Photonic crystal fibers supporting fully separated eigenmodes

Shi Chen; Jian Wang

doi:10.1364/OL.44.003046

Optics Letters
Vol. 44,
Issue 12,
pp. 3046-3049
(2019)
•https://doi.org/10.1364/OL.44.003046

Photonic crystal fibers supporting fully separated eigenmodes

Shi Chen and Jian Wang

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Shi Chen and Jian Wang, "Photonic crystal fibers supporting fully separated eigenmodes," Opt. Lett. 44, 3046-3049 (2019)

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Table of Contents Category
- Fiber Optics and Optical Communications
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About this Article
History
- Original Manuscript: April 25, 2019
- Revised Manuscript: May 15, 2019
- Manuscript Accepted: May 15, 2019
- Published: June 7, 2019

Abstract

We present two kinds of fully degeneracy-lifted solid-core photonic crystal multi-mode fibers aiming at multiple-input multiple-output-free direct fiber vector eigenmode multiplexing transmission. One of the target fiber structures is able to support 52 fully separated eigenmodes with effective index difference above $1.37 \times 10^{- 4}$ and confinement loss below $3.28 \times 10^{- 5} dB / km$ over the whole $C + L$ band (1530–1625 nm). Specifically, it is suggested that $> 10^{- 4}$ effective index separation is sufficient to possess polarization-maintaining properties, while for short-reach stable mode-division multiplexing transmission, the effective index difference $> 10^{- 3}$ is highly desired. In particular, the other target fiber structure can further increase effective index separation above $1.10 \times 10^{- 3}$ among 24 eigenmodes with confinement loss below $6.68 \times 10^{- 4} dB / km$ over the whole $C + L$ band.

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$b / a$	0.2	0.4	0.6	0.8	1.0	1.2	1.4	1.6
( $a$ (μm), $2 a / Λ$ )	(1.4, 0.92)	(2.4, 0.90)	(2.6, 0.90)	(1.6, 0.90)	\	(3.0, 0.90)	(1.4, 0.82)	(2.0, 0.76)
Mode number	38	52	49	33	\	20	8	8
Min ( $Δ n_{eff}$ )	$2.19 e - 4$	$1.32 e - 4$	$1.13 e - 4$	$1.34 e - 4$	\	$1.18 e - 4$	$1.90 e - 4$	$1.13 e - 4$

$b / a$		0.3	0.35	0.4	0.45	0.5
( $a$ (μm), $2 a / Λ$ )		(2.1, 0.885)	(2.45, 0.9)	(2.4, 0.895)	(2.35, 0.895)	(1.9, 0.89)
Mode number, $\min (Δ n_{eff})$		49, $1.91 e - 4$	54, $1.33 e - 4$	52, $1.48 e - 4$	52, $1.28 e - 4$	42, $1.32 e - 4$
Tolerance	$a$ (μm)	[1.9, 2.15]	[2.35, 2.5]	[2.35, 2.45]	[2.3, 2.45]	[1.9, 1.95]
	b/a	[0.3, 0.35]	[0.35, 0.40]	[0.4, 0.45]	[0.4, 0.45]	[0.45, 0.50]
	$2 a / Λ$	[0.88, 0.895]	[0.90, 0.91]	[0.89, 0.90]	[0.895, 0.90]	[0.89, 0.895]
	Mode number	[46, 50]	[52, 54]	52	[47, 52]	[41, 43]

