Fig. 1. (a) Schematic of the intramodal and intermodal FWM processes. The colors represent the spatial modes of the waves. (b) The inverse group velocity (β1) versus angular frequency relation required for phase matching in the intermodal processes. The dashed lines indicate the β1 values at the average frequency of the two waves in each mode, which should be equal.

Fig. 2. (a) Designed and measured refractive index profiles of the fabricated HNL-FMF at 1550 nm. The effective refractive index of the supported modes and their transverse mode profiles are also shown. (b) Relative inverse group velocity curves of the modes of the designed fiber and (c) those of the modes when the core radius or α parameters are changed ±1% from their optimal values.

Fig. 3. SLM apparatus when used as the MMUX for mode excitation of the fabricated HNL-FMF. PBS, polarizing beam splitter; λ/2, half-wave plate.

Fig. 4. Measured OTDR curves of both MGs.

Fig. 5. Setup of time-domain pulse response measurement, where GSa/s stands for gigasamples per second.

Fig. 6. Spectrogram of fiber pulse response over the C band. Inset: β2 of each eigenmode over the C band.

Fig. 7. Setup of CW-SPM nonlinear coefficient measurement.

Fig. 8. SPM spectra of the beating signal after propagation in different MGs. Inset: relationship between the SPM phase shift and the power ratio of the zero- and first-order harmonics, according to Ref. [36]. The two markers in the inset correspond to the power ratios of MGs labeled in the main figure.

Fig. 9. Experimental setup for intermodal FWM. Signal and Pump 1 are connected with the HE11 port of the MMUX, while Pump 2 and Pump 3 are connected with the HE21 port and TE01 port, respectively.

Fig. 10. Output spectra after mode demultiplexing. Two different MGs are received separately by changing the corresponding phase pattern in the MDMUX. For easier observation, a redshift of 0.1 nm is intentionally added on the spectrum when receiving the HE11 mode. Dashed lines indicate the cross talk from one MG to the other.

Fig. 11. Spectra of conversion efficiency when the signal wavelength varies from 1549.6 to 1546 nm. The blue curves correspond to the BS idlers, while the orange curves correspond to the PC idlers. The dashed-dotted curves correspond to the CE curves found through simulations, and the black dashed line shows where Pump 2 is located.