Harnessing Low-Threshold Nonlinear Effects in Cascaded Multimode Fiber Systems

Introduction

Nonlinear effects in multimode fibers (MMFs) have generated immense interest in recent years due to their potential applications in nonlinear fiber optics and optical fiber communications. Various nonlinear processes such as self-phase modulation (SPM), cross-phase modulation (XPM), intermodal four-wave mixing (IMFWM), and Raman scattering occur among the multiple spatial modes supported by MMFs, leading to intriguing nonlinear dynamics and the generation of new optical frequencies. Two key nonlinear processes contributing to broadband generation in MMFs are cascaded Raman scattering (CRS) and IMFWM.

In CRS, energy from the pump wavelength is transferred to longer wavelengths in the form of Stokes beams. The initial Raman Stokes line draws power from the pump to seed the formation of subsequent Stokes lines via a cascaded process. On the other hand, IMFWM is a phase-matched nonlinear process rigorously observed during the generation of MMF-based broadband continuum. Graded-index multimode (GRIN) fibers and few-mode fibers have gained significant attention due to their negligible intermodal dispersion and fascinating nonlinear effects.

However, a major challenge in exploiting these nonlinear processes in standard telecom-grade MMFs is the large amount of power required to trigger and maintain the effects. This tutorial presents an innovative solution to this problem by demonstrating a cascaded multimode fiber system that effectively reduces the Raman threshold, enabling the generation of broadband spectra through CRS and IMFWM at relatively low input pump powers.

Experimental Setup

The experimental setup for broadband generation in a cascaded fiber system (CFS) is illustrated in Figure 1. A passively Q-switched Nd:YAG laser with a 770 ps pulse duration, 23 kHz repetition rate, and a wavelength of 1064 nm is coupled into the device under test (DUT), which comprises a GRIN fiber (Thorlabs GIF625) and a few-mode non-zero dispersion-shifted (NZDS) fiber (Corning LEAF) of equal lengths spliced together.

The laser beam is routed towards a combination of a half-wave plate (HWP) and a polarizing beam splitter (PBS) cube, which controls the pump power and maintains the polarization of the incoming laser beam. The output from the PBS is focused onto the input end of the DUT (the GRIN fiber side) using a 20X microscope objective. The launching conditions can be controlled using a six-axis stage.

At the output end of the DUT (the NZDS fiber side), a plate beam splitter (BS) separates the optical power, with one portion directed to an optical spectrum analyzer (OSA) for spectral measurement (600-1700 nm range), and the other portion directed to a beam profiler for observing the respective spatial modes. Wavelength-specific bandpass filters isolate individual spatial modes at specific wavelengths.

Figure 1. Schematic diagram of the experimental set-up. Here, M1 and M2 are the routing mirrors, HWP: Half-wave Plate, PBS: Polarizing Beam Splitter, MO: Microscope Objective, DUT: Device Under Test (Cascaded Fiber Systems), BS: Plate Beam Splitter, OSA: Optical Spectrum Analyzer. The LP01 mode profile as observed in the beam profiler is also shown.

Cascaded Raman Scattering in the Cascaded Fiber System

The key advantage of the proposed cascaded fiber system is its ability to reduce the Raman threshold power, enabling the generation of higher-order Raman Stokes lines at relatively low input pump powers. Figure 2 shows the spectral power variation for different input pump peak powers in CFS1, a 100-m-long system comprising a 50-m-long GRIN fiber and a 50-m-long NZDS fiber.

At a peak power of 339 W (average power of 6 mW), Raman Stokes lines up to the fourth order are observed on the red side of the pump wavelength (1064 nm), indicating the occurrence of CRS. In contrast, individual 100-m-long GRIN and NZDS fibers pumped at a higher peak power of 3.2 kW (average power of 57 mW) produce Raman Stokes lines only up to the third and fourth orders, respectively (Figure 3).

The reduction in the Raman threshold power in the cascaded system can be understood by considering the effective mode area (Aeff) of the fibers. Fibers with smaller Aeff require less input pump power compared to fibers with larger Aeff of the same length to generate the same number of Raman peaks. Since the NZDS fiber has a smaller Aeff than the GRIN fiber at 1064 nm, the cascaded system benefits from the smaller Aeff of the NZDS fiber section, effectively reducing the Raman threshold.

Figure 2. Spectral power variation for different input pump peak power in CFS1 [GRIN (50 m) and NZDS (50 m) fiber], when the GRIN fiber side is pumped at 1064 nm. The black arrow denotes the location of the pump wavelength. IMFWM: Intermodal four-wave mixing; R1, R2, R3, and R4 are the first, second, third, and fourth-order Stokes lines, respectively.