Mode	$Δ n_{eff}$	$α$ (dB/km)	$D$ (ps/ nm/km)	$A_{eff}$ ( ${μm}^{2}$ )	Mode	$Δ n_{eff}$	$α$ (dB/km)	$D$ (ps/ nm/km)	$A_{eff}$ ( ${μm}^{2}$ )	Mode	$Δ n_{eff}$	$α$ (dB/km)	$D$ (ps/ nm/km)	$A_{eff}$ ( ${μm}^{2}$ )
${EM}_{1}$	$3.10 e - 4$	$6.38 e - 8$	49.36	24.15	${EM}_{19}$	$2.24 e - 3$	$1.81 e - 6$	155.13	42.09	${EM}_{37}$	$4.95 e - 4$	$2.37 e - 7$	290.13	41.43
${EM}_{2}$	$7.56 e - 3$	$4.11 e - 7$	52.83	23.62	${EM}_{20}$	$1.90 e - 3$	$9.69 e - 7$	178.92	41.99	${EM}_{38}$	$8.86 e - 4$	$2.57 e - 6$	290.38	34.72
${EM}_{3}$	$4.61 e - 4$	$1.97 e - 6$	73.56	25.32	${EM}_{21}$	$4.59 e - 4$	$2.30 e - 6$	168.60	43.62	${EM}_{39}$	$1.43 e - 3$	$9.41 e - 7$	310.34	38.99
${EM}_{4}$	$8.48 e - 3$	$7.80 e - 7$	78.84	24.34	${EM}_{22}$	$9.00 e - 4$	$1.12 e - 6$	175.82	45.99	${EM}_{40}$	$4.41 e - 3$	$1.68 e - 5$	339.94	47.81
${EM}_{5}$	$2.50 e - 4$	$3.23 e - 6$	90.55	39.02	${EM}_{23}$	$2.09 e - 3$	$7.47 e - 6$	179.76	44.03	${EM}_{41}$	$2.33 e - 3$	$2.52 e - 6$	317.88	34.89
${EM}_{6}$	$2.36 e - 4$	$1.20 e - 6$	95.56	34.67	${EM}_{24}$	$1.99 e - 3$	$5.02 e - 6$	201.88	43.94	${EM}_{42}$	$3.07 e - 4$	$8.53 e - 6$	341.61	41.84
${EM}_{7}$	$8.14 e - 4$	$3.22 e - 6$	105.24	20.76	${EM}_{25}$	$8.92 e - 4$	$6.24 e - 6$	208.93	44.08	${EM}_{43}$	$1.58 e - 3$	$1.64 e - 5$	355.49	37.02
${EM}_{8}$	$3.65 e - 3$	$4.81 e - 7$	114.54	19.20	${EM}_{26}$	$2.42 e - 4$	$6.98 e - 6$	224.04	47.36	${EM}_{44}$	$1.59 e - 3$	$1.52 e - 6$	348.82	44.78
${EM}_{9}$	$1.54 e - 4$	$2.23 e - 6$	81.93	28.71	${EM}_{27}$	$1.48 e - 4$	$1.02 e - 6$	199.98	19.44	${EM}_{45}$	$1.20 e - 3$	$7.41 e - 6$	348.30	32.55
${EM}_{10}$	$5.48 e - 4$	$3.76 e - 7$	84.33	36.46	${EM}_{28}$	$2.33 e - 3$	$9.76 e - 6$	208.20	19.53	${EM}_{46}$	$4.77 e - 3$	$7.49 e - 6$	389.02	40.26
${EM}_{11}$	$6.86 e - 4$	$2.29 e - 6$	94.15	29.79	${EM}_{29}$	$1.62 e - 3$	$9.57 e - 6$	213.10	45.60	${EM}_{47}$	$2.00 e - 4$	$3.34 e - 6$	313.14	47.76
${EM}_{12}$	$1.01 e - 3$	$1.07 e - 6$	102.05	35.49	${EM}_{30}$	$4.17 e - 3$	$4.01 e - 6$	230.94	44.32	${EM}_{48}$	$6.36 e - 4$	$5.75 e - 6$	371.50	41.81
${EM}_{13}$	$8.42 e - 4$	$3.49 e - 6$	103.24	47.01	${EM}_{31}$	$9.20 e - 4$	$3.59 e - 6$	241.72	45.55	${EM}_{49}$	$6.60 e - 4$	$6.73 e - 6$	342.13	54.98
${EM}_{14}$	$1.35 e - 3$	$4.70 e - 8$	106.37	37.78	${EM}_{32}$	$4.51 e - 3$	$2.32 e - 6$	248.42	45.07	${EM}_{50}$	$1.22 e - 3$	$8.51 e - 6$	348.77	51.45
${EM}_{15}$	$4.05 e - 4$	$1.65 e - 6$	120.27	44.18	${EM}_{33}$	$9.25 e - 4$	$2.83 e - 6$	279.09	33.54	${EM}_{51}$	$6.46 e - 4$	$6.52 e - 6$	390.07	54.19
${EM}_{16}$	$4.11 e - 3$	$2.43 e - 6$	116.30	38.64	${EM}_{34}$	$2.38 e - 3$	$5.07 e - 7$	290.80	40.29	${EM}_{52}$	—	$1.13 e - 5$	405.89	45.52
${EM}_{17}$	$7.29 e - 4$	$3.82 e - 6$	149.98	48.61	${EM}_{35}$	$3.48 e - 4$	$1.07 e - 5$	295.28	49.68
${EM}_{18}$	$7.86 e - 4$	$9.32 e - 7$	155.93	52.95	${EM}_{36}$	$6.06 e - 3$	$2.14 e - 5$	296.45	48.56

