section, refractive index distribution and dispersion curves of ring-core fiber^[68]. (a) Cross-section and refractive index distribution of ring-core fiber; (b) dispersion curves of weakly-guiding ring-core fiber, when d/(2a)=0.20; (c) dispersion curves of weakly-guiding ring-core fiber, when d/(2a)=0.25; (d) dispersion curves of weakly-guiding ring-core fiber, when d/(2a)=0.30

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Table 1. Core arrangement of the reported trench-assisted single-mode multi-core fibers

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Table 1. Core arrangement of the reported trench-assisted single-mode multi-core fibers

Fiber	In Ref. [22]	In Ref. [23]	In Ref. [24]	In Ref. [25]	In Ref. [26]	In Ref. [27]
Cross section of thereported MCFs
Fiber structure	ORS	DRS	HCPS	TLS	New-typeHCPS	SLS
Core number	12	12	19	22	30	32
Core pitch /μm	37	44.6	35	41	30	29
Cladding diameter /μm	225	230	200	260	229	243
Average crosstalk@1550 nm	-32 dB/52 km	<-30 dB/1000 km	-42 dB/1 km	-45 dB/km	-50 dB/9.6 km	<-34.5dB/51.4 km
Loss /(dB·km-1)@1550 nm	0.199	0.186	0.227	0.21	—	0.24
Transmissioncapacity /(Tb·s-1)	1010	409	305	2150	—	—

Table 2. Reported OAM strongly-guiding and weakly-coupling ring-core fibers

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Table 2. Reported OAM strongly-guiding and weakly-coupling ring-core fibers

Fiber	In Ref. [59]	In Ref. [60]	In Ref. [61]	In Ref. [62]	In Ref. [63]
Cross sectionof strongly-guidedOAM fiber			—
Refractiveindexdistribution				—	—
OAM modegroup	OAM5,1,OAM5,1,OAM7,1(12 OAMmodes in all)	OAM0,1,OAM1,1,OAM2,1 ,…,OAM7,1 (28 OAMmodes in all)	OAM1,1(2 OAMmodes in all)	OAM+1,1,OAM+2,1,OAM+3,1,OAM+4,1(4 OAMmodes in all)	OAM+1,1,OAM+2,1 (2 OAMmodes in all)
Min Δneff /10-4	~1	1.1	2.1	~2	~7

Table 3. Correction of propagation constant for each CV mode
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Table 3. Correction of propagation constant for each CV mode
CV mode dβ
H $E_{1,1}^{even}$ ,H $E_{1,1}^{odd}$ I₁
TE_0,1 0
TM_0,1 2(I₁+I₂)
H $E_{l + 1,1}^{even}$ ,H $E_{l + 1,1}^{odd}$ (l≥1) I₁- I₂
E $H_{l - 1,1}^{even}$ ,E $H_{l - 1,1}^{odd}$ (l≥2) I₁+I₂

Table 4. Comparison among three SDM fiber schemes

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Table 4. Comparison among three SDM fiber schemes

Fiber	Multi-core fiber	Few-mode fiber	Few-mode multi-core fiber
Fiber fabrication	Mature	A bit complicated	Complicated
Fiber loss	Low	A bit high	High
Crosstalk	Low	Moderate/high	High
Alignment/splicer	Marker assisted/specialfusion splicer	Existing device	Marker assisted/specialfusion splicer
MUX/DEMUX	Space/waveguide/fiber	Space/waveguide/fiber	To be studied
Amplifier	Core/cladding pump	Core/cladding pump	Cladding pump
MIMO-DSP	N_core×(2×2)	2N_mode×2N_mode	N_core×(2N_mode×2N_mode)