Figure 3. Comparison of individual fiber and CFS spectral response where individual fiber alone is pumped with 3.2 kW of peak power to produce several Raman stokes. The solid blue curve shows the output spectra from CFS1 observed at 339 W pump power. The black arrow denotes the pump wavelength λp; λas denotes the anti-Stokes line observed in the spectrum for the GRIN fiber, whereas the four black downward arrows mark the IMFWM generated sidelobes.

Intermodal Four-Wave Mixing in the Cascaded Fiber System

In addition to CRS, the output spectrum from CFS1 at 339 W coupled power exhibits intense sidelobes on the blue side of the pump wavelength, generated mainly through the process of IMFWM. The experimentally observed peaks located at 844, 812, and 789 nm are the most intense.

To verify the IMFWM-generated sidelobes, the phase-matching conditions for IMFWM are solved semi-numerically for both the GRIN and NZDS fibers separately. Table I summarizes the estimated and experimentally obtained IMFWM-generated wavelengths, showing good agreement between theory and experiment.

Notably, the signals at 1447 and 1549 nm predicted by theory are not observed in the spectra because these IMFWM-generated signals are outside the Raman gain bandwidth of both fibers and are therefore suppressed.

TABLE I IMFWM-GENERATED SIDELOBES FOR THE PUMP WAVELENGTH AT 1064 NM (THEORY VS. EXPERIMENT)

Effect of Asymmetric Cascading on CRS and IMFWM

The effect of unequal or asymmetric cascading on the output spectrum of the CFS is investigated by varying the individual fiber lengths while keeping the total CFS length fixed at 100 m. Figures 4 and 5 depict the spectral variations for asymmetric CFSs with different length ratios of the GRIN and NZDS fiber sections.

For CFS2 (30-m-long GRIN fiber and 70-m-long NZDS fiber) and CFS3 (70-m-long GRIN fiber and 30-m-long NZDS fiber), both systems exhibit Raman Stokes lines up to the fourth order, as well as the appearance of a fifth-order Stokes line around 1400 nm due to the higher input pump power of 395 W (Figure 4).

When the length ratio is further changed to 1:4 (CFS4: 20-m-long GRIN fiber and 80-m-long NZDS fiber, and CFS5: 80-m-long GRIN fiber and 20-m-long NZDS fiber), interesting observations are made (Figure 5). CFS4, with a longer NZDS fiber section, exhibits intense Raman Stokes lines up to the fifth order, while CFS5, with a longer GRIN fiber section, maintains a high-intensity continuum up to 1400 nm.

These findings suggest that a longer NZDS fiber section is beneficial for increasing the number of Raman Stokes lines, whereas a longer GRIN fiber section maintains a high power level with promising spectral features. Additionally, since CRS is a length-dependent process, higher-order Stokes lines can be observed by increasing the total length of the cascaded system with a comparatively longer NZDS fiber section while maintaining a lower Raman threshold.

Figure 4. Spectral variation for CFS2 [GRIN (30 m) + NZDS (70 m)] and CFS3 [GRIN (70 m) + NZDS (30 m)] at a peak power of 395 W centered at 1064 nm. The input wavelength is denoted by the black arrow.

Figure 5. Spectral variation for CFS4 [GRIN (20 m) + NZDS (80 m)] and CFS5 [GRIN (80 m) + NZDS (20 m)] at a peak power of 395 W centered at 1064 nm. The input wavelength is denoted by the black arrow.

Conclusion

This tutorial has presented a cascaded multimode fiber system comprising a GRIN fiber and a few-mode NZDS fiber, which effectively reduces the Raman threshold and enables the generation of broadband spectra through CRS and IMFWM at relatively low input pump powers. The experimental results demonstrate the generation of Raman Stokes lines up to the fourth order and IMFWM-generated sidelobes at an average input pump power of only 6 mW (corresponding peak power of 339 W) in a 100-m-long cascaded system.

The cascaded approach significantly improves the process of optical continuum generation compared to prior efforts employing single fibers of nearly the same length, making this system highly efficient for applications such as Raman spectroscopy, broadband tunable light sources, and various sensing techniques. The combined use of readily available GRIN and NZDS fibers offers unprecedented opportunities for power-scalable nonlinear fiber light sources and efficient frequency conversion.

Reference

[2] M. Rehan, R. Chowdhury, P. Biswas, M. S. Kang, and S. K. Varshney, "Low-threshold Cascaded Raman Scattering and Intermodal Four-wave Mixing in Cascaded Multimode Fiber System," IEEE/OSA Journal of Lightwave Technology, accepted for publication, [Online]. Available: DOI 10.1109/JLT.2024.3369933, 2024.