Mode	$Δ n_{eff}$	$α$ (dB/km)	$D$ (ps/ nm/km)	$A_{eff}$ ( ${μm}^{2}$ )	Mode	$Δ n_{eff}$	$α$ (dB/km)	$D$ (ps/ nm/km)	$A_{eff}$ ( ${μm}^{2}$ )	Mode	$Δ n_{eff}$	$α$ (dB/km)	$D$ (ps/ nm/km)	$A_{eff}$ ( ${μm}^{2}$ )
${EM}_{1}$	$2.44 e - 3$	$9.25 e - 7$	100.80	5.63	${EM}_{9}$	$1.96 e - 3$	$2.65 e - 5$	−4.92	7.21	${EM}_{17}$	$6.83 e - 3$	$5.06 e - 6$	416.85	12.53
${EM}_{2}$	$3.72 e - 2$	$9.13 e - 7$	121.31	5.54	${EM}_{10}$	$1.39 e - 3$	$2.42 e - 5$	8.26	10.56	${EM}_{18}$	$6.37 e - 3$	$1.38 e - 5$	332.04	15.02
${EM}_{3}$	$3.26 e - 3$	$6.32 e - 6$	138.72	6.55	${EM}_{11}$	$7.64 e - 3$	$1.47 e - 6$	307.35	13.35	${EM}_{19}$	$5.52 e - 3$	$8.22 e - 6$	193.56	16.10
${EM}_{4}$	$2.97 e - 2$	$4.46 e - 7$	173.79	5.94	${EM}_{12}$	$1.77 e - 3$	$4.92 e - 7$	276.61	13.96	${EM}_{20}$	$2.78 e - 3$	$5.16 e - 6$	481.97	13.66
${EM}_{5}$	$6.60 e - 3$	$2.80 e - 6$	212.13	5.84	${EM}_{13}$	$3.89 e - 3$	$2.49 e - 6$	322.92	17.02	${EM}_{21}$	$6.07 e - 3$	$7.48 e - 5$	185.22	15.16
${EM}_{6}$	$3.24 e - 3$	$1.86 e - 5$	246.46	5.45	${EM}_{14}$	$1.24 e - 2$	$2.01 e - 5$	228.94	11.41	${EM}_{22}$	$4.27 e - 3$	$3.05 e - 5$	371.46	16.57
${EM}_{7}$	$2.93 e - 3$	$2.97 e - 6$	−124.64	14.68	${EM}_{15}$	$2.90 e - 3$	$2.96 e - 5$	172.54	12.34	${EM}_{23}$	$1.12 e - 2$	$3.33 e - 5$	386.31	14.22
${EM}_{8}$	$1.02 e - 2$	$1.50 e - 5$	−215.72	13.59	${EM}_{16}$	$1.56 e - 2$	$1.17 e - 5$	190.86	17.58	${EM}_{24}$	—	$3.80 e - 5$	35.73	8.45

$b / a$	0.2	0.4	0.6	0.8	1.0	1.2	1.4	1.6
( $a$ (μm), $2 a / Λ$ )	(1.4, 0.92)	(2.4, 0.90)	(2.6, 0.90)	(1.6, 0.90)	\	(3.0, 0.90)	(1.4, 0.82)	(2.0, 0.76)
Mode number	38	52	49	33	\	20	8	8
Min ( $Δ n_{eff}$ )	$2.19 e - 4$	$1.32 e - 4$	$1.13 e - 4$	$1.34 e - 4$	\	$1.18 e - 4$	$1.90 e - 4$	$1.13 e - 4$

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Optics Letters