Fig. 1. Effective indices of different modes in the SMF (LP₀₁ mode) and MMF (LP_/1 modes) at a wavelength of 1550 nm.The black curve shows the effective index of the fundamental mode in the SMF as a function of the core radius. The horizontal lines show the effective indices of the LP_/1 modes in the MMF³².

Fig. 2. Normalized power conversion (a) from the LP₀₁ mode to the $$\text{Unknown environment 'document'}$$ mode in MSC₁, (b) from the LP₀₁ mode to the $$\text{Unknown environment 'document'}$$ mode in MSC₂, and (c) from the LP₀₁ mode to the $$\text{Unknown environment 'document'}$$ mode in MSC3 between the SMF and MMF as a function of coupling length L.Insets: simulated intensity profiles of the LP₀₁ and $$\text{Unknown environment 'document'}$$ modes.

Fig. 3. (a) Cross section and refractive-index distribution of the IECF. (b) Three-dimensional structure of the IECF.

Fig. 4. Evolution diagrams of intensity and phase from the LP₀₁ mode to the $$\text{Unknown environment 'document'}$$, $$\text{Unknown environment 'document'}$$, and $$\text{Unknown environment 'document'}$$ modes by coupling in the designed MSCs and those from the $$\text{Unknown environment 'document'}$$, $$\text{Unknown environment 'document'}$$, and $$\text{Unknown environment 'document'}$$ modes to the OAM_±11, OAM_±21, and OAM_±31 modes after passing through the designed IECFs with different splicing angles of 45°, 22.5°, and 15°³⁴.

Fig. 5. Normalized power evolution between the $$\text{Unknown environment 'document'}$$ modes and $$\text{Unknown environment 'document'}$$ modes along the propagation length of IECFs. The intersection points of each pair of curves are the corresponding positions of generation of OAM_±l1 modes.

Fig. 6. Intensity, phase, interference, and local helicity distributions of the OAM mode with TCs of / = ±1 generated by MSC₁ and IECF₁ at different values of L_IECF.

Fig. 7. Purity of the first-order OAM mode generated by MSC₁ cascaded with IECF₁ at different values of L_IECF.