# Real-Time Access to Collisions between a Two-Soliton Molecule and a Soliton Singlet in an Ultrafast Fiber Laser

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experimental Setup

^{2}/km. The other fibers in the cavity are a 12.7 m standard single-mode fiber (SMF) and a 0.5 m HI 1060 Flex fiber with dispersion parameters of −23 and −10 ps

^{2}/km, respectively. The cavity dispersion can be estimated to be −0.3 ps

^{2}. A polarization-dependent optical integrated component (PD-OIC) is employed in the laser cavity, which possesses the combined functions of a polarization-dependent isolator (PD-ISO), a wavelength-division multiplexer (WDM), and a 10% output coupler (OC). This PD-OIC has been detailed in our published paper [39]. The gain in the laser is provided by the EDF, which is pumped by a 980 nm laser diode (LD). An in-line polarization controller (PC) is adopted to adjust the net cavity birefringence. The PD-OIC works with the PC to form an artificial saturable absorber.

## 3. Results and Discussion

^{2}profile. The time–bandwidth product of the pulses is 0.37, indicating that the pulses are slightly chirped. Figure 2d maps the single-shot spectra of output pulses measured by the DFT technique, verifying that the laser operates in a stationary single-soliton state. As shown in Figure 2b, the average (red dashed curve) of the shot-to-shot spectra agrees well with the OSA-measured optical spectrum, which demonstrates the accuracy of our DFT measurement.

_{1}. The separation between the central peak and peak 2 stands for the separation between soliton 1 and soliton 2, labeled as τ

_{2}, and the separation between the central peak and peak 3 corresponds to the separation between soliton 1 and soliton 3, denoted by τ

_{3}. Figure 5d shows the retrieved soliton-separation evolution of a single collision event. The collision event can be divided into three stages, i.e., approaching, colliding, and being far away.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Single-soliton state. (

**a**) Pulse train, (

**b**) OSA-measured optical spectrum (black curve) and the average (red dashed curve) of the DFT single-shot spectra, (

**c**) corresponding RF spectrum (inset shows the autocorrelation trace), and (

**d**) shot-to-shot spectra of 1000 roundtrips.

**Figure 3.**Repeated collisions between a soliton molecule and a soliton singlet. (

**a**) Pulse train (inset shows the pulse train with a large scanning range), (

**b**) the corresponding pulse train after DFT, (

**c**) OSA-measured optical spectrum, and (

**d**) autocorrelation trace.

**Figure 4.**A typical single collision event. (

**a**) Shot-to-shot spectra of 14,000 roundtrips, (

**b**) the field autocorrelation traces obtained by Fourier transform of the shot-shot spectra in (

**a**), and (

**c**) zoom-in plot of the dashed rectangle in (

**b**) which shows the bond exchange.

**Figure 5.**Retrieval of soliton separations. (

**a**) The DFT spectrum at the roundtrip of 3600, (

**b**) the corresponding field autocorrelation trace, (

**c**) the actual temporal distribution of the solitons at the 3600th roundtrip, and (

**d**) the retrieved separation evolution of the solitons.

**Figure 6.**Annihilation of an initial soliton. (

**a**) The real-time spectral evolution measured by the DFT technique, (

**b**) zoom-in plot of the dashed rectangle in (

**a**), (

**c**) the field autocorrelation traces, and (

**d**) zoom-in plot of the dashed rectangle in (

**b**).

**Figure 7.**Formation of an unequally spaced soliton triplet. (

**a**) The real-time spectral evolution measured by the DFT technique, (

**b**) the corresponding field autocorrelation traces, (

**c**) shot-to-shot spectra of the formed stabilized soliton triplet, and (

**d**) the field autocorrelation traces of the stationary soliton triplet.

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**MDPI and ACS Style**

Li, J.; Li, H.; Wang, Z.; Zhang, Z.; Zhang, S.; Liu, Y.
Real-Time Access to Collisions between a Two-Soliton Molecule and a Soliton Singlet in an Ultrafast Fiber Laser. *Photonics* **2022**, *9*, 489.
https://doi.org/10.3390/photonics9070489

**AMA Style**

Li J, Li H, Wang Z, Zhang Z, Zhang S, Liu Y.
Real-Time Access to Collisions between a Two-Soliton Molecule and a Soliton Singlet in an Ultrafast Fiber Laser. *Photonics*. 2022; 9(7):489.
https://doi.org/10.3390/photonics9070489

**Chicago/Turabian Style**

Li, Junwen, Heping Li, Zhuang Wang, Zhiyao Zhang, Shangjian Zhang, and Yong Liu.
2022. "Real-Time Access to Collisions between a Two-Soliton Molecule and a Soliton Singlet in an Ultrafast Fiber Laser" *Photonics* 9, no. 7: 489.
https://doi.org/10.3390/photonics9070489