Theoretical analyses on orbital angular momentum modes in conventional graded-index multimode fibre

Abstract

Orbital angular momentum (OAM) modes are another mode basis to represent spatial modes. There have been increasing interests in exploiting OAM modes in specialty fibres. In this paper, we present a comprehensive characterisation of OAM modes in conventional graded-index multimode fibre (MMF). 1) We synthesise the circularly polarized OAM modes by properly combining two fold degenerate cylindrical vector modes (eigenmodes) and analyse the total angular momentum, i.e. spin angular momentum and orbital angular momentum. 2) We divide all the OAM modes of the conventional graded-index MMF into 10 OAM mode groups with effective refractive index differences between different mode groups above 10^-4 enabling low-level inter-group crosstalk. 3) We study the chromatic dispersion, differential group delay, effective mode area, and nonlinearity for each OAM mode group over a wide wavelength ranging from 1520 to 1630 nm covering the whole C band and L band. 4) We discuss the performance tolerance to fibre ellipticity and bending. 5) We further address the robustness of performance against fibre perturbations including the core size, index contrast and the imperfect index profile of the practically fabricated MMFs. The obtained results may provide theoretical basis for further space-division multiplexing applications employing OAM modes in conventional graded-index MMF.

Figure 1

(a) Index profile of an idealized conventional graded-index MMF (e.g. OM3) with parameters: r_core = 25 μm, n ₁ = 1.458369, n ₂ = 1.4440 at 1550 nm. (b) n_eff of all 110 fibre cylindrical vector modes (eigenmodes) at 1550 nm. (c) 10 mode groups in conventional graded-index MMF at 1550 nm. Each $H{E}_{mn}^{e/o}$ or $E{H}_{mn}^{e/o}$ mode is two fold degenerate, comprising even and odd modes. (d) n_eff differences in two adjacent vector modes. Top elliptical circle: n_eff differences between different mode groups. Middle elliptical circle: n_eff differences between different HE/EH/TE/TM modes in the same groups. Bottom elliptical circle: n_eff differences between the two fold degenerate modes.

Figure 2

Part of spatial phase distributions of the x-component electric field and intensity profiles of the OAM modes in conventional graded-index MMF.

Figure 3

OAM mode groups in conventional graded-index MMF at 1550 nm. Each $OA{M}_{\pm l,m}^{L/R}(l>0)$ is four fold degenerate including polarization and rotation, while $OA{M}_{0,m}^{L/R}$ is two fold degenerate including only polarization.

Figure 4

Guided eigenmode number in conventional graded-index MMF versus wavelength.

Figure 5

(a) Chromatic dispersion and (b) differential group delay of typical OAM modes over ten OAM mode groups versus wavelength ranging from 1524 nm to 1626 nm. Each OAM _l,m mode denotes one of the degenerate $OA{M}_{\pm l,m}^{L/R}$ modes as the degenerate OAM modes have similar dispersion and differential group delay.

Figure 6

Differential group delay of all 30 degenerate OAM modes at 1550 nm.

Figure 7

(a) Effective mode area and (b) nonlinearity of different OAM modes versus wavelength. Each OAM _l,m mode denotes one of the degenerate $OA{M}_{\pm l,m}^{L/R}$ modes as the degenerate OAM modes have similar effective mode area and nonlinearity.

Figure 8

(a) The outer 1/e ² modal field radius (in blue) and inner radius (in red) and (b) effective mode area of all 30 degenerate OAM modes at 1550 nm.

Figure 9

(a) n_eff difference and (b) 2π walk-off length and 10-ps walk-off length between the even and odd fibre eigenmodes versus fibre ellipticity. (c) OAM crosstalks for the lowest-order HE₂₁ related $OA{M}_{-1,1}^{\mathrm{R}}$ mode and highest-order HE _10,1 related $OA{M}_{+9,1}^{\mathrm{L}}$ mode under an ellipticity of 0.5%. (d) Minimum n_eff differences between different mode groups with ellipticity varying from 0 to 5%.

Figure 10

(a) n_eff difference and (b) 2π walk-off length and 10-ps walk-off length between the even and odd fibre eigenmodes versus fibre bend radius. (c) OAM crosstalks for the lowest-order HE₂₁ related ${\mathrm{OAM}}_{-1,1}^{\mathrm{R}}$ mode and highest-order HE₉₁ related ${\mathrm{OAM}}_{+8,1}^{\mathrm{L}}$ mode or HE_10,1 related ${\mathrm{OAM}}_{+9,1}^{\mathrm{L}}$ mode under fibre bend radii of 2 cm and 10 cm, respectively. (d) Minimum n_eff differences between different mode groups with bend radius varying from 1 cm to 100 cm. ‘None’ means no bending.

Figure 11

(a) Guided mode number and (b) n_eff distribution versus fibre core radius. (c) All 124 fibre modes when the fibre core radius takes 26.5 µm.

Figure 12

(a) Chromatic dispersion, (b) differential group delay, (c) effective mode area, and (d) nonlinearity coefficient for the typical fourteen OAM modes versus fibre core radius.

Figure 13

(a) Guided mode number and (b) n_eff distribution versus fibre relative refractive index difference. (c) All 132 fibre modes when the fibre relative refractive index difference is 1.2%.

Figure 14

(a) Chromatic dispersion, (b) differential group delay, (c) effective mode area, and (d) nonlinearity coefficient for the typical fourteen OAM modes versus fibre relative refractive index difference.

Figure 15

(a) Simulated refractive index profile distorted by random ripples with ripple amplitude of 0.5‰. (b) All 110 fibre modes when the ripple amplitude is 0.5‰.

Figure 16

(a) Chromatic dispersion, (b) differential group delay, (c) effective mode area, and (d) nonlinearity coefficient for the typical thirteen OAM modes versus ripple amplitude.

Figure 17

Chromatic dispersion versus number of mesh element and average mesh size for different OAM modes at 1530 nm, 1580 nm and 1625 nm, respectively.

Figure 18

(a–c) Effective mode area versus number of mesh element/average mesh size across the C band and L band. The integral radius is 45 µm. (d–f) Effective mode area versus integral radius across the C band and L band. The average mesh size is 158 nm. (a,d) 1530 m; (b,e) 1580 nm. (c,f) 1625 nm.